% 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_243__5369868_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:28:27.104

% Could-be-implicit typings (6)
thf(ty_n_t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J, type,
    set_set_nat : $tType).
thf(ty_n_t__Set__Oset_It__Real__Oreal_J, type,
    set_real : $tType).
thf(ty_n_t__Set__Oset_It__Nat__Onat_J, type,
    set_nat : $tType).
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 (35)
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_Finite__Set_Ofinite_001t__Nat__Onat, type,
    finite_finite_nat : set_nat > $o).
thf(sy_c_Finite__Set_Ofinite_001t__Real__Oreal, type,
    finite_finite_real : set_real > $o).
thf(sy_c_Finite__Set_Ofinite_001t__Set__Oset_It__Nat__Onat_J, type,
    finite2012248349et_nat : set_set_nat > $o).
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__Real__Oreal_001t__Real__Oreal_001t__Real__Oreal, type,
    comp_real_real_real : (real > real) > (real > real) > 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_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_Oord__class_Oless__eq_001t__Set__Oset_It__Nat__Onat_J, type,
    ord_less_eq_set_nat : set_nat > set_nat > $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_Set_OCollect_001t__Nat__Onat, type,
    collect_nat : (nat > $o) > set_nat).
thf(sy_c_Set_OCollect_001t__Set__Oset_It__Nat__Onat_J, type,
    collect_set_nat : (set_nat > $o) > set_set_nat).
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_c_member_001t__Nat__Onat, type,
    member_nat : nat > set_nat > $o).
thf(sy_c_member_001t__Real__Oreal, type,
    member_real : real > set_real > $o).
thf(sy_v_r, type,
    r : real).
thf(sy_v_s, type,
    s : nat > complex).
thf(sy_v_thesis____, type,
    thesis : $o).

% Relevant facts (240)
thf(fact_0__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_1_seq__monosub, axiom,
    ((![S : nat > real]: (?[F : nat > nat]: ((order_769474267at_nat @ F) & (topolo144289241q_real @ (^[N : nat]: (S @ (F @ N))))))))). % seq_monosub
thf(fact_2_strict__mono__compose, axiom,
    ((![R : real > real, S : real > real]: ((order_1818878995l_real @ R) => ((order_1818878995l_real @ S) => (order_1818878995l_real @ (^[X : real]: (R @ (S @ X))))))))). % strict_mono_compose
thf(fact_3_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_4_strict__mono__eq, axiom,
    ((![F2 : real > real, X2 : real, Y : real]: ((order_1818878995l_real @ F2) => (((F2 @ X2) = (F2 @ Y)) = (X2 = Y)))))). % strict_mono_eq
thf(fact_5_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_6_r, axiom,
    ((![N2 : nat]: (ord_less_eq_real @ (real_V638595069omplex @ (s @ N2)) @ r)))). % r
thf(fact_7_Re__def, axiom,
    ((re = (case_complex_real @ (^[X1 : real]: (^[X22 : real]: X1)))))). % Re_def
thf(fact_8_monoseq__minus, axiom,
    ((![A : nat > real]: ((topolo144289241q_real @ A) => (topolo144289241q_real @ (^[N : nat]: (uminus_uminus_real @ (A @ N)))))))). % monoseq_minus
thf(fact_9_strict__mono__add, axiom,
    ((![K : real]: (order_1818878995l_real @ (^[N : real]: (plus_plus_real @ N @ K)))))). % strict_mono_add
thf(fact_10_strict__mono__add, axiom,
    ((![K : nat]: (order_769474267at_nat @ (^[N : nat]: (plus_plus_nat @ N @ K)))))). % strict_mono_add
thf(fact_11_decseq__imp__monoseq, axiom,
    ((![X3 : nat > real]: ((order_106095024t_real @ X3) => (topolo144289241q_real @ X3))))). % decseq_imp_monoseq
thf(fact_12_strict__mono__imp__increasing, axiom,
    ((![F2 : nat > nat, N3 : nat]: ((order_769474267at_nat @ F2) => (ord_less_eq_nat @ N3 @ (F2 @ N3)))))). % strict_mono_imp_increasing
thf(fact_13_infinite__enumerate, axiom,
    ((![S2 : set_nat]: ((~ ((finite_finite_nat @ S2))) => (?[R2 : nat > nat]: ((order_769474267at_nat @ R2) & (![N2 : nat]: (member_nat @ (R2 @ N2) @ S2)))))))). % infinite_enumerate
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_nat__add__left__cancel__le, axiom,
    ((![K : nat, M : nat, N3 : nat]: ((ord_less_eq_nat @ (plus_plus_nat @ K @ M) @ (plus_plus_nat @ K @ N3)) = (ord_less_eq_nat @ M @ N3))))). % nat_add_left_cancel_le
thf(fact_17_decseq__const, axiom,
    ((![K : real]: (order_106095024t_real @ (^[X : nat]: K))))). % decseq_const
thf(fact_18_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_19_uminus__complex_Osimps_I1_J, axiom,
    ((![X2 : complex]: ((re @ (uminus1204672759omplex @ X2)) = (uminus_uminus_real @ (re @ X2)))))). % uminus_complex.simps(1)
thf(fact_20_add__leE, axiom,
    ((![M : nat, K : nat, N3 : nat]: ((ord_less_eq_nat @ (plus_plus_nat @ M @ K) @ N3) => (~ (((ord_less_eq_nat @ M @ N3) => (~ ((ord_less_eq_nat @ K @ N3)))))))))). % add_leE
thf(fact_21_le__add1, axiom,
    ((![N3 : nat, M : nat]: (ord_less_eq_nat @ N3 @ (plus_plus_nat @ N3 @ M))))). % le_add1
thf(fact_22_le__add2, axiom,
    ((![N3 : nat, M : nat]: (ord_less_eq_nat @ N3 @ (plus_plus_nat @ M @ N3))))). % le_add2
thf(fact_23_le__refl, axiom,
    ((![N3 : nat]: (ord_less_eq_nat @ N3 @ N3)))). % le_refl
thf(fact_24_add__leD1, axiom,
    ((![M : nat, K : nat, N3 : nat]: ((ord_less_eq_nat @ (plus_plus_nat @ M @ K) @ N3) => (ord_less_eq_nat @ M @ N3))))). % add_leD1
thf(fact_25_add__leD2, axiom,
    ((![M : nat, K : nat, N3 : nat]: ((ord_less_eq_nat @ (plus_plus_nat @ M @ K) @ N3) => (ord_less_eq_nat @ K @ N3))))). % add_leD2
thf(fact_26_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_27_eq__imp__le, axiom,
    ((![M : nat, N3 : nat]: ((M = N3) => (ord_less_eq_nat @ M @ N3))))). % eq_imp_le
thf(fact_28_le__Suc__ex, axiom,
    ((![K : nat, L : nat]: ((ord_less_eq_nat @ K @ L) => (?[N4 : nat]: (L = (plus_plus_nat @ K @ N4))))))). % le_Suc_ex
thf(fact_29_le__antisym, axiom,
    ((![M : nat, N3 : nat]: ((ord_less_eq_nat @ M @ N3) => ((ord_less_eq_nat @ N3 @ M) => (M = N3)))))). % le_antisym
thf(fact_30_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_31_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_32_nat__le__linear, axiom,
    ((![M : nat, N3 : nat]: ((ord_less_eq_nat @ M @ N3) | (ord_less_eq_nat @ N3 @ M))))). % nat_le_linear
thf(fact_33_trans__le__add1, axiom,
    ((![I : nat, J : nat, M : nat]: ((ord_less_eq_nat @ I @ J) => (ord_less_eq_nat @ I @ (plus_plus_nat @ J @ M)))))). % trans_le_add1
thf(fact_34_trans__le__add2, axiom,
    ((![I : nat, J : nat, M : nat]: ((ord_less_eq_nat @ I @ J) => (ord_less_eq_nat @ I @ (plus_plus_nat @ M @ J)))))). % trans_le_add2
thf(fact_35_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_36_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_37_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_38_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_39_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_40_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_41_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_42_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_43_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_44_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) & (![Y3 : nat]: ((P @ Y3) => (ord_less_eq_nat @ Y3 @ X4)))))))))). % Nat.ex_has_greatest_nat
thf(fact_45_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_46_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_47_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_48_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_49_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_50_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_51_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_52_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_53_monoI1, axiom,
    ((![X3 : nat > real]: ((![M3 : nat, N4 : nat]: ((ord_less_eq_nat @ M3 @ N4) => (ord_less_eq_real @ (X3 @ M3) @ (X3 @ N4)))) => (topolo144289241q_real @ X3))))). % monoI1
thf(fact_54_monoI1, axiom,
    ((![X3 : nat > nat]: ((![M3 : nat, N4 : nat]: ((ord_less_eq_nat @ M3 @ N4) => (ord_less_eq_nat @ (X3 @ M3) @ (X3 @ N4)))) => (topolo1922093437eq_nat @ X3))))). % monoI1
thf(fact_55_monoI2, axiom,
    ((![X3 : nat > real]: ((![M3 : nat, N4 : nat]: ((ord_less_eq_nat @ M3 @ N4) => (ord_less_eq_real @ (X3 @ N4) @ (X3 @ M3)))) => (topolo144289241q_real @ X3))))). % monoI2
thf(fact_56_monoI2, axiom,
    ((![X3 : nat > nat]: ((![M3 : nat, N4 : nat]: ((ord_less_eq_nat @ M3 @ N4) => (ord_less_eq_nat @ (X3 @ N4) @ (X3 @ M3)))) => (topolo1922093437eq_nat @ X3))))). % monoI2
thf(fact_57_mem__Collect__eq, axiom,
    ((![A : nat, P : nat > $o]: ((member_nat @ A @ (collect_nat @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_58_Collect__mem__eq, axiom,
    ((![A2 : set_nat]: ((collect_nat @ (^[X : nat]: (member_nat @ X @ A2))) = A2)))). % Collect_mem_eq
thf(fact_59_Collect__cong, axiom,
    ((![P : nat > $o, Q : nat > $o]: ((![X4 : nat]: ((P @ X4) = (Q @ X4))) => ((collect_nat @ P) = (collect_nat @ Q)))))). % Collect_cong
thf(fact_60_complex__Re__le__cmod, axiom,
    ((![X2 : complex]: (ord_less_eq_real @ (re @ X2) @ (real_V638595069omplex @ X2))))). % complex_Re_le_cmod
thf(fact_61_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_62_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_63_complex_Ocase__distrib, axiom,
    ((![H : real > real, F2 : real > real > real, Complex : complex]: ((H @ (case_complex_real @ F2 @ Complex)) = (case_complex_real @ (^[X1 : real]: (^[X22 : real]: (H @ (F2 @ X1 @ X22)))) @ Complex))))). % complex.case_distrib
thf(fact_64_eq__iff, axiom,
    (((^[Y4 : real]: (^[Z : real]: (Y4 = Z))) = (^[X : real]: (^[Y5 : real]: (((ord_less_eq_real @ X @ Y5)) & ((ord_less_eq_real @ Y5 @ X)))))))). % eq_iff
thf(fact_65_eq__iff, axiom,
    (((^[Y4 : nat]: (^[Z : nat]: (Y4 = Z))) = (^[X : nat]: (^[Y5 : nat]: (((ord_less_eq_nat @ X @ Y5)) & ((ord_less_eq_nat @ Y5 @ X)))))))). % eq_iff
thf(fact_66_antisym, axiom,
    ((![X2 : real, Y : real]: ((ord_less_eq_real @ X2 @ Y) => ((ord_less_eq_real @ Y @ X2) => (X2 = Y)))))). % antisym
thf(fact_67_antisym, axiom,
    ((![X2 : nat, Y : nat]: ((ord_less_eq_nat @ X2 @ Y) => ((ord_less_eq_nat @ Y @ X2) => (X2 = Y)))))). % antisym
thf(fact_68_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_69_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_70_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_71_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_72_linear, axiom,
    ((![X2 : real, Y : real]: ((ord_less_eq_real @ X2 @ Y) | (ord_less_eq_real @ Y @ X2))))). % linear
thf(fact_73_linear, axiom,
    ((![X2 : nat, Y : nat]: ((ord_less_eq_nat @ X2 @ Y) | (ord_less_eq_nat @ Y @ X2))))). % linear
thf(fact_74_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_75_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_76_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_77_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_78_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_79_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_80_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_81_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_82_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_83_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_84_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_85_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_86_eq__refl, axiom,
    ((![X2 : real, Y : real]: ((X2 = Y) => (ord_less_eq_real @ X2 @ Y))))). % eq_refl
thf(fact_87_eq__refl, axiom,
    ((![X2 : nat, Y : nat]: ((X2 = Y) => (ord_less_eq_nat @ X2 @ Y))))). % eq_refl
thf(fact_88_le__cases, axiom,
    ((![X2 : real, Y : real]: ((~ ((ord_less_eq_real @ X2 @ Y))) => (ord_less_eq_real @ Y @ X2))))). % le_cases
thf(fact_89_le__cases, axiom,
    ((![X2 : nat, Y : nat]: ((~ ((ord_less_eq_nat @ X2 @ Y))) => (ord_less_eq_nat @ Y @ X2))))). % le_cases
thf(fact_90_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_91_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_92_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_93_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_94_antimono__def, axiom,
    ((order_537808140l_real = (^[F3 : real > real]: (![X : real]: (![Y5 : real]: (((ord_less_eq_real @ X @ Y5)) => ((ord_less_eq_real @ (F3 @ Y5) @ (F3 @ X)))))))))). % antimono_def
thf(fact_95_antimono__def, axiom,
    ((order_1598331440al_nat = (^[F3 : real > nat]: (![X : real]: (![Y5 : real]: (((ord_less_eq_real @ X @ Y5)) => ((ord_less_eq_nat @ (F3 @ Y5) @ (F3 @ X)))))))))). % antimono_def
thf(fact_96_antimono__def, axiom,
    ((order_1631207636at_nat = (^[F3 : nat > nat]: (![X : nat]: (![Y5 : nat]: (((ord_less_eq_nat @ X @ Y5)) => ((ord_less_eq_nat @ (F3 @ Y5) @ (F3 @ X)))))))))). % antimono_def
thf(fact_97_antimono__def, axiom,
    ((order_106095024t_real = (^[F3 : nat > real]: (![X : nat]: (![Y5 : nat]: (((ord_less_eq_nat @ X @ Y5)) => ((ord_less_eq_real @ (F3 @ Y5) @ (F3 @ X)))))))))). % antimono_def
thf(fact_98_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_99_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_100_order__class_Oorder_Oeq__iff, axiom,
    (((^[Y4 : real]: (^[Z : real]: (Y4 = Z))) = (^[A3 : real]: (^[B2 : real]: (((ord_less_eq_real @ A3 @ B2)) & ((ord_less_eq_real @ B2 @ A3)))))))). % order_class.order.eq_iff
thf(fact_101_order__class_Oorder_Oeq__iff, axiom,
    (((^[Y4 : nat]: (^[Z : nat]: (Y4 = Z))) = (^[A3 : nat]: (^[B2 : nat]: (((ord_less_eq_nat @ A3 @ B2)) & ((ord_less_eq_nat @ B2 @ A3)))))))). % order_class.order.eq_iff
thf(fact_102_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_103_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_104_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_105_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_106_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_107_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_108_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_109_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_110_dual__order_Orefl, axiom,
    ((![A : real]: (ord_less_eq_real @ A @ A)))). % dual_order.refl
thf(fact_111_dual__order_Orefl, axiom,
    ((![A : nat]: (ord_less_eq_nat @ A @ A)))). % dual_order.refl
thf(fact_112_linorder__wlog, axiom,
    ((![P : real > real > $o, A : real, B : real]: ((![A4 : real, B3 : real]: ((ord_less_eq_real @ A4 @ B3) => (P @ A4 @ B3))) => ((![A4 : real, B3 : real]: ((P @ B3 @ A4) => (P @ A4 @ B3))) => (P @ A @ B)))))). % linorder_wlog
thf(fact_113_linorder__wlog, axiom,
    ((![P : nat > nat > $o, A : nat, B : nat]: ((![A4 : nat, B3 : nat]: ((ord_less_eq_nat @ A4 @ B3) => (P @ A4 @ B3))) => ((![A4 : nat, B3 : nat]: ((P @ B3 @ A4) => (P @ A4 @ B3))) => (P @ A @ B)))))). % linorder_wlog
thf(fact_114_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_115_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_116_dual__order_Oeq__iff, axiom,
    (((^[Y4 : real]: (^[Z : real]: (Y4 = Z))) = (^[A3 : real]: (^[B2 : real]: (((ord_less_eq_real @ B2 @ A3)) & ((ord_less_eq_real @ A3 @ B2)))))))). % dual_order.eq_iff
thf(fact_117_dual__order_Oeq__iff, axiom,
    (((^[Y4 : nat]: (^[Z : nat]: (Y4 = Z))) = (^[A3 : nat]: (^[B2 : nat]: (((ord_less_eq_nat @ B2 @ A3)) & ((ord_less_eq_nat @ A3 @ B2)))))))). % dual_order.eq_iff
thf(fact_118_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_119_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_120_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_121_infinite__nat__iff__unbounded__le, axiom,
    ((![S2 : set_nat]: ((~ ((finite_finite_nat @ S2))) = (![M2 : nat]: (?[N : nat]: (((ord_less_eq_nat @ M2 @ N)) & ((member_nat @ N @ S2))))))))). % infinite_nat_iff_unbounded_le
thf(fact_122_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_123_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_124_strict__mono__o, axiom,
    ((![R : real > real, S : real > real]: ((order_1818878995l_real @ R) => ((order_1818878995l_real @ S) => (order_1818878995l_real @ (comp_real_real_real @ R @ S))))))). % strict_mono_o
thf(fact_125_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_126_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_127_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_128_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_129_strict__mono__leD, axiom,
    ((![R : real > nat, M : real, N3 : real]: ((order_297469111al_nat @ R) => ((ord_less_eq_real @ M @ N3) => (ord_less_eq_nat @ (R @ M) @ (R @ N3))))))). % strict_mono_leD
thf(fact_130_strict__mono__leD, axiom,
    ((![R : nat > real, M : nat, N3 : nat]: ((order_952716343t_real @ R) => ((ord_less_eq_nat @ M @ N3) => (ord_less_eq_real @ (R @ M) @ (R @ N3))))))). % strict_mono_leD
thf(fact_131_strict__mono__leD, axiom,
    ((![R : nat > nat, M : nat, N3 : nat]: ((order_769474267at_nat @ R) => ((ord_less_eq_nat @ M @ N3) => (ord_less_eq_nat @ (R @ M) @ (R @ N3))))))). % strict_mono_leD
thf(fact_132_strict__mono__leD, axiom,
    ((![R : real > real, M : real, N3 : real]: ((order_1818878995l_real @ R) => ((ord_less_eq_real @ M @ N3) => (ord_less_eq_real @ (R @ M) @ (R @ N3))))))). % strict_mono_leD
thf(fact_133_finite__Collect__le__nat, axiom,
    ((![K : nat]: (finite_finite_nat @ (collect_nat @ (^[N : nat]: (ord_less_eq_nat @ N @ K))))))). % finite_Collect_le_nat
thf(fact_134_norm__minus__cancel, axiom,
    ((![X2 : real]: ((real_V646646907m_real @ (uminus_uminus_real @ X2)) = (real_V646646907m_real @ X2))))). % norm_minus_cancel
thf(fact_135_norm__minus__cancel, axiom,
    ((![X2 : complex]: ((real_V638595069omplex @ (uminus1204672759omplex @ X2)) = (real_V638595069omplex @ X2))))). % norm_minus_cancel
thf(fact_136_add__minus__cancel, axiom,
    ((![A : complex, B : complex]: ((plus_plus_complex @ A @ (plus_plus_complex @ (uminus1204672759omplex @ A) @ B)) = B)))). % add_minus_cancel
thf(fact_137_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_138_minus__add__cancel, axiom,
    ((![A : complex, B : complex]: ((plus_plus_complex @ (uminus1204672759omplex @ A) @ (plus_plus_complex @ A @ B)) = B)))). % minus_add_cancel
thf(fact_139_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_140_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_141_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_142_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_143_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_144_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_145_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_146_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_147_finite__Collect__conjI, axiom,
    ((![P : nat > $o, Q : nat > $o]: (((finite_finite_nat @ (collect_nat @ P)) | (finite_finite_nat @ (collect_nat @ Q))) => (finite_finite_nat @ (collect_nat @ (^[X : nat]: (((P @ X)) & ((Q @ X)))))))))). % finite_Collect_conjI
thf(fact_148_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_149_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_150_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_151_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_152_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_153_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_154_neg__equal__iff__equal, axiom,
    ((![A : complex, B : complex]: (((uminus1204672759omplex @ A) = (uminus1204672759omplex @ B)) = (A = B))))). % neg_equal_iff_equal
thf(fact_155_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_156_add_Oinverse__inverse, axiom,
    ((![A : complex]: ((uminus1204672759omplex @ (uminus1204672759omplex @ A)) = A)))). % add.inverse_inverse
thf(fact_157_add_Oinverse__inverse, axiom,
    ((![A : real]: ((uminus_uminus_real @ (uminus_uminus_real @ A)) = A)))). % add.inverse_inverse
thf(fact_158_finite__Collect__subsets, axiom,
    ((![A2 : set_nat]: ((finite_finite_nat @ A2) => (finite2012248349et_nat @ (collect_set_nat @ (^[B4 : set_nat]: (ord_less_eq_set_nat @ B4 @ A2)))))))). % finite_Collect_subsets
thf(fact_159_finite__Collect__disjI, axiom,
    ((![P : nat > $o, Q : nat > $o]: ((finite_finite_nat @ (collect_nat @ (^[X : nat]: (((P @ X)) | ((Q @ X)))))) = (((finite_finite_nat @ (collect_nat @ P))) & ((finite_finite_nat @ (collect_nat @ Q)))))))). % finite_Collect_disjI
thf(fact_160_rev__finite__subset, axiom,
    ((![B5 : set_nat, A2 : set_nat]: ((finite_finite_nat @ B5) => ((ord_less_eq_set_nat @ A2 @ B5) => (finite_finite_nat @ A2)))))). % rev_finite_subset
thf(fact_161_infinite__super, axiom,
    ((![S2 : set_nat, T : set_nat]: ((ord_less_eq_set_nat @ S2 @ T) => ((~ ((finite_finite_nat @ S2))) => (~ ((finite_finite_nat @ T)))))))). % infinite_super
thf(fact_162_finite__subset, axiom,
    ((![A2 : set_nat, B5 : set_nat]: ((ord_less_eq_set_nat @ A2 @ B5) => ((finite_finite_nat @ B5) => (finite_finite_nat @ A2)))))). % finite_subset
thf(fact_163_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_164_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_165_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_166_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_167_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_168_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_169_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_170_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_171_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_172_add_Ocommute, axiom,
    ((plus_plus_nat = (^[A3 : nat]: (^[B2 : nat]: (plus_plus_nat @ B2 @ A3)))))). % add.commute
thf(fact_173_add_Ocommute, axiom,
    ((plus_plus_complex = (^[A3 : complex]: (^[B2 : complex]: (plus_plus_complex @ B2 @ A3)))))). % add.commute
thf(fact_174_add_Ocommute, axiom,
    ((plus_plus_real = (^[A3 : real]: (^[B2 : real]: (plus_plus_real @ B2 @ A3)))))). % add.commute
thf(fact_175_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_176_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_177_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_178_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_179_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_180_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_181_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_182_group__cancel_Oadd2, axiom,
    ((![B5 : nat, K : nat, B : nat, A : nat]: ((B5 = (plus_plus_nat @ K @ B)) => ((plus_plus_nat @ A @ B5) = (plus_plus_nat @ K @ (plus_plus_nat @ A @ B))))))). % group_cancel.add2
thf(fact_183_group__cancel_Oadd2, axiom,
    ((![B5 : complex, K : complex, B : complex, A : complex]: ((B5 = (plus_plus_complex @ K @ B)) => ((plus_plus_complex @ A @ B5) = (plus_plus_complex @ K @ (plus_plus_complex @ A @ B))))))). % group_cancel.add2
thf(fact_184_group__cancel_Oadd2, axiom,
    ((![B5 : real, K : real, B : real, A : real]: ((B5 = (plus_plus_real @ K @ B)) => ((plus_plus_real @ A @ B5) = (plus_plus_real @ K @ (plus_plus_real @ A @ B))))))). % group_cancel.add2
thf(fact_185_group__cancel_Oadd1, axiom,
    ((![A2 : nat, K : nat, A : nat, B : nat]: ((A2 = (plus_plus_nat @ K @ A)) => ((plus_plus_nat @ A2 @ B) = (plus_plus_nat @ K @ (plus_plus_nat @ A @ B))))))). % group_cancel.add1
thf(fact_186_group__cancel_Oadd1, axiom,
    ((![A2 : complex, K : complex, A : complex, B : complex]: ((A2 = (plus_plus_complex @ K @ A)) => ((plus_plus_complex @ A2 @ B) = (plus_plus_complex @ K @ (plus_plus_complex @ A @ B))))))). % group_cancel.add1
thf(fact_187_group__cancel_Oadd1, axiom,
    ((![A2 : real, K : real, A : real, B : real]: ((A2 = (plus_plus_real @ K @ A)) => ((plus_plus_real @ A2 @ B) = (plus_plus_real @ K @ (plus_plus_real @ A @ B))))))). % group_cancel.add1
thf(fact_188_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_189_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_190_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_191_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_192_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_193_minus__equation__iff, axiom,
    ((![A : complex, B : complex]: (((uminus1204672759omplex @ A) = B) = ((uminus1204672759omplex @ B) = A))))). % minus_equation_iff
thf(fact_194_minus__equation__iff, axiom,
    ((![A : real, B : real]: (((uminus_uminus_real @ A) = B) = ((uminus_uminus_real @ B) = A))))). % minus_equation_iff
thf(fact_195_equation__minus__iff, axiom,
    ((![A : complex, B : complex]: ((A = (uminus1204672759omplex @ B)) = (B = (uminus1204672759omplex @ A)))))). % equation_minus_iff
thf(fact_196_equation__minus__iff, axiom,
    ((![A : real, B : real]: ((A = (uminus_uminus_real @ B)) = (B = (uminus_uminus_real @ A)))))). % equation_minus_iff
thf(fact_197_pigeonhole__infinite__rel, axiom,
    ((![A2 : set_nat, B5 : set_nat, R3 : nat > nat > $o]: ((~ ((finite_finite_nat @ A2))) => ((finite_finite_nat @ B5) => ((![X4 : nat]: ((member_nat @ X4 @ A2) => (?[Xa : nat]: ((member_nat @ Xa @ B5) & (R3 @ X4 @ Xa))))) => (?[X4 : nat]: ((member_nat @ X4 @ B5) & (~ ((finite_finite_nat @ (collect_nat @ (^[A3 : nat]: (((member_nat @ A3 @ A2)) & ((R3 @ A3 @ X4)))))))))))))))). % pigeonhole_infinite_rel
thf(fact_198_not__finite__existsD, axiom,
    ((![P : nat > $o]: ((~ ((finite_finite_nat @ (collect_nat @ P)))) => (?[X_1 : nat]: (P @ X_1)))))). % not_finite_existsD
thf(fact_199_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_200_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_201_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_202_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_203_le__iff__add, axiom,
    ((ord_less_eq_nat = (^[A3 : nat]: (^[B2 : nat]: (?[C2 : nat]: (B2 = (plus_plus_nat @ A3 @ C2)))))))). % le_iff_add
thf(fact_204_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_205_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_206_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_207_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_208_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_209_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_210_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_211_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_212_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_213_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_214_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_215_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_216_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_217_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_218_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_219_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_220_finite__has__minimal2, axiom,
    ((![A2 : set_real, A : real]: ((finite_finite_real @ A2) => ((member_real @ A @ A2) => (?[X4 : real]: ((member_real @ X4 @ A2) & ((ord_less_eq_real @ X4 @ A) & (![Xa : real]: ((member_real @ Xa @ A2) => ((ord_less_eq_real @ Xa @ X4) => (X4 = Xa)))))))))))). % finite_has_minimal2
thf(fact_221_finite__has__minimal2, axiom,
    ((![A2 : set_nat, A : nat]: ((finite_finite_nat @ A2) => ((member_nat @ A @ A2) => (?[X4 : nat]: ((member_nat @ X4 @ A2) & ((ord_less_eq_nat @ X4 @ A) & (![Xa : nat]: ((member_nat @ Xa @ A2) => ((ord_less_eq_nat @ Xa @ X4) => (X4 = Xa)))))))))))). % finite_has_minimal2
thf(fact_222_finite__has__maximal2, axiom,
    ((![A2 : set_real, A : real]: ((finite_finite_real @ A2) => ((member_real @ A @ A2) => (?[X4 : real]: ((member_real @ X4 @ A2) & ((ord_less_eq_real @ A @ X4) & (![Xa : real]: ((member_real @ Xa @ A2) => ((ord_less_eq_real @ X4 @ Xa) => (X4 = Xa)))))))))))). % finite_has_maximal2
thf(fact_223_finite__has__maximal2, axiom,
    ((![A2 : set_nat, A : nat]: ((finite_finite_nat @ A2) => ((member_nat @ A @ A2) => (?[X4 : nat]: ((member_nat @ X4 @ A2) & ((ord_less_eq_nat @ A @ X4) & (![Xa : nat]: ((member_nat @ Xa @ A2) => ((ord_less_eq_nat @ X4 @ Xa) => (X4 = Xa)))))))))))). % finite_has_maximal2
thf(fact_224_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_225_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_226_group__cancel_Oneg1, axiom,
    ((![A2 : complex, K : complex, A : complex]: ((A2 = (plus_plus_complex @ K @ A)) => ((uminus1204672759omplex @ A2) = (plus_plus_complex @ (uminus1204672759omplex @ K) @ (uminus1204672759omplex @ A))))))). % group_cancel.neg1
thf(fact_227_group__cancel_Oneg1, axiom,
    ((![A2 : real, K : real, A : real]: ((A2 = (plus_plus_real @ K @ A)) => ((uminus_uminus_real @ A2) = (plus_plus_real @ (uminus_uminus_real @ K) @ (uminus_uminus_real @ A))))))). % group_cancel.neg1
thf(fact_228_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_229_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_230_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_231_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_232_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_233_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_234_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_235_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_236_finite__less__ub, axiom,
    ((![F2 : nat > nat, U : nat]: ((![N4 : nat]: (ord_less_eq_nat @ N4 @ (F2 @ N4))) => (finite_finite_nat @ (collect_nat @ (^[N : nat]: (ord_less_eq_nat @ (F2 @ N) @ U)))))))). % finite_less_ub
thf(fact_237_comp__apply, axiom,
    ((comp_c1631780367al_nat = (^[F3 : complex > real]: (^[G : nat > complex]: (^[X : nat]: (F3 @ (G @ X)))))))). % comp_apply
thf(fact_238_verit__minus__simplify_I4_J, axiom,
    ((![B : complex]: ((uminus1204672759omplex @ (uminus1204672759omplex @ B)) = B)))). % verit_minus_simplify(4)
thf(fact_239_verit__minus__simplify_I4_J, axiom,
    ((![B : real]: ((uminus_uminus_real @ (uminus_uminus_real @ B)) = B)))). % verit_minus_simplify(4)

% Conjectures (2)
thf(conj_0, hypothesis,
    ((![F4 : nat > nat]: ((order_769474267at_nat @ F4) => ((topolo144289241q_real @ (^[N : nat]: (re @ (s @ (F4 @ N))))) => thesis))))).
thf(conj_1, conjecture,
    (thesis)).
