% 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_49__5367118_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:26:36.301

% Could-be-implicit typings (7)
thf(ty_n_t__Polynomial__Opoly_It__Polynomial__Opoly_It__Polynomial__Opoly_Itf__a_J_J_J, type,
    poly_poly_poly_a : $tType).
thf(ty_n_t__Polynomial__Opoly_It__Polynomial__Opoly_It__Real__Oreal_J_J, type,
    poly_poly_real : $tType).
thf(ty_n_t__Polynomial__Opoly_It__Polynomial__Opoly_Itf__a_J_J, type,
    poly_poly_a : $tType).
thf(ty_n_t__Polynomial__Opoly_It__Real__Oreal_J, type,
    poly_real : $tType).
thf(ty_n_t__Polynomial__Opoly_Itf__a_J, type,
    poly_a : $tType).
thf(ty_n_t__Real__Oreal, type,
    real : $tType).
thf(ty_n_tf__a, type,
    a : $tType).

% Explicit typings (42)
thf(sy_c_Groups_Oabs__class_Oabs_001t__Polynomial__Opoly_It__Real__Oreal_J, type,
    abs_abs_poly_real : poly_real > poly_real).
thf(sy_c_Groups_Oabs__class_Oabs_001t__Real__Oreal, type,
    abs_abs_real : real > real).
thf(sy_c_Groups_Oone__class_Oone_001t__Polynomial__Opoly_It__Real__Oreal_J, type,
    one_one_poly_real : poly_real).
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__Polynomial__Opoly_It__Polynomial__Opoly_Itf__a_J_J, type,
    plus_p1976640465poly_a : poly_poly_a > poly_poly_a > poly_poly_a).
thf(sy_c_Groups_Oplus__class_Oplus_001t__Polynomial__Opoly_It__Real__Oreal_J, type,
    plus_plus_poly_real : poly_real > poly_real > poly_real).
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__Polynomial__Opoly_It__Polynomial__Opoly_Itf__a_J_J, type,
    times_545135445poly_a : poly_poly_a > poly_poly_a > poly_poly_a).
thf(sy_c_Groups_Otimes__class_Otimes_001t__Polynomial__Opoly_It__Real__Oreal_J, type,
    times_775122617y_real : poly_real > poly_real > poly_real).
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__Polynomial__Opoly_It__Polynomial__Opoly_It__Polynomial__Opoly_Itf__a_J_J_J, type,
    zero_z2064990175poly_a : poly_poly_poly_a).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Real__Oreal_J_J, type,
    zero_z1423781445y_real : poly_poly_real).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Polynomial__Opoly_Itf__a_J_J, type,
    zero_z2096148049poly_a : poly_poly_a).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Real__Oreal_J, type,
    zero_zero_poly_real : poly_real).
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__Polynomial__Opoly_It__Real__Oreal_J, type,
    ord_less_poly_real : poly_real > poly_real > $o).
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__Polynomial__Opoly_It__Real__Oreal_J, type,
    ord_le1180086932y_real : poly_real > poly_real > $o).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Real__Oreal, type,
    ord_less_eq_real : real > real > $o).
thf(sy_c_Polynomial_OpCons_001t__Polynomial__Opoly_It__Polynomial__Opoly_Itf__a_J_J, type,
    pCons_poly_poly_a : poly_poly_a > poly_poly_poly_a > poly_poly_poly_a).
thf(sy_c_Polynomial_OpCons_001t__Polynomial__Opoly_It__Real__Oreal_J, type,
    pCons_poly_real : poly_real > poly_poly_real > poly_poly_real).
thf(sy_c_Polynomial_OpCons_001t__Polynomial__Opoly_Itf__a_J, type,
    pCons_poly_a : poly_a > poly_poly_a > poly_poly_a).
thf(sy_c_Polynomial_OpCons_001t__Real__Oreal, type,
    pCons_real : real > poly_real > poly_real).
thf(sy_c_Polynomial_OpCons_001tf__a, type,
    pCons_a : a > poly_a > poly_a).
thf(sy_c_Polynomial_Opoly_001t__Polynomial__Opoly_It__Polynomial__Opoly_Itf__a_J_J, type,
    poly_poly_poly_a2 : poly_poly_poly_a > poly_poly_a > poly_poly_a).
thf(sy_c_Polynomial_Opoly_001t__Polynomial__Opoly_It__Real__Oreal_J, type,
    poly_poly_real2 : poly_poly_real > poly_real > poly_real).
thf(sy_c_Polynomial_Opoly_001t__Polynomial__Opoly_Itf__a_J, type,
    poly_poly_a2 : poly_poly_a > poly_a > poly_a).
thf(sy_c_Polynomial_Opoly_001t__Real__Oreal, type,
    poly_real2 : poly_real > real > real).
thf(sy_c_Polynomial_Opoly_001tf__a, type,
    poly_a2 : poly_a > a > a).
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 (247)
thf(fact_0_m, axiom,
    ((![Z : a]: ((ord_less_eq_real @ (real_V1022479215norm_a @ Z) @ r) => (ord_less_eq_real @ (real_V1022479215norm_a @ (poly_a2 @ cs @ Z)) @ m))))). % m
thf(fact_1_pCons_Ohyps_I2_J, axiom,
    ((?[M : real]: ((ord_less_real @ zero_zero_real @ M) & (![Z : a]: ((ord_less_eq_real @ (real_V1022479215norm_a @ Z) @ r) => (ord_less_eq_real @ (real_V1022479215norm_a @ (poly_a2 @ cs @ Z)) @ M))))))). % pCons.hyps(2)
thf(fact_2__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062m_O_A_092_060forall_062z_O_Anorm_Az_A_092_060le_062_Ar_A_092_060longrightarrow_062_Anorm_A_Ipoly_Acs_Az_J_A_092_060le_062_Am_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom,
    ((~ ((![M : real]: (~ ((![Z : a]: ((ord_less_eq_real @ (real_V1022479215norm_a @ Z) @ r) => (ord_less_eq_real @ (real_V1022479215norm_a @ (poly_a2 @ cs @ Z)) @ M)))))))))). % \<open>\<And>thesis. (\<And>m. \<forall>z. norm z \<le> r \<longrightarrow> norm (poly cs z) \<le> m \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_3_kp, axiom,
    ((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)))))). % kp
thf(fact_4__092_060open_062_092_060And_062z_O_Anorm_Az_A_092_060le_062_Ar_A_092_060Longrightarrow_062_Anorm_A_Ipoly_A_IpCons_Ac_Acs_J_Az_J_A_092_060le_062_A1_A_L_Anorm_Ac_A_L_A_092_060bar_062r_A_K_Am_092_060bar_062_092_060close_062, axiom,
    ((![Z2 : a]: ((ord_less_eq_real @ (real_V1022479215norm_a @ Z2) @ r) => (ord_less_eq_real @ (real_V1022479215norm_a @ (poly_a2 @ (pCons_a @ c @ cs) @ Z2)) @ (plus_plus_real @ (plus_plus_real @ one_one_real @ (real_V1022479215norm_a @ c)) @ (abs_abs_real @ (times_times_real @ r @ m)))))))). % \<open>\<And>z. norm z \<le> r \<Longrightarrow> norm (poly (pCons c cs) z) \<le> 1 + norm c + \<bar>r * m\<bar>\<close>
thf(fact_5_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_6_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_7_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_8_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_9_norm__zero, axiom,
    (((real_V1022479215norm_a @ zero_zero_a) = zero_zero_real))). % norm_zero
thf(fact_10_norm__zero, axiom,
    (((real_V646646907m_real @ zero_zero_real) = zero_zero_real))). % norm_zero
thf(fact_11_norm__eq__zero, axiom,
    ((![X : a]: (((real_V1022479215norm_a @ X) = zero_zero_real) = (X = zero_zero_a))))). % norm_eq_zero
thf(fact_12_norm__eq__zero, axiom,
    ((![X : real]: (((real_V646646907m_real @ X) = zero_zero_real) = (X = zero_zero_real))))). % norm_eq_zero
thf(fact_13_poly__0, axiom,
    ((![X : poly_poly_a]: ((poly_poly_poly_a2 @ zero_z2064990175poly_a @ X) = zero_z2096148049poly_a)))). % poly_0
thf(fact_14_poly__0, axiom,
    ((![X : poly_real]: ((poly_poly_real2 @ zero_z1423781445y_real @ X) = zero_zero_poly_real)))). % poly_0
thf(fact_15_poly__0, axiom,
    ((![X : real]: ((poly_real2 @ zero_zero_poly_real @ X) = zero_zero_real)))). % poly_0
thf(fact_16_poly__0, axiom,
    ((![X : poly_a]: ((poly_poly_a2 @ zero_z2096148049poly_a @ X) = zero_zero_poly_a)))). % poly_0
thf(fact_17_poly__0, axiom,
    ((![X : a]: ((poly_a2 @ zero_zero_poly_a @ X) = zero_zero_a)))). % poly_0
thf(fact_18_pCons__0__0, axiom,
    (((pCons_real @ zero_zero_real @ zero_zero_poly_real) = zero_zero_poly_real))). % pCons_0_0
thf(fact_19_pCons__0__0, axiom,
    (((pCons_a @ zero_zero_a @ zero_zero_poly_a) = zero_zero_poly_a))). % pCons_0_0
thf(fact_20_pCons__0__0, axiom,
    (((pCons_poly_a @ zero_zero_poly_a @ zero_z2096148049poly_a) = zero_z2096148049poly_a))). % pCons_0_0
thf(fact_21_pCons__0__0, axiom,
    (((pCons_poly_poly_a @ zero_z2096148049poly_a @ zero_z2064990175poly_a) = zero_z2064990175poly_a))). % pCons_0_0
thf(fact_22_pCons__0__0, axiom,
    (((pCons_poly_real @ zero_zero_poly_real @ zero_z1423781445y_real) = zero_z1423781445y_real))). % pCons_0_0
thf(fact_23_pCons__eq__0__iff, axiom,
    ((![A : poly_poly_a, P : poly_poly_poly_a]: (((pCons_poly_poly_a @ A @ P) = zero_z2064990175poly_a) = (((A = zero_z2096148049poly_a)) & ((P = zero_z2064990175poly_a))))))). % pCons_eq_0_iff
thf(fact_24_pCons__eq__0__iff, axiom,
    ((![A : poly_real, P : poly_poly_real]: (((pCons_poly_real @ A @ P) = zero_z1423781445y_real) = (((A = zero_zero_poly_real)) & ((P = zero_z1423781445y_real))))))). % pCons_eq_0_iff
thf(fact_25_pCons__eq__0__iff, axiom,
    ((![A : a, P : poly_a]: (((pCons_a @ A @ P) = zero_zero_poly_a) = (((A = zero_zero_a)) & ((P = zero_zero_poly_a))))))). % pCons_eq_0_iff
thf(fact_26_pCons__eq__0__iff, axiom,
    ((![A : poly_a, P : poly_poly_a]: (((pCons_poly_a @ A @ P) = zero_z2096148049poly_a) = (((A = zero_zero_poly_a)) & ((P = zero_z2096148049poly_a))))))). % pCons_eq_0_iff
thf(fact_27_pCons__eq__0__iff, axiom,
    ((![A : real, P : poly_real]: (((pCons_real @ A @ P) = zero_zero_poly_real) = (((A = zero_zero_real)) & ((P = zero_zero_poly_real))))))). % pCons_eq_0_iff
thf(fact_28_norm__ge__zero, axiom,
    ((![X : a]: (ord_less_eq_real @ zero_zero_real @ (real_V1022479215norm_a @ X))))). % norm_ge_zero
thf(fact_29_norm__ge__zero, axiom,
    ((![X : real]: (ord_less_eq_real @ zero_zero_real @ (real_V646646907m_real @ X))))). % norm_ge_zero
thf(fact_30_norm__not__less__zero, axiom,
    ((![X : a]: (~ ((ord_less_real @ (real_V1022479215norm_a @ X) @ zero_zero_real)))))). % norm_not_less_zero
thf(fact_31_norm__not__less__zero, axiom,
    ((![X : real]: (~ ((ord_less_real @ (real_V646646907m_real @ X) @ zero_zero_real)))))). % norm_not_less_zero
thf(fact_32_pCons__eq__iff, axiom,
    ((![A : a, P : poly_a, B : a, Q : poly_a]: (((pCons_a @ A @ P) = (pCons_a @ B @ Q)) = (((A = B)) & ((P = Q))))))). % pCons_eq_iff
thf(fact_33_pCons_Ohyps_I1_J, axiom,
    (((~ ((c = zero_zero_a))) | (~ ((cs = zero_zero_poly_a)))))). % pCons.hyps(1)
thf(fact_34_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_35_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_36_abs__idempotent, axiom,
    ((![A : real]: ((abs_abs_real @ (abs_abs_real @ A)) = (abs_abs_real @ A))))). % abs_idempotent
thf(fact_37_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_38_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_39_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_40_add__cancel__right__right, axiom,
    ((![A : poly_poly_a, B : poly_poly_a]: ((A = (plus_p1976640465poly_a @ A @ B)) = (B = zero_z2096148049poly_a))))). % add_cancel_right_right
thf(fact_41_add__cancel__right__right, axiom,
    ((![A : poly_real, B : poly_real]: ((A = (plus_plus_poly_real @ A @ B)) = (B = zero_zero_poly_real))))). % add_cancel_right_right
thf(fact_42_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_43_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_44_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_45_add__cancel__right__left, axiom,
    ((![A : poly_poly_a, B : poly_poly_a]: ((A = (plus_p1976640465poly_a @ B @ A)) = (B = zero_z2096148049poly_a))))). % add_cancel_right_left
thf(fact_46_add__cancel__right__left, axiom,
    ((![A : poly_real, B : poly_real]: ((A = (plus_plus_poly_real @ B @ A)) = (B = zero_zero_poly_real))))). % add_cancel_right_left
thf(fact_47_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_48_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_49_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_50_add__cancel__left__right, axiom,
    ((![A : poly_poly_a, B : poly_poly_a]: (((plus_p1976640465poly_a @ A @ B) = A) = (B = zero_z2096148049poly_a))))). % add_cancel_left_right
thf(fact_51_add__cancel__left__right, axiom,
    ((![A : poly_real, B : poly_real]: (((plus_plus_poly_real @ A @ B) = A) = (B = zero_zero_poly_real))))). % add_cancel_left_right
thf(fact_52_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_53_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_54_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_55_add__cancel__left__left, axiom,
    ((![B : poly_poly_a, A : poly_poly_a]: (((plus_p1976640465poly_a @ B @ A) = A) = (B = zero_z2096148049poly_a))))). % add_cancel_left_left
thf(fact_56_add__cancel__left__left, axiom,
    ((![B : poly_real, A : poly_real]: (((plus_plus_poly_real @ B @ A) = A) = (B = zero_zero_poly_real))))). % add_cancel_left_left
thf(fact_57_double__zero__sym, axiom,
    ((![A : real]: ((zero_zero_real = (plus_plus_real @ A @ A)) = (A = zero_zero_real))))). % double_zero_sym
thf(fact_58_double__zero__sym, axiom,
    ((![A : poly_real]: ((zero_zero_poly_real = (plus_plus_poly_real @ A @ A)) = (A = zero_zero_poly_real))))). % double_zero_sym
thf(fact_59_double__zero, axiom,
    ((![A : real]: (((plus_plus_real @ A @ A) = zero_zero_real) = (A = zero_zero_real))))). % double_zero
thf(fact_60_double__zero, axiom,
    ((![A : poly_real]: (((plus_plus_poly_real @ A @ A) = zero_zero_poly_real) = (A = zero_zero_poly_real))))). % double_zero
thf(fact_61_add_Oright__neutral, axiom,
    ((![A : real]: ((plus_plus_real @ A @ zero_zero_real) = A)))). % add.right_neutral
thf(fact_62_add_Oright__neutral, axiom,
    ((![A : a]: ((plus_plus_a @ A @ zero_zero_a) = A)))). % add.right_neutral
thf(fact_63_add_Oright__neutral, axiom,
    ((![A : poly_a]: ((plus_plus_poly_a @ A @ zero_zero_poly_a) = A)))). % add.right_neutral
thf(fact_64_add_Oright__neutral, axiom,
    ((![A : poly_poly_a]: ((plus_p1976640465poly_a @ A @ zero_z2096148049poly_a) = A)))). % add.right_neutral
thf(fact_65_add_Oright__neutral, axiom,
    ((![A : poly_real]: ((plus_plus_poly_real @ A @ zero_zero_poly_real) = A)))). % add.right_neutral
thf(fact_66_add_Oleft__neutral, axiom,
    ((![A : real]: ((plus_plus_real @ zero_zero_real @ A) = A)))). % add.left_neutral
thf(fact_67_add_Oleft__neutral, axiom,
    ((![A : a]: ((plus_plus_a @ zero_zero_a @ A) = A)))). % add.left_neutral
thf(fact_68_add_Oleft__neutral, axiom,
    ((![A : poly_a]: ((plus_plus_poly_a @ zero_zero_poly_a @ A) = A)))). % add.left_neutral
thf(fact_69_add_Oleft__neutral, axiom,
    ((![A : poly_poly_a]: ((plus_p1976640465poly_a @ zero_z2096148049poly_a @ A) = A)))). % add.left_neutral
thf(fact_70_add_Oleft__neutral, axiom,
    ((![A : poly_real]: ((plus_plus_poly_real @ zero_zero_poly_real @ A) = A)))). % add.left_neutral
thf(fact_71_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_72_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_73_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_74_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_75_mult_Oleft__neutral, axiom,
    ((![A : real]: ((times_times_real @ one_one_real @ A) = A)))). % mult.left_neutral
thf(fact_76_mult_Oright__neutral, axiom,
    ((![A : real]: ((times_times_real @ A @ one_one_real) = A)))). % mult.right_neutral
thf(fact_77_abs__zero, axiom,
    (((abs_abs_real @ zero_zero_real) = zero_zero_real))). % abs_zero
thf(fact_78_abs__zero, axiom,
    (((abs_abs_poly_real @ zero_zero_poly_real) = zero_zero_poly_real))). % abs_zero
thf(fact_79_abs__eq__0, axiom,
    ((![A : real]: (((abs_abs_real @ A) = zero_zero_real) = (A = zero_zero_real))))). % abs_eq_0
thf(fact_80_abs__eq__0, axiom,
    ((![A : poly_real]: (((abs_abs_poly_real @ A) = zero_zero_poly_real) = (A = zero_zero_poly_real))))). % abs_eq_0
thf(fact_81_abs__0__eq, axiom,
    ((![A : real]: ((zero_zero_real = (abs_abs_real @ A)) = (A = zero_zero_real))))). % abs_0_eq
thf(fact_82_abs__0__eq, axiom,
    ((![A : poly_real]: ((zero_zero_poly_real = (abs_abs_poly_real @ A)) = (A = zero_zero_poly_real))))). % abs_0_eq
thf(fact_83_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_84_add__pCons, axiom,
    ((![A : a, P : poly_a, B : a, Q : poly_a]: ((plus_plus_poly_a @ (pCons_a @ A @ P) @ (pCons_a @ B @ Q)) = (pCons_a @ (plus_plus_a @ A @ B) @ (plus_plus_poly_a @ P @ Q)))))). % add_pCons
thf(fact_85_add__pCons, axiom,
    ((![A : real, P : poly_real, B : real, Q : poly_real]: ((plus_plus_poly_real @ (pCons_real @ A @ P) @ (pCons_real @ B @ Q)) = (pCons_real @ (plus_plus_real @ A @ B) @ (plus_plus_poly_real @ P @ Q)))))). % add_pCons
thf(fact_86_poly__mult, axiom,
    ((![P : poly_a, Q : poly_a, X : a]: ((poly_a2 @ (times_times_poly_a @ P @ Q) @ X) = (times_times_a @ (poly_a2 @ P @ X) @ (poly_a2 @ Q @ X)))))). % poly_mult
thf(fact_87_poly__mult, axiom,
    ((![P : poly_poly_a, Q : poly_poly_a, X : poly_a]: ((poly_poly_a2 @ (times_545135445poly_a @ P @ Q) @ X) = (times_times_poly_a @ (poly_poly_a2 @ P @ X) @ (poly_poly_a2 @ Q @ X)))))). % poly_mult
thf(fact_88_poly__mult, axiom,
    ((![P : poly_real, Q : poly_real, X : real]: ((poly_real2 @ (times_775122617y_real @ P @ Q) @ X) = (times_times_real @ (poly_real2 @ P @ X) @ (poly_real2 @ Q @ X)))))). % poly_mult
thf(fact_89_poly__add, axiom,
    ((![P : poly_a, Q : poly_a, X : a]: ((poly_a2 @ (plus_plus_poly_a @ P @ Q) @ X) = (plus_plus_a @ (poly_a2 @ P @ X) @ (poly_a2 @ Q @ X)))))). % poly_add
thf(fact_90_poly__add, axiom,
    ((![P : poly_poly_a, Q : poly_poly_a, X : poly_a]: ((poly_poly_a2 @ (plus_p1976640465poly_a @ P @ Q) @ X) = (plus_plus_poly_a @ (poly_poly_a2 @ P @ X) @ (poly_poly_a2 @ Q @ X)))))). % poly_add
thf(fact_91_poly__add, axiom,
    ((![P : poly_real, Q : poly_real, X : real]: ((poly_real2 @ (plus_plus_poly_real @ P @ Q) @ X) = (plus_plus_real @ (poly_real2 @ P @ X) @ (poly_real2 @ Q @ X)))))). % poly_add
thf(fact_92_poly__1, axiom,
    ((![X : real]: ((poly_real2 @ one_one_poly_real @ X) = one_one_real)))). % poly_1
thf(fact_93_abs__norm__cancel, axiom,
    ((![A : a]: ((abs_abs_real @ (real_V1022479215norm_a @ A)) = (real_V1022479215norm_a @ A))))). % abs_norm_cancel
thf(fact_94_abs__norm__cancel, axiom,
    ((![A : real]: ((abs_abs_real @ (real_V646646907m_real @ A)) = (real_V646646907m_real @ A))))). % abs_norm_cancel
thf(fact_95_zero__le__double__add__iff__zero__le__single__add, axiom,
    ((![A : poly_real]: ((ord_le1180086932y_real @ zero_zero_poly_real @ (plus_plus_poly_real @ A @ A)) = (ord_le1180086932y_real @ zero_zero_poly_real @ A))))). % zero_le_double_add_iff_zero_le_single_add
thf(fact_96_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_97_double__add__le__zero__iff__single__add__le__zero, axiom,
    ((![A : poly_real]: ((ord_le1180086932y_real @ (plus_plus_poly_real @ A @ A) @ zero_zero_poly_real) = (ord_le1180086932y_real @ A @ zero_zero_poly_real))))). % double_add_le_zero_iff_single_add_le_zero
thf(fact_98_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_99_le__add__same__cancel2, axiom,
    ((![A : poly_real, B : poly_real]: ((ord_le1180086932y_real @ A @ (plus_plus_poly_real @ B @ A)) = (ord_le1180086932y_real @ zero_zero_poly_real @ B))))). % le_add_same_cancel2
thf(fact_100_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_101_le__add__same__cancel1, axiom,
    ((![A : poly_real, B : poly_real]: ((ord_le1180086932y_real @ A @ (plus_plus_poly_real @ A @ B)) = (ord_le1180086932y_real @ zero_zero_poly_real @ B))))). % le_add_same_cancel1
thf(fact_102_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_103_add__le__same__cancel2, axiom,
    ((![A : poly_real, B : poly_real]: ((ord_le1180086932y_real @ (plus_plus_poly_real @ A @ B) @ B) = (ord_le1180086932y_real @ A @ zero_zero_poly_real))))). % add_le_same_cancel2
thf(fact_104_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_105_add__le__same__cancel1, axiom,
    ((![B : poly_real, A : poly_real]: ((ord_le1180086932y_real @ (plus_plus_poly_real @ B @ A) @ B) = (ord_le1180086932y_real @ A @ zero_zero_poly_real))))). % add_le_same_cancel1
thf(fact_106_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_107_zero__less__double__add__iff__zero__less__single__add, axiom,
    ((![A : poly_real]: ((ord_less_poly_real @ zero_zero_poly_real @ (plus_plus_poly_real @ A @ A)) = (ord_less_poly_real @ zero_zero_poly_real @ A))))). % zero_less_double_add_iff_zero_less_single_add
thf(fact_108_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_109_double__add__less__zero__iff__single__add__less__zero, axiom,
    ((![A : poly_real]: ((ord_less_poly_real @ (plus_plus_poly_real @ A @ A) @ zero_zero_poly_real) = (ord_less_poly_real @ A @ zero_zero_poly_real))))). % double_add_less_zero_iff_single_add_less_zero
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 : poly_real, B : poly_real]: ((ord_less_poly_real @ A @ (plus_plus_poly_real @ B @ A)) = (ord_less_poly_real @ zero_zero_poly_real @ B))))). % less_add_same_cancel2
thf(fact_112_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_113_less__add__same__cancel1, axiom,
    ((![A : poly_real, B : poly_real]: ((ord_less_poly_real @ A @ (plus_plus_poly_real @ A @ B)) = (ord_less_poly_real @ zero_zero_poly_real @ B))))). % less_add_same_cancel1
thf(fact_114_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_115_add__less__same__cancel2, axiom,
    ((![A : poly_real, B : poly_real]: ((ord_less_poly_real @ (plus_plus_poly_real @ A @ B) @ B) = (ord_less_poly_real @ A @ zero_zero_poly_real))))). % add_less_same_cancel2
thf(fact_116_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_117_add__less__same__cancel1, axiom,
    ((![B : poly_real, A : poly_real]: ((ord_less_poly_real @ (plus_plus_poly_real @ B @ A) @ B) = (ord_less_poly_real @ A @ zero_zero_poly_real))))). % add_less_same_cancel1
thf(fact_118_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_119_abs__le__zero__iff, axiom,
    ((![A : poly_real]: ((ord_le1180086932y_real @ (abs_abs_poly_real @ A) @ zero_zero_poly_real) = (A = zero_zero_poly_real))))). % abs_le_zero_iff
thf(fact_120_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_121_abs__le__self__iff, axiom,
    ((![A : poly_real]: ((ord_le1180086932y_real @ (abs_abs_poly_real @ A) @ A) = (ord_le1180086932y_real @ zero_zero_poly_real @ A))))). % abs_le_self_iff
thf(fact_122_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_123_abs__of__nonneg, axiom,
    ((![A : poly_real]: ((ord_le1180086932y_real @ zero_zero_poly_real @ A) => ((abs_abs_poly_real @ A) = A))))). % abs_of_nonneg
thf(fact_124_abs__of__nonneg, axiom,
    ((![A : real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((abs_abs_real @ A) = A))))). % abs_of_nonneg
thf(fact_125_zero__less__abs__iff, axiom,
    ((![A : poly_real]: ((ord_less_poly_real @ zero_zero_poly_real @ (abs_abs_poly_real @ A)) = (~ ((A = zero_zero_poly_real))))))). % zero_less_abs_iff
thf(fact_126_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_127_norm__one, axiom,
    (((real_V1022479215norm_a @ one_one_a) = one_one_real))). % norm_one
thf(fact_128_norm__one, axiom,
    (((real_V646646907m_real @ one_one_real) = one_one_real))). % norm_one
thf(fact_129_one__poly__eq__simps_I2_J, axiom,
    (((pCons_real @ one_one_real @ zero_zero_poly_real) = one_one_poly_real))). % one_poly_eq_simps(2)
thf(fact_130_one__poly__eq__simps_I1_J, axiom,
    ((one_one_poly_real = (pCons_real @ one_one_real @ zero_zero_poly_real)))). % one_poly_eq_simps(1)
thf(fact_131_poly__pCons, axiom,
    ((![A : poly_a, P : poly_poly_a, X : poly_a]: ((poly_poly_a2 @ (pCons_poly_a @ A @ P) @ X) = (plus_plus_poly_a @ A @ (times_times_poly_a @ X @ (poly_poly_a2 @ P @ X))))))). % poly_pCons
thf(fact_132_poly__pCons, axiom,
    ((![A : a, P : poly_a, X : a]: ((poly_a2 @ (pCons_a @ A @ P) @ X) = (plus_plus_a @ A @ (times_times_a @ X @ (poly_a2 @ P @ X))))))). % poly_pCons
thf(fact_133_poly__pCons, axiom,
    ((![A : real, P : poly_real, X : real]: ((poly_real2 @ (pCons_real @ A @ P) @ X) = (plus_plus_real @ A @ (times_times_real @ X @ (poly_real2 @ P @ X))))))). % poly_pCons
thf(fact_134_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_135_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_136_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_137_one__reorient, axiom,
    ((![X : real]: ((one_one_real = X) = (X = one_one_real))))). % one_reorient
thf(fact_138_pCons__one, axiom,
    (((pCons_real @ one_one_real @ zero_zero_poly_real) = one_one_poly_real))). % pCons_one
thf(fact_139_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_140_group__cancel_Oadd2, axiom,
    ((![B2 : real, K : real, B : real, A : real]: ((B2 = (plus_plus_real @ K @ B)) => ((plus_plus_real @ A @ B2) = (plus_plus_real @ K @ (plus_plus_real @ A @ B))))))). % group_cancel.add2
thf(fact_141_real__norm__def, axiom,
    ((real_V646646907m_real = abs_abs_real))). % real_norm_def
thf(fact_142_comm__monoid__mult__class_Omult__1, axiom,
    ((![A : real]: ((times_times_real @ one_one_real @ A) = A)))). % comm_monoid_mult_class.mult_1
thf(fact_143_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_144_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_145_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_146_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_147_add_Ocommute, axiom,
    ((plus_plus_real = (^[A3 : real]: (^[B3 : real]: (plus_plus_real @ B3 @ A3)))))). % add.commute
thf(fact_148_mult_Ocommute, axiom,
    ((times_times_real = (^[A3 : real]: (^[B3 : real]: (times_times_real @ B3 @ A3)))))). % mult.commute
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_mult_Ocomm__neutral, axiom,
    ((![A : real]: ((times_times_real @ A @ one_one_real) = A)))). % mult.comm_neutral
thf(fact_151_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_152_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_153_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_154_pderiv_Oinduct, axiom,
    ((![P2 : poly_real > $o, A0 : poly_real]: ((![A4 : real, P3 : poly_real]: (((~ ((P3 = zero_zero_poly_real))) => (P2 @ P3)) => (P2 @ (pCons_real @ A4 @ P3)))) => (P2 @ A0))))). % pderiv.induct
thf(fact_155_poly__induct2, axiom,
    ((![P2 : poly_a > poly_a > $o, P : poly_a, Q : poly_a]: ((P2 @ zero_zero_poly_a @ zero_zero_poly_a) => ((![A4 : a, P3 : poly_a, B4 : a, Q2 : poly_a]: ((P2 @ P3 @ Q2) => (P2 @ (pCons_a @ A4 @ P3) @ (pCons_a @ B4 @ Q2)))) => (P2 @ P @ Q)))))). % poly_induct2
thf(fact_156_poly__induct2, axiom,
    ((![P2 : poly_a > poly_poly_a > $o, P : poly_a, Q : poly_poly_a]: ((P2 @ zero_zero_poly_a @ zero_z2096148049poly_a) => ((![A4 : a, P3 : poly_a, B4 : poly_a, Q2 : poly_poly_a]: ((P2 @ P3 @ Q2) => (P2 @ (pCons_a @ A4 @ P3) @ (pCons_poly_a @ B4 @ Q2)))) => (P2 @ P @ Q)))))). % poly_induct2
thf(fact_157_poly__induct2, axiom,
    ((![P2 : poly_a > poly_real > $o, P : poly_a, Q : poly_real]: ((P2 @ zero_zero_poly_a @ zero_zero_poly_real) => ((![A4 : a, P3 : poly_a, B4 : real, Q2 : poly_real]: ((P2 @ P3 @ Q2) => (P2 @ (pCons_a @ A4 @ P3) @ (pCons_real @ B4 @ Q2)))) => (P2 @ P @ Q)))))). % poly_induct2
thf(fact_158_poly__induct2, axiom,
    ((![P2 : poly_poly_a > poly_a > $o, P : poly_poly_a, Q : poly_a]: ((P2 @ zero_z2096148049poly_a @ zero_zero_poly_a) => ((![A4 : poly_a, P3 : poly_poly_a, B4 : a, Q2 : poly_a]: ((P2 @ P3 @ Q2) => (P2 @ (pCons_poly_a @ A4 @ P3) @ (pCons_a @ B4 @ Q2)))) => (P2 @ P @ Q)))))). % poly_induct2
thf(fact_159_poly__induct2, axiom,
    ((![P2 : poly_poly_a > poly_poly_a > $o, P : poly_poly_a, Q : poly_poly_a]: ((P2 @ zero_z2096148049poly_a @ zero_z2096148049poly_a) => ((![A4 : poly_a, P3 : poly_poly_a, B4 : poly_a, Q2 : poly_poly_a]: ((P2 @ P3 @ Q2) => (P2 @ (pCons_poly_a @ A4 @ P3) @ (pCons_poly_a @ B4 @ Q2)))) => (P2 @ P @ Q)))))). % poly_induct2
thf(fact_160_poly__induct2, axiom,
    ((![P2 : poly_poly_a > poly_real > $o, P : poly_poly_a, Q : poly_real]: ((P2 @ zero_z2096148049poly_a @ zero_zero_poly_real) => ((![A4 : poly_a, P3 : poly_poly_a, B4 : real, Q2 : poly_real]: ((P2 @ P3 @ Q2) => (P2 @ (pCons_poly_a @ A4 @ P3) @ (pCons_real @ B4 @ Q2)))) => (P2 @ P @ Q)))))). % poly_induct2
thf(fact_161_poly__induct2, axiom,
    ((![P2 : poly_real > poly_a > $o, P : poly_real, Q : poly_a]: ((P2 @ zero_zero_poly_real @ zero_zero_poly_a) => ((![A4 : real, P3 : poly_real, B4 : a, Q2 : poly_a]: ((P2 @ P3 @ Q2) => (P2 @ (pCons_real @ A4 @ P3) @ (pCons_a @ B4 @ Q2)))) => (P2 @ P @ Q)))))). % poly_induct2
thf(fact_162_poly__induct2, axiom,
    ((![P2 : poly_real > poly_poly_a > $o, P : poly_real, Q : poly_poly_a]: ((P2 @ zero_zero_poly_real @ zero_z2096148049poly_a) => ((![A4 : real, P3 : poly_real, B4 : poly_a, Q2 : poly_poly_a]: ((P2 @ P3 @ Q2) => (P2 @ (pCons_real @ A4 @ P3) @ (pCons_poly_a @ B4 @ Q2)))) => (P2 @ P @ Q)))))). % poly_induct2
thf(fact_163_poly__induct2, axiom,
    ((![P2 : poly_real > poly_real > $o, P : poly_real, Q : poly_real]: ((P2 @ zero_zero_poly_real @ zero_zero_poly_real) => ((![A4 : real, P3 : poly_real, B4 : real, Q2 : poly_real]: ((P2 @ P3 @ Q2) => (P2 @ (pCons_real @ A4 @ P3) @ (pCons_real @ B4 @ Q2)))) => (P2 @ P @ Q)))))). % poly_induct2
thf(fact_164_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_165_poly__IVT, axiom,
    ((![A : real, B : real, P : poly_real]: ((ord_less_real @ A @ B) => ((ord_less_real @ (times_times_real @ (poly_real2 @ P @ A) @ (poly_real2 @ P @ B)) @ zero_zero_real) => (?[X2 : real]: ((ord_less_real @ A @ X2) & ((ord_less_real @ X2 @ B) & ((poly_real2 @ P @ X2) = zero_zero_real))))))))). % poly_IVT
thf(fact_166_norm__mult, axiom,
    ((![X : a, Y : a]: ((real_V1022479215norm_a @ (times_times_a @ X @ Y)) = (times_times_real @ (real_V1022479215norm_a @ X) @ (real_V1022479215norm_a @ Y)))))). % norm_mult
thf(fact_167_norm__mult, axiom,
    ((![X : real, Y : real]: ((real_V646646907m_real @ (times_times_real @ X @ Y)) = (times_times_real @ (real_V646646907m_real @ X) @ (real_V646646907m_real @ Y)))))). % norm_mult
thf(fact_168_poly__IVT__pos, axiom,
    ((![A : real, B : real, P : poly_real]: ((ord_less_real @ A @ B) => ((ord_less_real @ (poly_real2 @ P @ A) @ zero_zero_real) => ((ord_less_real @ zero_zero_real @ (poly_real2 @ P @ B)) => (?[X2 : real]: ((ord_less_real @ A @ X2) & ((ord_less_real @ X2 @ B) & ((poly_real2 @ P @ X2) = zero_zero_real)))))))))). % poly_IVT_pos
thf(fact_169_poly__IVT__neg, axiom,
    ((![A : real, B : real, P : poly_real]: ((ord_less_real @ A @ B) => ((ord_less_real @ zero_zero_real @ (poly_real2 @ P @ A)) => ((ord_less_real @ (poly_real2 @ P @ B) @ zero_zero_real) => (?[X2 : real]: ((ord_less_real @ A @ X2) & ((ord_less_real @ X2 @ B) & ((poly_real2 @ P @ X2) = zero_zero_real)))))))))). % poly_IVT_neg
thf(fact_170_abs__ge__self, axiom,
    ((![A : real]: (ord_less_eq_real @ A @ (abs_abs_real @ A))))). % abs_ge_self
thf(fact_171_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_172_add_Ogroup__left__neutral, axiom,
    ((![A : real]: ((plus_plus_real @ zero_zero_real @ A) = A)))). % add.group_left_neutral
thf(fact_173_add_Ogroup__left__neutral, axiom,
    ((![A : a]: ((plus_plus_a @ zero_zero_a @ A) = A)))). % add.group_left_neutral
thf(fact_174_add_Ogroup__left__neutral, axiom,
    ((![A : poly_a]: ((plus_plus_poly_a @ zero_zero_poly_a @ A) = A)))). % add.group_left_neutral
thf(fact_175_add_Ogroup__left__neutral, axiom,
    ((![A : poly_poly_a]: ((plus_p1976640465poly_a @ zero_z2096148049poly_a @ A) = A)))). % add.group_left_neutral
thf(fact_176_add_Ogroup__left__neutral, axiom,
    ((![A : poly_real]: ((plus_plus_poly_real @ zero_zero_poly_real @ A) = A)))). % add.group_left_neutral
thf(fact_177_add_Ocomm__neutral, axiom,
    ((![A : real]: ((plus_plus_real @ A @ zero_zero_real) = A)))). % add.comm_neutral
thf(fact_178_add_Ocomm__neutral, axiom,
    ((![A : a]: ((plus_plus_a @ A @ zero_zero_a) = A)))). % add.comm_neutral
thf(fact_179_add_Ocomm__neutral, axiom,
    ((![A : poly_a]: ((plus_plus_poly_a @ A @ zero_zero_poly_a) = A)))). % add.comm_neutral
thf(fact_180_add_Ocomm__neutral, axiom,
    ((![A : poly_poly_a]: ((plus_p1976640465poly_a @ A @ zero_z2096148049poly_a) = A)))). % add.comm_neutral
thf(fact_181_add_Ocomm__neutral, axiom,
    ((![A : poly_real]: ((plus_plus_poly_real @ A @ zero_zero_poly_real) = A)))). % add.comm_neutral
thf(fact_182_comm__monoid__add__class_Oadd__0, axiom,
    ((![A : real]: ((plus_plus_real @ zero_zero_real @ A) = A)))). % comm_monoid_add_class.add_0
thf(fact_183_comm__monoid__add__class_Oadd__0, axiom,
    ((![A : a]: ((plus_plus_a @ zero_zero_a @ A) = A)))). % comm_monoid_add_class.add_0
thf(fact_184_comm__monoid__add__class_Oadd__0, axiom,
    ((![A : poly_a]: ((plus_plus_poly_a @ zero_zero_poly_a @ A) = A)))). % comm_monoid_add_class.add_0
thf(fact_185_comm__monoid__add__class_Oadd__0, axiom,
    ((![A : poly_poly_a]: ((plus_p1976640465poly_a @ zero_z2096148049poly_a @ A) = A)))). % comm_monoid_add_class.add_0
thf(fact_186_comm__monoid__add__class_Oadd__0, axiom,
    ((![A : poly_real]: ((plus_plus_poly_real @ zero_zero_poly_real @ A) = A)))). % comm_monoid_add_class.add_0
thf(fact_187_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_188_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_189_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_190_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_191_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_192_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_193_add__mono__thms__linordered__semiring_I2_J, axiom,
    ((![I : real, J : real, K : real, L : real]: (((I = J) & (ord_less_eq_real @ K @ L)) => (ord_less_eq_real @ (plus_plus_real @ I @ K) @ (plus_plus_real @ J @ L)))))). % add_mono_thms_linordered_semiring(2)
thf(fact_194_add__mono__thms__linordered__semiring_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_195_add__less__imp__less__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_imp_less_right
thf(fact_196_add__less__imp__less__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_imp_less_left
thf(fact_197_add__strict__right__mono, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_real @ A @ B) => (ord_less_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ C)))))). % add_strict_right_mono
thf(fact_198_add__strict__left__mono, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_real @ A @ B) => (ord_less_real @ (plus_plus_real @ C @ A) @ (plus_plus_real @ C @ B)))))). % add_strict_left_mono
thf(fact_199_add__strict__mono, axiom,
    ((![A : real, B : real, C : real, D : real]: ((ord_less_real @ A @ B) => ((ord_less_real @ C @ D) => (ord_less_real @ (plus_plus_real @ A @ C) @ (plus_plus_real @ B @ D))))))). % add_strict_mono
thf(fact_200_add__mono__thms__linordered__field_I1_J, axiom,
    ((![I : real, J : real, K : real, L : real]: (((ord_less_real @ I @ J) & (K = L)) => (ord_less_real @ (plus_plus_real @ I @ K) @ (plus_plus_real @ J @ L)))))). % add_mono_thms_linordered_field(1)
thf(fact_201_add__mono__thms__linordered__field_I2_J, axiom,
    ((![I : real, J : real, K : real, L : 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(2)
thf(fact_202_add__mono__thms__linordered__field_I5_J, axiom,
    ((![I : real, J : real, K : real, L : real]: (((ord_less_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(5)
thf(fact_203_norm__triangle__lt, axiom,
    ((![X : a, Y : a, E : real]: ((ord_less_real @ (plus_plus_real @ (real_V1022479215norm_a @ X) @ (real_V1022479215norm_a @ Y)) @ E) => (ord_less_real @ (real_V1022479215norm_a @ (plus_plus_a @ X @ Y)) @ E))))). % norm_triangle_lt
thf(fact_204_norm__triangle__lt, axiom,
    ((![X : real, Y : real, E : real]: ((ord_less_real @ (plus_plus_real @ (real_V646646907m_real @ X) @ (real_V646646907m_real @ Y)) @ E) => (ord_less_real @ (real_V646646907m_real @ (plus_plus_real @ X @ Y)) @ E))))). % norm_triangle_lt
thf(fact_205_norm__add__less, axiom,
    ((![X : a, R : real, Y : a, S : real]: ((ord_less_real @ (real_V1022479215norm_a @ X) @ R) => ((ord_less_real @ (real_V1022479215norm_a @ Y) @ S) => (ord_less_real @ (real_V1022479215norm_a @ (plus_plus_a @ X @ Y)) @ (plus_plus_real @ R @ S))))))). % norm_add_less
thf(fact_206_norm__add__less, axiom,
    ((![X : real, R : real, Y : real, S : real]: ((ord_less_real @ (real_V646646907m_real @ X) @ R) => ((ord_less_real @ (real_V646646907m_real @ Y) @ S) => (ord_less_real @ (real_V646646907m_real @ (plus_plus_real @ X @ Y)) @ (plus_plus_real @ R @ S))))))). % norm_add_less
thf(fact_207_norm__triangle__mono, axiom,
    ((![A : a, R : real, B : a, S : real]: ((ord_less_eq_real @ (real_V1022479215norm_a @ A) @ R) => ((ord_less_eq_real @ (real_V1022479215norm_a @ B) @ S) => (ord_less_eq_real @ (real_V1022479215norm_a @ (plus_plus_a @ A @ B)) @ (plus_plus_real @ R @ S))))))). % norm_triangle_mono
thf(fact_208_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_209_norm__triangle__ineq, axiom,
    ((![X : a, Y : a]: (ord_less_eq_real @ (real_V1022479215norm_a @ (plus_plus_a @ X @ Y)) @ (plus_plus_real @ (real_V1022479215norm_a @ X) @ (real_V1022479215norm_a @ Y)))))). % norm_triangle_ineq
thf(fact_210_norm__triangle__ineq, axiom,
    ((![X : real, Y : real]: (ord_less_eq_real @ (real_V646646907m_real @ (plus_plus_real @ X @ Y)) @ (plus_plus_real @ (real_V646646907m_real @ X) @ (real_V646646907m_real @ Y)))))). % norm_triangle_ineq
thf(fact_211_norm__triangle__le, axiom,
    ((![X : a, Y : a, E : real]: ((ord_less_eq_real @ (plus_plus_real @ (real_V1022479215norm_a @ X) @ (real_V1022479215norm_a @ Y)) @ E) => (ord_less_eq_real @ (real_V1022479215norm_a @ (plus_plus_a @ X @ Y)) @ E))))). % norm_triangle_le
thf(fact_212_norm__triangle__le, axiom,
    ((![X : real, Y : real, E : real]: ((ord_less_eq_real @ (plus_plus_real @ (real_V646646907m_real @ X) @ (real_V646646907m_real @ Y)) @ E) => (ord_less_eq_real @ (real_V646646907m_real @ (plus_plus_real @ X @ Y)) @ E))))). % norm_triangle_le
thf(fact_213_norm__add__leD, axiom,
    ((![A : a, B : a, C : real]: ((ord_less_eq_real @ (real_V1022479215norm_a @ (plus_plus_a @ A @ B)) @ C) => (ord_less_eq_real @ (real_V1022479215norm_a @ B) @ (plus_plus_real @ (real_V1022479215norm_a @ A) @ C)))))). % norm_add_leD
thf(fact_214_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_215_norm__mult__less, axiom,
    ((![X : a, R : real, Y : a, S : real]: ((ord_less_real @ (real_V1022479215norm_a @ X) @ R) => ((ord_less_real @ (real_V1022479215norm_a @ Y) @ S) => (ord_less_real @ (real_V1022479215norm_a @ (times_times_a @ X @ Y)) @ (times_times_real @ R @ S))))))). % norm_mult_less
thf(fact_216_norm__mult__less, axiom,
    ((![X : real, R : real, Y : real, S : real]: ((ord_less_real @ (real_V646646907m_real @ X) @ R) => ((ord_less_real @ (real_V646646907m_real @ Y) @ S) => (ord_less_real @ (real_V646646907m_real @ (times_times_real @ X @ Y)) @ (times_times_real @ R @ S))))))). % norm_mult_less
thf(fact_217_norm__mult__ineq, axiom,
    ((![X : a, Y : a]: (ord_less_eq_real @ (real_V1022479215norm_a @ (times_times_a @ X @ Y)) @ (times_times_real @ (real_V1022479215norm_a @ X) @ (real_V1022479215norm_a @ Y)))))). % norm_mult_ineq
thf(fact_218_norm__mult__ineq, axiom,
    ((![X : real, Y : real]: (ord_less_eq_real @ (real_V646646907m_real @ (times_times_real @ X @ Y)) @ (times_times_real @ (real_V646646907m_real @ X) @ (real_V646646907m_real @ Y)))))). % norm_mult_ineq
thf(fact_219_zero__reorient, axiom,
    ((![X : real]: ((zero_zero_real = X) = (X = zero_zero_real))))). % zero_reorient
thf(fact_220_zero__reorient, axiom,
    ((![X : a]: ((zero_zero_a = X) = (X = zero_zero_a))))). % zero_reorient
thf(fact_221_zero__reorient, axiom,
    ((![X : poly_a]: ((zero_zero_poly_a = X) = (X = zero_zero_poly_a))))). % zero_reorient
thf(fact_222_zero__reorient, axiom,
    ((![X : poly_poly_a]: ((zero_z2096148049poly_a = X) = (X = zero_z2096148049poly_a))))). % zero_reorient
thf(fact_223_zero__reorient, axiom,
    ((![X : poly_real]: ((zero_zero_poly_real = X) = (X = zero_zero_poly_real))))). % zero_reorient
thf(fact_224_abs__ge__zero, axiom,
    ((![A : poly_real]: (ord_le1180086932y_real @ zero_zero_poly_real @ (abs_abs_poly_real @ A))))). % abs_ge_zero
thf(fact_225_abs__ge__zero, axiom,
    ((![A : real]: (ord_less_eq_real @ zero_zero_real @ (abs_abs_real @ A))))). % abs_ge_zero
thf(fact_226_abs__not__less__zero, axiom,
    ((![A : poly_real]: (~ ((ord_less_poly_real @ (abs_abs_poly_real @ A) @ zero_zero_poly_real)))))). % abs_not_less_zero
thf(fact_227_abs__not__less__zero, axiom,
    ((![A : real]: (~ ((ord_less_real @ (abs_abs_real @ A) @ zero_zero_real)))))). % abs_not_less_zero
thf(fact_228_abs__of__pos, axiom,
    ((![A : poly_real]: ((ord_less_poly_real @ zero_zero_poly_real @ A) => ((abs_abs_poly_real @ A) = A))))). % abs_of_pos
thf(fact_229_abs__of__pos, axiom,
    ((![A : real]: ((ord_less_real @ zero_zero_real @ A) => ((abs_abs_real @ A) = A))))). % abs_of_pos
thf(fact_230_add__nonpos__eq__0__iff, axiom,
    ((![X : poly_real, Y : poly_real]: ((ord_le1180086932y_real @ X @ zero_zero_poly_real) => ((ord_le1180086932y_real @ Y @ zero_zero_poly_real) => (((plus_plus_poly_real @ X @ Y) = zero_zero_poly_real) = (((X = zero_zero_poly_real)) & ((Y = zero_zero_poly_real))))))))). % add_nonpos_eq_0_iff
thf(fact_231_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_232_add__nonneg__eq__0__iff, axiom,
    ((![X : poly_real, Y : poly_real]: ((ord_le1180086932y_real @ zero_zero_poly_real @ X) => ((ord_le1180086932y_real @ zero_zero_poly_real @ Y) => (((plus_plus_poly_real @ X @ Y) = zero_zero_poly_real) = (((X = zero_zero_poly_real)) & ((Y = zero_zero_poly_real))))))))). % add_nonneg_eq_0_iff
thf(fact_233_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_234_add__nonpos__nonpos, axiom,
    ((![A : poly_real, B : poly_real]: ((ord_le1180086932y_real @ A @ zero_zero_poly_real) => ((ord_le1180086932y_real @ B @ zero_zero_poly_real) => (ord_le1180086932y_real @ (plus_plus_poly_real @ A @ B) @ zero_zero_poly_real)))))). % add_nonpos_nonpos
thf(fact_235_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_236_add__nonneg__nonneg, axiom,
    ((![A : poly_real, B : poly_real]: ((ord_le1180086932y_real @ zero_zero_poly_real @ A) => ((ord_le1180086932y_real @ zero_zero_poly_real @ B) => (ord_le1180086932y_real @ zero_zero_poly_real @ (plus_plus_poly_real @ A @ B))))))). % add_nonneg_nonneg
thf(fact_237_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_238_add__increasing2, axiom,
    ((![C : poly_real, B : poly_real, A : poly_real]: ((ord_le1180086932y_real @ zero_zero_poly_real @ C) => ((ord_le1180086932y_real @ B @ A) => (ord_le1180086932y_real @ B @ (plus_plus_poly_real @ A @ C))))))). % add_increasing2
thf(fact_239_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_240_add__decreasing2, axiom,
    ((![C : poly_real, A : poly_real, B : poly_real]: ((ord_le1180086932y_real @ C @ zero_zero_poly_real) => ((ord_le1180086932y_real @ A @ B) => (ord_le1180086932y_real @ (plus_plus_poly_real @ A @ C) @ B)))))). % add_decreasing2
thf(fact_241_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_242_add__increasing, axiom,
    ((![A : poly_real, B : poly_real, C : poly_real]: ((ord_le1180086932y_real @ zero_zero_poly_real @ A) => ((ord_le1180086932y_real @ B @ C) => (ord_le1180086932y_real @ B @ (plus_plus_poly_real @ A @ C))))))). % add_increasing
thf(fact_243_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_244_add__decreasing, axiom,
    ((![A : poly_real, C : poly_real, B : poly_real]: ((ord_le1180086932y_real @ A @ zero_zero_poly_real) => ((ord_le1180086932y_real @ C @ B) => (ord_le1180086932y_real @ (plus_plus_poly_real @ A @ C) @ B)))))). % add_decreasing
thf(fact_245_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_246_pos__add__strict, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ B @ C) => (ord_less_real @ B @ (plus_plus_real @ A @ C))))))). % pos_add_strict

% Conjectures (1)
thf(conj_0, conjecture,
    ((?[M2 : real]: ((ord_less_real @ zero_zero_real @ M2) & (![Z3 : a]: ((~ ((ord_less_eq_real @ (real_V1022479215norm_a @ Z3) @ r))) | (ord_less_eq_real @ (real_V1022479215norm_a @ (poly_a2 @ (pCons_a @ c @ cs) @ Z3)) @ M2))))))).
