% 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_335__5370826_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:29:18.793

% Could-be-implicit typings (8)
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__Set__Oset_It__Real__Oreal_J, type,
    set_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_t__Nat__Onat, type,
    nat : $tType).
thf(ty_n_tf__a, type,
    a : $tType).

% Explicit typings (33)
thf(sy_c_Groups_Ominus__class_Ominus_001t__Polynomial__Opoly_It__Real__Oreal_J, type,
    minus_240770701y_real : poly_real > poly_real > poly_real).
thf(sy_c_Groups_Ominus__class_Ominus_001t__Polynomial__Opoly_Itf__a_J, type,
    minus_minus_poly_a : poly_a > poly_a > poly_a).
thf(sy_c_Groups_Ominus__class_Ominus_001t__Real__Oreal, type,
    minus_minus_real : real > real > real).
thf(sy_c_Groups_Ominus__class_Ominus_001tf__a, type,
    minus_minus_a : a > a > a).
thf(sy_c_Groups_Oone__class_Oone_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Real__Oreal_J_J, type,
    one_on501200385y_real : poly_poly_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_Ozero__class_Ozero_001t__Nat__Onat, type,
    zero_zero_nat : nat).
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_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_Polynomial_Opoly__cutoff_001t__Real__Oreal, type,
    poly_cutoff_real : nat > poly_real > poly_real).
thf(sy_c_Polynomial_Opoly__cutoff_001tf__a, type,
    poly_cutoff_a : nat > poly_a > poly_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_c_Set_OCollect_001t__Real__Oreal, type,
    collect_real : (real > $o) > set_real).
thf(sy_c_member_001t__Real__Oreal, type,
    member_real : real > set_real > $o).
thf(sy_v_c____, type,
    c : a).
thf(sy_v_cs____, type,
    cs : poly_a).
thf(sy_v_e, type,
    e : real).
thf(sy_v_thesis____, type,
    thesis : $o).
thf(sy_v_z, type,
    z : a).

% Relevant facts (170)
thf(fact_0_ep, axiom,
    ((ord_less_real @ zero_zero_real @ e))). % ep
thf(fact_1__092_060open_062_092_060exists_062m_0620_O_A_092_060forall_062z_O_Anorm_Az_A_092_060le_062_A1_A_092_060longrightarrow_062_Anorm_A_Ipoly_Acs_Az_J_A_092_060le_062_Am_092_060close_062, axiom,
    ((?[M : real]: ((ord_less_real @ zero_zero_real @ M) & (![Z : a]: ((ord_less_eq_real @ (real_V1022479215norm_a @ Z) @ one_one_real) => (ord_less_eq_real @ (real_V1022479215norm_a @ (poly_a2 @ cs @ Z)) @ M))))))). % \<open>\<exists>m>0. \<forall>z. norm z \<le> 1 \<longrightarrow> norm (poly cs z) \<le> m\<close>
thf(fact_2_real__sup__exists, axiom,
    ((![P : real > $o]: ((?[X_1 : real]: (P @ X_1)) => ((?[Z : real]: (![X : real]: ((P @ X) => (ord_less_real @ X @ Z)))) => (?[S : real]: (![Y : real]: ((?[X2 : real]: (((P @ X2)) & ((ord_less_real @ Y @ X2)))) = (ord_less_real @ Y @ S))))))))). % real_sup_exists
thf(fact_3_poly__bound__exists, axiom,
    ((![R : real, P2 : poly_real]: (?[M : real]: ((ord_less_real @ zero_zero_real @ M) & (![Z : real]: ((ord_less_eq_real @ (real_V646646907m_real @ Z) @ R) => (ord_less_eq_real @ (real_V646646907m_real @ (poly_real2 @ P2 @ Z)) @ M)))))))). % poly_bound_exists
thf(fact_4_poly__bound__exists, axiom,
    ((![R : real, P2 : poly_a]: (?[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 @ P2 @ Z)) @ M)))))))). % poly_bound_exists
thf(fact_5_norm__le__zero__iff, axiom,
    ((![X3 : real]: ((ord_less_eq_real @ (real_V646646907m_real @ X3) @ zero_zero_real) = (X3 = zero_zero_real))))). % norm_le_zero_iff
thf(fact_6_norm__le__zero__iff, axiom,
    ((![X3 : a]: ((ord_less_eq_real @ (real_V1022479215norm_a @ X3) @ zero_zero_real) = (X3 = zero_zero_a))))). % norm_le_zero_iff
thf(fact_7_zero__less__norm__iff, axiom,
    ((![X3 : real]: ((ord_less_real @ zero_zero_real @ (real_V646646907m_real @ X3)) = (~ ((X3 = zero_zero_real))))))). % zero_less_norm_iff
thf(fact_8_zero__less__norm__iff, axiom,
    ((![X3 : a]: ((ord_less_real @ zero_zero_real @ (real_V1022479215norm_a @ X3)) = (~ ((X3 = zero_zero_a))))))). % zero_less_norm_iff
thf(fact_9_norm__one, axiom,
    (((real_V646646907m_real @ one_one_real) = one_one_real))). % norm_one
thf(fact_10_norm__one, axiom,
    (((real_V1022479215norm_a @ one_one_a) = one_one_real))). % norm_one
thf(fact_11_norm__zero, axiom,
    (((real_V646646907m_real @ zero_zero_real) = zero_zero_real))). % norm_zero
thf(fact_12_norm__zero, axiom,
    (((real_V1022479215norm_a @ zero_zero_a) = zero_zero_real))). % norm_zero
thf(fact_13_norm__eq__zero, axiom,
    ((![X3 : real]: (((real_V646646907m_real @ X3) = zero_zero_real) = (X3 = zero_zero_real))))). % norm_eq_zero
thf(fact_14_norm__eq__zero, axiom,
    ((![X3 : a]: (((real_V1022479215norm_a @ X3) = zero_zero_real) = (X3 = zero_zero_a))))). % norm_eq_zero
thf(fact_15_poly__1, axiom,
    ((![X3 : poly_real]: ((poly_poly_real2 @ one_on501200385y_real @ X3) = one_one_poly_real)))). % poly_1
thf(fact_16_poly__1, axiom,
    ((![X3 : real]: ((poly_real2 @ one_one_poly_real @ X3) = one_one_real)))). % poly_1
thf(fact_17_poly__0, axiom,
    ((![X3 : real]: ((poly_real2 @ zero_zero_poly_real @ X3) = zero_zero_real)))). % poly_0
thf(fact_18_poly__0, axiom,
    ((![X3 : poly_a]: ((poly_poly_a2 @ zero_z2096148049poly_a @ X3) = zero_zero_poly_a)))). % poly_0
thf(fact_19_poly__0, axiom,
    ((![X3 : a]: ((poly_a2 @ zero_zero_poly_a @ X3) = zero_zero_a)))). % poly_0
thf(fact_20_norm__ge__zero, axiom,
    ((![X3 : a]: (ord_less_eq_real @ zero_zero_real @ (real_V1022479215norm_a @ X3))))). % norm_ge_zero
thf(fact_21_norm__ge__zero, axiom,
    ((![X3 : real]: (ord_less_eq_real @ zero_zero_real @ (real_V646646907m_real @ X3))))). % norm_ge_zero
thf(fact_22_norm__not__less__zero, axiom,
    ((![X3 : a]: (~ ((ord_less_real @ (real_V1022479215norm_a @ X3) @ zero_zero_real)))))). % norm_not_less_zero
thf(fact_23_norm__not__less__zero, axiom,
    ((![X3 : real]: (~ ((ord_less_real @ (real_V646646907m_real @ X3) @ zero_zero_real)))))). % norm_not_less_zero
thf(fact_24_less__numeral__extra_I1_J, axiom,
    ((ord_less_poly_real @ zero_zero_poly_real @ one_one_poly_real))). % less_numeral_extra(1)
thf(fact_25_less__numeral__extra_I1_J, axiom,
    ((ord_less_real @ zero_zero_real @ one_one_real))). % less_numeral_extra(1)
thf(fact_26_pCons_Ohyps_I1_J, axiom,
    (((~ ((c = zero_zero_a))) | (~ ((cs = zero_zero_poly_a)))))). % pCons.hyps(1)
thf(fact_27_poly__IVT__pos, axiom,
    ((![A : real, B : real, P2 : poly_real]: ((ord_less_real @ A @ B) => ((ord_less_real @ (poly_real2 @ P2 @ A) @ zero_zero_real) => ((ord_less_real @ zero_zero_real @ (poly_real2 @ P2 @ B)) => (?[X : real]: ((ord_less_real @ A @ X) & ((ord_less_real @ X @ B) & ((poly_real2 @ P2 @ X) = zero_zero_real)))))))))). % poly_IVT_pos
thf(fact_28_poly__IVT__neg, axiom,
    ((![A : real, B : real, P2 : poly_real]: ((ord_less_real @ A @ B) => ((ord_less_real @ zero_zero_real @ (poly_real2 @ P2 @ A)) => ((ord_less_real @ (poly_real2 @ P2 @ B) @ zero_zero_real) => (?[X : real]: ((ord_less_real @ A @ X) & ((ord_less_real @ X @ B) & ((poly_real2 @ P2 @ X) = zero_zero_real)))))))))). % poly_IVT_neg
thf(fact_29_zero__reorient, axiom,
    ((![X3 : real]: ((zero_zero_real = X3) = (X3 = zero_zero_real))))). % zero_reorient
thf(fact_30_zero__reorient, axiom,
    ((![X3 : a]: ((zero_zero_a = X3) = (X3 = zero_zero_a))))). % zero_reorient
thf(fact_31_zero__reorient, axiom,
    ((![X3 : poly_a]: ((zero_zero_poly_a = X3) = (X3 = zero_zero_poly_a))))). % zero_reorient
thf(fact_32_one__reorient, axiom,
    ((![X3 : real]: ((one_one_real = X3) = (X3 = one_one_real))))). % one_reorient
thf(fact_33_one__reorient, axiom,
    ((![X3 : a]: ((one_one_a = X3) = (X3 = one_one_a))))). % one_reorient
thf(fact_34_one__reorient, axiom,
    ((![X3 : poly_real]: ((one_one_poly_real = X3) = (X3 = one_one_poly_real))))). % one_reorient
thf(fact_35_poly__eq__poly__eq__iff, axiom,
    ((![P2 : poly_real, Q : poly_real]: (((poly_real2 @ P2) = (poly_real2 @ Q)) = (P2 = Q))))). % poly_eq_poly_eq_iff
thf(fact_36_le__numeral__extra_I3_J, axiom,
    ((ord_less_eq_real @ zero_zero_real @ zero_zero_real))). % le_numeral_extra(3)
thf(fact_37_less__numeral__extra_I3_J, axiom,
    ((~ ((ord_less_real @ zero_zero_real @ zero_zero_real))))). % less_numeral_extra(3)
thf(fact_38_le__numeral__extra_I4_J, axiom,
    ((ord_le1180086932y_real @ one_one_poly_real @ one_one_poly_real))). % le_numeral_extra(4)
thf(fact_39_le__numeral__extra_I4_J, axiom,
    ((ord_less_eq_real @ one_one_real @ one_one_real))). % le_numeral_extra(4)
thf(fact_40_less__numeral__extra_I4_J, axiom,
    ((~ ((ord_less_poly_real @ one_one_poly_real @ one_one_poly_real))))). % less_numeral_extra(4)
thf(fact_41_less__numeral__extra_I4_J, axiom,
    ((~ ((ord_less_real @ one_one_real @ one_one_real))))). % less_numeral_extra(4)
thf(fact_42_poly__all__0__iff__0, axiom,
    ((![P2 : poly_real]: ((![X2 : real]: ((poly_real2 @ P2 @ X2) = zero_zero_real)) = (P2 = zero_zero_poly_real))))). % poly_all_0_iff_0
thf(fact_43_pCons_Ohyps_I2_J, axiom,
    ((?[D : real]: ((ord_less_real @ zero_zero_real @ D) & (![W : a]: (((ord_less_real @ zero_zero_real @ (real_V1022479215norm_a @ (minus_minus_a @ W @ z))) & (ord_less_real @ (real_V1022479215norm_a @ (minus_minus_a @ W @ z)) @ D)) => (ord_less_real @ (real_V1022479215norm_a @ (minus_minus_a @ (poly_a2 @ cs @ (minus_minus_a @ W @ z)) @ (poly_a2 @ cs @ (minus_minus_a @ z @ z)))) @ e))))))). % pCons.hyps(2)
thf(fact_44_not__one__less__zero, axiom,
    ((~ ((ord_less_poly_real @ one_one_poly_real @ zero_zero_poly_real))))). % not_one_less_zero
thf(fact_45_not__one__less__zero, axiom,
    ((~ ((ord_less_real @ one_one_real @ zero_zero_real))))). % not_one_less_zero
thf(fact_46_zero__less__one, axiom,
    ((ord_less_poly_real @ zero_zero_poly_real @ one_one_poly_real))). % zero_less_one
thf(fact_47_zero__less__one, axiom,
    ((ord_less_real @ zero_zero_real @ one_one_real))). % zero_less_one
thf(fact_48_not__one__le__zero, axiom,
    ((~ ((ord_le1180086932y_real @ one_one_poly_real @ zero_zero_poly_real))))). % not_one_le_zero
thf(fact_49_not__one__le__zero, axiom,
    ((~ ((ord_less_eq_real @ one_one_real @ zero_zero_real))))). % not_one_le_zero
thf(fact_50_zero__le__one, axiom,
    ((ord_le1180086932y_real @ zero_zero_poly_real @ one_one_poly_real))). % zero_le_one
thf(fact_51_zero__le__one, axiom,
    ((ord_less_eq_real @ zero_zero_real @ one_one_real))). % zero_le_one
thf(fact_52_poly__cutoff__1, axiom,
    ((![N : nat]: (((N = zero_zero_nat) => ((poly_cutoff_real @ N @ one_one_poly_real) = zero_zero_poly_real)) & ((~ ((N = zero_zero_nat))) => ((poly_cutoff_real @ N @ one_one_poly_real) = one_one_poly_real)))))). % poly_cutoff_1
thf(fact_53_order__refl, axiom,
    ((![X3 : real]: (ord_less_eq_real @ X3 @ X3)))). % order_refl
thf(fact_54_less__eq__real__def, axiom,
    ((ord_less_eq_real = (^[X2 : real]: (^[Y2 : real]: (((ord_less_real @ X2 @ Y2)) | ((X2 = Y2)))))))). % less_eq_real_def
thf(fact_55_zero__neq__one, axiom,
    ((~ ((zero_zero_poly_real = one_one_poly_real))))). % zero_neq_one
thf(fact_56_zero__neq__one, axiom,
    ((~ ((zero_zero_real = one_one_real))))). % zero_neq_one
thf(fact_57_zero__neq__one, axiom,
    ((~ ((zero_zero_a = one_one_a))))). % zero_neq_one
thf(fact_58_diff__self, axiom,
    ((![A : real]: ((minus_minus_real @ A @ A) = zero_zero_real)))). % diff_self
thf(fact_59_diff__self, axiom,
    ((![A : poly_a]: ((minus_minus_poly_a @ A @ A) = zero_zero_poly_a)))). % diff_self
thf(fact_60_diff__self, axiom,
    ((![A : a]: ((minus_minus_a @ A @ A) = zero_zero_a)))). % diff_self
thf(fact_61_diff__0__right, axiom,
    ((![A : real]: ((minus_minus_real @ A @ zero_zero_real) = A)))). % diff_0_right
thf(fact_62_diff__0__right, axiom,
    ((![A : poly_a]: ((minus_minus_poly_a @ A @ zero_zero_poly_a) = A)))). % diff_0_right
thf(fact_63_diff__0__right, axiom,
    ((![A : a]: ((minus_minus_a @ A @ zero_zero_a) = A)))). % diff_0_right
thf(fact_64_mem__Collect__eq, axiom,
    ((![A : real, P : real > $o]: ((member_real @ A @ (collect_real @ P)) = (P @ A))))). % mem_Collect_eq
thf(fact_65_Collect__mem__eq, axiom,
    ((![A2 : set_real]: ((collect_real @ (^[X2 : real]: (member_real @ X2 @ A2))) = A2)))). % Collect_mem_eq
thf(fact_66_diff__zero, axiom,
    ((![A : real]: ((minus_minus_real @ A @ zero_zero_real) = A)))). % diff_zero
thf(fact_67_diff__zero, axiom,
    ((![A : poly_a]: ((minus_minus_poly_a @ A @ zero_zero_poly_a) = A)))). % diff_zero
thf(fact_68_diff__zero, axiom,
    ((![A : a]: ((minus_minus_a @ A @ zero_zero_a) = A)))). % diff_zero
thf(fact_69_cancel__comm__monoid__add__class_Odiff__cancel, axiom,
    ((![A : real]: ((minus_minus_real @ A @ A) = zero_zero_real)))). % cancel_comm_monoid_add_class.diff_cancel
thf(fact_70_cancel__comm__monoid__add__class_Odiff__cancel, axiom,
    ((![A : poly_a]: ((minus_minus_poly_a @ A @ A) = zero_zero_poly_a)))). % cancel_comm_monoid_add_class.diff_cancel
thf(fact_71_cancel__comm__monoid__add__class_Odiff__cancel, axiom,
    ((![A : a]: ((minus_minus_a @ A @ A) = zero_zero_a)))). % cancel_comm_monoid_add_class.diff_cancel
thf(fact_72_poly__diff, axiom,
    ((![P2 : poly_real, Q : poly_real, X3 : real]: ((poly_real2 @ (minus_240770701y_real @ P2 @ Q) @ X3) = (minus_minus_real @ (poly_real2 @ P2 @ X3) @ (poly_real2 @ Q @ X3)))))). % poly_diff
thf(fact_73_poly__cutoff__0, axiom,
    ((![N : nat]: ((poly_cutoff_a @ N @ zero_zero_poly_a) = zero_zero_poly_a)))). % poly_cutoff_0
thf(fact_74_diff__ge__0__iff__ge, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ zero_zero_real @ (minus_minus_real @ A @ B)) = (ord_less_eq_real @ B @ A))))). % diff_ge_0_iff_ge
thf(fact_75_diff__gt__0__iff__gt, axiom,
    ((![A : real, B : real]: ((ord_less_real @ zero_zero_real @ (minus_minus_real @ A @ B)) = (ord_less_real @ B @ A))))). % diff_gt_0_iff_gt
thf(fact_76_diff__numeral__special_I9_J, axiom,
    (((minus_240770701y_real @ one_one_poly_real @ one_one_poly_real) = zero_zero_poly_real))). % diff_numeral_special(9)
thf(fact_77_diff__numeral__special_I9_J, axiom,
    (((minus_minus_real @ one_one_real @ one_one_real) = zero_zero_real))). % diff_numeral_special(9)
thf(fact_78_diff__numeral__special_I9_J, axiom,
    (((minus_minus_a @ one_one_a @ one_one_a) = zero_zero_a))). % diff_numeral_special(9)
thf(fact_79_diff__eq__diff__eq, axiom,
    ((![A : a, B : a, C : a, D2 : a]: (((minus_minus_a @ A @ B) = (minus_minus_a @ C @ D2)) => ((A = B) = (C = D2)))))). % diff_eq_diff_eq
thf(fact_80_cancel__ab__semigroup__add__class_Odiff__right__commute, axiom,
    ((![A : a, C : a, B : a]: ((minus_minus_a @ (minus_minus_a @ A @ C) @ B) = (minus_minus_a @ (minus_minus_a @ A @ B) @ C))))). % cancel_ab_semigroup_add_class.diff_right_commute
thf(fact_81_norm__triangle__ineq2, axiom,
    ((![A : a, B : a]: (ord_less_eq_real @ (minus_minus_real @ (real_V1022479215norm_a @ A) @ (real_V1022479215norm_a @ B)) @ (real_V1022479215norm_a @ (minus_minus_a @ A @ B)))))). % norm_triangle_ineq2
thf(fact_82_norm__triangle__ineq2, axiom,
    ((![A : real, B : real]: (ord_less_eq_real @ (minus_minus_real @ (real_V646646907m_real @ A) @ (real_V646646907m_real @ B)) @ (real_V646646907m_real @ (minus_minus_real @ A @ B)))))). % norm_triangle_ineq2
thf(fact_83_eq__iff__diff__eq__0, axiom,
    (((^[Y3 : real]: (^[Z2 : real]: (Y3 = Z2))) = (^[A3 : real]: (^[B2 : real]: ((minus_minus_real @ A3 @ B2) = zero_zero_real)))))). % eq_iff_diff_eq_0
thf(fact_84_eq__iff__diff__eq__0, axiom,
    (((^[Y3 : poly_a]: (^[Z2 : poly_a]: (Y3 = Z2))) = (^[A3 : poly_a]: (^[B2 : poly_a]: ((minus_minus_poly_a @ A3 @ B2) = zero_zero_poly_a)))))). % eq_iff_diff_eq_0
thf(fact_85_eq__iff__diff__eq__0, axiom,
    (((^[Y3 : a]: (^[Z2 : a]: (Y3 = Z2))) = (^[A3 : a]: (^[B2 : a]: ((minus_minus_a @ A3 @ B2) = zero_zero_a)))))). % eq_iff_diff_eq_0
thf(fact_86_diff__mono, axiom,
    ((![A : real, B : real, D2 : real, C : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ D2 @ C) => (ord_less_eq_real @ (minus_minus_real @ A @ C) @ (minus_minus_real @ B @ D2))))))). % diff_mono
thf(fact_87_diff__left__mono, axiom,
    ((![B : real, A : real, C : real]: ((ord_less_eq_real @ B @ A) => (ord_less_eq_real @ (minus_minus_real @ C @ A) @ (minus_minus_real @ C @ B)))))). % diff_left_mono
thf(fact_88_diff__right__mono, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_eq_real @ A @ B) => (ord_less_eq_real @ (minus_minus_real @ A @ C) @ (minus_minus_real @ B @ C)))))). % diff_right_mono
thf(fact_89_diff__eq__diff__less__eq, axiom,
    ((![A : real, B : real, C : real, D2 : real]: (((minus_minus_real @ A @ B) = (minus_minus_real @ C @ D2)) => ((ord_less_eq_real @ A @ B) = (ord_less_eq_real @ C @ D2)))))). % diff_eq_diff_less_eq
thf(fact_90_diff__strict__mono, axiom,
    ((![A : real, B : real, D2 : real, C : real]: ((ord_less_real @ A @ B) => ((ord_less_real @ D2 @ C) => (ord_less_real @ (minus_minus_real @ A @ C) @ (minus_minus_real @ B @ D2))))))). % diff_strict_mono
thf(fact_91_diff__eq__diff__less, axiom,
    ((![A : real, B : real, C : real, D2 : real]: (((minus_minus_real @ A @ B) = (minus_minus_real @ C @ D2)) => ((ord_less_real @ A @ B) = (ord_less_real @ C @ D2)))))). % diff_eq_diff_less
thf(fact_92_diff__strict__left__mono, axiom,
    ((![B : real, A : real, C : real]: ((ord_less_real @ B @ A) => (ord_less_real @ (minus_minus_real @ C @ A) @ (minus_minus_real @ C @ B)))))). % diff_strict_left_mono
thf(fact_93_diff__strict__right__mono, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_real @ A @ B) => (ord_less_real @ (minus_minus_real @ A @ C) @ (minus_minus_real @ B @ C)))))). % diff_strict_right_mono
thf(fact_94_norm__minus__commute, axiom,
    ((![A : a, B : a]: ((real_V1022479215norm_a @ (minus_minus_a @ A @ B)) = (real_V1022479215norm_a @ (minus_minus_a @ B @ A)))))). % norm_minus_commute
thf(fact_95_norm__minus__commute, axiom,
    ((![A : real, B : real]: ((real_V646646907m_real @ (minus_minus_real @ A @ B)) = (real_V646646907m_real @ (minus_minus_real @ B @ A)))))). % norm_minus_commute
thf(fact_96_le__iff__diff__le__0, axiom,
    ((ord_less_eq_real = (^[A3 : real]: (^[B2 : real]: (ord_less_eq_real @ (minus_minus_real @ A3 @ B2) @ zero_zero_real)))))). % le_iff_diff_le_0
thf(fact_97_less__iff__diff__less__0, axiom,
    ((ord_less_real = (^[A3 : real]: (^[B2 : real]: (ord_less_real @ (minus_minus_real @ A3 @ B2) @ zero_zero_real)))))). % less_iff_diff_less_0
thf(fact_98_order__subst1, axiom,
    ((![A : real, F : real > real, B : real, C : real]: ((ord_less_eq_real @ A @ (F @ B)) => ((ord_less_eq_real @ B @ C) => ((![X : real, Y4 : real]: ((ord_less_eq_real @ X @ Y4) => (ord_less_eq_real @ (F @ X) @ (F @ Y4)))) => (ord_less_eq_real @ A @ (F @ C)))))))). % order_subst1
thf(fact_99_order__subst2, axiom,
    ((![A : real, B : real, F : real > real, C : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ (F @ B) @ C) => ((![X : real, Y4 : real]: ((ord_less_eq_real @ X @ Y4) => (ord_less_eq_real @ (F @ X) @ (F @ Y4)))) => (ord_less_eq_real @ (F @ A) @ C))))))). % order_subst2
thf(fact_100_ord__eq__le__subst, axiom,
    ((![A : real, F : real > real, B : real, C : real]: ((A = (F @ B)) => ((ord_less_eq_real @ B @ C) => ((![X : real, Y4 : real]: ((ord_less_eq_real @ X @ Y4) => (ord_less_eq_real @ (F @ X) @ (F @ Y4)))) => (ord_less_eq_real @ A @ (F @ C)))))))). % ord_eq_le_subst
thf(fact_101_ord__le__eq__subst, axiom,
    ((![A : real, B : real, F : real > real, C : real]: ((ord_less_eq_real @ A @ B) => (((F @ B) = C) => ((![X : real, Y4 : real]: ((ord_less_eq_real @ X @ Y4) => (ord_less_eq_real @ (F @ X) @ (F @ Y4)))) => (ord_less_eq_real @ (F @ A) @ C))))))). % ord_le_eq_subst
thf(fact_102_eq__iff, axiom,
    (((^[Y3 : real]: (^[Z2 : real]: (Y3 = Z2))) = (^[X2 : real]: (^[Y2 : real]: (((ord_less_eq_real @ X2 @ Y2)) & ((ord_less_eq_real @ Y2 @ X2)))))))). % eq_iff
thf(fact_103_antisym, axiom,
    ((![X3 : real, Y5 : real]: ((ord_less_eq_real @ X3 @ Y5) => ((ord_less_eq_real @ Y5 @ X3) => (X3 = Y5)))))). % antisym
thf(fact_104_linear, axiom,
    ((![X3 : real, Y5 : real]: ((ord_less_eq_real @ X3 @ Y5) | (ord_less_eq_real @ Y5 @ X3))))). % linear
thf(fact_105_eq__refl, axiom,
    ((![X3 : real, Y5 : real]: ((X3 = Y5) => (ord_less_eq_real @ X3 @ Y5))))). % eq_refl
thf(fact_106_le__cases, axiom,
    ((![X3 : real, Y5 : real]: ((~ ((ord_less_eq_real @ X3 @ Y5))) => (ord_less_eq_real @ Y5 @ X3))))). % le_cases
thf(fact_107_order_Otrans, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ B @ C) => (ord_less_eq_real @ A @ C)))))). % order.trans
thf(fact_108_le__cases3, axiom,
    ((![X3 : real, Y5 : real, Z3 : real]: (((ord_less_eq_real @ X3 @ Y5) => (~ ((ord_less_eq_real @ Y5 @ Z3)))) => (((ord_less_eq_real @ Y5 @ X3) => (~ ((ord_less_eq_real @ X3 @ Z3)))) => (((ord_less_eq_real @ X3 @ Z3) => (~ ((ord_less_eq_real @ Z3 @ Y5)))) => (((ord_less_eq_real @ Z3 @ Y5) => (~ ((ord_less_eq_real @ Y5 @ X3)))) => (((ord_less_eq_real @ Y5 @ Z3) => (~ ((ord_less_eq_real @ Z3 @ X3)))) => (~ (((ord_less_eq_real @ Z3 @ X3) => (~ ((ord_less_eq_real @ X3 @ Y5)))))))))))))). % le_cases3
thf(fact_109_antisym__conv, axiom,
    ((![Y5 : real, X3 : real]: ((ord_less_eq_real @ Y5 @ X3) => ((ord_less_eq_real @ X3 @ Y5) = (X3 = Y5)))))). % antisym_conv
thf(fact_110_order__class_Oorder_Oeq__iff, axiom,
    (((^[Y3 : real]: (^[Z2 : real]: (Y3 = Z2))) = (^[A3 : real]: (^[B2 : real]: (((ord_less_eq_real @ A3 @ B2)) & ((ord_less_eq_real @ B2 @ A3)))))))). % order_class.order.eq_iff
thf(fact_111_ord__eq__le__trans, axiom,
    ((![A : real, B : real, C : real]: ((A = B) => ((ord_less_eq_real @ B @ C) => (ord_less_eq_real @ A @ C)))))). % ord_eq_le_trans
thf(fact_112_ord__le__eq__trans, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_eq_real @ A @ B) => ((B = C) => (ord_less_eq_real @ A @ C)))))). % ord_le_eq_trans
thf(fact_113_order__class_Oorder_Oantisym, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ B @ A) => (A = B)))))). % order_class.order.antisym
thf(fact_114_order__trans, axiom,
    ((![X3 : real, Y5 : real, Z3 : real]: ((ord_less_eq_real @ X3 @ Y5) => ((ord_less_eq_real @ Y5 @ Z3) => (ord_less_eq_real @ X3 @ Z3)))))). % order_trans
thf(fact_115_dual__order_Orefl, axiom,
    ((![A : real]: (ord_less_eq_real @ A @ A)))). % dual_order.refl
thf(fact_116_linorder__wlog, axiom,
    ((![P : real > real > $o, A : real, B : real]: ((![A4 : real, B3 : real]: ((ord_less_eq_real @ A4 @ B3) => (P @ A4 @ B3))) => ((![A4 : real, B3 : real]: ((P @ B3 @ A4) => (P @ A4 @ B3))) => (P @ A @ B)))))). % linorder_wlog
thf(fact_117_dual__order_Otrans, axiom,
    ((![B : real, A : real, C : real]: ((ord_less_eq_real @ B @ A) => ((ord_less_eq_real @ C @ B) => (ord_less_eq_real @ C @ A)))))). % dual_order.trans
thf(fact_118_dual__order_Oeq__iff, axiom,
    (((^[Y3 : real]: (^[Z2 : real]: (Y3 = Z2))) = (^[A3 : real]: (^[B2 : real]: (((ord_less_eq_real @ B2 @ A3)) & ((ord_less_eq_real @ A3 @ B2)))))))). % dual_order.eq_iff
thf(fact_119_dual__order_Oantisym, axiom,
    ((![B : real, A : real]: ((ord_less_eq_real @ B @ A) => ((ord_less_eq_real @ A @ B) => (A = B)))))). % dual_order.antisym
thf(fact_120_ord__eq__less__subst, axiom,
    ((![A : real, F : real > real, B : real, C : real]: ((A = (F @ B)) => ((ord_less_real @ B @ C) => ((![X : real, Y4 : real]: ((ord_less_real @ X @ Y4) => (ord_less_real @ (F @ X) @ (F @ Y4)))) => (ord_less_real @ A @ (F @ C)))))))). % ord_eq_less_subst
thf(fact_121_ord__less__eq__subst, axiom,
    ((![A : real, B : real, F : real > real, C : real]: ((ord_less_real @ A @ B) => (((F @ B) = C) => ((![X : real, Y4 : real]: ((ord_less_real @ X @ Y4) => (ord_less_real @ (F @ X) @ (F @ Y4)))) => (ord_less_real @ (F @ A) @ C))))))). % ord_less_eq_subst
thf(fact_122_order__less__subst1, axiom,
    ((![A : real, F : real > real, B : real, C : real]: ((ord_less_real @ A @ (F @ B)) => ((ord_less_real @ B @ C) => ((![X : real, Y4 : real]: ((ord_less_real @ X @ Y4) => (ord_less_real @ (F @ X) @ (F @ Y4)))) => (ord_less_real @ A @ (F @ C)))))))). % order_less_subst1
thf(fact_123_order__less__subst2, axiom,
    ((![A : real, B : real, F : real > real, C : real]: ((ord_less_real @ A @ B) => ((ord_less_real @ (F @ B) @ C) => ((![X : real, Y4 : real]: ((ord_less_real @ X @ Y4) => (ord_less_real @ (F @ X) @ (F @ Y4)))) => (ord_less_real @ (F @ A) @ C))))))). % order_less_subst2
thf(fact_124_lt__ex, axiom,
    ((![X3 : real]: (?[Y4 : real]: (ord_less_real @ Y4 @ X3))))). % lt_ex
thf(fact_125_gt__ex, axiom,
    ((![X3 : real]: (?[X_12 : real]: (ord_less_real @ X3 @ X_12))))). % gt_ex
thf(fact_126_neqE, axiom,
    ((![X3 : real, Y5 : real]: ((~ ((X3 = Y5))) => ((~ ((ord_less_real @ X3 @ Y5))) => (ord_less_real @ Y5 @ X3)))))). % neqE
thf(fact_127_neq__iff, axiom,
    ((![X3 : real, Y5 : real]: ((~ ((X3 = Y5))) = (((ord_less_real @ X3 @ Y5)) | ((ord_less_real @ Y5 @ X3))))))). % neq_iff
thf(fact_128_order_Oasym, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ B) => (~ ((ord_less_real @ B @ A))))))). % order.asym
thf(fact_129_dense, axiom,
    ((![X3 : real, Y5 : real]: ((ord_less_real @ X3 @ Y5) => (?[Z4 : real]: ((ord_less_real @ X3 @ Z4) & (ord_less_real @ Z4 @ Y5))))))). % dense
thf(fact_130_less__imp__neq, axiom,
    ((![X3 : real, Y5 : real]: ((ord_less_real @ X3 @ Y5) => (~ ((X3 = Y5))))))). % less_imp_neq
thf(fact_131_less__asym, axiom,
    ((![X3 : real, Y5 : real]: ((ord_less_real @ X3 @ Y5) => (~ ((ord_less_real @ Y5 @ X3))))))). % less_asym
thf(fact_132_less__asym_H, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ B) => (~ ((ord_less_real @ B @ A))))))). % less_asym'
thf(fact_133_less__trans, axiom,
    ((![X3 : real, Y5 : real, Z3 : real]: ((ord_less_real @ X3 @ Y5) => ((ord_less_real @ Y5 @ Z3) => (ord_less_real @ X3 @ Z3)))))). % less_trans
thf(fact_134_less__linear, axiom,
    ((![X3 : real, Y5 : real]: ((ord_less_real @ X3 @ Y5) | ((X3 = Y5) | (ord_less_real @ Y5 @ X3)))))). % less_linear
thf(fact_135_less__irrefl, axiom,
    ((![X3 : real]: (~ ((ord_less_real @ X3 @ X3)))))). % less_irrefl
thf(fact_136_ord__eq__less__trans, axiom,
    ((![A : real, B : real, C : real]: ((A = B) => ((ord_less_real @ B @ C) => (ord_less_real @ A @ C)))))). % ord_eq_less_trans
thf(fact_137_ord__less__eq__trans, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_real @ A @ B) => ((B = C) => (ord_less_real @ A @ C)))))). % ord_less_eq_trans
thf(fact_138_dual__order_Oasym, axiom,
    ((![B : real, A : real]: ((ord_less_real @ B @ A) => (~ ((ord_less_real @ A @ B))))))). % dual_order.asym
thf(fact_139_less__imp__not__eq, axiom,
    ((![X3 : real, Y5 : real]: ((ord_less_real @ X3 @ Y5) => (~ ((X3 = Y5))))))). % less_imp_not_eq
thf(fact_140_less__not__sym, axiom,
    ((![X3 : real, Y5 : real]: ((ord_less_real @ X3 @ Y5) => (~ ((ord_less_real @ Y5 @ X3))))))). % less_not_sym
thf(fact_141_antisym__conv3, axiom,
    ((![Y5 : real, X3 : real]: ((~ ((ord_less_real @ Y5 @ X3))) => ((~ ((ord_less_real @ X3 @ Y5))) = (X3 = Y5)))))). % antisym_conv3
thf(fact_142_less__imp__not__eq2, axiom,
    ((![X3 : real, Y5 : real]: ((ord_less_real @ X3 @ Y5) => (~ ((Y5 = X3))))))). % less_imp_not_eq2
thf(fact_143_less__imp__triv, axiom,
    ((![X3 : real, Y5 : real, P : $o]: ((ord_less_real @ X3 @ Y5) => ((ord_less_real @ Y5 @ X3) => P))))). % less_imp_triv
thf(fact_144_linorder__cases, axiom,
    ((![X3 : real, Y5 : real]: ((~ ((ord_less_real @ X3 @ Y5))) => ((~ ((X3 = Y5))) => (ord_less_real @ Y5 @ X3)))))). % linorder_cases
thf(fact_145_dual__order_Oirrefl, axiom,
    ((![A : real]: (~ ((ord_less_real @ A @ A)))))). % dual_order.irrefl
thf(fact_146_order_Ostrict__trans, axiom,
    ((![A : real, B : real, C : real]: ((ord_less_real @ A @ B) => ((ord_less_real @ B @ C) => (ord_less_real @ A @ C)))))). % order.strict_trans
thf(fact_147_less__imp__not__less, axiom,
    ((![X3 : real, Y5 : real]: ((ord_less_real @ X3 @ Y5) => (~ ((ord_less_real @ Y5 @ X3))))))). % less_imp_not_less
thf(fact_148_linorder__less__wlog, axiom,
    ((![P : real > real > $o, A : real, B : real]: ((![A4 : real, B3 : real]: ((ord_less_real @ A4 @ B3) => (P @ A4 @ B3))) => ((![A4 : real]: (P @ A4 @ A4)) => ((![A4 : real, B3 : real]: ((P @ B3 @ A4) => (P @ A4 @ B3))) => (P @ A @ B))))))). % linorder_less_wlog
thf(fact_149_dual__order_Ostrict__trans, axiom,
    ((![B : real, A : real, C : real]: ((ord_less_real @ B @ A) => ((ord_less_real @ C @ B) => (ord_less_real @ C @ A)))))). % dual_order.strict_trans
thf(fact_150_not__less__iff__gr__or__eq, axiom,
    ((![X3 : real, Y5 : real]: ((~ ((ord_less_real @ X3 @ Y5))) = (((ord_less_real @ Y5 @ X3)) | ((X3 = Y5))))))). % not_less_iff_gr_or_eq
thf(fact_151_order_Ostrict__implies__not__eq, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ B) => (~ ((A = B))))))). % order.strict_implies_not_eq
thf(fact_152_dual__order_Ostrict__implies__not__eq, axiom,
    ((![B : real, A : real]: ((ord_less_real @ B @ A) => (~ ((A = B))))))). % dual_order.strict_implies_not_eq
thf(fact_153_linorder__neqE__linordered__idom, axiom,
    ((![X3 : real, Y5 : real]: ((~ ((X3 = Y5))) => ((~ ((ord_less_real @ X3 @ Y5))) => (ord_less_real @ Y5 @ X3)))))). % linorder_neqE_linordered_idom
thf(fact_154_complete__real, axiom,
    ((![S2 : set_real]: ((?[X4 : real]: (member_real @ X4 @ S2)) => ((?[Z : real]: (![X : real]: ((member_real @ X @ S2) => (ord_less_eq_real @ X @ Z)))) => (?[Y4 : real]: ((![X4 : real]: ((member_real @ X4 @ S2) => (ord_less_eq_real @ X4 @ Y4))) & (![Z : real]: ((![X : real]: ((member_real @ X @ S2) => (ord_less_eq_real @ X @ Z))) => (ord_less_eq_real @ Y4 @ Z)))))))))). % complete_real
thf(fact_155_field__lbound__gt__zero, axiom,
    ((![D1 : real, D22 : real]: ((ord_less_real @ zero_zero_real @ D1) => ((ord_less_real @ zero_zero_real @ D22) => (?[E : real]: ((ord_less_real @ zero_zero_real @ E) & ((ord_less_real @ E @ D1) & (ord_less_real @ E @ D22))))))))). % field_lbound_gt_zero
thf(fact_156_leD, axiom,
    ((![Y5 : real, X3 : real]: ((ord_less_eq_real @ Y5 @ X3) => (~ ((ord_less_real @ X3 @ Y5))))))). % leD
thf(fact_157_leI, axiom,
    ((![X3 : real, Y5 : real]: ((~ ((ord_less_real @ X3 @ Y5))) => (ord_less_eq_real @ Y5 @ X3))))). % leI
thf(fact_158_le__less, axiom,
    ((ord_less_eq_real = (^[X2 : real]: (^[Y2 : real]: (((ord_less_real @ X2 @ Y2)) | ((X2 = Y2)))))))). % le_less
thf(fact_159_less__le, axiom,
    ((ord_less_real = (^[X2 : real]: (^[Y2 : real]: (((ord_less_eq_real @ X2 @ Y2)) & ((~ ((X2 = Y2)))))))))). % less_le
thf(fact_160_order__le__less__subst1, axiom,
    ((![A : real, F : real > real, B : real, C : real]: ((ord_less_eq_real @ A @ (F @ B)) => ((ord_less_real @ B @ C) => ((![X : real, Y4 : real]: ((ord_less_real @ X @ Y4) => (ord_less_real @ (F @ X) @ (F @ Y4)))) => (ord_less_real @ A @ (F @ C)))))))). % order_le_less_subst1
thf(fact_161_order__le__less__subst2, axiom,
    ((![A : real, B : real, F : real > real, C : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_real @ (F @ B) @ C) => ((![X : real, Y4 : real]: ((ord_less_eq_real @ X @ Y4) => (ord_less_eq_real @ (F @ X) @ (F @ Y4)))) => (ord_less_real @ (F @ A) @ C))))))). % order_le_less_subst2
thf(fact_162_order__less__le__subst1, axiom,
    ((![A : real, F : real > real, B : real, C : real]: ((ord_less_real @ A @ (F @ B)) => ((ord_less_eq_real @ B @ C) => ((![X : real, Y4 : real]: ((ord_less_eq_real @ X @ Y4) => (ord_less_eq_real @ (F @ X) @ (F @ Y4)))) => (ord_less_real @ A @ (F @ C)))))))). % order_less_le_subst1
thf(fact_163_order__less__le__subst2, axiom,
    ((![A : real, B : real, F : real > real, C : real]: ((ord_less_real @ A @ B) => ((ord_less_eq_real @ (F @ B) @ C) => ((![X : real, Y4 : real]: ((ord_less_real @ X @ Y4) => (ord_less_real @ (F @ X) @ (F @ Y4)))) => (ord_less_real @ (F @ A) @ C))))))). % order_less_le_subst2
thf(fact_164_not__le, axiom,
    ((![X3 : real, Y5 : real]: ((~ ((ord_less_eq_real @ X3 @ Y5))) = (ord_less_real @ Y5 @ X3))))). % not_le
thf(fact_165_not__less, axiom,
    ((![X3 : real, Y5 : real]: ((~ ((ord_less_real @ X3 @ Y5))) = (ord_less_eq_real @ Y5 @ X3))))). % not_less
thf(fact_166_le__neq__trans, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ A @ B) => ((~ ((A = B))) => (ord_less_real @ A @ B)))))). % le_neq_trans
thf(fact_167_antisym__conv1, axiom,
    ((![X3 : real, Y5 : real]: ((~ ((ord_less_real @ X3 @ Y5))) => ((ord_less_eq_real @ X3 @ Y5) = (X3 = Y5)))))). % antisym_conv1
thf(fact_168_antisym__conv2, axiom,
    ((![X3 : real, Y5 : real]: ((ord_less_eq_real @ X3 @ Y5) => ((~ ((ord_less_real @ X3 @ Y5))) = (X3 = Y5)))))). % antisym_conv2
thf(fact_169_less__imp__le, axiom,
    ((![X3 : real, Y5 : real]: ((ord_less_real @ X3 @ Y5) => (ord_less_eq_real @ X3 @ Y5))))). % less_imp_le

% Conjectures (2)
thf(conj_0, hypothesis,
    ((![M2 : real]: ((ord_less_real @ zero_zero_real @ M2) => ((![Z4 : a]: ((ord_less_eq_real @ (real_V1022479215norm_a @ Z4) @ one_one_real) => (ord_less_eq_real @ (real_V1022479215norm_a @ (poly_a2 @ cs @ Z4)) @ M2))) => thesis))))).
thf(conj_1, conjecture,
    (thesis)).
