% 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_246__5369898_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:28:29.951

% 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 (36)
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__Complex__Ocomplex_001t__Nat__Onat, type,
    comp_c438056209ex_nat : (complex > complex) > (nat > complex) > nat > complex).
thf(sy_c_Fun_Ocomp_001t__Complex__Ocomplex_001t__Nat__Onat_001t__Nat__Onat, type,
    comp_complex_nat_nat : (complex > nat) > (nat > complex) > nat > nat).
thf(sy_c_Fun_Ocomp_001t__Complex__Ocomplex_001t__Real__Oreal_001t__Complex__Ocomplex, type,
    comp_c317287661omplex : (complex > real) > (complex > complex) > 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__Complex__Ocomplex_001t__Nat__Onat, type,
    comp_nat_complex_nat : (nat > complex) > (nat > nat) > nat > complex).
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__Complex__Ocomplex, type,
    comp_n1816297743omplex : (nat > real) > (complex > nat) > complex > real).
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_Fun_Ocomp_001t__Real__Oreal_001t__Real__Oreal_001t__Complex__Ocomplex, type,
    comp_r422820971omplex : (real > real) > (complex > real) > complex > real).
thf(sy_c_Fun_Ocomp_001t__Real__Oreal_001t__Real__Oreal_001t__Nat__Onat, type,
    comp_real_real_nat : (real > real) > (nat > real) > nat > 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_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__Nat__Onat, type,
    order_1631207636at_nat : (nat > nat) > $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_Oantimono_001t__Real__Oreal_001t__Nat__Onat, type,
    order_1598331440al_nat : (real > nat) > $o).
thf(sy_c_Orderings_Oorder__class_Oantimono_001t__Real__Oreal_001t__Real__Oreal, type,
    order_537808140l_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_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__Nat__Onat, type,
    order_297469111al_nat : (real > nat) > $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__Nat__Onat, type,
    topolo1922093437eq_nat : (nat > nat) > $o).
thf(sy_c_Topological__Spaces_Omonoseq_001t__Real__Oreal, type,
    topolo144289241q_real : (nat > real) > $o).
thf(sy_v_f____, type,
    f : nat > nat).
thf(sy_v_r, type,
    r : real).
thf(sy_v_s, type,
    s : nat > complex).
thf(sy_v_thesis____, type,
    thesis : $o).

% Relevant facts (249)
thf(fact_0_f_I1_J, axiom,
    ((order_769474267at_nat @ f))). % f(1)
thf(fact_1_f_I2_J, axiom,
    ((topolo144289241q_real @ (^[N : nat]: (re @ (s @ (f @ N))))))). % f(2)
thf(fact_2__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_3_seq__monosub, axiom,
    ((![S : nat > real]: (?[F : nat > nat]: ((order_769474267at_nat @ F) & (topolo144289241q_real @ (^[N : nat]: (S @ (F @ N))))))))). % seq_monosub
thf(fact_4__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_5_strict__mono__compose, axiom,
    ((![R : nat > nat, S : nat > nat]: ((order_769474267at_nat @ R) => ((order_769474267at_nat @ S) => (order_769474267at_nat @ (^[X : nat]: (R @ (S @ X))))))))). % strict_mono_compose
thf(fact_6_strict__mono__eq, axiom,
    ((![F2 : nat > nat, X2 : nat, Y : nat]: ((order_769474267at_nat @ F2) => (((F2 @ X2) = (F2 @ Y)) = (X2 = Y)))))). % strict_mono_eq
thf(fact_7__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_8_r, axiom,
    ((![N2 : nat]: (ord_less_eq_real @ (real_V638595069omplex @ (s @ N2)) @ r)))). % r
thf(fact_9_Im__def, axiom,
    ((im = (case_complex_real @ (^[X1 : real]: (^[X22 : real]: X22)))))). % Im_def
thf(fact_10_monoseq__minus, axiom,
    ((![A : nat > real]: ((topolo144289241q_real @ A) => (topolo144289241q_real @ (^[N : nat]: (uminus_uminus_real @ (A @ N)))))))). % monoseq_minus
thf(fact_11_strict__mono__add, axiom,
    ((![K : real]: (order_1818878995l_real @ (^[N : real]: (plus_plus_real @ N @ K)))))). % strict_mono_add
thf(fact_12_strict__mono__add, axiom,
    ((![K : nat]: (order_769474267at_nat @ (^[N : nat]: (plus_plus_nat @ N @ K)))))). % strict_mono_add
thf(fact_13_decseq__imp__monoseq, axiom,
    ((![X3 : nat > real]: ((order_106095024t_real @ X3) => (topolo144289241q_real @ X3))))). % decseq_imp_monoseq
thf(fact_14_order__refl, axiom,
    ((![X2 : real]: (ord_less_eq_real @ X2 @ X2)))). % order_refl
thf(fact_15_order__refl, axiom,
    ((![X2 : nat]: (ord_less_eq_nat @ X2 @ X2)))). % order_refl
thf(fact_16_plus__complex_Osimps_I2_J, axiom,
    ((![X2 : complex, Y : complex]: ((im @ (plus_plus_complex @ X2 @ Y)) = (plus_plus_real @ (im @ X2) @ (im @ Y)))))). % plus_complex.simps(2)
thf(fact_17_plus__complex_Osimps_I1_J, axiom,
    ((![X2 : complex, Y : complex]: ((re @ (plus_plus_complex @ X2 @ Y)) = (plus_plus_real @ (re @ X2) @ (re @ Y)))))). % plus_complex.simps(1)
thf(fact_18_uminus__complex_Osimps_I2_J, axiom,
    ((![X2 : complex]: ((im @ (uminus1204672759omplex @ X2)) = (uminus_uminus_real @ (im @ X2)))))). % uminus_complex.simps(2)
thf(fact_19_uminus__complex_Osimps_I1_J, axiom,
    ((![X2 : complex]: ((re @ (uminus1204672759omplex @ X2)) = (uminus_uminus_real @ (re @ X2)))))). % uminus_complex.simps(1)
thf(fact_20_Re__def, axiom,
    ((re = (case_complex_real @ (^[X1 : real]: (^[X22 : real]: X1)))))). % Re_def
thf(fact_21_order__subst1, axiom,
    ((![A : real, F2 : real > real, B : real, C : real]: ((ord_less_eq_real @ A @ (F2 @ B)) => ((ord_less_eq_real @ B @ C) => ((![X4 : real, Y2 : real]: ((ord_less_eq_real @ X4 @ Y2) => (ord_less_eq_real @ (F2 @ X4) @ (F2 @ Y2)))) => (ord_less_eq_real @ A @ (F2 @ C)))))))). % order_subst1
thf(fact_22_order__subst1, axiom,
    ((![A : real, F2 : nat > real, B : nat, C : nat]: ((ord_less_eq_real @ A @ (F2 @ B)) => ((ord_less_eq_nat @ B @ C) => ((![X4 : nat, Y2 : nat]: ((ord_less_eq_nat @ X4 @ Y2) => (ord_less_eq_real @ (F2 @ X4) @ (F2 @ Y2)))) => (ord_less_eq_real @ A @ (F2 @ C)))))))). % order_subst1
thf(fact_23_order__subst1, axiom,
    ((![A : nat, F2 : real > nat, B : real, C : real]: ((ord_less_eq_nat @ A @ (F2 @ B)) => ((ord_less_eq_real @ B @ C) => ((![X4 : real, Y2 : real]: ((ord_less_eq_real @ X4 @ Y2) => (ord_less_eq_nat @ (F2 @ X4) @ (F2 @ Y2)))) => (ord_less_eq_nat @ A @ (F2 @ C)))))))). % order_subst1
thf(fact_24_order__subst1, axiom,
    ((![A : nat, F2 : nat > nat, B : nat, C : nat]: ((ord_less_eq_nat @ A @ (F2 @ B)) => ((ord_less_eq_nat @ B @ C) => ((![X4 : nat, Y2 : nat]: ((ord_less_eq_nat @ X4 @ Y2) => (ord_less_eq_nat @ (F2 @ X4) @ (F2 @ Y2)))) => (ord_less_eq_nat @ A @ (F2 @ C)))))))). % order_subst1
thf(fact_25_order__subst2, axiom,
    ((![A : real, B : real, F2 : real > real, C : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ (F2 @ B) @ C) => ((![X4 : real, Y2 : real]: ((ord_less_eq_real @ X4 @ Y2) => (ord_less_eq_real @ (F2 @ X4) @ (F2 @ Y2)))) => (ord_less_eq_real @ (F2 @ A) @ C))))))). % order_subst2
thf(fact_26_order__subst2, axiom,
    ((![A : real, B : real, F2 : real > nat, C : nat]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_nat @ (F2 @ B) @ C) => ((![X4 : real, Y2 : real]: ((ord_less_eq_real @ X4 @ Y2) => (ord_less_eq_nat @ (F2 @ X4) @ (F2 @ Y2)))) => (ord_less_eq_nat @ (F2 @ A) @ C))))))). % order_subst2
thf(fact_27_order__subst2, axiom,
    ((![A : nat, B : nat, F2 : nat > real, C : real]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_real @ (F2 @ B) @ C) => ((![X4 : nat, Y2 : nat]: ((ord_less_eq_nat @ X4 @ Y2) => (ord_less_eq_real @ (F2 @ X4) @ (F2 @ Y2)))) => (ord_less_eq_real @ (F2 @ A) @ C))))))). % order_subst2
thf(fact_28_order__subst2, axiom,
    ((![A : nat, B : nat, F2 : nat > nat, C : nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ (F2 @ B) @ C) => ((![X4 : nat, Y2 : nat]: ((ord_less_eq_nat @ X4 @ Y2) => (ord_less_eq_nat @ (F2 @ X4) @ (F2 @ Y2)))) => (ord_less_eq_nat @ (F2 @ A) @ C))))))). % order_subst2
thf(fact_29_ord__eq__le__subst, axiom,
    ((![A : real, F2 : real > real, B : real, C : real]: ((A = (F2 @ B)) => ((ord_less_eq_real @ B @ C) => ((![X4 : real, Y2 : real]: ((ord_less_eq_real @ X4 @ Y2) => (ord_less_eq_real @ (F2 @ X4) @ (F2 @ Y2)))) => (ord_less_eq_real @ A @ (F2 @ C)))))))). % ord_eq_le_subst
thf(fact_30_ord__eq__le__subst, axiom,
    ((![A : nat, F2 : real > nat, B : real, C : real]: ((A = (F2 @ B)) => ((ord_less_eq_real @ B @ C) => ((![X4 : real, Y2 : real]: ((ord_less_eq_real @ X4 @ Y2) => (ord_less_eq_nat @ (F2 @ X4) @ (F2 @ Y2)))) => (ord_less_eq_nat @ A @ (F2 @ C)))))))). % ord_eq_le_subst
thf(fact_31_ord__eq__le__subst, axiom,
    ((![A : real, F2 : nat > real, B : nat, C : nat]: ((A = (F2 @ B)) => ((ord_less_eq_nat @ B @ C) => ((![X4 : nat, Y2 : nat]: ((ord_less_eq_nat @ X4 @ Y2) => (ord_less_eq_real @ (F2 @ X4) @ (F2 @ Y2)))) => (ord_less_eq_real @ A @ (F2 @ C)))))))). % ord_eq_le_subst
thf(fact_32_ord__eq__le__subst, axiom,
    ((![A : nat, F2 : nat > nat, B : nat, C : nat]: ((A = (F2 @ B)) => ((ord_less_eq_nat @ B @ C) => ((![X4 : nat, Y2 : nat]: ((ord_less_eq_nat @ X4 @ Y2) => (ord_less_eq_nat @ (F2 @ X4) @ (F2 @ Y2)))) => (ord_less_eq_nat @ A @ (F2 @ C)))))))). % ord_eq_le_subst
thf(fact_33_ord__le__eq__subst, axiom,
    ((![A : real, B : real, F2 : real > real, C : real]: ((ord_less_eq_real @ A @ B) => (((F2 @ B) = C) => ((![X4 : real, Y2 : real]: ((ord_less_eq_real @ X4 @ Y2) => (ord_less_eq_real @ (F2 @ X4) @ (F2 @ Y2)))) => (ord_less_eq_real @ (F2 @ A) @ C))))))). % ord_le_eq_subst
thf(fact_34_ord__le__eq__subst, axiom,
    ((![A : real, B : real, F2 : real > nat, C : nat]: ((ord_less_eq_real @ A @ B) => (((F2 @ B) = C) => ((![X4 : real, Y2 : real]: ((ord_less_eq_real @ X4 @ Y2) => (ord_less_eq_nat @ (F2 @ X4) @ (F2 @ Y2)))) => (ord_less_eq_nat @ (F2 @ A) @ C))))))). % ord_le_eq_subst
thf(fact_35_ord__le__eq__subst, axiom,
    ((![A : nat, B : nat, F2 : nat > real, C : real]: ((ord_less_eq_nat @ A @ B) => (((F2 @ B) = C) => ((![X4 : nat, Y2 : nat]: ((ord_less_eq_nat @ X4 @ Y2) => (ord_less_eq_real @ (F2 @ X4) @ (F2 @ Y2)))) => (ord_less_eq_real @ (F2 @ A) @ C))))))). % ord_le_eq_subst
thf(fact_36_ord__le__eq__subst, axiom,
    ((![A : nat, B : nat, F2 : nat > nat, C : nat]: ((ord_less_eq_nat @ A @ B) => (((F2 @ B) = C) => ((![X4 : nat, Y2 : nat]: ((ord_less_eq_nat @ X4 @ Y2) => (ord_less_eq_nat @ (F2 @ X4) @ (F2 @ Y2)))) => (ord_less_eq_nat @ (F2 @ A) @ C))))))). % ord_le_eq_subst
thf(fact_37_monoI1, axiom,
    ((![X3 : nat > real]: ((![M : nat, N3 : nat]: ((ord_less_eq_nat @ M @ N3) => (ord_less_eq_real @ (X3 @ M) @ (X3 @ N3)))) => (topolo144289241q_real @ X3))))). % monoI1
thf(fact_38_monoI1, axiom,
    ((![X3 : nat > nat]: ((![M : nat, N3 : nat]: ((ord_less_eq_nat @ M @ N3) => (ord_less_eq_nat @ (X3 @ M) @ (X3 @ N3)))) => (topolo1922093437eq_nat @ X3))))). % monoI1
thf(fact_39_monoI2, axiom,
    ((![X3 : nat > real]: ((![M : nat, N3 : nat]: ((ord_less_eq_nat @ M @ N3) => (ord_less_eq_real @ (X3 @ N3) @ (X3 @ M)))) => (topolo144289241q_real @ X3))))). % monoI2
thf(fact_40_monoI2, axiom,
    ((![X3 : nat > nat]: ((![M : nat, N3 : nat]: ((ord_less_eq_nat @ M @ N3) => (ord_less_eq_nat @ (X3 @ N3) @ (X3 @ M)))) => (topolo1922093437eq_nat @ X3))))). % monoI2
thf(fact_41_complex_Ocase__eq__if, axiom,
    ((case_complex_real = (^[F3 : real > real > real]: (^[Complex : complex]: (F3 @ (re @ Complex) @ (im @ Complex))))))). % complex.case_eq_if
thf(fact_42_complex__Re__le__cmod, axiom,
    ((![X2 : complex]: (ord_less_eq_real @ (re @ X2) @ (real_V638595069omplex @ X2))))). % complex_Re_le_cmod
thf(fact_43_decseqD, axiom,
    ((![F2 : nat > real, I : nat, J : nat]: ((order_106095024t_real @ F2) => ((ord_less_eq_nat @ I @ J) => (ord_less_eq_real @ (F2 @ J) @ (F2 @ I))))))). % decseqD
thf(fact_44_decseqD, axiom,
    ((![F2 : nat > nat, I : nat, J : nat]: ((order_1631207636at_nat @ F2) => ((ord_less_eq_nat @ I @ J) => (ord_less_eq_nat @ (F2 @ J) @ (F2 @ I))))))). % decseqD
thf(fact_45_complex_Ocase__distrib, axiom,
    ((![H : real > real, F2 : real > real > real, Complex2 : complex]: ((H @ (case_complex_real @ F2 @ Complex2)) = (case_complex_real @ (^[X1 : real]: (^[X22 : real]: (H @ (F2 @ X1 @ X22)))) @ Complex2))))). % complex.case_distrib
thf(fact_46_eq__iff, axiom,
    (((^[Y3 : real]: (^[Z : real]: (Y3 = Z))) = (^[X : real]: (^[Y4 : real]: (((ord_less_eq_real @ X @ Y4)) & ((ord_less_eq_real @ Y4 @ X)))))))). % eq_iff
thf(fact_47_eq__iff, axiom,
    (((^[Y3 : nat]: (^[Z : nat]: (Y3 = Z))) = (^[X : nat]: (^[Y4 : nat]: (((ord_less_eq_nat @ X @ Y4)) & ((ord_less_eq_nat @ Y4 @ X)))))))). % eq_iff
thf(fact_48_antisym, axiom,
    ((![X2 : real, Y : real]: ((ord_less_eq_real @ X2 @ Y) => ((ord_less_eq_real @ Y @ X2) => (X2 = Y)))))). % antisym
thf(fact_49_antisym, axiom,
    ((![X2 : nat, Y : nat]: ((ord_less_eq_nat @ X2 @ Y) => ((ord_less_eq_nat @ Y @ X2) => (X2 = Y)))))). % antisym
thf(fact_50_decseq__def, axiom,
    ((order_106095024t_real = (^[X5 : nat > real]: (![M2 : nat]: (![N : nat]: (((ord_less_eq_nat @ M2 @ N)) => ((ord_less_eq_real @ (X5 @ N) @ (X5 @ M2)))))))))). % decseq_def
thf(fact_51_decseq__def, axiom,
    ((order_1631207636at_nat = (^[X5 : nat > nat]: (![M2 : nat]: (![N : nat]: (((ord_less_eq_nat @ M2 @ N)) => ((ord_less_eq_nat @ (X5 @ N) @ (X5 @ M2)))))))))). % decseq_def
thf(fact_52_monoseq__def, axiom,
    ((topolo144289241q_real = (^[X5 : nat > real]: (((![M2 : nat]: (![N : nat]: (((ord_less_eq_nat @ M2 @ N)) => ((ord_less_eq_real @ (X5 @ M2) @ (X5 @ N))))))) | ((![M2 : nat]: (![N : nat]: (((ord_less_eq_nat @ M2 @ N)) => ((ord_less_eq_real @ (X5 @ N) @ (X5 @ M2)))))))))))). % monoseq_def
thf(fact_53_monoseq__def, axiom,
    ((topolo1922093437eq_nat = (^[X5 : nat > nat]: (((![M2 : nat]: (![N : nat]: (((ord_less_eq_nat @ M2 @ N)) => ((ord_less_eq_nat @ (X5 @ M2) @ (X5 @ N))))))) | ((![M2 : nat]: (![N : nat]: (((ord_less_eq_nat @ M2 @ N)) => ((ord_less_eq_nat @ (X5 @ N) @ (X5 @ M2)))))))))))). % monoseq_def
thf(fact_54_linear, axiom,
    ((![X2 : real, Y : real]: ((ord_less_eq_real @ X2 @ Y) | (ord_less_eq_real @ Y @ X2))))). % linear
thf(fact_55_linear, axiom,
    ((![X2 : nat, Y : nat]: ((ord_less_eq_nat @ X2 @ Y) | (ord_less_eq_nat @ Y @ X2))))). % linear
thf(fact_56_antimonoD, axiom,
    ((![F2 : real > real, X2 : real, Y : real]: ((order_537808140l_real @ F2) => ((ord_less_eq_real @ X2 @ Y) => (ord_less_eq_real @ (F2 @ Y) @ (F2 @ X2))))))). % antimonoD
thf(fact_57_antimonoD, axiom,
    ((![F2 : real > nat, X2 : real, Y : real]: ((order_1598331440al_nat @ F2) => ((ord_less_eq_real @ X2 @ Y) => (ord_less_eq_nat @ (F2 @ Y) @ (F2 @ X2))))))). % antimonoD
thf(fact_58_antimonoD, axiom,
    ((![F2 : nat > real, X2 : nat, Y : nat]: ((order_106095024t_real @ F2) => ((ord_less_eq_nat @ X2 @ Y) => (ord_less_eq_real @ (F2 @ Y) @ (F2 @ X2))))))). % antimonoD
thf(fact_59_antimonoD, axiom,
    ((![F2 : nat > nat, X2 : nat, Y : nat]: ((order_1631207636at_nat @ F2) => ((ord_less_eq_nat @ X2 @ Y) => (ord_less_eq_nat @ (F2 @ Y) @ (F2 @ X2))))))). % antimonoD
thf(fact_60_antimonoE, axiom,
    ((![F2 : real > real, X2 : real, Y : real]: ((order_537808140l_real @ F2) => ((ord_less_eq_real @ X2 @ Y) => (ord_less_eq_real @ (F2 @ Y) @ (F2 @ X2))))))). % antimonoE
thf(fact_61_antimonoE, axiom,
    ((![F2 : real > nat, X2 : real, Y : real]: ((order_1598331440al_nat @ F2) => ((ord_less_eq_real @ X2 @ Y) => (ord_less_eq_nat @ (F2 @ Y) @ (F2 @ X2))))))). % antimonoE
thf(fact_62_antimonoE, axiom,
    ((![F2 : nat > real, X2 : nat, Y : nat]: ((order_106095024t_real @ F2) => ((ord_less_eq_nat @ X2 @ Y) => (ord_less_eq_real @ (F2 @ Y) @ (F2 @ X2))))))). % antimonoE
thf(fact_63_antimonoE, axiom,
    ((![F2 : nat > nat, X2 : nat, Y : nat]: ((order_1631207636at_nat @ F2) => ((ord_less_eq_nat @ X2 @ Y) => (ord_less_eq_nat @ (F2 @ Y) @ (F2 @ X2))))))). % antimonoE
thf(fact_64_antimonoI, axiom,
    ((![F2 : real > real]: ((![X4 : real, Y2 : real]: ((ord_less_eq_real @ X4 @ Y2) => (ord_less_eq_real @ (F2 @ Y2) @ (F2 @ X4)))) => (order_537808140l_real @ F2))))). % antimonoI
thf(fact_65_antimonoI, axiom,
    ((![F2 : real > nat]: ((![X4 : real, Y2 : real]: ((ord_less_eq_real @ X4 @ Y2) => (ord_less_eq_nat @ (F2 @ Y2) @ (F2 @ X4)))) => (order_1598331440al_nat @ F2))))). % antimonoI
thf(fact_66_antimonoI, axiom,
    ((![F2 : nat > real]: ((![X4 : nat, Y2 : nat]: ((ord_less_eq_nat @ X4 @ Y2) => (ord_less_eq_real @ (F2 @ Y2) @ (F2 @ X4)))) => (order_106095024t_real @ F2))))). % antimonoI
thf(fact_67_antimonoI, axiom,
    ((![F2 : nat > nat]: ((![X4 : nat, Y2 : nat]: ((ord_less_eq_nat @ X4 @ Y2) => (ord_less_eq_nat @ (F2 @ Y2) @ (F2 @ X4)))) => (order_1631207636at_nat @ F2))))). % antimonoI
thf(fact_68_eq__refl, axiom,
    ((![X2 : real, Y : real]: ((X2 = Y) => (ord_less_eq_real @ X2 @ Y))))). % eq_refl
thf(fact_69_eq__refl, axiom,
    ((![X2 : nat, Y : nat]: ((X2 = Y) => (ord_less_eq_nat @ X2 @ Y))))). % eq_refl
thf(fact_70_le__cases, axiom,
    ((![X2 : real, Y : real]: ((~ ((ord_less_eq_real @ X2 @ Y))) => (ord_less_eq_real @ Y @ X2))))). % le_cases
thf(fact_71_le__cases, axiom,
    ((![X2 : nat, Y : nat]: ((~ ((ord_less_eq_nat @ X2 @ Y))) => (ord_less_eq_nat @ Y @ X2))))). % le_cases
thf(fact_72_order_Otrans, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ B @ C) => (ord_less_eq_real @ A @ C)))))). % order.trans
thf(fact_73_order_Otrans, axiom,
    ((![A : nat, B : nat, C : nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ A @ C)))))). % order.trans
thf(fact_74_le__cases3, axiom,
    ((![X2 : real, Y : real, Z2 : real]: (((ord_less_eq_real @ X2 @ Y) => (~ ((ord_less_eq_real @ Y @ Z2)))) => (((ord_less_eq_real @ Y @ X2) => (~ ((ord_less_eq_real @ X2 @ Z2)))) => (((ord_less_eq_real @ X2 @ Z2) => (~ ((ord_less_eq_real @ Z2 @ Y)))) => (((ord_less_eq_real @ Z2 @ Y) => (~ ((ord_less_eq_real @ Y @ X2)))) => (((ord_less_eq_real @ Y @ Z2) => (~ ((ord_less_eq_real @ Z2 @ X2)))) => (~ (((ord_less_eq_real @ Z2 @ X2) => (~ ((ord_less_eq_real @ X2 @ Y)))))))))))))). % le_cases3
thf(fact_75_le__cases3, axiom,
    ((![X2 : nat, Y : nat, Z2 : nat]: (((ord_less_eq_nat @ X2 @ Y) => (~ ((ord_less_eq_nat @ Y @ Z2)))) => (((ord_less_eq_nat @ Y @ X2) => (~ ((ord_less_eq_nat @ X2 @ Z2)))) => (((ord_less_eq_nat @ X2 @ Z2) => (~ ((ord_less_eq_nat @ Z2 @ Y)))) => (((ord_less_eq_nat @ Z2 @ Y) => (~ ((ord_less_eq_nat @ Y @ X2)))) => (((ord_less_eq_nat @ Y @ Z2) => (~ ((ord_less_eq_nat @ Z2 @ X2)))) => (~ (((ord_less_eq_nat @ Z2 @ X2) => (~ ((ord_less_eq_nat @ X2 @ Y)))))))))))))). % le_cases3
thf(fact_76_antimono__def, axiom,
    ((order_537808140l_real = (^[F3 : real > real]: (![X : real]: (![Y4 : real]: (((ord_less_eq_real @ X @ Y4)) => ((ord_less_eq_real @ (F3 @ Y4) @ (F3 @ X)))))))))). % antimono_def
thf(fact_77_antimono__def, axiom,
    ((order_1598331440al_nat = (^[F3 : real > nat]: (![X : real]: (![Y4 : real]: (((ord_less_eq_real @ X @ Y4)) => ((ord_less_eq_nat @ (F3 @ Y4) @ (F3 @ X)))))))))). % antimono_def
thf(fact_78_antimono__def, axiom,
    ((order_106095024t_real = (^[F3 : nat > real]: (![X : nat]: (![Y4 : nat]: (((ord_less_eq_nat @ X @ Y4)) => ((ord_less_eq_real @ (F3 @ Y4) @ (F3 @ X)))))))))). % antimono_def
thf(fact_79_antimono__def, axiom,
    ((order_1631207636at_nat = (^[F3 : nat > nat]: (![X : nat]: (![Y4 : nat]: (((ord_less_eq_nat @ X @ Y4)) => ((ord_less_eq_nat @ (F3 @ Y4) @ (F3 @ X)))))))))). % antimono_def
thf(fact_80_antisym__conv, axiom,
    ((![Y : real, X2 : real]: ((ord_less_eq_real @ Y @ X2) => ((ord_less_eq_real @ X2 @ Y) = (X2 = Y)))))). % antisym_conv
thf(fact_81_antisym__conv, axiom,
    ((![Y : nat, X2 : nat]: ((ord_less_eq_nat @ Y @ X2) => ((ord_less_eq_nat @ X2 @ Y) = (X2 = Y)))))). % antisym_conv
thf(fact_82_order__class_Oorder_Oeq__iff, axiom,
    (((^[Y3 : real]: (^[Z : real]: (Y3 = Z))) = (^[A2 : real]: (^[B2 : real]: (((ord_less_eq_real @ A2 @ B2)) & ((ord_less_eq_real @ B2 @ A2)))))))). % order_class.order.eq_iff
thf(fact_83_order__class_Oorder_Oeq__iff, axiom,
    (((^[Y3 : nat]: (^[Z : nat]: (Y3 = Z))) = (^[A2 : nat]: (^[B2 : nat]: (((ord_less_eq_nat @ A2 @ B2)) & ((ord_less_eq_nat @ B2 @ A2)))))))). % order_class.order.eq_iff
thf(fact_84_ord__eq__le__trans, axiom,
    ((![A : real, B : real, C : real]: ((A = B) => ((ord_less_eq_real @ B @ C) => (ord_less_eq_real @ A @ C)))))). % ord_eq_le_trans
thf(fact_85_ord__eq__le__trans, axiom,
    ((![A : nat, B : nat, C : nat]: ((A = B) => ((ord_less_eq_nat @ B @ C) => (ord_less_eq_nat @ A @ C)))))). % ord_eq_le_trans
thf(fact_86_ord__le__eq__trans, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_eq_real @ A @ B) => ((B = C) => (ord_less_eq_real @ A @ C)))))). % ord_le_eq_trans
thf(fact_87_ord__le__eq__trans, axiom,
    ((![A : nat, B : nat, C : nat]: ((ord_less_eq_nat @ A @ B) => ((B = C) => (ord_less_eq_nat @ A @ C)))))). % ord_le_eq_trans
thf(fact_88_order__class_Oorder_Oantisym, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ B @ A) => (A = B)))))). % order_class.order.antisym
thf(fact_89_order__class_Oorder_Oantisym, axiom,
    ((![A : nat, B : nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ B @ A) => (A = B)))))). % order_class.order.antisym
thf(fact_90_order__trans, axiom,
    ((![X2 : real, Y : real, Z2 : real]: ((ord_less_eq_real @ X2 @ Y) => ((ord_less_eq_real @ Y @ Z2) => (ord_less_eq_real @ X2 @ Z2)))))). % order_trans
thf(fact_91_order__trans, axiom,
    ((![X2 : nat, Y : nat, Z2 : nat]: ((ord_less_eq_nat @ X2 @ Y) => ((ord_less_eq_nat @ Y @ Z2) => (ord_less_eq_nat @ X2 @ Z2)))))). % order_trans
thf(fact_92_dual__order_Orefl, axiom,
    ((![A : real]: (ord_less_eq_real @ A @ A)))). % dual_order.refl
thf(fact_93_dual__order_Orefl, axiom,
    ((![A : nat]: (ord_less_eq_nat @ A @ A)))). % dual_order.refl
thf(fact_94_linorder__wlog, axiom,
    ((![P : real > real > $o, A : real, B : real]: ((![A3 : real, B3 : real]: ((ord_less_eq_real @ A3 @ B3) => (P @ A3 @ B3))) => ((![A3 : real, B3 : real]: ((P @ B3 @ A3) => (P @ A3 @ B3))) => (P @ A @ B)))))). % linorder_wlog
thf(fact_95_linorder__wlog, axiom,
    ((![P : nat > nat > $o, A : nat, B : nat]: ((![A3 : nat, B3 : nat]: ((ord_less_eq_nat @ A3 @ B3) => (P @ A3 @ B3))) => ((![A3 : nat, B3 : nat]: ((P @ B3 @ A3) => (P @ A3 @ B3))) => (P @ A @ B)))))). % linorder_wlog
thf(fact_96_dual__order_Otrans, axiom,
    ((![B : real, A : real, C : real]: ((ord_less_eq_real @ B @ A) => ((ord_less_eq_real @ C @ B) => (ord_less_eq_real @ C @ A)))))). % dual_order.trans
thf(fact_97_dual__order_Otrans, axiom,
    ((![B : nat, A : nat, C : nat]: ((ord_less_eq_nat @ B @ A) => ((ord_less_eq_nat @ C @ B) => (ord_less_eq_nat @ C @ A)))))). % dual_order.trans
thf(fact_98_dual__order_Oeq__iff, axiom,
    (((^[Y3 : real]: (^[Z : real]: (Y3 = Z))) = (^[A2 : real]: (^[B2 : real]: (((ord_less_eq_real @ B2 @ A2)) & ((ord_less_eq_real @ A2 @ B2)))))))). % dual_order.eq_iff
thf(fact_99_dual__order_Oeq__iff, axiom,
    (((^[Y3 : nat]: (^[Z : nat]: (Y3 = Z))) = (^[A2 : nat]: (^[B2 : nat]: (((ord_less_eq_nat @ B2 @ A2)) & ((ord_less_eq_nat @ A2 @ B2)))))))). % dual_order.eq_iff
thf(fact_100_complex__mod__minus__le__complex__mod, axiom,
    ((![X2 : complex]: (ord_less_eq_real @ (uminus_uminus_real @ (real_V638595069omplex @ X2)) @ (real_V638595069omplex @ X2))))). % complex_mod_minus_le_complex_mod
thf(fact_101_dual__order_Oantisym, axiom,
    ((![B : real, A : real]: ((ord_less_eq_real @ B @ A) => ((ord_less_eq_real @ A @ B) => (A = B)))))). % dual_order.antisym
thf(fact_102_dual__order_Oantisym, axiom,
    ((![B : nat, A : nat]: ((ord_less_eq_nat @ B @ A) => ((ord_less_eq_nat @ A @ B) => (A = B)))))). % dual_order.antisym
thf(fact_103_complex__mod__triangle__sub, axiom,
    ((![W : complex, Z2 : complex]: (ord_less_eq_real @ (real_V638595069omplex @ W) @ (plus_plus_real @ (real_V638595069omplex @ (plus_plus_complex @ W @ Z2)) @ (real_V638595069omplex @ Z2)))))). % complex_mod_triangle_sub
thf(fact_104_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_105_complex__eq__iff, axiom,
    (((^[Y3 : complex]: (^[Z : complex]: (Y3 = Z))) = (^[X : complex]: (^[Y4 : complex]: ((((re @ X) = (re @ Y4))) & (((im @ X) = (im @ Y4))))))))). % complex_eq_iff
thf(fact_106_complex_Oexpand, axiom,
    ((![Complex2 : complex, Complex3 : complex]: ((((re @ Complex2) = (re @ Complex3)) & ((im @ Complex2) = (im @ Complex3))) => (Complex2 = Complex3))))). % complex.expand
thf(fact_107_complex__eqI, axiom,
    ((![X2 : complex, Y : complex]: (((re @ X2) = (re @ Y)) => (((im @ X2) = (im @ Y)) => (X2 = Y)))))). % complex_eqI
thf(fact_108_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_109_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_110_strict__mono__less__eq, axiom,
    ((![F2 : real > real, X2 : real, Y : real]: ((order_1818878995l_real @ F2) => ((ord_less_eq_real @ (F2 @ X2) @ (F2 @ Y)) = (ord_less_eq_real @ X2 @ Y)))))). % strict_mono_less_eq
thf(fact_111_strict__mono__less__eq, axiom,
    ((![F2 : nat > real, X2 : nat, Y : nat]: ((order_952716343t_real @ F2) => ((ord_less_eq_real @ (F2 @ X2) @ (F2 @ Y)) = (ord_less_eq_nat @ X2 @ Y)))))). % strict_mono_less_eq
thf(fact_112_strict__mono__less__eq, axiom,
    ((![F2 : real > nat, X2 : real, Y : real]: ((order_297469111al_nat @ F2) => ((ord_less_eq_nat @ (F2 @ X2) @ (F2 @ Y)) = (ord_less_eq_real @ X2 @ Y)))))). % strict_mono_less_eq
thf(fact_113_strict__mono__less__eq, axiom,
    ((![F2 : nat > nat, X2 : nat, Y : nat]: ((order_769474267at_nat @ F2) => ((ord_less_eq_nat @ (F2 @ X2) @ (F2 @ Y)) = (ord_less_eq_nat @ X2 @ Y)))))). % strict_mono_less_eq
thf(fact_114_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_115_strict__mono__leD, axiom,
    ((![R : real > nat, M3 : real, N4 : real]: ((order_297469111al_nat @ R) => ((ord_less_eq_real @ M3 @ N4) => (ord_less_eq_nat @ (R @ M3) @ (R @ N4))))))). % strict_mono_leD
thf(fact_116_strict__mono__leD, axiom,
    ((![R : nat > real, M3 : nat, N4 : nat]: ((order_952716343t_real @ R) => ((ord_less_eq_nat @ M3 @ N4) => (ord_less_eq_real @ (R @ M3) @ (R @ N4))))))). % strict_mono_leD
thf(fact_117_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_118_norm__minus__cancel, axiom,
    ((![X2 : real]: ((real_V646646907m_real @ (uminus_uminus_real @ X2)) = (real_V646646907m_real @ X2))))). % norm_minus_cancel
thf(fact_119_norm__minus__cancel, axiom,
    ((![X2 : complex]: ((real_V638595069omplex @ (uminus1204672759omplex @ X2)) = (real_V638595069omplex @ X2))))). % norm_minus_cancel
thf(fact_120_add__minus__cancel, axiom,
    ((![A : complex, B : complex]: ((plus_plus_complex @ A @ (plus_plus_complex @ (uminus1204672759omplex @ A) @ B)) = B)))). % add_minus_cancel
thf(fact_121_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_122_minus__add__cancel, axiom,
    ((![A : complex, B : complex]: ((plus_plus_complex @ (uminus1204672759omplex @ A) @ (plus_plus_complex @ A @ B)) = B)))). % minus_add_cancel
thf(fact_123_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_124_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_125_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_126_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_127_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_128_add__le__cancel__left, axiom,
    ((![C : nat, A : nat, B : nat]: ((ord_less_eq_nat @ (plus_plus_nat @ C @ A) @ (plus_plus_nat @ C @ B)) = (ord_less_eq_nat @ A @ B))))). % add_le_cancel_left
thf(fact_129_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_130_add__le__cancel__right, axiom,
    ((![A : nat, C : nat, B : nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ C)) = (ord_less_eq_nat @ A @ B))))). % add_le_cancel_right
thf(fact_131_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_132_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_133_norm__triangle__le, axiom,
    ((![X2 : real, Y : real, E : real]: ((ord_less_eq_real @ (plus_plus_real @ (real_V646646907m_real @ X2) @ (real_V646646907m_real @ Y)) @ E) => (ord_less_eq_real @ (real_V646646907m_real @ (plus_plus_real @ X2 @ Y)) @ E))))). % norm_triangle_le
thf(fact_134_norm__triangle__le, axiom,
    ((![X2 : complex, Y : complex, E : real]: ((ord_less_eq_real @ (plus_plus_real @ (real_V638595069omplex @ X2) @ (real_V638595069omplex @ Y)) @ E) => (ord_less_eq_real @ (real_V638595069omplex @ (plus_plus_complex @ X2 @ Y)) @ E))))). % norm_triangle_le
thf(fact_135_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_136_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_137_add__right__cancel, axiom,
    ((![B : nat, A : nat, C : nat]: (((plus_plus_nat @ B @ A) = (plus_plus_nat @ C @ A)) = (B = C))))). % add_right_cancel
thf(fact_138_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_139_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_140_add__left__cancel, axiom,
    ((![A : nat, B : nat, C : nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ A @ C)) = (B = C))))). % add_left_cancel
thf(fact_141_neg__equal__iff__equal, axiom,
    ((![A : complex, B : complex]: (((uminus1204672759omplex @ A) = (uminus1204672759omplex @ B)) = (A = B))))). % neg_equal_iff_equal
thf(fact_142_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_143_add_Oinverse__inverse, axiom,
    ((![A : complex]: ((uminus1204672759omplex @ (uminus1204672759omplex @ A)) = A)))). % add.inverse_inverse
thf(fact_144_add_Oinverse__inverse, axiom,
    ((![A : real]: ((uminus_uminus_real @ (uminus_uminus_real @ A)) = A)))). % add.inverse_inverse
thf(fact_145_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_146_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_147_add__right__imp__eq, axiom,
    ((![B : nat, A : nat, C : nat]: (((plus_plus_nat @ B @ A) = (plus_plus_nat @ C @ A)) => (B = C))))). % add_right_imp_eq
thf(fact_148_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_149_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_150_add__left__imp__eq, axiom,
    ((![A : nat, B : nat, C : nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ A @ C)) => (B = C))))). % add_left_imp_eq
thf(fact_151_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_152_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_153_add_Oleft__commute, axiom,
    ((![B : nat, A : nat, C : nat]: ((plus_plus_nat @ B @ (plus_plus_nat @ A @ C)) = (plus_plus_nat @ A @ (plus_plus_nat @ B @ C)))))). % add.left_commute
thf(fact_154_add_Ocommute, axiom,
    ((plus_plus_complex = (^[A2 : complex]: (^[B2 : complex]: (plus_plus_complex @ B2 @ A2)))))). % add.commute
thf(fact_155_add_Ocommute, axiom,
    ((plus_plus_real = (^[A2 : real]: (^[B2 : real]: (plus_plus_real @ B2 @ A2)))))). % add.commute
thf(fact_156_add_Ocommute, axiom,
    ((plus_plus_nat = (^[A2 : nat]: (^[B2 : nat]: (plus_plus_nat @ B2 @ A2)))))). % add.commute
thf(fact_157_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_158_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_159_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
thf(fact_160_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_161_add_Oassoc, axiom,
    ((![A : complex, B : complex, C : complex]: ((plus_plus_complex @ (plus_plus_complex @ A @ B) @ C) = (plus_plus_complex @ A @ (plus_plus_complex @ B @ C)))))). % add.assoc
thf(fact_162_add_Oassoc, 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)))))). % add.assoc
thf(fact_163_add_Oassoc, axiom,
    ((![A : nat, B : nat, C : nat]: ((plus_plus_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ A @ (plus_plus_nat @ B @ C)))))). % add.assoc
thf(fact_164_group__cancel_Oadd2, axiom,
    ((![B4 : complex, K : complex, B : complex, A : complex]: ((B4 = (plus_plus_complex @ K @ B)) => ((plus_plus_complex @ A @ B4) = (plus_plus_complex @ K @ (plus_plus_complex @ A @ B))))))). % group_cancel.add2
thf(fact_165_group__cancel_Oadd2, axiom,
    ((![B4 : real, K : real, B : real, A : real]: ((B4 = (plus_plus_real @ K @ B)) => ((plus_plus_real @ A @ B4) = (plus_plus_real @ K @ (plus_plus_real @ A @ B))))))). % group_cancel.add2
thf(fact_166_group__cancel_Oadd2, axiom,
    ((![B4 : nat, K : nat, B : nat, A : nat]: ((B4 = (plus_plus_nat @ K @ B)) => ((plus_plus_nat @ A @ B4) = (plus_plus_nat @ K @ (plus_plus_nat @ A @ B))))))). % group_cancel.add2
thf(fact_167_group__cancel_Oadd1, axiom,
    ((![A4 : complex, K : complex, A : complex, B : complex]: ((A4 = (plus_plus_complex @ K @ A)) => ((plus_plus_complex @ A4 @ B) = (plus_plus_complex @ K @ (plus_plus_complex @ A @ B))))))). % group_cancel.add1
thf(fact_168_group__cancel_Oadd1, axiom,
    ((![A4 : real, K : real, A : real, B : real]: ((A4 = (plus_plus_real @ K @ A)) => ((plus_plus_real @ A4 @ B) = (plus_plus_real @ K @ (plus_plus_real @ A @ B))))))). % group_cancel.add1
thf(fact_169_group__cancel_Oadd1, axiom,
    ((![A4 : nat, K : nat, A : nat, B : nat]: ((A4 = (plus_plus_nat @ K @ A)) => ((plus_plus_nat @ A4 @ B) = (plus_plus_nat @ K @ (plus_plus_nat @ A @ B))))))). % group_cancel.add1
thf(fact_170_add__mono__thms__linordered__semiring_I4_J, axiom,
    ((![I : real, J : real, K : real, L : real]: (((I = J) & (K = L)) => ((plus_plus_real @ I @ K) = (plus_plus_real @ J @ L)))))). % add_mono_thms_linordered_semiring(4)
thf(fact_171_add__mono__thms__linordered__semiring_I4_J, axiom,
    ((![I : nat, J : nat, K : nat, L : nat]: (((I = J) & (K = L)) => ((plus_plus_nat @ I @ K) = (plus_plus_nat @ J @ L)))))). % add_mono_thms_linordered_semiring(4)
thf(fact_172_ab__semigroup__add__class_Oadd__ac_I1_J, axiom,
    ((![A : complex, B : complex, C : complex]: ((plus_plus_complex @ (plus_plus_complex @ A @ B) @ C) = (plus_plus_complex @ A @ (plus_plus_complex @ B @ C)))))). % ab_semigroup_add_class.add_ac(1)
thf(fact_173_ab__semigroup__add__class_Oadd__ac_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)))))). % ab_semigroup_add_class.add_ac(1)
thf(fact_174_ab__semigroup__add__class_Oadd__ac_I1_J, axiom,
    ((![A : nat, B : nat, C : nat]: ((plus_plus_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ A @ (plus_plus_nat @ B @ C)))))). % ab_semigroup_add_class.add_ac(1)
thf(fact_175_minus__equation__iff, axiom,
    ((![A : complex, B : complex]: (((uminus1204672759omplex @ A) = B) = ((uminus1204672759omplex @ B) = A))))). % minus_equation_iff
thf(fact_176_minus__equation__iff, axiom,
    ((![A : real, B : real]: (((uminus_uminus_real @ A) = B) = ((uminus_uminus_real @ B) = A))))). % minus_equation_iff
thf(fact_177_equation__minus__iff, axiom,
    ((![A : complex, B : complex]: ((A = (uminus1204672759omplex @ B)) = (B = (uminus1204672759omplex @ A)))))). % equation_minus_iff
thf(fact_178_equation__minus__iff, axiom,
    ((![A : real, B : real]: ((A = (uminus_uminus_real @ B)) = (B = (uminus_uminus_real @ A)))))). % equation_minus_iff
thf(fact_179_add__le__imp__le__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_imp_le_right
thf(fact_180_add__le__imp__le__right, axiom,
    ((![A : nat, C : nat, B : nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ C)) => (ord_less_eq_nat @ A @ B))))). % add_le_imp_le_right
thf(fact_181_add__le__imp__le__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_imp_le_left
thf(fact_182_add__le__imp__le__left, axiom,
    ((![C : nat, A : nat, B : nat]: ((ord_less_eq_nat @ (plus_plus_nat @ C @ A) @ (plus_plus_nat @ C @ B)) => (ord_less_eq_nat @ A @ B))))). % add_le_imp_le_left
thf(fact_183_le__iff__add, axiom,
    ((ord_less_eq_nat = (^[A2 : nat]: (^[B2 : nat]: (?[C2 : nat]: (B2 = (plus_plus_nat @ A2 @ C2)))))))). % le_iff_add
thf(fact_184_add__right__mono, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_eq_real @ A @ B) => (ord_less_eq_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ C)))))). % add_right_mono
thf(fact_185_add__right__mono, axiom,
    ((![A : nat, B : nat, C : nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ C)))))). % add_right_mono
thf(fact_186_less__eqE, axiom,
    ((![A : nat, B : nat]: ((ord_less_eq_nat @ A @ B) => (~ ((![C3 : nat]: (~ ((B = (plus_plus_nat @ A @ C3))))))))))). % less_eqE
thf(fact_187_add__left__mono, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_eq_real @ A @ B) => (ord_less_eq_real @ (plus_plus_real @ C @ A) @ (plus_plus_real @ C @ B)))))). % add_left_mono
thf(fact_188_add__left__mono, axiom,
    ((![A : nat, B : nat, C : nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (plus_plus_nat @ C @ A) @ (plus_plus_nat @ C @ B)))))). % add_left_mono
thf(fact_189_add__mono, axiom,
    ((![A : real, B : real, C : real, D : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ C @ D) => (ord_less_eq_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ D))))))). % add_mono
thf(fact_190_add__mono, axiom,
    ((![A : nat, B : nat, C : nat, D : nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ C @ D) => (ord_less_eq_nat @ (plus_plus_nat @ A @ C) @ (plus_plus_nat @ B @ D))))))). % add_mono
thf(fact_191_add__mono__thms__linordered__semiring_I1_J, axiom,
    ((![I : real, J : real, K : real, L : real]: (((ord_less_eq_real @ I @ J) & (ord_less_eq_real @ K @ L)) => (ord_less_eq_real @ (plus_plus_real @ I @ K) @ (plus_plus_real @ J @ L)))))). % add_mono_thms_linordered_semiring(1)
thf(fact_192_add__mono__thms__linordered__semiring_I1_J, axiom,
    ((![I : nat, J : nat, K : nat, L : nat]: (((ord_less_eq_nat @ I @ J) & (ord_less_eq_nat @ K @ L)) => (ord_less_eq_nat @ (plus_plus_nat @ I @ K) @ (plus_plus_nat @ J @ L)))))). % add_mono_thms_linordered_semiring(1)
thf(fact_193_add__mono__thms__linordered__semiring_I2_J, axiom,
    ((![I : real, J : real, K : real, L : real]: (((I = J) & (ord_less_eq_real @ K @ L)) => (ord_less_eq_real @ (plus_plus_real @ I @ K) @ (plus_plus_real @ J @ L)))))). % add_mono_thms_linordered_semiring(2)
thf(fact_194_add__mono__thms__linordered__semiring_I2_J, axiom,
    ((![I : nat, J : nat, K : nat, L : nat]: (((I = J) & (ord_less_eq_nat @ K @ L)) => (ord_less_eq_nat @ (plus_plus_nat @ I @ K) @ (plus_plus_nat @ J @ L)))))). % add_mono_thms_linordered_semiring(2)
thf(fact_195_add__mono__thms__linordered__semiring_I3_J, axiom,
    ((![I : real, J : real, K : real, L : real]: (((ord_less_eq_real @ I @ J) & (K = L)) => (ord_less_eq_real @ (plus_plus_real @ I @ K) @ (plus_plus_real @ J @ L)))))). % add_mono_thms_linordered_semiring(3)
thf(fact_196_add__mono__thms__linordered__semiring_I3_J, axiom,
    ((![I : nat, J : nat, K : nat, L : nat]: (((ord_less_eq_nat @ I @ J) & (K = L)) => (ord_less_eq_nat @ (plus_plus_nat @ I @ K) @ (plus_plus_nat @ J @ L)))))). % add_mono_thms_linordered_semiring(3)
thf(fact_197_le__imp__neg__le, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ A @ B) => (ord_less_eq_real @ (uminus_uminus_real @ B) @ (uminus_uminus_real @ A)))))). % le_imp_neg_le
thf(fact_198_minus__le__iff, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ (uminus_uminus_real @ A) @ B) = (ord_less_eq_real @ (uminus_uminus_real @ B) @ A))))). % minus_le_iff
thf(fact_199_le__minus__iff, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ A @ (uminus_uminus_real @ B)) = (ord_less_eq_real @ B @ (uminus_uminus_real @ A)))))). % le_minus_iff
thf(fact_200_add_Oinverse__distrib__swap, axiom,
    ((![A : complex, B : complex]: ((uminus1204672759omplex @ (plus_plus_complex @ A @ B)) = (plus_plus_complex @ (uminus1204672759omplex @ B) @ (uminus1204672759omplex @ A)))))). % add.inverse_distrib_swap
thf(fact_201_add_Oinverse__distrib__swap, axiom,
    ((![A : real, B : real]: ((uminus_uminus_real @ (plus_plus_real @ A @ B)) = (plus_plus_real @ (uminus_uminus_real @ B) @ (uminus_uminus_real @ A)))))). % add.inverse_distrib_swap
thf(fact_202_group__cancel_Oneg1, axiom,
    ((![A4 : complex, K : complex, A : complex]: ((A4 = (plus_plus_complex @ K @ A)) => ((uminus1204672759omplex @ A4) = (plus_plus_complex @ (uminus1204672759omplex @ K) @ (uminus1204672759omplex @ A))))))). % group_cancel.neg1
thf(fact_203_group__cancel_Oneg1, axiom,
    ((![A4 : real, K : real, A : real]: ((A4 = (plus_plus_real @ K @ A)) => ((uminus_uminus_real @ A4) = (plus_plus_real @ (uminus_uminus_real @ K) @ (uminus_uminus_real @ A))))))). % group_cancel.neg1
thf(fact_204_norm__triangle__mono, axiom,
    ((![A : real, R : real, B : real, S : real]: ((ord_less_eq_real @ (real_V646646907m_real @ A) @ R) => ((ord_less_eq_real @ (real_V646646907m_real @ B) @ S) => (ord_less_eq_real @ (real_V646646907m_real @ (plus_plus_real @ A @ B)) @ (plus_plus_real @ R @ S))))))). % norm_triangle_mono
thf(fact_205_norm__triangle__mono, axiom,
    ((![A : complex, R : real, B : complex, S : real]: ((ord_less_eq_real @ (real_V638595069omplex @ A) @ R) => ((ord_less_eq_real @ (real_V638595069omplex @ B) @ S) => (ord_less_eq_real @ (real_V638595069omplex @ (plus_plus_complex @ A @ B)) @ (plus_plus_real @ R @ S))))))). % norm_triangle_mono
thf(fact_206_norm__triangle__ineq, axiom,
    ((![X2 : real, Y : real]: (ord_less_eq_real @ (real_V646646907m_real @ (plus_plus_real @ X2 @ Y)) @ (plus_plus_real @ (real_V646646907m_real @ X2) @ (real_V646646907m_real @ Y)))))). % norm_triangle_ineq
thf(fact_207_norm__triangle__ineq, axiom,
    ((![X2 : complex, Y : complex]: (ord_less_eq_real @ (real_V638595069omplex @ (plus_plus_complex @ X2 @ Y)) @ (plus_plus_real @ (real_V638595069omplex @ X2) @ (real_V638595069omplex @ Y)))))). % norm_triangle_ineq
thf(fact_208_comp__apply, axiom,
    ((comp_nat_real_nat = (^[F3 : nat > real]: (^[G : nat > nat]: (^[X : nat]: (F3 @ (G @ X)))))))). % comp_apply
thf(fact_209_comp__apply, axiom,
    ((comp_c1631780367al_nat = (^[F3 : complex > real]: (^[G : nat > complex]: (^[X : nat]: (F3 @ (G @ X)))))))). % comp_apply
thf(fact_210_nat__add__left__cancel__le, axiom,
    ((![K : nat, M3 : nat, N4 : nat]: ((ord_less_eq_nat @ (plus_plus_nat @ K @ M3) @ (plus_plus_nat @ K @ N4)) = (ord_less_eq_nat @ M3 @ N4))))). % nat_add_left_cancel_le
thf(fact_211_verit__minus__simplify_I4_J, axiom,
    ((![B : complex]: ((uminus1204672759omplex @ (uminus1204672759omplex @ B)) = B)))). % verit_minus_simplify(4)
thf(fact_212_verit__minus__simplify_I4_J, axiom,
    ((![B : real]: ((uminus_uminus_real @ (uminus_uminus_real @ B)) = B)))). % verit_minus_simplify(4)
thf(fact_213_strict__mono__imp__increasing, axiom,
    ((![F2 : nat > nat, N4 : nat]: ((order_769474267at_nat @ F2) => (ord_less_eq_nat @ N4 @ (F2 @ N4)))))). % strict_mono_imp_increasing
thf(fact_214_verit__la__disequality, axiom,
    ((![A : real, B : real]: ((A = B) | ((~ ((ord_less_eq_real @ A @ B))) | (~ ((ord_less_eq_real @ B @ A)))))))). % verit_la_disequality
thf(fact_215_verit__la__disequality, axiom,
    ((![A : nat, B : nat]: ((A = B) | ((~ ((ord_less_eq_nat @ A @ B))) | (~ ((ord_less_eq_nat @ B @ A)))))))). % verit_la_disequality
thf(fact_216_verit__negate__coefficient_I3_J, axiom,
    ((![A : real, B : real]: ((A = B) => ((uminus_uminus_real @ A) = (uminus_uminus_real @ B)))))). % verit_negate_coefficient(3)
thf(fact_217_Nat_Oex__has__greatest__nat, axiom,
    ((![P : nat > $o, K : nat, B : nat]: ((P @ K) => ((![Y2 : nat]: ((P @ Y2) => (ord_less_eq_nat @ Y2 @ B))) => (?[X4 : nat]: ((P @ X4) & (![Y5 : nat]: ((P @ Y5) => (ord_less_eq_nat @ Y5 @ X4)))))))))). % Nat.ex_has_greatest_nat
thf(fact_218_nat__le__iff__add, axiom,
    ((ord_less_eq_nat = (^[M2 : nat]: (^[N : nat]: (?[K2 : nat]: (N = (plus_plus_nat @ M2 @ K2)))))))). % nat_le_iff_add
thf(fact_219_trans__le__add2, axiom,
    ((![I : nat, J : nat, M3 : nat]: ((ord_less_eq_nat @ I @ J) => (ord_less_eq_nat @ I @ (plus_plus_nat @ M3 @ J)))))). % trans_le_add2
thf(fact_220_trans__le__add1, axiom,
    ((![I : nat, J : nat, M3 : nat]: ((ord_less_eq_nat @ I @ J) => (ord_less_eq_nat @ I @ (plus_plus_nat @ J @ M3)))))). % trans_le_add1
thf(fact_221_nat__le__linear, axiom,
    ((![M3 : nat, N4 : nat]: ((ord_less_eq_nat @ M3 @ N4) | (ord_less_eq_nat @ N4 @ M3))))). % nat_le_linear
thf(fact_222_add__le__mono1, axiom,
    ((![I : nat, J : nat, K : nat]: ((ord_less_eq_nat @ I @ J) => (ord_less_eq_nat @ (plus_plus_nat @ I @ K) @ (plus_plus_nat @ J @ K)))))). % add_le_mono1
thf(fact_223_add__le__mono, axiom,
    ((![I : nat, J : nat, K : nat, L : nat]: ((ord_less_eq_nat @ I @ J) => ((ord_less_eq_nat @ K @ L) => (ord_less_eq_nat @ (plus_plus_nat @ I @ K) @ (plus_plus_nat @ J @ L))))))). % add_le_mono
thf(fact_224_le__antisym, axiom,
    ((![M3 : nat, N4 : nat]: ((ord_less_eq_nat @ M3 @ N4) => ((ord_less_eq_nat @ N4 @ M3) => (M3 = N4)))))). % le_antisym
thf(fact_225_le__Suc__ex, axiom,
    ((![K : nat, L : nat]: ((ord_less_eq_nat @ K @ L) => (?[N3 : nat]: (L = (plus_plus_nat @ K @ N3))))))). % le_Suc_ex
thf(fact_226_eq__imp__le, axiom,
    ((![M3 : nat, N4 : nat]: ((M3 = N4) => (ord_less_eq_nat @ M3 @ N4))))). % eq_imp_le
thf(fact_227_le__trans, axiom,
    ((![I : nat, J : nat, K : nat]: ((ord_less_eq_nat @ I @ J) => ((ord_less_eq_nat @ J @ K) => (ord_less_eq_nat @ I @ K)))))). % le_trans
thf(fact_228_add__leD2, axiom,
    ((![M3 : nat, K : nat, N4 : nat]: ((ord_less_eq_nat @ (plus_plus_nat @ M3 @ K) @ N4) => (ord_less_eq_nat @ K @ N4))))). % add_leD2
thf(fact_229_add__leD1, axiom,
    ((![M3 : nat, K : nat, N4 : nat]: ((ord_less_eq_nat @ (plus_plus_nat @ M3 @ K) @ N4) => (ord_less_eq_nat @ M3 @ N4))))). % add_leD1
thf(fact_230_le__refl, axiom,
    ((![N4 : nat]: (ord_less_eq_nat @ N4 @ N4)))). % le_refl
thf(fact_231_le__add2, axiom,
    ((![N4 : nat, M3 : nat]: (ord_less_eq_nat @ N4 @ (plus_plus_nat @ M3 @ N4))))). % le_add2
thf(fact_232_le__add1, axiom,
    ((![N4 : nat, M3 : nat]: (ord_less_eq_nat @ N4 @ (plus_plus_nat @ N4 @ M3))))). % le_add1
thf(fact_233_add__leE, axiom,
    ((![M3 : nat, K : nat, N4 : nat]: ((ord_less_eq_nat @ (plus_plus_nat @ M3 @ K) @ N4) => (~ (((ord_less_eq_nat @ M3 @ N4) => (~ ((ord_less_eq_nat @ K @ N4)))))))))). % add_leE
thf(fact_234_comp__def, axiom,
    ((comp_nat_real_nat = (^[F3 : nat > real]: (^[G : nat > nat]: (^[X : nat]: (F3 @ (G @ X)))))))). % comp_def
thf(fact_235_comp__def, axiom,
    ((comp_c1631780367al_nat = (^[F3 : complex > real]: (^[G : nat > complex]: (^[X : nat]: (F3 @ (G @ X)))))))). % comp_def
thf(fact_236_comp__assoc, axiom,
    ((![F2 : real > real, G2 : nat > real, H : nat > nat]: ((comp_nat_real_nat @ (comp_real_real_nat @ F2 @ G2) @ H) = (comp_real_real_nat @ F2 @ (comp_nat_real_nat @ G2 @ H)))))). % comp_assoc
thf(fact_237_comp__assoc, axiom,
    ((![F2 : nat > real, G2 : nat > nat, H : nat > nat]: ((comp_nat_real_nat @ (comp_nat_real_nat @ F2 @ G2) @ H) = (comp_nat_real_nat @ F2 @ (comp_nat_nat_nat @ G2 @ H)))))). % comp_assoc
thf(fact_238_comp__assoc, axiom,
    ((![F2 : complex > real, G2 : nat > complex, H : nat > nat]: ((comp_nat_real_nat @ (comp_c1631780367al_nat @ F2 @ G2) @ H) = (comp_c1631780367al_nat @ F2 @ (comp_nat_complex_nat @ G2 @ H)))))). % comp_assoc
thf(fact_239_comp__assoc, axiom,
    ((![F2 : real > real, G2 : complex > real, H : nat > complex]: ((comp_c1631780367al_nat @ (comp_r422820971omplex @ F2 @ G2) @ H) = (comp_real_real_nat @ F2 @ (comp_c1631780367al_nat @ G2 @ H)))))). % comp_assoc
thf(fact_240_comp__assoc, axiom,
    ((![F2 : nat > real, G2 : complex > nat, H : nat > complex]: ((comp_c1631780367al_nat @ (comp_n1816297743omplex @ F2 @ G2) @ H) = (comp_nat_real_nat @ F2 @ (comp_complex_nat_nat @ G2 @ H)))))). % comp_assoc
thf(fact_241_comp__assoc, axiom,
    ((![F2 : complex > real, G2 : complex > complex, H : nat > complex]: ((comp_c1631780367al_nat @ (comp_c317287661omplex @ F2 @ G2) @ H) = (comp_c1631780367al_nat @ F2 @ (comp_c438056209ex_nat @ G2 @ H)))))). % comp_assoc
thf(fact_242_comp__eq__dest, axiom,
    ((![A : nat > real, B : nat > nat, C : nat > real, D : nat > nat, V : nat]: (((comp_nat_real_nat @ A @ B) = (comp_nat_real_nat @ C @ D)) => ((A @ (B @ V)) = (C @ (D @ V))))))). % comp_eq_dest
thf(fact_243_comp__eq__dest, axiom,
    ((![A : nat > real, B : nat > nat, C : complex > real, D : nat > complex, V : nat]: (((comp_nat_real_nat @ A @ B) = (comp_c1631780367al_nat @ C @ D)) => ((A @ (B @ V)) = (C @ (D @ V))))))). % comp_eq_dest
thf(fact_244_comp__eq__dest, axiom,
    ((![A : complex > real, B : nat > complex, C : nat > real, D : nat > nat, V : nat]: (((comp_c1631780367al_nat @ A @ B) = (comp_nat_real_nat @ C @ D)) => ((A @ (B @ V)) = (C @ (D @ V))))))). % comp_eq_dest
thf(fact_245_comp__eq__dest, axiom,
    ((![A : complex > real, B : nat > complex, C : complex > real, D : nat > complex, V : nat]: (((comp_c1631780367al_nat @ A @ B) = (comp_c1631780367al_nat @ C @ D)) => ((A @ (B @ V)) = (C @ (D @ V))))))). % comp_eq_dest
thf(fact_246_comp__eq__elim, axiom,
    ((![A : nat > real, B : nat > nat, C : complex > real, D : nat > complex]: (((comp_nat_real_nat @ A @ B) = (comp_c1631780367al_nat @ C @ D)) => (![V2 : nat]: ((A @ (B @ V2)) = (C @ (D @ V2)))))))). % comp_eq_elim
thf(fact_247_comp__eq__elim, axiom,
    ((![A : complex > real, B : nat > complex, C : nat > real, D : nat > nat]: (((comp_c1631780367al_nat @ A @ B) = (comp_nat_real_nat @ C @ D)) => (![V2 : nat]: ((A @ (B @ V2)) = (C @ (D @ V2)))))))). % comp_eq_elim
thf(fact_248_comp__eq__elim, axiom,
    ((![A : complex > real, B : nat > complex, C : complex > real, D : nat > complex]: (((comp_c1631780367al_nat @ A @ B) = (comp_c1631780367al_nat @ C @ D)) => (![V2 : nat]: ((A @ (B @ V2)) = (C @ (D @ V2)))))))). % comp_eq_elim

% Conjectures (2)
thf(conj_0, hypothesis,
    ((![G3 : nat > nat]: ((order_769474267at_nat @ G3) => ((topolo144289241q_real @ (^[N : nat]: (im @ (s @ (f @ (G3 @ N)))))) => thesis))))).
thf(conj_1, conjecture,
    (thesis)).
