% 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_33__5366972_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:26:25.946

% Could-be-implicit typings (4)
thf(ty_n_t__Polynomial__Opoly_Itf__a_J, type,
    poly_a : $tType).
thf(ty_n_t__Complex__Ocomplex, type,
    complex : $tType).
thf(ty_n_t__Real__Oreal, type,
    real : $tType).
thf(ty_n_tf__a, type,
    a : $tType).

% Explicit typings (26)
thf(sy_c_Groups_Oabs__class_Oabs_001t__Complex__Ocomplex, type,
    abs_abs_complex : complex > complex).
thf(sy_c_Groups_Oabs__class_Oabs_001t__Real__Oreal, type,
    abs_abs_real : real > real).
thf(sy_c_Groups_Oone__class_Oone_001t__Complex__Ocomplex, type,
    one_one_complex : complex).
thf(sy_c_Groups_Oone__class_Oone_001t__Real__Oreal, type,
    one_one_real : real).
thf(sy_c_Groups_Oone__class_Oone_001tf__a, type,
    one_one_a : a).
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__Polynomial__Opoly_Itf__a_J, type,
    plus_plus_poly_a : poly_a > poly_a > poly_a).
thf(sy_c_Groups_Oplus__class_Oplus_001t__Real__Oreal, type,
    plus_plus_real : real > real > real).
thf(sy_c_Groups_Oplus__class_Oplus_001tf__a, type,
    plus_plus_a : a > a > a).
thf(sy_c_Groups_Otimes__class_Otimes_001t__Complex__Ocomplex, type,
    times_times_complex : complex > complex > complex).
thf(sy_c_Groups_Otimes__class_Otimes_001t__Polynomial__Opoly_Itf__a_J, type,
    times_times_poly_a : poly_a > poly_a > poly_a).
thf(sy_c_Groups_Otimes__class_Otimes_001t__Real__Oreal, type,
    times_times_real : real > real > real).
thf(sy_c_Groups_Otimes__class_Otimes_001tf__a, type,
    times_times_a : a > a > a).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Complex__Ocomplex, type,
    zero_zero_complex : complex).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_Itf__a_J, type,
    zero_zero_poly_a : poly_a).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Real__Oreal, type,
    zero_zero_real : real).
thf(sy_c_Groups_Ozero__class_Ozero_001tf__a, type,
    zero_zero_a : a).
thf(sy_c_Orderings_Oord__class_Oless_001t__Real__Oreal, type,
    ord_less_real : real > real > $o).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Real__Oreal, type,
    ord_less_eq_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_Real__Vector__Spaces_Onorm__class_Onorm_001tf__a, type,
    real_V1022479215norm_a : a > real).
thf(sy_v_c____, type,
    c : a).
thf(sy_v_cs____, type,
    cs : poly_a).
thf(sy_v_m____, type,
    m : real).
thf(sy_v_r, type,
    r : real).

% Relevant facts (221)
thf(fact_0__092_060open_0620_A_092_060le_062_Anorm_Ac_092_060close_062, axiom,
    ((ord_less_eq_real @ zero_zero_real @ (real_V1022479215norm_a @ c)))). % \<open>0 \<le> norm c\<close>
thf(fact_1__092_060open_0620_A_092_060le_062_A_092_060bar_062r_A_K_Am_092_060bar_062_092_060close_062, axiom,
    ((ord_less_eq_real @ zero_zero_real @ (abs_abs_real @ (times_times_real @ r @ m))))). % \<open>0 \<le> \<bar>r * m\<bar>\<close>
thf(fact_2_zero__less__norm__iff, axiom,
    ((![X : a]: ((ord_less_real @ zero_zero_real @ (real_V1022479215norm_a @ X)) = (~ ((X = zero_zero_a))))))). % zero_less_norm_iff
thf(fact_3_zero__less__norm__iff, axiom,
    ((![X : complex]: ((ord_less_real @ zero_zero_real @ (real_V638595069omplex @ X)) = (~ ((X = zero_zero_complex))))))). % zero_less_norm_iff
thf(fact_4_zero__less__norm__iff, axiom,
    ((![X : real]: ((ord_less_real @ zero_zero_real @ (real_V646646907m_real @ X)) = (~ ((X = zero_zero_real))))))). % zero_less_norm_iff
thf(fact_5_norm__one, axiom,
    (((real_V1022479215norm_a @ one_one_a) = one_one_real))). % norm_one
thf(fact_6_norm__one, axiom,
    (((real_V638595069omplex @ one_one_complex) = one_one_real))). % norm_one
thf(fact_7_norm__one, axiom,
    (((real_V646646907m_real @ one_one_real) = one_one_real))). % norm_one
thf(fact_8_not__real__square__gt__zero, axiom,
    ((![X : real]: ((~ ((ord_less_real @ zero_zero_real @ (times_times_real @ X @ X)))) = (X = zero_zero_real))))). % not_real_square_gt_zero
thf(fact_9_norm__zero, axiom,
    (((real_V1022479215norm_a @ zero_zero_a) = zero_zero_real))). % norm_zero
thf(fact_10_norm__zero, axiom,
    (((real_V638595069omplex @ zero_zero_complex) = zero_zero_real))). % norm_zero
thf(fact_11_norm__zero, axiom,
    (((real_V646646907m_real @ zero_zero_real) = zero_zero_real))). % norm_zero
thf(fact_12_norm__eq__zero, axiom,
    ((![X : a]: (((real_V1022479215norm_a @ X) = zero_zero_real) = (X = zero_zero_a))))). % norm_eq_zero
thf(fact_13_norm__eq__zero, axiom,
    ((![X : complex]: (((real_V638595069omplex @ X) = zero_zero_real) = (X = zero_zero_complex))))). % norm_eq_zero
thf(fact_14_norm__eq__zero, axiom,
    ((![X : real]: (((real_V646646907m_real @ X) = zero_zero_real) = (X = zero_zero_real))))). % norm_eq_zero
thf(fact_15_zero__less__abs__iff, axiom,
    ((![A : real]: ((ord_less_real @ zero_zero_real @ (abs_abs_real @ A)) = (~ ((A = zero_zero_real))))))). % zero_less_abs_iff
thf(fact_16_mult__cancel__left1, axiom,
    ((![C : complex, B : complex]: ((C = (times_times_complex @ C @ B)) = (((C = zero_zero_complex)) | ((B = one_one_complex))))))). % mult_cancel_left1
thf(fact_17_mult__cancel__left1, axiom,
    ((![C : a, B : a]: ((C = (times_times_a @ C @ B)) = (((C = zero_zero_a)) | ((B = one_one_a))))))). % mult_cancel_left1
thf(fact_18_mult__cancel__left1, axiom,
    ((![C : real, B : real]: ((C = (times_times_real @ C @ B)) = (((C = zero_zero_real)) | ((B = one_one_real))))))). % mult_cancel_left1
thf(fact_19_mult__cancel__left2, axiom,
    ((![C : complex, A : complex]: (((times_times_complex @ C @ A) = C) = (((C = zero_zero_complex)) | ((A = one_one_complex))))))). % mult_cancel_left2
thf(fact_20_mult__cancel__left2, axiom,
    ((![C : a, A : a]: (((times_times_a @ C @ A) = C) = (((C = zero_zero_a)) | ((A = one_one_a))))))). % mult_cancel_left2
thf(fact_21_mult__cancel__left2, axiom,
    ((![C : real, A : real]: (((times_times_real @ C @ A) = C) = (((C = zero_zero_real)) | ((A = one_one_real))))))). % mult_cancel_left2
thf(fact_22_mult__cancel__right1, axiom,
    ((![C : complex, B : complex]: ((C = (times_times_complex @ B @ C)) = (((C = zero_zero_complex)) | ((B = one_one_complex))))))). % mult_cancel_right1
thf(fact_23_mult__cancel__right1, axiom,
    ((![C : real, B : real]: ((C = (times_times_real @ B @ C)) = (((C = zero_zero_real)) | ((B = one_one_real))))))). % mult_cancel_right1
thf(fact_24_mult__cancel__right1, axiom,
    ((![C : a, B : a]: ((C = (times_times_a @ B @ C)) = (((C = zero_zero_a)) | ((B = one_one_a))))))). % mult_cancel_right1
thf(fact_25_mult__cancel__right2, axiom,
    ((![A : complex, C : complex]: (((times_times_complex @ A @ C) = C) = (((C = zero_zero_complex)) | ((A = one_one_complex))))))). % mult_cancel_right2
thf(fact_26_mult__cancel__right2, axiom,
    ((![A : real, C : real]: (((times_times_real @ A @ C) = C) = (((C = zero_zero_real)) | ((A = one_one_real))))))). % mult_cancel_right2
thf(fact_27_mult__cancel__right2, axiom,
    ((![A : a, C : a]: (((times_times_a @ A @ C) = C) = (((C = zero_zero_a)) | ((A = one_one_a))))))). % mult_cancel_right2
thf(fact_28_sum__squares__eq__zero__iff, axiom,
    ((![X : real, Y : real]: (((plus_plus_real @ (times_times_real @ X @ X) @ (times_times_real @ Y @ Y)) = zero_zero_real) = (((X = zero_zero_real)) & ((Y = zero_zero_real))))))). % sum_squares_eq_zero_iff
thf(fact_29_add__less__same__cancel1, axiom,
    ((![B : real, A : real]: ((ord_less_real @ (plus_plus_real @ B @ A) @ B) = (ord_less_real @ A @ zero_zero_real))))). % add_less_same_cancel1
thf(fact_30_pCons_Ohyps_I1_J, axiom,
    (((~ ((c = zero_zero_a))) | (~ ((cs = zero_zero_poly_a)))))). % pCons.hyps(1)
thf(fact_31_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_32_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_33_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_34_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_35_abs__idempotent, axiom,
    ((![A : real]: ((abs_abs_real @ (abs_abs_real @ A)) = (abs_abs_real @ A))))). % abs_idempotent
thf(fact_36_abs__abs, axiom,
    ((![A : real]: ((abs_abs_real @ (abs_abs_real @ A)) = (abs_abs_real @ A))))). % abs_abs
thf(fact_37_mult__cancel__right, axiom,
    ((![A : complex, C : complex, B : complex]: (((times_times_complex @ A @ C) = (times_times_complex @ B @ C)) = (((C = zero_zero_complex)) | ((A = B))))))). % mult_cancel_right
thf(fact_38_mult__cancel__right, axiom,
    ((![A : real, C : real, B : real]: (((times_times_real @ A @ C) = (times_times_real @ B @ C)) = (((C = zero_zero_real)) | ((A = B))))))). % mult_cancel_right
thf(fact_39_mult__cancel__right, axiom,
    ((![A : a, C : a, B : a]: (((times_times_a @ A @ C) = (times_times_a @ B @ C)) = (((C = zero_zero_a)) | ((A = B))))))). % mult_cancel_right
thf(fact_40_mult__cancel__left, axiom,
    ((![C : complex, A : complex, B : complex]: (((times_times_complex @ C @ A) = (times_times_complex @ C @ B)) = (((C = zero_zero_complex)) | ((A = B))))))). % mult_cancel_left
thf(fact_41_mult__cancel__left, axiom,
    ((![C : real, A : real, B : real]: (((times_times_real @ C @ A) = (times_times_real @ C @ B)) = (((C = zero_zero_real)) | ((A = B))))))). % mult_cancel_left
thf(fact_42_mult__cancel__left, axiom,
    ((![C : a, A : a, B : a]: (((times_times_a @ C @ A) = (times_times_a @ C @ B)) = (((C = zero_zero_a)) | ((A = B))))))). % mult_cancel_left
thf(fact_43_mult__eq__0__iff, axiom,
    ((![A : poly_a, B : poly_a]: (((times_times_poly_a @ A @ B) = zero_zero_poly_a) = (((A = zero_zero_poly_a)) | ((B = zero_zero_poly_a))))))). % mult_eq_0_iff
thf(fact_44_mult__eq__0__iff, axiom,
    ((![A : complex, B : complex]: (((times_times_complex @ A @ B) = zero_zero_complex) = (((A = zero_zero_complex)) | ((B = zero_zero_complex))))))). % mult_eq_0_iff
thf(fact_45_mult__eq__0__iff, axiom,
    ((![A : real, B : real]: (((times_times_real @ A @ B) = zero_zero_real) = (((A = zero_zero_real)) | ((B = zero_zero_real))))))). % mult_eq_0_iff
thf(fact_46_mult__eq__0__iff, axiom,
    ((![A : a, B : a]: (((times_times_a @ A @ B) = zero_zero_a) = (((A = zero_zero_a)) | ((B = zero_zero_a))))))). % mult_eq_0_iff
thf(fact_47_mult__zero__right, axiom,
    ((![A : poly_a]: ((times_times_poly_a @ A @ zero_zero_poly_a) = zero_zero_poly_a)))). % mult_zero_right
thf(fact_48_mult__zero__right, axiom,
    ((![A : complex]: ((times_times_complex @ A @ zero_zero_complex) = zero_zero_complex)))). % mult_zero_right
thf(fact_49_mult__zero__right, axiom,
    ((![A : real]: ((times_times_real @ A @ zero_zero_real) = zero_zero_real)))). % mult_zero_right
thf(fact_50_mult__zero__right, axiom,
    ((![A : a]: ((times_times_a @ A @ zero_zero_a) = zero_zero_a)))). % mult_zero_right
thf(fact_51_mult__zero__left, axiom,
    ((![A : poly_a]: ((times_times_poly_a @ zero_zero_poly_a @ A) = zero_zero_poly_a)))). % mult_zero_left
thf(fact_52_mult__zero__left, axiom,
    ((![A : complex]: ((times_times_complex @ zero_zero_complex @ A) = zero_zero_complex)))). % mult_zero_left
thf(fact_53_mult__zero__left, axiom,
    ((![A : real]: ((times_times_real @ zero_zero_real @ A) = zero_zero_real)))). % mult_zero_left
thf(fact_54_mult__zero__left, axiom,
    ((![A : a]: ((times_times_a @ zero_zero_a @ A) = zero_zero_a)))). % mult_zero_left
thf(fact_55_add__cancel__right__right, axiom,
    ((![A : real, B : real]: ((A = (plus_plus_real @ A @ B)) = (B = zero_zero_real))))). % add_cancel_right_right
thf(fact_56_add__cancel__right__right, axiom,
    ((![A : a, B : a]: ((A = (plus_plus_a @ A @ B)) = (B = zero_zero_a))))). % add_cancel_right_right
thf(fact_57_add__cancel__right__right, axiom,
    ((![A : poly_a, B : poly_a]: ((A = (plus_plus_poly_a @ A @ B)) = (B = zero_zero_poly_a))))). % add_cancel_right_right
thf(fact_58_add__cancel__right__right, axiom,
    ((![A : complex, B : complex]: ((A = (plus_plus_complex @ A @ B)) = (B = zero_zero_complex))))). % add_cancel_right_right
thf(fact_59_add__cancel__right__left, axiom,
    ((![A : real, B : real]: ((A = (plus_plus_real @ B @ A)) = (B = zero_zero_real))))). % add_cancel_right_left
thf(fact_60_add__cancel__right__left, axiom,
    ((![A : a, B : a]: ((A = (plus_plus_a @ B @ A)) = (B = zero_zero_a))))). % add_cancel_right_left
thf(fact_61_add__cancel__right__left, axiom,
    ((![A : poly_a, B : poly_a]: ((A = (plus_plus_poly_a @ B @ A)) = (B = zero_zero_poly_a))))). % add_cancel_right_left
thf(fact_62_add__cancel__right__left, axiom,
    ((![A : complex, B : complex]: ((A = (plus_plus_complex @ B @ A)) = (B = zero_zero_complex))))). % add_cancel_right_left
thf(fact_63_add__cancel__left__right, axiom,
    ((![A : real, B : real]: (((plus_plus_real @ A @ B) = A) = (B = zero_zero_real))))). % add_cancel_left_right
thf(fact_64_add__cancel__left__right, axiom,
    ((![A : a, B : a]: (((plus_plus_a @ A @ B) = A) = (B = zero_zero_a))))). % add_cancel_left_right
thf(fact_65_add__cancel__left__right, axiom,
    ((![A : poly_a, B : poly_a]: (((plus_plus_poly_a @ A @ B) = A) = (B = zero_zero_poly_a))))). % add_cancel_left_right
thf(fact_66_add__cancel__left__right, axiom,
    ((![A : complex, B : complex]: (((plus_plus_complex @ A @ B) = A) = (B = zero_zero_complex))))). % add_cancel_left_right
thf(fact_67_add__cancel__left__left, axiom,
    ((![B : real, A : real]: (((plus_plus_real @ B @ A) = A) = (B = zero_zero_real))))). % add_cancel_left_left
thf(fact_68_add__cancel__left__left, axiom,
    ((![B : a, A : a]: (((plus_plus_a @ B @ A) = A) = (B = zero_zero_a))))). % add_cancel_left_left
thf(fact_69_add__cancel__left__left, axiom,
    ((![B : poly_a, A : poly_a]: (((plus_plus_poly_a @ B @ A) = A) = (B = zero_zero_poly_a))))). % add_cancel_left_left
thf(fact_70_add__cancel__left__left, axiom,
    ((![B : complex, A : complex]: (((plus_plus_complex @ B @ A) = A) = (B = zero_zero_complex))))). % add_cancel_left_left
thf(fact_71_double__zero__sym, axiom,
    ((![A : real]: ((zero_zero_real = (plus_plus_real @ A @ A)) = (A = zero_zero_real))))). % double_zero_sym
thf(fact_72_double__zero, axiom,
    ((![A : real]: (((plus_plus_real @ A @ A) = zero_zero_real) = (A = zero_zero_real))))). % double_zero
thf(fact_73_add_Oright__neutral, axiom,
    ((![A : real]: ((plus_plus_real @ A @ zero_zero_real) = A)))). % add.right_neutral
thf(fact_74_add_Oright__neutral, axiom,
    ((![A : a]: ((plus_plus_a @ A @ zero_zero_a) = A)))). % add.right_neutral
thf(fact_75_add_Oright__neutral, axiom,
    ((![A : poly_a]: ((plus_plus_poly_a @ A @ zero_zero_poly_a) = A)))). % add.right_neutral
thf(fact_76_add_Oright__neutral, axiom,
    ((![A : complex]: ((plus_plus_complex @ A @ zero_zero_complex) = A)))). % add.right_neutral
thf(fact_77_add_Oleft__neutral, axiom,
    ((![A : real]: ((plus_plus_real @ zero_zero_real @ A) = A)))). % add.left_neutral
thf(fact_78_add_Oleft__neutral, axiom,
    ((![A : a]: ((plus_plus_a @ zero_zero_a @ A) = A)))). % add.left_neutral
thf(fact_79_add_Oleft__neutral, axiom,
    ((![A : poly_a]: ((plus_plus_poly_a @ zero_zero_poly_a @ A) = A)))). % add.left_neutral
thf(fact_80_add_Oleft__neutral, axiom,
    ((![A : complex]: ((plus_plus_complex @ zero_zero_complex @ A) = A)))). % add.left_neutral
thf(fact_81_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_82_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_83_add__less__cancel__right, axiom,
    ((![A : real, C : real, B : real]: ((ord_less_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ C)) = (ord_less_real @ A @ B))))). % add_less_cancel_right
thf(fact_84_add__less__cancel__left, axiom,
    ((![C : real, A : real, B : real]: ((ord_less_real @ (plus_plus_real @ C @ A) @ (plus_plus_real @ C @ B)) = (ord_less_real @ A @ B))))). % add_less_cancel_left
thf(fact_85_mult_Oright__neutral, axiom,
    ((![A : complex]: ((times_times_complex @ A @ one_one_complex) = A)))). % mult.right_neutral
thf(fact_86_mult_Oright__neutral, axiom,
    ((![A : real]: ((times_times_real @ A @ one_one_real) = A)))). % mult.right_neutral
thf(fact_87_mult_Oright__neutral, axiom,
    ((![A : a]: ((times_times_a @ A @ one_one_a) = A)))). % mult.right_neutral
thf(fact_88_mult_Oleft__neutral, axiom,
    ((![A : complex]: ((times_times_complex @ one_one_complex @ A) = A)))). % mult.left_neutral
thf(fact_89_mult_Oleft__neutral, axiom,
    ((![A : real]: ((times_times_real @ one_one_real @ A) = A)))). % mult.left_neutral
thf(fact_90_mult_Oleft__neutral, axiom,
    ((![A : a]: ((times_times_a @ one_one_a @ A) = A)))). % mult.left_neutral
thf(fact_91_abs__zero, axiom,
    (((abs_abs_real @ zero_zero_real) = zero_zero_real))). % abs_zero
thf(fact_92_abs__eq__0, axiom,
    ((![A : real]: (((abs_abs_real @ A) = zero_zero_real) = (A = zero_zero_real))))). % abs_eq_0
thf(fact_93_abs__0__eq, axiom,
    ((![A : real]: ((zero_zero_real = (abs_abs_real @ A)) = (A = zero_zero_real))))). % abs_0_eq
thf(fact_94_abs__0, axiom,
    (((abs_abs_real @ zero_zero_real) = zero_zero_real))). % abs_0
thf(fact_95_abs__0, axiom,
    (((abs_abs_complex @ zero_zero_complex) = zero_zero_complex))). % abs_0
thf(fact_96_abs__mult__self__eq, axiom,
    ((![A : real]: ((times_times_real @ (abs_abs_real @ A) @ (abs_abs_real @ A)) = (times_times_real @ A @ A))))). % abs_mult_self_eq
thf(fact_97_abs__add__abs, axiom,
    ((![A : real, B : real]: ((abs_abs_real @ (plus_plus_real @ (abs_abs_real @ A) @ (abs_abs_real @ B))) = (plus_plus_real @ (abs_abs_real @ A) @ (abs_abs_real @ B)))))). % abs_add_abs
thf(fact_98_abs__1, axiom,
    (((abs_abs_real @ one_one_real) = one_one_real))). % abs_1
thf(fact_99_abs__1, axiom,
    (((abs_abs_complex @ one_one_complex) = one_one_complex))). % abs_1
thf(fact_100_abs__norm__cancel, axiom,
    ((![A : a]: ((abs_abs_real @ (real_V1022479215norm_a @ A)) = (real_V1022479215norm_a @ A))))). % abs_norm_cancel
thf(fact_101_abs__norm__cancel, axiom,
    ((![A : complex]: ((abs_abs_real @ (real_V638595069omplex @ A)) = (real_V638595069omplex @ A))))). % abs_norm_cancel
thf(fact_102_abs__norm__cancel, axiom,
    ((![A : real]: ((abs_abs_real @ (real_V646646907m_real @ A)) = (real_V646646907m_real @ A))))). % abs_norm_cancel
thf(fact_103_zero__le__double__add__iff__zero__le__single__add, axiom,
    ((![A : real]: ((ord_less_eq_real @ zero_zero_real @ (plus_plus_real @ A @ A)) = (ord_less_eq_real @ zero_zero_real @ A))))). % zero_le_double_add_iff_zero_le_single_add
thf(fact_104_double__add__le__zero__iff__single__add__le__zero, axiom,
    ((![A : real]: ((ord_less_eq_real @ (plus_plus_real @ A @ A) @ zero_zero_real) = (ord_less_eq_real @ A @ zero_zero_real))))). % double_add_le_zero_iff_single_add_le_zero
thf(fact_105_le__add__same__cancel2, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ A @ (plus_plus_real @ B @ A)) = (ord_less_eq_real @ zero_zero_real @ B))))). % le_add_same_cancel2
thf(fact_106_le__add__same__cancel1, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ A @ (plus_plus_real @ A @ B)) = (ord_less_eq_real @ zero_zero_real @ B))))). % le_add_same_cancel1
thf(fact_107_add__le__same__cancel2, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ (plus_plus_real @ A @ B) @ B) = (ord_less_eq_real @ A @ zero_zero_real))))). % add_le_same_cancel2
thf(fact_108_add__le__same__cancel1, axiom,
    ((![B : real, A : real]: ((ord_less_eq_real @ (plus_plus_real @ B @ A) @ B) = (ord_less_eq_real @ A @ zero_zero_real))))). % add_le_same_cancel1
thf(fact_109_zero__less__double__add__iff__zero__less__single__add, axiom,
    ((![A : real]: ((ord_less_real @ zero_zero_real @ (plus_plus_real @ A @ A)) = (ord_less_real @ zero_zero_real @ A))))). % zero_less_double_add_iff_zero_less_single_add
thf(fact_110_double__add__less__zero__iff__single__add__less__zero, axiom,
    ((![A : real]: ((ord_less_real @ (plus_plus_real @ A @ A) @ zero_zero_real) = (ord_less_real @ A @ zero_zero_real))))). % double_add_less_zero_iff_single_add_less_zero
thf(fact_111_less__add__same__cancel2, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ (plus_plus_real @ B @ A)) = (ord_less_real @ zero_zero_real @ B))))). % less_add_same_cancel2
thf(fact_112_less__add__same__cancel1, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ (plus_plus_real @ A @ B)) = (ord_less_real @ zero_zero_real @ B))))). % less_add_same_cancel1
thf(fact_113_add__less__same__cancel2, axiom,
    ((![A : real, B : real]: ((ord_less_real @ (plus_plus_real @ A @ B) @ B) = (ord_less_real @ A @ zero_zero_real))))). % add_less_same_cancel2
thf(fact_114_abs__le__zero__iff, axiom,
    ((![A : real]: ((ord_less_eq_real @ (abs_abs_real @ A) @ zero_zero_real) = (A = zero_zero_real))))). % abs_le_zero_iff
thf(fact_115_abs__le__self__iff, axiom,
    ((![A : real]: ((ord_less_eq_real @ (abs_abs_real @ A) @ A) = (ord_less_eq_real @ zero_zero_real @ A))))). % abs_le_self_iff
thf(fact_116_abs__of__nonneg, axiom,
    ((![A : real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((abs_abs_real @ A) = A))))). % abs_of_nonneg
thf(fact_117_norm__le__zero__iff, axiom,
    ((![X : a]: ((ord_less_eq_real @ (real_V1022479215norm_a @ X) @ zero_zero_real) = (X = zero_zero_a))))). % norm_le_zero_iff
thf(fact_118_norm__le__zero__iff, axiom,
    ((![X : complex]: ((ord_less_eq_real @ (real_V638595069omplex @ X) @ zero_zero_real) = (X = zero_zero_complex))))). % norm_le_zero_iff
thf(fact_119_norm__le__zero__iff, axiom,
    ((![X : real]: ((ord_less_eq_real @ (real_V646646907m_real @ X) @ zero_zero_real) = (X = zero_zero_real))))). % norm_le_zero_iff
thf(fact_120_complex__mod__triangle__sub, axiom,
    ((![W : complex, Z : complex]: (ord_less_eq_real @ (real_V638595069omplex @ W) @ (plus_plus_real @ (real_V638595069omplex @ (plus_plus_complex @ W @ Z)) @ (real_V638595069omplex @ Z)))))). % complex_mod_triangle_sub
thf(fact_121_real__norm__def, axiom,
    ((real_V646646907m_real = abs_abs_real))). % real_norm_def
thf(fact_122_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_123_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_124_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_125_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_126_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_127_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_128_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_129_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_130_abs__ge__self, axiom,
    ((![A : real]: (ord_less_eq_real @ A @ (abs_abs_real @ A))))). % abs_ge_self
thf(fact_131_abs__le__D1, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ (abs_abs_real @ A) @ B) => (ord_less_eq_real @ A @ B))))). % abs_le_D1
thf(fact_132_zero__reorient, axiom,
    ((![X : real]: ((zero_zero_real = X) = (X = zero_zero_real))))). % zero_reorient
thf(fact_133_zero__reorient, axiom,
    ((![X : a]: ((zero_zero_a = X) = (X = zero_zero_a))))). % zero_reorient
thf(fact_134_zero__reorient, axiom,
    ((![X : poly_a]: ((zero_zero_poly_a = X) = (X = zero_zero_poly_a))))). % zero_reorient
thf(fact_135_zero__reorient, axiom,
    ((![X : complex]: ((zero_zero_complex = X) = (X = zero_zero_complex))))). % zero_reorient
thf(fact_136_linorder__neqE__linordered__idom, axiom,
    ((![X : real, Y : real]: ((~ ((X = Y))) => ((~ ((ord_less_real @ X @ Y))) => (ord_less_real @ Y @ X)))))). % linorder_neqE_linordered_idom
thf(fact_137_mult_Oleft__commute, axiom,
    ((![B : real, A : real, C : real]: ((times_times_real @ B @ (times_times_real @ A @ C)) = (times_times_real @ A @ (times_times_real @ B @ C)))))). % mult.left_commute
thf(fact_138_mult_Oleft__commute, axiom,
    ((![B : a, A : a, C : a]: ((times_times_a @ B @ (times_times_a @ A @ C)) = (times_times_a @ A @ (times_times_a @ B @ C)))))). % mult.left_commute
thf(fact_139_mult_Ocommute, axiom,
    ((times_times_real = (^[A2 : real]: (^[B2 : real]: (times_times_real @ B2 @ A2)))))). % mult.commute
thf(fact_140_mult_Ocommute, axiom,
    ((times_times_a = (^[A2 : a]: (^[B2 : a]: (times_times_a @ B2 @ A2)))))). % mult.commute
thf(fact_141_mult_Oassoc, axiom,
    ((![A : real, B : real, C : real]: ((times_times_real @ (times_times_real @ A @ B) @ C) = (times_times_real @ A @ (times_times_real @ B @ C)))))). % mult.assoc
thf(fact_142_mult_Oassoc, axiom,
    ((![A : a, B : a, C : a]: ((times_times_a @ (times_times_a @ A @ B) @ C) = (times_times_a @ A @ (times_times_a @ B @ C)))))). % mult.assoc
thf(fact_143_ab__semigroup__mult__class_Omult__ac_I1_J, axiom,
    ((![A : real, B : real, C : real]: ((times_times_real @ (times_times_real @ A @ B) @ C) = (times_times_real @ A @ (times_times_real @ B @ C)))))). % ab_semigroup_mult_class.mult_ac(1)
thf(fact_144_ab__semigroup__mult__class_Omult__ac_I1_J, axiom,
    ((![A : a, B : a, C : a]: ((times_times_a @ (times_times_a @ A @ B) @ C) = (times_times_a @ A @ (times_times_a @ B @ C)))))). % ab_semigroup_mult_class.mult_ac(1)
thf(fact_145_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_146_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_147_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_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_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_150_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_151_add_Ocommute, axiom,
    ((plus_plus_real = (^[A2 : real]: (^[B2 : real]: (plus_plus_real @ B2 @ A2)))))). % add.commute
thf(fact_152_add_Ocommute, axiom,
    ((plus_plus_complex = (^[A2 : complex]: (^[B2 : complex]: (plus_plus_complex @ B2 @ A2)))))). % add.commute
thf(fact_153_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_154_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_155_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_156_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_157_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_158_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_159_group__cancel_Oadd2, axiom,
    ((![B3 : real, K : real, B : real, A : real]: ((B3 = (plus_plus_real @ K @ B)) => ((plus_plus_real @ A @ B3) = (plus_plus_real @ K @ (plus_plus_real @ A @ B))))))). % group_cancel.add2
thf(fact_160_group__cancel_Oadd2, axiom,
    ((![B3 : complex, K : complex, B : complex, A : complex]: ((B3 = (plus_plus_complex @ K @ B)) => ((plus_plus_complex @ A @ B3) = (plus_plus_complex @ K @ (plus_plus_complex @ A @ B))))))). % group_cancel.add2
thf(fact_161_group__cancel_Oadd1, axiom,
    ((![A3 : real, K : real, A : real, B : real]: ((A3 = (plus_plus_real @ K @ A)) => ((plus_plus_real @ A3 @ B) = (plus_plus_real @ K @ (plus_plus_real @ A @ B))))))). % group_cancel.add1
thf(fact_162_group__cancel_Oadd1, axiom,
    ((![A3 : complex, K : complex, A : complex, B : complex]: ((A3 = (plus_plus_complex @ K @ A)) => ((plus_plus_complex @ A3 @ B) = (plus_plus_complex @ K @ (plus_plus_complex @ A @ B))))))). % group_cancel.add1
thf(fact_163_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_164_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_165_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_166_one__reorient, axiom,
    ((![X : real]: ((one_one_real = X) = (X = one_one_real))))). % one_reorient
thf(fact_167_one__reorient, axiom,
    ((![X : complex]: ((one_one_complex = X) = (X = one_one_complex))))). % one_reorient
thf(fact_168_one__reorient, axiom,
    ((![X : a]: ((one_one_a = X) = (X = one_one_a))))). % one_reorient
thf(fact_169_ordered__comm__semiring__class_Ocomm__mult__left__mono, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ zero_zero_real @ C) => (ord_less_eq_real @ (times_times_real @ C @ A) @ (times_times_real @ C @ B))))))). % ordered_comm_semiring_class.comm_mult_left_mono
thf(fact_170_zero__le__mult__iff, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ zero_zero_real @ (times_times_real @ A @ B)) = (((((ord_less_eq_real @ zero_zero_real @ A)) & ((ord_less_eq_real @ zero_zero_real @ B)))) | ((((ord_less_eq_real @ A @ zero_zero_real)) & ((ord_less_eq_real @ B @ zero_zero_real))))))))). % zero_le_mult_iff
thf(fact_171_mult__nonneg__nonpos2, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ B @ zero_zero_real) => (ord_less_eq_real @ (times_times_real @ B @ A) @ zero_zero_real)))))). % mult_nonneg_nonpos2
thf(fact_172_mult__nonpos__nonneg, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ A @ zero_zero_real) => ((ord_less_eq_real @ zero_zero_real @ B) => (ord_less_eq_real @ (times_times_real @ A @ B) @ zero_zero_real)))))). % mult_nonpos_nonneg
thf(fact_173_mult__nonneg__nonpos, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ B @ zero_zero_real) => (ord_less_eq_real @ (times_times_real @ A @ B) @ zero_zero_real)))))). % mult_nonneg_nonpos
thf(fact_174_mult__nonneg__nonneg, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ zero_zero_real @ B) => (ord_less_eq_real @ zero_zero_real @ (times_times_real @ A @ B))))))). % mult_nonneg_nonneg
thf(fact_175_split__mult__neg__le, axiom,
    ((![A : real, B : real]: ((((ord_less_eq_real @ zero_zero_real @ A) & (ord_less_eq_real @ B @ zero_zero_real)) | ((ord_less_eq_real @ A @ zero_zero_real) & (ord_less_eq_real @ zero_zero_real @ B))) => (ord_less_eq_real @ (times_times_real @ A @ B) @ zero_zero_real))))). % split_mult_neg_le
thf(fact_176_mult__le__0__iff, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ (times_times_real @ A @ B) @ zero_zero_real) = (((((ord_less_eq_real @ zero_zero_real @ A)) & ((ord_less_eq_real @ B @ zero_zero_real)))) | ((((ord_less_eq_real @ A @ zero_zero_real)) & ((ord_less_eq_real @ zero_zero_real @ B))))))))). % mult_le_0_iff
thf(fact_177_mult__right__mono, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ zero_zero_real @ C) => (ord_less_eq_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ C))))))). % mult_right_mono
thf(fact_178_mult__right__mono__neg, axiom,
    ((![B : real, A : real, C : real]: ((ord_less_eq_real @ B @ A) => ((ord_less_eq_real @ C @ zero_zero_real) => (ord_less_eq_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ C))))))). % mult_right_mono_neg
thf(fact_179_mult__left__mono, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ zero_zero_real @ C) => (ord_less_eq_real @ (times_times_real @ C @ A) @ (times_times_real @ C @ B))))))). % mult_left_mono
thf(fact_180_mult__nonpos__nonpos, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ A @ zero_zero_real) => ((ord_less_eq_real @ B @ zero_zero_real) => (ord_less_eq_real @ zero_zero_real @ (times_times_real @ A @ B))))))). % mult_nonpos_nonpos
thf(fact_181_mult__left__mono__neg, axiom,
    ((![B : real, A : real, C : real]: ((ord_less_eq_real @ B @ A) => ((ord_less_eq_real @ C @ zero_zero_real) => (ord_less_eq_real @ (times_times_real @ C @ A) @ (times_times_real @ C @ B))))))). % mult_left_mono_neg
thf(fact_182_split__mult__pos__le, axiom,
    ((![A : real, B : real]: ((((ord_less_eq_real @ zero_zero_real @ A) & (ord_less_eq_real @ zero_zero_real @ B)) | ((ord_less_eq_real @ A @ zero_zero_real) & (ord_less_eq_real @ B @ zero_zero_real))) => (ord_less_eq_real @ zero_zero_real @ (times_times_real @ A @ B)))))). % split_mult_pos_le
thf(fact_183_zero__le__square, axiom,
    ((![A : real]: (ord_less_eq_real @ zero_zero_real @ (times_times_real @ A @ A))))). % zero_le_square
thf(fact_184_mult__mono_H, 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 @ zero_zero_real @ A) => ((ord_less_eq_real @ zero_zero_real @ C) => (ord_less_eq_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ D))))))))). % mult_mono'
thf(fact_185_mult__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 @ zero_zero_real @ B) => ((ord_less_eq_real @ zero_zero_real @ C) => (ord_less_eq_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ D))))))))). % mult_mono
thf(fact_186_add__nonpos__eq__0__iff, axiom,
    ((![X : real, Y : real]: ((ord_less_eq_real @ X @ zero_zero_real) => ((ord_less_eq_real @ Y @ zero_zero_real) => (((plus_plus_real @ X @ Y) = zero_zero_real) = (((X = zero_zero_real)) & ((Y = zero_zero_real))))))))). % add_nonpos_eq_0_iff
thf(fact_187_add__nonneg__eq__0__iff, axiom,
    ((![X : real, Y : real]: ((ord_less_eq_real @ zero_zero_real @ X) => ((ord_less_eq_real @ zero_zero_real @ Y) => (((plus_plus_real @ X @ Y) = zero_zero_real) = (((X = zero_zero_real)) & ((Y = zero_zero_real))))))))). % add_nonneg_eq_0_iff
thf(fact_188_add__nonpos__nonpos, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ A @ zero_zero_real) => ((ord_less_eq_real @ B @ zero_zero_real) => (ord_less_eq_real @ (plus_plus_real @ A @ B) @ zero_zero_real)))))). % add_nonpos_nonpos
thf(fact_189_add__nonneg__nonneg, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ zero_zero_real @ B) => (ord_less_eq_real @ zero_zero_real @ (plus_plus_real @ A @ B))))))). % add_nonneg_nonneg
thf(fact_190_add__increasing2, axiom,
    ((![C : real, B : real, A : real]: ((ord_less_eq_real @ zero_zero_real @ C) => ((ord_less_eq_real @ B @ A) => (ord_less_eq_real @ B @ (plus_plus_real @ A @ C))))))). % add_increasing2
thf(fact_191_add__decreasing2, axiom,
    ((![C : real, A : real, B : real]: ((ord_less_eq_real @ C @ zero_zero_real) => ((ord_less_eq_real @ A @ B) => (ord_less_eq_real @ (plus_plus_real @ A @ C) @ B)))))). % add_decreasing2
thf(fact_192_add__increasing, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ B @ C) => (ord_less_eq_real @ B @ (plus_plus_real @ A @ C))))))). % add_increasing
thf(fact_193_add__decreasing, axiom,
    ((![A : real, C : real, B : real]: ((ord_less_eq_real @ A @ zero_zero_real) => ((ord_less_eq_real @ C @ B) => (ord_less_eq_real @ (plus_plus_real @ A @ C) @ B)))))). % add_decreasing
thf(fact_194_not__one__le__zero, axiom,
    ((~ ((ord_less_eq_real @ one_one_real @ zero_zero_real))))). % not_one_le_zero
thf(fact_195_zero__le__one, axiom,
    ((ord_less_eq_real @ zero_zero_real @ one_one_real))). % zero_le_one
thf(fact_196_add__less__le__mono, axiom,
    ((![A : real, B : real, C : real, D : real]: ((ord_less_real @ A @ B) => ((ord_less_eq_real @ C @ D) => (ord_less_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ D))))))). % add_less_le_mono
thf(fact_197_add__le__less__mono, axiom,
    ((![A : real, B : real, C : real, D : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_real @ C @ D) => (ord_less_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ D))))))). % add_le_less_mono
thf(fact_198_add__mono__thms__linordered__field_I3_J, axiom,
    ((![I : real, J : real, K : real, L : real]: (((ord_less_real @ I @ J) & (ord_less_eq_real @ K @ L)) => (ord_less_real @ (plus_plus_real @ I @ K) @ (plus_plus_real @ J @ L)))))). % add_mono_thms_linordered_field(3)
thf(fact_199_add__mono__thms__linordered__field_I4_J, axiom,
    ((![I : real, J : real, K : real, L : real]: (((ord_less_eq_real @ I @ J) & (ord_less_real @ K @ L)) => (ord_less_real @ (plus_plus_real @ I @ K) @ (plus_plus_real @ J @ L)))))). % add_mono_thms_linordered_field(4)
thf(fact_200_abs__ge__zero, axiom,
    ((![A : real]: (ord_less_eq_real @ zero_zero_real @ (abs_abs_real @ A))))). % abs_ge_zero
thf(fact_201_abs__triangle__ineq, axiom,
    ((![A : real, B : real]: (ord_less_eq_real @ (abs_abs_real @ (plus_plus_real @ A @ B)) @ (plus_plus_real @ (abs_abs_real @ A) @ (abs_abs_real @ B)))))). % abs_triangle_ineq
thf(fact_202_norm__ge__zero, axiom,
    ((![X : a]: (ord_less_eq_real @ zero_zero_real @ (real_V1022479215norm_a @ X))))). % norm_ge_zero
thf(fact_203_norm__ge__zero, axiom,
    ((![X : complex]: (ord_less_eq_real @ zero_zero_real @ (real_V638595069omplex @ X))))). % norm_ge_zero
thf(fact_204_norm__ge__zero, axiom,
    ((![X : real]: (ord_less_eq_real @ zero_zero_real @ (real_V646646907m_real @ X))))). % norm_ge_zero
thf(fact_205_mult__less__le__imp__less, axiom,
    ((![A : real, B : real, C : real, D : real]: ((ord_less_real @ A @ B) => ((ord_less_eq_real @ C @ D) => ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_real @ zero_zero_real @ C) => (ord_less_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ D))))))))). % mult_less_le_imp_less
thf(fact_206_mult__le__less__imp__less, axiom,
    ((![A : real, B : real, C : real, D : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_real @ C @ D) => ((ord_less_real @ zero_zero_real @ A) => ((ord_less_eq_real @ zero_zero_real @ C) => (ord_less_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ D))))))))). % mult_le_less_imp_less
thf(fact_207_mult__right__le__imp__le, axiom,
    ((![A : real, C : real, B : real]: ((ord_less_eq_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ C)) => ((ord_less_real @ zero_zero_real @ C) => (ord_less_eq_real @ A @ B)))))). % mult_right_le_imp_le
thf(fact_208_mult__left__le__imp__le, axiom,
    ((![C : real, A : real, B : real]: ((ord_less_eq_real @ (times_times_real @ C @ A) @ (times_times_real @ C @ B)) => ((ord_less_real @ zero_zero_real @ C) => (ord_less_eq_real @ A @ B)))))). % mult_left_le_imp_le
thf(fact_209_mult__le__cancel__left__pos, axiom,
    ((![C : real, A : real, B : real]: ((ord_less_real @ zero_zero_real @ C) => ((ord_less_eq_real @ (times_times_real @ C @ A) @ (times_times_real @ C @ B)) = (ord_less_eq_real @ A @ B)))))). % mult_le_cancel_left_pos
thf(fact_210_mult__le__cancel__left__neg, axiom,
    ((![C : real, A : real, B : real]: ((ord_less_real @ C @ zero_zero_real) => ((ord_less_eq_real @ (times_times_real @ C @ A) @ (times_times_real @ C @ B)) = (ord_less_eq_real @ B @ A)))))). % mult_le_cancel_left_neg
thf(fact_211_mult__less__cancel__right, axiom,
    ((![A : real, C : real, B : real]: ((ord_less_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ C)) = (((((ord_less_eq_real @ zero_zero_real @ C)) => ((ord_less_real @ A @ B)))) & ((((ord_less_eq_real @ C @ zero_zero_real)) => ((ord_less_real @ B @ A))))))))). % mult_less_cancel_right
thf(fact_212_mult__strict__mono_H, axiom,
    ((![A : real, B : real, C : real, D : real]: ((ord_less_real @ A @ B) => ((ord_less_real @ C @ D) => ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ zero_zero_real @ C) => (ord_less_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ D))))))))). % mult_strict_mono'
thf(fact_213_mult__right__less__imp__less, axiom,
    ((![A : real, C : real, B : real]: ((ord_less_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ C)) => ((ord_less_eq_real @ zero_zero_real @ C) => (ord_less_real @ A @ B)))))). % mult_right_less_imp_less
thf(fact_214_mult__less__cancel__left, axiom,
    ((![C : real, A : real, B : real]: ((ord_less_real @ (times_times_real @ C @ A) @ (times_times_real @ C @ B)) = (((((ord_less_eq_real @ zero_zero_real @ C)) => ((ord_less_real @ A @ B)))) & ((((ord_less_eq_real @ C @ zero_zero_real)) => ((ord_less_real @ B @ A))))))))). % mult_less_cancel_left
thf(fact_215_mult__strict__mono, axiom,
    ((![A : real, B : real, C : real, D : real]: ((ord_less_real @ A @ B) => ((ord_less_real @ C @ D) => ((ord_less_real @ zero_zero_real @ B) => ((ord_less_eq_real @ zero_zero_real @ C) => (ord_less_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ D))))))))). % mult_strict_mono
thf(fact_216_mult__left__less__imp__less, axiom,
    ((![C : real, A : real, B : real]: ((ord_less_real @ (times_times_real @ C @ A) @ (times_times_real @ C @ B)) => ((ord_less_eq_real @ zero_zero_real @ C) => (ord_less_real @ A @ B)))))). % mult_left_less_imp_less
thf(fact_217_mult__le__cancel__right, axiom,
    ((![A : real, C : real, B : real]: ((ord_less_eq_real @ (times_times_real @ A @ C) @ (times_times_real @ B @ C)) = (((((ord_less_real @ zero_zero_real @ C)) => ((ord_less_eq_real @ A @ B)))) & ((((ord_less_real @ C @ zero_zero_real)) => ((ord_less_eq_real @ B @ A))))))))). % mult_le_cancel_right
thf(fact_218_mult__le__cancel__left, axiom,
    ((![C : real, A : real, B : real]: ((ord_less_eq_real @ (times_times_real @ C @ A) @ (times_times_real @ C @ B)) = (((((ord_less_real @ zero_zero_real @ C)) => ((ord_less_eq_real @ A @ B)))) & ((((ord_less_real @ C @ zero_zero_real)) => ((ord_less_eq_real @ B @ A))))))))). % mult_le_cancel_left
thf(fact_219_add__strict__increasing2, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_real @ B @ C) => (ord_less_real @ B @ (plus_plus_real @ A @ C))))))). % add_strict_increasing2
thf(fact_220_add__strict__increasing, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_eq_real @ B @ C) => (ord_less_real @ B @ (plus_plus_real @ A @ C))))))). % add_strict_increasing

% Conjectures (1)
thf(conj_0, conjecture,
    ((ord_less_real @ zero_zero_real @ (plus_plus_real @ (plus_plus_real @ one_one_real @ (real_V1022479215norm_a @ c)) @ (abs_abs_real @ (times_times_real @ r @ m)))))).
