% 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_71__5367494_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:26:43.611

% 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__Nat__Onat_J_J, type,
    poly_poly_nat : $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__Nat__Onat_J, type,
    poly_nat : $tType).
thf(ty_n_t__Polynomial__Opoly_Itf__a_J, type,
    poly_a : $tType).
thf(ty_n_t__Nat__Onat, type,
    nat : $tType).
thf(ty_n_tf__a, type,
    a : $tType).

% Explicit typings (63)
thf(sy_c_Fundamental__Theorem__Algebra__Mirabelle__sywschxjbb_Ooffset__poly_001t__Nat__Onat, type,
    fundam170929432ly_nat : poly_nat > nat > poly_nat).
thf(sy_c_Fundamental__Theorem__Algebra__Mirabelle__sywschxjbb_Ooffset__poly_001t__Polynomial__Opoly_Itf__a_J, type,
    fundam1343031620poly_a : poly_poly_a > poly_a > poly_poly_a).
thf(sy_c_Fundamental__Theorem__Algebra__Mirabelle__sywschxjbb_Ooffset__poly_001tf__a, type,
    fundam1358810038poly_a : poly_a > a > poly_a).
thf(sy_c_Groups_Oone__class_Oone_001t__Nat__Onat, type,
    one_one_nat : nat).
thf(sy_c_Groups_Oone__class_Oone_001t__Polynomial__Opoly_It__Nat__Onat_J, type,
    one_one_poly_nat : poly_nat).
thf(sy_c_Groups_Oplus__class_Oplus_001t__Nat__Onat, type,
    plus_plus_nat : nat > nat > nat).
thf(sy_c_Groups_Oplus__class_Oplus_001t__Polynomial__Opoly_It__Nat__Onat_J, type,
    plus_plus_poly_nat : poly_nat > poly_nat > poly_nat).
thf(sy_c_Groups_Oplus__class_Oplus_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Nat__Onat_J_J, type,
    plus_p1835221865ly_nat : poly_poly_nat > poly_poly_nat > poly_poly_nat).
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_Itf__a_J, type,
    plus_plus_poly_a : poly_a > poly_a > poly_a).
thf(sy_c_Groups_Oplus__class_Oplus_001tf__a, type,
    plus_plus_a : a > 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__Nat__Onat_J, type,
    zero_zero_poly_nat : poly_nat).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Nat__Onat_J_J, type,
    zero_z1059985641ly_nat : poly_poly_nat).
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_Itf__a_J_J, type,
    zero_z2096148049poly_a : poly_poly_a).
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_001tf__a, type,
    zero_zero_a : a).
thf(sy_c_If_001t__Polynomial__Opoly_It__Nat__Onat_J, type,
    if_poly_nat : $o > poly_nat > poly_nat > poly_nat).
thf(sy_c_If_001t__Polynomial__Opoly_It__Polynomial__Opoly_Itf__a_J_J, type,
    if_poly_poly_a : $o > poly_poly_a > poly_poly_a > poly_poly_a).
thf(sy_c_Polynomial_Ocontent_001t__Nat__Onat, type,
    content_nat : poly_nat > nat).
thf(sy_c_Polynomial_Odegree_001t__Nat__Onat, type,
    degree_nat : poly_nat > nat).
thf(sy_c_Polynomial_Odegree_001t__Polynomial__Opoly_It__Nat__Onat_J, type,
    degree_poly_nat : poly_poly_nat > nat).
thf(sy_c_Polynomial_Odegree_001t__Polynomial__Opoly_It__Polynomial__Opoly_Itf__a_J_J, type,
    degree_poly_poly_a : poly_poly_poly_a > nat).
thf(sy_c_Polynomial_Odegree_001t__Polynomial__Opoly_Itf__a_J, type,
    degree_poly_a : poly_poly_a > nat).
thf(sy_c_Polynomial_Odegree_001tf__a, type,
    degree_a : poly_a > nat).
thf(sy_c_Polynomial_Ois__zero_001t__Nat__Onat, type,
    is_zero_nat : poly_nat > $o).
thf(sy_c_Polynomial_Ois__zero_001t__Polynomial__Opoly_Itf__a_J, type,
    is_zero_poly_a : poly_poly_a > $o).
thf(sy_c_Polynomial_Ois__zero_001tf__a, type,
    is_zero_a : poly_a > $o).
thf(sy_c_Polynomial_Omonom_001t__Nat__Onat, type,
    monom_nat : nat > nat > poly_nat).
thf(sy_c_Polynomial_Omonom_001t__Polynomial__Opoly_It__Nat__Onat_J, type,
    monom_poly_nat : poly_nat > nat > poly_poly_nat).
thf(sy_c_Polynomial_Omonom_001t__Polynomial__Opoly_It__Polynomial__Opoly_Itf__a_J_J, type,
    monom_poly_poly_a : poly_poly_a > nat > poly_poly_poly_a).
thf(sy_c_Polynomial_Omonom_001t__Polynomial__Opoly_Itf__a_J, type,
    monom_poly_a : poly_a > nat > poly_poly_a).
thf(sy_c_Polynomial_Omonom_001tf__a, type,
    monom_a : a > nat > poly_a).
thf(sy_c_Polynomial_Opoly_001t__Nat__Onat, type,
    poly_nat2 : poly_nat > nat > nat).
thf(sy_c_Polynomial_Opoly_001t__Polynomial__Opoly_It__Nat__Onat_J, type,
    poly_poly_nat2 : poly_poly_nat > poly_nat > poly_nat).
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_Itf__a_J, type,
    poly_poly_a2 : poly_poly_a > poly_a > poly_a).
thf(sy_c_Polynomial_Opoly_001tf__a, type,
    poly_a2 : poly_a > a > a).
thf(sy_c_Polynomial_Opoly_Ocoeff_001t__Nat__Onat, type,
    coeff_nat : poly_nat > nat > nat).
thf(sy_c_Polynomial_Opoly_Ocoeff_001t__Polynomial__Opoly_It__Nat__Onat_J, type,
    coeff_poly_nat : poly_poly_nat > nat > poly_nat).
thf(sy_c_Polynomial_Opoly_Ocoeff_001t__Polynomial__Opoly_It__Polynomial__Opoly_Itf__a_J_J, type,
    coeff_poly_poly_a : poly_poly_poly_a > nat > poly_poly_a).
thf(sy_c_Polynomial_Opoly_Ocoeff_001t__Polynomial__Opoly_Itf__a_J, type,
    coeff_poly_a : poly_poly_a > nat > poly_a).
thf(sy_c_Polynomial_Opoly_Ocoeff_001tf__a, type,
    coeff_a : poly_a > nat > a).
thf(sy_c_Polynomial_Opoly__cutoff_001t__Nat__Onat, type,
    poly_cutoff_nat : nat > poly_nat > poly_nat).
thf(sy_c_Polynomial_Opoly__cutoff_001t__Polynomial__Opoly_Itf__a_J, type,
    poly_cutoff_poly_a : nat > poly_poly_a > poly_poly_a).
thf(sy_c_Polynomial_Opoly__cutoff_001tf__a, type,
    poly_cutoff_a : nat > poly_a > poly_a).
thf(sy_c_Polynomial_Opoly__shift_001t__Nat__Onat, type,
    poly_shift_nat : nat > poly_nat > poly_nat).
thf(sy_c_Polynomial_Opoly__shift_001t__Polynomial__Opoly_Itf__a_J, type,
    poly_shift_poly_a : nat > poly_poly_a > poly_poly_a).
thf(sy_c_Polynomial_Opoly__shift_001tf__a, type,
    poly_shift_a : nat > poly_a > poly_a).
thf(sy_c_Polynomial_Oprimitive__part_001t__Nat__Onat, type,
    primitive_part_nat : poly_nat > poly_nat).
thf(sy_c_Polynomial_Oreflect__poly_001t__Nat__Onat, type,
    reflect_poly_nat : poly_nat > poly_nat).
thf(sy_c_Polynomial_Oreflect__poly_001t__Polynomial__Opoly_It__Nat__Onat_J, type,
    reflec781175074ly_nat : poly_poly_nat > poly_poly_nat).
thf(sy_c_Polynomial_Oreflect__poly_001t__Polynomial__Opoly_It__Polynomial__Opoly_Itf__a_J_J, type,
    reflec581648976poly_a : poly_poly_poly_a > poly_poly_poly_a).
thf(sy_c_Polynomial_Oreflect__poly_001t__Polynomial__Opoly_Itf__a_J, type,
    reflect_poly_poly_a : poly_poly_a > poly_poly_a).
thf(sy_c_Polynomial_Oreflect__poly_001tf__a, type,
    reflect_poly_a : poly_a > poly_a).
thf(sy_c_Polynomial_Osynthetic__div_001t__Nat__Onat, type,
    synthetic_div_nat : poly_nat > nat > poly_nat).
thf(sy_c_Polynomial_Osynthetic__div_001t__Polynomial__Opoly_Itf__a_J, type,
    synthetic_div_poly_a : poly_poly_a > poly_a > poly_poly_a).
thf(sy_c_Polynomial_Osynthetic__div_001tf__a, type,
    synthetic_div_a : poly_a > a > poly_a).
thf(sy_c_Rings_Odvd__class_Odvd_001t__Nat__Onat, type,
    dvd_dvd_nat : nat > nat > $o).
thf(sy_c_Rings_Odvd__class_Odvd_001t__Polynomial__Opoly_It__Nat__Onat_J, type,
    dvd_dvd_poly_nat : poly_nat > poly_nat > $o).
thf(sy_v_h, type,
    h : a).
thf(sy_v_x, type,
    x : a).

% Relevant facts (246)
thf(fact_0_offset__poly__0, axiom,
    ((![H : nat]: ((fundam170929432ly_nat @ zero_zero_poly_nat @ H) = zero_zero_poly_nat)))). % offset_poly_0
thf(fact_1_offset__poly__0, axiom,
    ((![H : poly_a]: ((fundam1343031620poly_a @ zero_z2096148049poly_a @ H) = zero_z2096148049poly_a)))). % offset_poly_0
thf(fact_2_offset__poly__0, axiom,
    ((![H : a]: ((fundam1358810038poly_a @ zero_zero_poly_a @ H) = zero_zero_poly_a)))). % offset_poly_0
thf(fact_3_poly__0, axiom,
    ((![X : poly_nat]: ((poly_poly_nat2 @ zero_z1059985641ly_nat @ X) = zero_zero_poly_nat)))). % poly_0
thf(fact_4_poly__0, axiom,
    ((![X : poly_poly_a]: ((poly_poly_poly_a2 @ zero_z2064990175poly_a @ X) = zero_z2096148049poly_a)))). % poly_0
thf(fact_5_poly__0, axiom,
    ((![X : poly_a]: ((poly_poly_a2 @ zero_z2096148049poly_a @ X) = zero_zero_poly_a)))). % poly_0
thf(fact_6_poly__0, axiom,
    ((![X : nat]: ((poly_nat2 @ zero_zero_poly_nat @ X) = zero_zero_nat)))). % poly_0
thf(fact_7_poly__0, axiom,
    ((![X : a]: ((poly_a2 @ zero_zero_poly_a @ X) = zero_zero_a)))). % poly_0
thf(fact_8_poly__add, axiom,
    ((![P : poly_poly_nat, Q : poly_poly_nat, X : poly_nat]: ((poly_poly_nat2 @ (plus_p1835221865ly_nat @ P @ Q) @ X) = (plus_plus_poly_nat @ (poly_poly_nat2 @ P @ X) @ (poly_poly_nat2 @ Q @ X)))))). % poly_add
thf(fact_9_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_10_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_11_poly__add, axiom,
    ((![P : poly_nat, Q : poly_nat, X : nat]: ((poly_nat2 @ (plus_plus_poly_nat @ P @ Q) @ X) = (plus_plus_nat @ (poly_nat2 @ P @ X) @ (poly_nat2 @ Q @ X)))))). % poly_add
thf(fact_12_add_Oleft__neutral, axiom,
    ((![A : poly_nat]: ((plus_plus_poly_nat @ zero_zero_poly_nat @ A) = A)))). % add.left_neutral
thf(fact_13_add_Oleft__neutral, axiom,
    ((![A : poly_poly_a]: ((plus_p1976640465poly_a @ zero_z2096148049poly_a @ A) = A)))). % add.left_neutral
thf(fact_14_add_Oleft__neutral, axiom,
    ((![A : a]: ((plus_plus_a @ zero_zero_a @ A) = A)))). % add.left_neutral
thf(fact_15_add_Oleft__neutral, axiom,
    ((![A : poly_a]: ((plus_plus_poly_a @ zero_zero_poly_a @ A) = A)))). % add.left_neutral
thf(fact_16_add_Oleft__neutral, axiom,
    ((![A : nat]: ((plus_plus_nat @ zero_zero_nat @ A) = A)))). % add.left_neutral
thf(fact_17_add_Oright__neutral, axiom,
    ((![A : poly_nat]: ((plus_plus_poly_nat @ A @ zero_zero_poly_nat) = A)))). % add.right_neutral
thf(fact_18_add_Oright__neutral, axiom,
    ((![A : poly_poly_a]: ((plus_p1976640465poly_a @ A @ zero_z2096148049poly_a) = A)))). % add.right_neutral
thf(fact_19_add_Oright__neutral, axiom,
    ((![A : a]: ((plus_plus_a @ A @ zero_zero_a) = A)))). % add.right_neutral
thf(fact_20_add_Oright__neutral, axiom,
    ((![A : poly_a]: ((plus_plus_poly_a @ A @ zero_zero_poly_a) = A)))). % add.right_neutral
thf(fact_21_add_Oright__neutral, axiom,
    ((![A : nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A)))). % add.right_neutral
thf(fact_22_add__cancel__left__left, axiom,
    ((![B : poly_nat, A : poly_nat]: (((plus_plus_poly_nat @ B @ A) = A) = (B = zero_zero_poly_nat))))). % add_cancel_left_left
thf(fact_23_add__cancel__left__left, axiom,
    ((![B : nat, A : nat]: (((plus_plus_nat @ B @ A) = A) = (B = zero_zero_nat))))). % add_cancel_left_left
thf(fact_24_add__cancel__left__right, axiom,
    ((![A : poly_nat, B : poly_nat]: (((plus_plus_poly_nat @ A @ B) = A) = (B = zero_zero_poly_nat))))). % add_cancel_left_right
thf(fact_25_add__cancel__left__right, axiom,
    ((![A : nat, B : nat]: (((plus_plus_nat @ A @ B) = A) = (B = zero_zero_nat))))). % add_cancel_left_right
thf(fact_26_add__cancel__right__left, axiom,
    ((![A : poly_nat, B : poly_nat]: ((A = (plus_plus_poly_nat @ B @ A)) = (B = zero_zero_poly_nat))))). % add_cancel_right_left
thf(fact_27_add__cancel__right__left, axiom,
    ((![A : nat, B : nat]: ((A = (plus_plus_nat @ B @ A)) = (B = zero_zero_nat))))). % add_cancel_right_left
thf(fact_28_add__cancel__right__right, axiom,
    ((![A : nat, B : nat]: ((A = (plus_plus_nat @ A @ B)) = (B = zero_zero_nat))))). % add_cancel_right_right
thf(fact_29_add__cancel__right__right, axiom,
    ((![A : poly_nat, B : poly_nat]: ((A = (plus_plus_poly_nat @ A @ B)) = (B = zero_zero_poly_nat))))). % add_cancel_right_right
thf(fact_30_add__eq__0__iff__both__eq__0, axiom,
    ((![X : nat, Y : nat]: (((plus_plus_nat @ X @ Y) = zero_zero_nat) = (((X = zero_zero_nat)) & ((Y = zero_zero_nat))))))). % add_eq_0_iff_both_eq_0
thf(fact_31_zero__eq__add__iff__both__eq__0, axiom,
    ((![X : nat, Y : nat]: ((zero_zero_nat = (plus_plus_nat @ X @ Y)) = (((X = zero_zero_nat)) & ((Y = zero_zero_nat))))))). % zero_eq_add_iff_both_eq_0
thf(fact_32_add__right__cancel, axiom,
    ((![B : nat, A : nat, C : nat]: (((plus_plus_nat @ B @ A) = (plus_plus_nat @ C @ A)) = (B = C))))). % add_right_cancel
thf(fact_33_add__right__cancel, axiom,
    ((![B : poly_nat, A : poly_nat, C : poly_nat]: (((plus_plus_poly_nat @ B @ A) = (plus_plus_poly_nat @ C @ A)) = (B = C))))). % add_right_cancel
thf(fact_34_add__left__cancel, axiom,
    ((![A : nat, B : nat, C : nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ A @ C)) = (B = C))))). % add_left_cancel
thf(fact_35_add__left__cancel, axiom,
    ((![A : poly_nat, B : poly_nat, C : poly_nat]: (((plus_plus_poly_nat @ A @ B) = (plus_plus_poly_nat @ A @ C)) = (B = C))))). % add_left_cancel
thf(fact_36_zero__reorient, axiom,
    ((![X : poly_a]: ((zero_zero_poly_a = X) = (X = zero_zero_poly_a))))). % zero_reorient
thf(fact_37_zero__reorient, axiom,
    ((![X : nat]: ((zero_zero_nat = X) = (X = zero_zero_nat))))). % zero_reorient
thf(fact_38_zero__reorient, axiom,
    ((![X : a]: ((zero_zero_a = X) = (X = zero_zero_a))))). % zero_reorient
thf(fact_39_zero__reorient, axiom,
    ((![X : poly_nat]: ((zero_zero_poly_nat = X) = (X = zero_zero_poly_nat))))). % zero_reorient
thf(fact_40_zero__reorient, axiom,
    ((![X : poly_poly_a]: ((zero_z2096148049poly_a = X) = (X = zero_z2096148049poly_a))))). % zero_reorient
thf(fact_41_add__right__imp__eq, axiom,
    ((![B : nat, A : nat, C : nat]: (((plus_plus_nat @ B @ A) = (plus_plus_nat @ C @ A)) => (B = C))))). % add_right_imp_eq
thf(fact_42_add__right__imp__eq, axiom,
    ((![B : poly_nat, A : poly_nat, C : poly_nat]: (((plus_plus_poly_nat @ B @ A) = (plus_plus_poly_nat @ C @ A)) => (B = C))))). % add_right_imp_eq
thf(fact_43_add__left__imp__eq, axiom,
    ((![A : nat, B : nat, C : nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ A @ C)) => (B = C))))). % add_left_imp_eq
thf(fact_44_add__left__imp__eq, axiom,
    ((![A : poly_nat, B : poly_nat, C : poly_nat]: (((plus_plus_poly_nat @ A @ B) = (plus_plus_poly_nat @ A @ C)) => (B = C))))). % add_left_imp_eq
thf(fact_45_add_Oleft__commute, axiom,
    ((![B : a, A : a, C : a]: ((plus_plus_a @ B @ (plus_plus_a @ A @ C)) = (plus_plus_a @ A @ (plus_plus_a @ B @ C)))))). % add.left_commute
thf(fact_46_add_Oleft__commute, axiom,
    ((![B : nat, A : nat, C : nat]: ((plus_plus_nat @ B @ (plus_plus_nat @ A @ C)) = (plus_plus_nat @ A @ (plus_plus_nat @ B @ C)))))). % add.left_commute
thf(fact_47_add_Oleft__commute, axiom,
    ((![B : poly_nat, A : poly_nat, C : poly_nat]: ((plus_plus_poly_nat @ B @ (plus_plus_poly_nat @ A @ C)) = (plus_plus_poly_nat @ A @ (plus_plus_poly_nat @ B @ C)))))). % add.left_commute
thf(fact_48_add_Oleft__commute, axiom,
    ((![B : poly_a, A : poly_a, C : poly_a]: ((plus_plus_poly_a @ B @ (plus_plus_poly_a @ A @ C)) = (plus_plus_poly_a @ A @ (plus_plus_poly_a @ B @ C)))))). % add.left_commute
thf(fact_49_add_Ocommute, axiom,
    ((plus_plus_a = (^[A2 : a]: (^[B2 : a]: (plus_plus_a @ B2 @ A2)))))). % add.commute
thf(fact_50_add_Ocommute, axiom,
    ((plus_plus_nat = (^[A2 : nat]: (^[B2 : nat]: (plus_plus_nat @ B2 @ A2)))))). % add.commute
thf(fact_51_add_Ocommute, axiom,
    ((plus_plus_poly_nat = (^[A2 : poly_nat]: (^[B2 : poly_nat]: (plus_plus_poly_nat @ B2 @ A2)))))). % add.commute
thf(fact_52_add_Ocommute, axiom,
    ((plus_plus_poly_a = (^[A2 : poly_a]: (^[B2 : poly_a]: (plus_plus_poly_a @ B2 @ A2)))))). % add.commute
thf(fact_53_add_Oassoc, axiom,
    ((![A : a, B : a, C : a]: ((plus_plus_a @ (plus_plus_a @ A @ B) @ C) = (plus_plus_a @ A @ (plus_plus_a @ B @ C)))))). % add.assoc
thf(fact_54_add_Oassoc, axiom,
    ((![A : nat, B : nat, C : nat]: ((plus_plus_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ A @ (plus_plus_nat @ B @ C)))))). % add.assoc
thf(fact_55_add_Oassoc, axiom,
    ((![A : poly_nat, B : poly_nat, C : poly_nat]: ((plus_plus_poly_nat @ (plus_plus_poly_nat @ A @ B) @ C) = (plus_plus_poly_nat @ A @ (plus_plus_poly_nat @ B @ C)))))). % add.assoc
thf(fact_56_add_Oassoc, axiom,
    ((![A : poly_a, B : poly_a, C : poly_a]: ((plus_plus_poly_a @ (plus_plus_poly_a @ A @ B) @ C) = (plus_plus_poly_a @ A @ (plus_plus_poly_a @ B @ C)))))). % add.assoc
thf(fact_57_group__cancel_Oadd2, axiom,
    ((![B3 : a, K : a, B : a, A : a]: ((B3 = (plus_plus_a @ K @ B)) => ((plus_plus_a @ A @ B3) = (plus_plus_a @ K @ (plus_plus_a @ A @ B))))))). % group_cancel.add2
thf(fact_58_group__cancel_Oadd2, axiom,
    ((![B3 : nat, K : nat, B : nat, A : nat]: ((B3 = (plus_plus_nat @ K @ B)) => ((plus_plus_nat @ A @ B3) = (plus_plus_nat @ K @ (plus_plus_nat @ A @ B))))))). % group_cancel.add2
thf(fact_59_group__cancel_Oadd2, axiom,
    ((![B3 : poly_nat, K : poly_nat, B : poly_nat, A : poly_nat]: ((B3 = (plus_plus_poly_nat @ K @ B)) => ((plus_plus_poly_nat @ A @ B3) = (plus_plus_poly_nat @ K @ (plus_plus_poly_nat @ A @ B))))))). % group_cancel.add2
thf(fact_60_group__cancel_Oadd2, axiom,
    ((![B3 : poly_a, K : poly_a, B : poly_a, A : poly_a]: ((B3 = (plus_plus_poly_a @ K @ B)) => ((plus_plus_poly_a @ A @ B3) = (plus_plus_poly_a @ K @ (plus_plus_poly_a @ A @ B))))))). % group_cancel.add2
thf(fact_61_group__cancel_Oadd1, axiom,
    ((![A3 : a, K : a, A : a, B : a]: ((A3 = (plus_plus_a @ K @ A)) => ((plus_plus_a @ A3 @ B) = (plus_plus_a @ K @ (plus_plus_a @ A @ B))))))). % group_cancel.add1
thf(fact_62_group__cancel_Oadd1, axiom,
    ((![A3 : nat, K : nat, A : nat, B : nat]: ((A3 = (plus_plus_nat @ K @ A)) => ((plus_plus_nat @ A3 @ B) = (plus_plus_nat @ K @ (plus_plus_nat @ A @ B))))))). % group_cancel.add1
thf(fact_63_group__cancel_Oadd1, axiom,
    ((![A3 : poly_nat, K : poly_nat, A : poly_nat, B : poly_nat]: ((A3 = (plus_plus_poly_nat @ K @ A)) => ((plus_plus_poly_nat @ A3 @ B) = (plus_plus_poly_nat @ K @ (plus_plus_poly_nat @ A @ B))))))). % group_cancel.add1
thf(fact_64_group__cancel_Oadd1, axiom,
    ((![A3 : poly_a, K : poly_a, A : poly_a, B : poly_a]: ((A3 = (plus_plus_poly_a @ K @ A)) => ((plus_plus_poly_a @ A3 @ B) = (plus_plus_poly_a @ K @ (plus_plus_poly_a @ A @ B))))))). % group_cancel.add1
thf(fact_65_add__mono__thms__linordered__semiring_I4_J, axiom,
    ((![I : nat, J : nat, K : nat, L : nat]: (((I = J) & (K = L)) => ((plus_plus_nat @ I @ K) = (plus_plus_nat @ J @ L)))))). % add_mono_thms_linordered_semiring(4)
thf(fact_66_ab__semigroup__add__class_Oadd__ac_I1_J, axiom,
    ((![A : a, B : a, C : a]: ((plus_plus_a @ (plus_plus_a @ A @ B) @ C) = (plus_plus_a @ A @ (plus_plus_a @ B @ C)))))). % ab_semigroup_add_class.add_ac(1)
thf(fact_67_ab__semigroup__add__class_Oadd__ac_I1_J, axiom,
    ((![A : nat, B : nat, C : nat]: ((plus_plus_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ A @ (plus_plus_nat @ B @ C)))))). % ab_semigroup_add_class.add_ac(1)
thf(fact_68_ab__semigroup__add__class_Oadd__ac_I1_J, axiom,
    ((![A : poly_nat, B : poly_nat, C : poly_nat]: ((plus_plus_poly_nat @ (plus_plus_poly_nat @ A @ B) @ C) = (plus_plus_poly_nat @ A @ (plus_plus_poly_nat @ B @ C)))))). % ab_semigroup_add_class.add_ac(1)
thf(fact_69_ab__semigroup__add__class_Oadd__ac_I1_J, axiom,
    ((![A : poly_a, B : poly_a, C : poly_a]: ((plus_plus_poly_a @ (plus_plus_poly_a @ A @ B) @ C) = (plus_plus_poly_a @ A @ (plus_plus_poly_a @ B @ C)))))). % ab_semigroup_add_class.add_ac(1)
thf(fact_70_add_Ocomm__neutral, axiom,
    ((![A : poly_a]: ((plus_plus_poly_a @ A @ zero_zero_poly_a) = A)))). % add.comm_neutral
thf(fact_71_add_Ocomm__neutral, axiom,
    ((![A : nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A)))). % add.comm_neutral
thf(fact_72_add_Ocomm__neutral, axiom,
    ((![A : a]: ((plus_plus_a @ A @ zero_zero_a) = A)))). % add.comm_neutral
thf(fact_73_add_Ocomm__neutral, axiom,
    ((![A : poly_nat]: ((plus_plus_poly_nat @ A @ zero_zero_poly_nat) = A)))). % add.comm_neutral
thf(fact_74_add_Ocomm__neutral, axiom,
    ((![A : poly_poly_a]: ((plus_p1976640465poly_a @ A @ zero_z2096148049poly_a) = A)))). % add.comm_neutral
thf(fact_75_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_76_comm__monoid__add__class_Oadd__0, axiom,
    ((![A : nat]: ((plus_plus_nat @ zero_zero_nat @ A) = A)))). % comm_monoid_add_class.add_0
thf(fact_77_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_78_comm__monoid__add__class_Oadd__0, axiom,
    ((![A : poly_nat]: ((plus_plus_poly_nat @ zero_zero_poly_nat @ A) = A)))). % comm_monoid_add_class.add_0
thf(fact_79_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_80_add__0__iff, axiom,
    ((![B : nat, A : nat]: ((B = (plus_plus_nat @ B @ A)) = (A = zero_zero_nat))))). % add_0_iff
thf(fact_81_verit__sum__simplify, axiom,
    ((![A : nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A)))). % verit_sum_simplify
thf(fact_82_verit__sum__simplify, axiom,
    ((![A : poly_nat]: ((plus_plus_poly_nat @ A @ zero_zero_poly_nat) = A)))). % verit_sum_simplify
thf(fact_83_is__zero__null, axiom,
    ((is_zero_a = (^[P2 : poly_a]: (P2 = zero_zero_poly_a))))). % is_zero_null
thf(fact_84_is__zero__null, axiom,
    ((is_zero_nat = (^[P2 : poly_nat]: (P2 = zero_zero_poly_nat))))). % is_zero_null
thf(fact_85_is__zero__null, axiom,
    ((is_zero_poly_a = (^[P2 : poly_poly_a]: (P2 = zero_z2096148049poly_a))))). % is_zero_null
thf(fact_86_poly__cutoff__0, axiom,
    ((![N : nat]: ((poly_cutoff_a @ N @ zero_zero_poly_a) = zero_zero_poly_a)))). % poly_cutoff_0
thf(fact_87_poly__cutoff__0, axiom,
    ((![N : nat]: ((poly_cutoff_nat @ N @ zero_zero_poly_nat) = zero_zero_poly_nat)))). % poly_cutoff_0
thf(fact_88_poly__cutoff__0, axiom,
    ((![N : nat]: ((poly_cutoff_poly_a @ N @ zero_z2096148049poly_a) = zero_z2096148049poly_a)))). % poly_cutoff_0
thf(fact_89_reflect__poly__at__0__eq__0__iff, axiom,
    ((![P : poly_poly_a]: (((poly_poly_a2 @ (reflect_poly_poly_a @ P) @ zero_zero_poly_a) = zero_zero_poly_a) = (P = zero_z2096148049poly_a))))). % reflect_poly_at_0_eq_0_iff
thf(fact_90_reflect__poly__at__0__eq__0__iff, axiom,
    ((![P : poly_nat]: (((poly_nat2 @ (reflect_poly_nat @ P) @ zero_zero_nat) = zero_zero_nat) = (P = zero_zero_poly_nat))))). % reflect_poly_at_0_eq_0_iff
thf(fact_91_reflect__poly__at__0__eq__0__iff, axiom,
    ((![P : poly_a]: (((poly_a2 @ (reflect_poly_a @ P) @ zero_zero_a) = zero_zero_a) = (P = zero_zero_poly_a))))). % reflect_poly_at_0_eq_0_iff
thf(fact_92_reflect__poly__at__0__eq__0__iff, axiom,
    ((![P : poly_poly_nat]: (((poly_poly_nat2 @ (reflec781175074ly_nat @ P) @ zero_zero_poly_nat) = zero_zero_poly_nat) = (P = zero_z1059985641ly_nat))))). % reflect_poly_at_0_eq_0_iff
thf(fact_93_reflect__poly__at__0__eq__0__iff, axiom,
    ((![P : poly_poly_poly_a]: (((poly_poly_poly_a2 @ (reflec581648976poly_a @ P) @ zero_z2096148049poly_a) = zero_z2096148049poly_a) = (P = zero_z2064990175poly_a))))). % reflect_poly_at_0_eq_0_iff
thf(fact_94_poly__shift__0, axiom,
    ((![N : nat]: ((poly_shift_a @ N @ zero_zero_poly_a) = zero_zero_poly_a)))). % poly_shift_0
thf(fact_95_poly__shift__0, axiom,
    ((![N : nat]: ((poly_shift_nat @ N @ zero_zero_poly_nat) = zero_zero_poly_nat)))). % poly_shift_0
thf(fact_96_poly__shift__0, axiom,
    ((![N : nat]: ((poly_shift_poly_a @ N @ zero_z2096148049poly_a) = zero_z2096148049poly_a)))). % poly_shift_0
thf(fact_97_content__eq__zero__iff, axiom,
    ((![P : poly_nat]: (((content_nat @ P) = zero_zero_nat) = (P = zero_zero_poly_nat))))). % content_eq_zero_iff
thf(fact_98_reflect__poly__0, axiom,
    (((reflect_poly_a @ zero_zero_poly_a) = zero_zero_poly_a))). % reflect_poly_0
thf(fact_99_reflect__poly__0, axiom,
    (((reflect_poly_nat @ zero_zero_poly_nat) = zero_zero_poly_nat))). % reflect_poly_0
thf(fact_100_reflect__poly__0, axiom,
    (((reflect_poly_poly_a @ zero_z2096148049poly_a) = zero_z2096148049poly_a))). % reflect_poly_0
thf(fact_101_content__0, axiom,
    (((content_nat @ zero_zero_poly_nat) = zero_zero_nat))). % content_0
thf(fact_102_add__is__0, axiom,
    ((![M : nat, N : nat]: (((plus_plus_nat @ M @ N) = zero_zero_nat) = (((M = zero_zero_nat)) & ((N = zero_zero_nat))))))). % add_is_0
thf(fact_103_Nat_Oadd__0__right, axiom,
    ((![M : nat]: ((plus_plus_nat @ M @ zero_zero_nat) = M)))). % Nat.add_0_right
thf(fact_104_poly__cutoff__1, axiom,
    ((![N : nat]: (((N = zero_zero_nat) => ((poly_cutoff_nat @ N @ one_one_poly_nat) = zero_zero_poly_nat)) & ((~ ((N = zero_zero_nat))) => ((poly_cutoff_nat @ N @ one_one_poly_nat) = one_one_poly_nat)))))). % poly_cutoff_1
thf(fact_105_coeff__0__reflect__poly__0__iff, axiom,
    ((![P : poly_poly_a]: (((coeff_poly_a @ (reflect_poly_poly_a @ P) @ zero_zero_nat) = zero_zero_poly_a) = (P = zero_z2096148049poly_a))))). % coeff_0_reflect_poly_0_iff
thf(fact_106_coeff__0__reflect__poly__0__iff, axiom,
    ((![P : poly_nat]: (((coeff_nat @ (reflect_poly_nat @ P) @ zero_zero_nat) = zero_zero_nat) = (P = zero_zero_poly_nat))))). % coeff_0_reflect_poly_0_iff
thf(fact_107_coeff__0__reflect__poly__0__iff, axiom,
    ((![P : poly_a]: (((coeff_a @ (reflect_poly_a @ P) @ zero_zero_nat) = zero_zero_a) = (P = zero_zero_poly_a))))). % coeff_0_reflect_poly_0_iff
thf(fact_108_coeff__0__reflect__poly__0__iff, axiom,
    ((![P : poly_poly_nat]: (((coeff_poly_nat @ (reflec781175074ly_nat @ P) @ zero_zero_nat) = zero_zero_poly_nat) = (P = zero_z1059985641ly_nat))))). % coeff_0_reflect_poly_0_iff
thf(fact_109_coeff__0__reflect__poly__0__iff, axiom,
    ((![P : poly_poly_poly_a]: (((coeff_poly_poly_a @ (reflec581648976poly_a @ P) @ zero_zero_nat) = zero_z2096148049poly_a) = (P = zero_z2064990175poly_a))))). % coeff_0_reflect_poly_0_iff
thf(fact_110_poly__shift__1, axiom,
    ((![N : nat]: (((N = zero_zero_nat) => ((poly_shift_nat @ N @ one_one_poly_nat) = one_one_poly_nat)) & ((~ ((N = zero_zero_nat))) => ((poly_shift_nat @ N @ one_one_poly_nat) = zero_zero_poly_nat)))))). % poly_shift_1
thf(fact_111_reflect__poly__reflect__poly, axiom,
    ((![P : poly_poly_a]: ((~ (((coeff_poly_a @ P @ zero_zero_nat) = zero_zero_poly_a))) => ((reflect_poly_poly_a @ (reflect_poly_poly_a @ P)) = P))))). % reflect_poly_reflect_poly
thf(fact_112_reflect__poly__reflect__poly, axiom,
    ((![P : poly_nat]: ((~ (((coeff_nat @ P @ zero_zero_nat) = zero_zero_nat))) => ((reflect_poly_nat @ (reflect_poly_nat @ P)) = P))))). % reflect_poly_reflect_poly
thf(fact_113_reflect__poly__reflect__poly, axiom,
    ((![P : poly_a]: ((~ (((coeff_a @ P @ zero_zero_nat) = zero_zero_a))) => ((reflect_poly_a @ (reflect_poly_a @ P)) = P))))). % reflect_poly_reflect_poly
thf(fact_114_reflect__poly__reflect__poly, axiom,
    ((![P : poly_poly_nat]: ((~ (((coeff_poly_nat @ P @ zero_zero_nat) = zero_zero_poly_nat))) => ((reflec781175074ly_nat @ (reflec781175074ly_nat @ P)) = P))))). % reflect_poly_reflect_poly
thf(fact_115_reflect__poly__reflect__poly, axiom,
    ((![P : poly_poly_poly_a]: ((~ (((coeff_poly_poly_a @ P @ zero_zero_nat) = zero_z2096148049poly_a))) => ((reflec581648976poly_a @ (reflec581648976poly_a @ P)) = P))))). % reflect_poly_reflect_poly
thf(fact_116_coeff__0, axiom,
    ((![N : nat]: ((coeff_poly_nat @ zero_z1059985641ly_nat @ N) = zero_zero_poly_nat)))). % coeff_0
thf(fact_117_coeff__0, axiom,
    ((![N : nat]: ((coeff_poly_poly_a @ zero_z2064990175poly_a @ N) = zero_z2096148049poly_a)))). % coeff_0
thf(fact_118_coeff__0, axiom,
    ((![N : nat]: ((coeff_a @ zero_zero_poly_a @ N) = zero_zero_a)))). % coeff_0
thf(fact_119_coeff__0, axiom,
    ((![N : nat]: ((coeff_nat @ zero_zero_poly_nat @ N) = zero_zero_nat)))). % coeff_0
thf(fact_120_coeff__0, axiom,
    ((![N : nat]: ((coeff_poly_a @ zero_z2096148049poly_a @ N) = zero_zero_poly_a)))). % coeff_0
thf(fact_121_coeff__add, axiom,
    ((![P : poly_poly_nat, Q : poly_poly_nat, N : nat]: ((coeff_poly_nat @ (plus_p1835221865ly_nat @ P @ Q) @ N) = (plus_plus_poly_nat @ (coeff_poly_nat @ P @ N) @ (coeff_poly_nat @ Q @ N)))))). % coeff_add
thf(fact_122_coeff__add, axiom,
    ((![P : poly_poly_a, Q : poly_poly_a, N : nat]: ((coeff_poly_a @ (plus_p1976640465poly_a @ P @ Q) @ N) = (plus_plus_poly_a @ (coeff_poly_a @ P @ N) @ (coeff_poly_a @ Q @ N)))))). % coeff_add
thf(fact_123_coeff__add, axiom,
    ((![P : poly_nat, Q : poly_nat, N : nat]: ((coeff_nat @ (plus_plus_poly_nat @ P @ Q) @ N) = (plus_plus_nat @ (coeff_nat @ P @ N) @ (coeff_nat @ Q @ N)))))). % coeff_add
thf(fact_124_coeff__add, axiom,
    ((![P : poly_a, Q : poly_a, N : nat]: ((coeff_a @ (plus_plus_poly_a @ P @ Q) @ N) = (plus_plus_a @ (coeff_a @ P @ N) @ (coeff_a @ Q @ N)))))). % coeff_add
thf(fact_125_poly__1, axiom,
    ((![X : nat]: ((poly_nat2 @ one_one_poly_nat @ X) = one_one_nat)))). % poly_1
thf(fact_126_content__1, axiom,
    (((content_nat @ one_one_poly_nat) = one_one_nat))). % content_1
thf(fact_127_one__reorient, axiom,
    ((![X : nat]: ((one_one_nat = X) = (X = one_one_nat))))). % one_reorient
thf(fact_128_zero__poly_Orep__eq, axiom,
    (((coeff_poly_nat @ zero_z1059985641ly_nat) = (^[Uu : nat]: zero_zero_poly_nat)))). % zero_poly.rep_eq
thf(fact_129_zero__poly_Orep__eq, axiom,
    (((coeff_poly_poly_a @ zero_z2064990175poly_a) = (^[Uu : nat]: zero_z2096148049poly_a)))). % zero_poly.rep_eq
thf(fact_130_zero__poly_Orep__eq, axiom,
    (((coeff_a @ zero_zero_poly_a) = (^[Uu : nat]: zero_zero_a)))). % zero_poly.rep_eq
thf(fact_131_zero__poly_Orep__eq, axiom,
    (((coeff_nat @ zero_zero_poly_nat) = (^[Uu : nat]: zero_zero_nat)))). % zero_poly.rep_eq
thf(fact_132_zero__poly_Orep__eq, axiom,
    (((coeff_poly_a @ zero_z2096148049poly_a) = (^[Uu : nat]: zero_zero_poly_a)))). % zero_poly.rep_eq
thf(fact_133_plus__poly_Orep__eq, axiom,
    ((![X : poly_poly_nat, Xa : poly_poly_nat]: ((coeff_poly_nat @ (plus_p1835221865ly_nat @ X @ Xa)) = (^[N2 : nat]: (plus_plus_poly_nat @ (coeff_poly_nat @ X @ N2) @ (coeff_poly_nat @ Xa @ N2))))))). % plus_poly.rep_eq
thf(fact_134_plus__poly_Orep__eq, axiom,
    ((![X : poly_poly_a, Xa : poly_poly_a]: ((coeff_poly_a @ (plus_p1976640465poly_a @ X @ Xa)) = (^[N2 : nat]: (plus_plus_poly_a @ (coeff_poly_a @ X @ N2) @ (coeff_poly_a @ Xa @ N2))))))). % plus_poly.rep_eq
thf(fact_135_plus__poly_Orep__eq, axiom,
    ((![X : poly_nat, Xa : poly_nat]: ((coeff_nat @ (plus_plus_poly_nat @ X @ Xa)) = (^[N2 : nat]: (plus_plus_nat @ (coeff_nat @ X @ N2) @ (coeff_nat @ Xa @ N2))))))). % plus_poly.rep_eq
thf(fact_136_plus__poly_Orep__eq, axiom,
    ((![X : poly_a, Xa : poly_a]: ((coeff_a @ (plus_plus_poly_a @ X @ Xa)) = (^[N2 : nat]: (plus_plus_a @ (coeff_a @ X @ N2) @ (coeff_a @ Xa @ N2))))))). % plus_poly.rep_eq
thf(fact_137_poly__0__coeff__0, axiom,
    ((![P : poly_poly_a]: ((poly_poly_a2 @ P @ zero_zero_poly_a) = (coeff_poly_a @ P @ zero_zero_nat))))). % poly_0_coeff_0
thf(fact_138_poly__0__coeff__0, axiom,
    ((![P : poly_nat]: ((poly_nat2 @ P @ zero_zero_nat) = (coeff_nat @ P @ zero_zero_nat))))). % poly_0_coeff_0
thf(fact_139_poly__0__coeff__0, axiom,
    ((![P : poly_a]: ((poly_a2 @ P @ zero_zero_a) = (coeff_a @ P @ zero_zero_nat))))). % poly_0_coeff_0
thf(fact_140_poly__0__coeff__0, axiom,
    ((![P : poly_poly_nat]: ((poly_poly_nat2 @ P @ zero_zero_poly_nat) = (coeff_poly_nat @ P @ zero_zero_nat))))). % poly_0_coeff_0
thf(fact_141_poly__0__coeff__0, axiom,
    ((![P : poly_poly_poly_a]: ((poly_poly_poly_a2 @ P @ zero_z2096148049poly_a) = (coeff_poly_poly_a @ P @ zero_zero_nat))))). % poly_0_coeff_0
thf(fact_142_add__eq__self__zero, axiom,
    ((![M : nat, N : nat]: (((plus_plus_nat @ M @ N) = M) => (N = zero_zero_nat))))). % add_eq_self_zero
thf(fact_143_plus__nat_Oadd__0, axiom,
    ((![N : nat]: ((plus_plus_nat @ zero_zero_nat @ N) = N)))). % plus_nat.add_0
thf(fact_144_Euclid__induct, axiom,
    ((![P3 : nat > nat > $o, A : nat, B : nat]: ((![A4 : nat, B4 : nat]: ((P3 @ A4 @ B4) = (P3 @ B4 @ A4))) => ((![A4 : nat]: (P3 @ A4 @ zero_zero_nat)) => ((![A4 : nat, B4 : nat]: ((P3 @ A4 @ B4) => (P3 @ A4 @ (plus_plus_nat @ A4 @ B4)))) => (P3 @ A @ B))))))). % Euclid_induct
thf(fact_145_content__primitive__part, axiom,
    ((![P : poly_nat]: ((~ ((P = zero_zero_poly_nat))) => ((content_nat @ (primitive_part_nat @ P)) = one_one_nat))))). % content_primitive_part
thf(fact_146_zero__neq__one, axiom,
    ((~ ((zero_zero_nat = one_one_nat))))). % zero_neq_one
thf(fact_147_zero__neq__one, axiom,
    ((~ ((zero_zero_poly_nat = one_one_poly_nat))))). % zero_neq_one
thf(fact_148_poly__reflect__poly__0, axiom,
    ((![P : poly_poly_a]: ((poly_poly_a2 @ (reflect_poly_poly_a @ P) @ zero_zero_poly_a) = (coeff_poly_a @ P @ (degree_poly_a @ P)))))). % poly_reflect_poly_0
thf(fact_149_poly__reflect__poly__0, axiom,
    ((![P : poly_nat]: ((poly_nat2 @ (reflect_poly_nat @ P) @ zero_zero_nat) = (coeff_nat @ P @ (degree_nat @ P)))))). % poly_reflect_poly_0
thf(fact_150_poly__reflect__poly__0, axiom,
    ((![P : poly_a]: ((poly_a2 @ (reflect_poly_a @ P) @ zero_zero_a) = (coeff_a @ P @ (degree_a @ P)))))). % poly_reflect_poly_0
thf(fact_151_poly__reflect__poly__0, axiom,
    ((![P : poly_poly_nat]: ((poly_poly_nat2 @ (reflec781175074ly_nat @ P) @ zero_zero_poly_nat) = (coeff_poly_nat @ P @ (degree_poly_nat @ P)))))). % poly_reflect_poly_0
thf(fact_152_poly__reflect__poly__0, axiom,
    ((![P : poly_poly_poly_a]: ((poly_poly_poly_a2 @ (reflec581648976poly_a @ P) @ zero_z2096148049poly_a) = (coeff_poly_poly_a @ P @ (degree_poly_poly_a @ P)))))). % poly_reflect_poly_0
thf(fact_153_primitive__part__0, axiom,
    (((primitive_part_nat @ zero_zero_poly_nat) = zero_zero_poly_nat))). % primitive_part_0
thf(fact_154_primitive__part__eq__0__iff, axiom,
    ((![P : poly_nat]: (((primitive_part_nat @ P) = zero_zero_poly_nat) = (P = zero_zero_poly_nat))))). % primitive_part_eq_0_iff
thf(fact_155_degree__0, axiom,
    (((degree_a @ zero_zero_poly_a) = zero_zero_nat))). % degree_0
thf(fact_156_degree__0, axiom,
    (((degree_nat @ zero_zero_poly_nat) = zero_zero_nat))). % degree_0
thf(fact_157_degree__0, axiom,
    (((degree_poly_a @ zero_z2096148049poly_a) = zero_zero_nat))). % degree_0
thf(fact_158_leading__coeff__0__iff, axiom,
    ((![P : poly_poly_a]: (((coeff_poly_a @ P @ (degree_poly_a @ P)) = zero_zero_poly_a) = (P = zero_z2096148049poly_a))))). % leading_coeff_0_iff
thf(fact_159_leading__coeff__0__iff, axiom,
    ((![P : poly_nat]: (((coeff_nat @ P @ (degree_nat @ P)) = zero_zero_nat) = (P = zero_zero_poly_nat))))). % leading_coeff_0_iff
thf(fact_160_leading__coeff__0__iff, axiom,
    ((![P : poly_a]: (((coeff_a @ P @ (degree_a @ P)) = zero_zero_a) = (P = zero_zero_poly_a))))). % leading_coeff_0_iff
thf(fact_161_leading__coeff__0__iff, axiom,
    ((![P : poly_poly_nat]: (((coeff_poly_nat @ P @ (degree_poly_nat @ P)) = zero_zero_poly_nat) = (P = zero_z1059985641ly_nat))))). % leading_coeff_0_iff
thf(fact_162_leading__coeff__0__iff, axiom,
    ((![P : poly_poly_poly_a]: (((coeff_poly_poly_a @ P @ (degree_poly_poly_a @ P)) = zero_z2096148049poly_a) = (P = zero_z2064990175poly_a))))). % leading_coeff_0_iff
thf(fact_163_lead__coeff__1, axiom,
    (((coeff_nat @ one_one_poly_nat @ (degree_nat @ one_one_poly_nat)) = one_one_nat))). % lead_coeff_1
thf(fact_164_degree__reflect__poly__eq, axiom,
    ((![P : poly_poly_a]: ((~ (((coeff_poly_a @ P @ zero_zero_nat) = zero_zero_poly_a))) => ((degree_poly_a @ (reflect_poly_poly_a @ P)) = (degree_poly_a @ P)))))). % degree_reflect_poly_eq
thf(fact_165_degree__reflect__poly__eq, axiom,
    ((![P : poly_nat]: ((~ (((coeff_nat @ P @ zero_zero_nat) = zero_zero_nat))) => ((degree_nat @ (reflect_poly_nat @ P)) = (degree_nat @ P)))))). % degree_reflect_poly_eq
thf(fact_166_degree__reflect__poly__eq, axiom,
    ((![P : poly_a]: ((~ (((coeff_a @ P @ zero_zero_nat) = zero_zero_a))) => ((degree_a @ (reflect_poly_a @ P)) = (degree_a @ P)))))). % degree_reflect_poly_eq
thf(fact_167_degree__reflect__poly__eq, axiom,
    ((![P : poly_poly_nat]: ((~ (((coeff_poly_nat @ P @ zero_zero_nat) = zero_zero_poly_nat))) => ((degree_poly_nat @ (reflec781175074ly_nat @ P)) = (degree_poly_nat @ P)))))). % degree_reflect_poly_eq
thf(fact_168_degree__reflect__poly__eq, axiom,
    ((![P : poly_poly_poly_a]: ((~ (((coeff_poly_poly_a @ P @ zero_zero_nat) = zero_z2096148049poly_a))) => ((degree_poly_poly_a @ (reflec581648976poly_a @ P)) = (degree_poly_poly_a @ P)))))). % degree_reflect_poly_eq
thf(fact_169_leading__coeff__neq__0, axiom,
    ((![P : poly_poly_nat]: ((~ ((P = zero_z1059985641ly_nat))) => (~ (((coeff_poly_nat @ P @ (degree_poly_nat @ P)) = zero_zero_poly_nat))))))). % leading_coeff_neq_0
thf(fact_170_leading__coeff__neq__0, axiom,
    ((![P : poly_poly_poly_a]: ((~ ((P = zero_z2064990175poly_a))) => (~ (((coeff_poly_poly_a @ P @ (degree_poly_poly_a @ P)) = zero_z2096148049poly_a))))))). % leading_coeff_neq_0
thf(fact_171_leading__coeff__neq__0, axiom,
    ((![P : poly_a]: ((~ ((P = zero_zero_poly_a))) => (~ (((coeff_a @ P @ (degree_a @ P)) = zero_zero_a))))))). % leading_coeff_neq_0
thf(fact_172_leading__coeff__neq__0, axiom,
    ((![P : poly_nat]: ((~ ((P = zero_zero_poly_nat))) => (~ (((coeff_nat @ P @ (degree_nat @ P)) = zero_zero_nat))))))). % leading_coeff_neq_0
thf(fact_173_leading__coeff__neq__0, axiom,
    ((![P : poly_poly_a]: ((~ ((P = zero_z2096148049poly_a))) => (~ (((coeff_poly_a @ P @ (degree_poly_a @ P)) = zero_zero_poly_a))))))). % leading_coeff_neq_0
thf(fact_174_primitive__part__prim, axiom,
    ((![P : poly_nat]: (((content_nat @ P) = one_one_nat) => ((primitive_part_nat @ P) = P))))). % primitive_part_prim
thf(fact_175_synthetic__div__eq__0__iff, axiom,
    ((![P : poly_a, C : a]: (((synthetic_div_a @ P @ C) = zero_zero_poly_a) = ((degree_a @ P) = zero_zero_nat))))). % synthetic_div_eq_0_iff
thf(fact_176_synthetic__div__eq__0__iff, axiom,
    ((![P : poly_nat, C : nat]: (((synthetic_div_nat @ P @ C) = zero_zero_poly_nat) = ((degree_nat @ P) = zero_zero_nat))))). % synthetic_div_eq_0_iff
thf(fact_177_synthetic__div__eq__0__iff, axiom,
    ((![P : poly_poly_a, C : poly_a]: (((synthetic_div_poly_a @ P @ C) = zero_z2096148049poly_a) = ((degree_poly_a @ P) = zero_zero_nat))))). % synthetic_div_eq_0_iff
thf(fact_178_dvd__0__left__iff, axiom,
    ((![A : nat]: ((dvd_dvd_nat @ zero_zero_nat @ A) = (A = zero_zero_nat))))). % dvd_0_left_iff
thf(fact_179_dvd__0__left__iff, axiom,
    ((![A : poly_nat]: ((dvd_dvd_poly_nat @ zero_zero_poly_nat @ A) = (A = zero_zero_poly_nat))))). % dvd_0_left_iff
thf(fact_180_dvd__0__right, axiom,
    ((![A : nat]: (dvd_dvd_nat @ A @ zero_zero_nat)))). % dvd_0_right
thf(fact_181_dvd__0__right, axiom,
    ((![A : poly_nat]: (dvd_dvd_poly_nat @ A @ zero_zero_poly_nat)))). % dvd_0_right
thf(fact_182_dvd__add__triv__left__iff, axiom,
    ((![A : nat, B : nat]: ((dvd_dvd_nat @ A @ (plus_plus_nat @ A @ B)) = (dvd_dvd_nat @ A @ B))))). % dvd_add_triv_left_iff
thf(fact_183_dvd__add__triv__right__iff, axiom,
    ((![A : nat, B : nat]: ((dvd_dvd_nat @ A @ (plus_plus_nat @ B @ A)) = (dvd_dvd_nat @ A @ B))))). % dvd_add_triv_right_iff
thf(fact_184_synthetic__div__0, axiom,
    ((![C : a]: ((synthetic_div_a @ zero_zero_poly_a @ C) = zero_zero_poly_a)))). % synthetic_div_0
thf(fact_185_synthetic__div__0, axiom,
    ((![C : nat]: ((synthetic_div_nat @ zero_zero_poly_nat @ C) = zero_zero_poly_nat)))). % synthetic_div_0
thf(fact_186_synthetic__div__0, axiom,
    ((![C : poly_a]: ((synthetic_div_poly_a @ zero_z2096148049poly_a @ C) = zero_z2096148049poly_a)))). % synthetic_div_0
thf(fact_187_is__unit__content__iff, axiom,
    ((![P : poly_nat]: ((dvd_dvd_nat @ (content_nat @ P) @ one_one_nat) = ((content_nat @ P) = one_one_nat))))). % is_unit_content_iff
thf(fact_188_content__dvd__contentI, axiom,
    ((![P : poly_nat, Q : poly_nat]: ((dvd_dvd_poly_nat @ P @ Q) => (dvd_dvd_nat @ (content_nat @ P) @ (content_nat @ Q)))))). % content_dvd_contentI
thf(fact_189_dvd__add, axiom,
    ((![A : nat, B : nat, C : nat]: ((dvd_dvd_nat @ A @ B) => ((dvd_dvd_nat @ A @ C) => (dvd_dvd_nat @ A @ (plus_plus_nat @ B @ C))))))). % dvd_add
thf(fact_190_dvd__add, axiom,
    ((![A : poly_nat, B : poly_nat, C : poly_nat]: ((dvd_dvd_poly_nat @ A @ B) => ((dvd_dvd_poly_nat @ A @ C) => (dvd_dvd_poly_nat @ A @ (plus_plus_poly_nat @ B @ C))))))). % dvd_add
thf(fact_191_dvd__add__left__iff, axiom,
    ((![A : nat, C : nat, B : nat]: ((dvd_dvd_nat @ A @ C) => ((dvd_dvd_nat @ A @ (plus_plus_nat @ B @ C)) = (dvd_dvd_nat @ A @ B)))))). % dvd_add_left_iff
thf(fact_192_dvd__add__right__iff, axiom,
    ((![A : nat, B : nat, C : nat]: ((dvd_dvd_nat @ A @ B) => ((dvd_dvd_nat @ A @ (plus_plus_nat @ B @ C)) = (dvd_dvd_nat @ A @ C)))))). % dvd_add_right_iff
thf(fact_193_one__dvd, axiom,
    ((![A : nat]: (dvd_dvd_nat @ one_one_nat @ A)))). % one_dvd
thf(fact_194_unit__imp__dvd, axiom,
    ((![B : nat, A : nat]: ((dvd_dvd_nat @ B @ one_one_nat) => (dvd_dvd_nat @ B @ A))))). % unit_imp_dvd
thf(fact_195_dvd__unit__imp__unit, axiom,
    ((![A : nat, B : nat]: ((dvd_dvd_nat @ A @ B) => ((dvd_dvd_nat @ B @ one_one_nat) => (dvd_dvd_nat @ A @ one_one_nat)))))). % dvd_unit_imp_unit
thf(fact_196_dvd__trans, axiom,
    ((![A : nat, B : nat, C : nat]: ((dvd_dvd_nat @ A @ B) => ((dvd_dvd_nat @ B @ C) => (dvd_dvd_nat @ A @ C)))))). % dvd_trans
thf(fact_197_dvd__refl, axiom,
    ((![A : nat]: (dvd_dvd_nat @ A @ A)))). % dvd_refl
thf(fact_198_dvd__0__left, axiom,
    ((![A : nat]: ((dvd_dvd_nat @ zero_zero_nat @ A) => (A = zero_zero_nat))))). % dvd_0_left
thf(fact_199_dvd__0__left, axiom,
    ((![A : poly_nat]: ((dvd_dvd_poly_nat @ zero_zero_poly_nat @ A) => (A = zero_zero_poly_nat))))). % dvd_0_left
thf(fact_200_not__is__unit__0, axiom,
    ((~ ((dvd_dvd_nat @ zero_zero_nat @ one_one_nat))))). % not_is_unit_0
thf(fact_201_content__dvd__coeff, axiom,
    ((![P : poly_nat, N : nat]: (dvd_dvd_nat @ (content_nat @ P) @ (coeff_nat @ P @ N))))). % content_dvd_coeff
thf(fact_202_nat__dvd__1__iff__1, axiom,
    ((![M : nat]: ((dvd_dvd_nat @ M @ one_one_nat) = (M = one_one_nat))))). % nat_dvd_1_iff_1
thf(fact_203_gcd__nat_Oextremum__uniqueI, axiom,
    ((![A : nat]: ((dvd_dvd_nat @ zero_zero_nat @ A) => (A = zero_zero_nat))))). % gcd_nat.extremum_uniqueI
thf(fact_204_gcd__nat_Onot__eq__extremum, axiom,
    ((![A : nat]: ((~ ((A = zero_zero_nat))) = (((dvd_dvd_nat @ A @ zero_zero_nat)) & ((~ ((A = zero_zero_nat))))))))). % gcd_nat.not_eq_extremum
thf(fact_205_gcd__nat_Oextremum__unique, axiom,
    ((![A : nat]: ((dvd_dvd_nat @ zero_zero_nat @ A) = (A = zero_zero_nat))))). % gcd_nat.extremum_unique
thf(fact_206_gcd__nat_Oextremum__strict, axiom,
    ((![A : nat]: (~ (((dvd_dvd_nat @ zero_zero_nat @ A) & (~ ((zero_zero_nat = A))))))))). % gcd_nat.extremum_strict
thf(fact_207_gcd__nat_Oextremum, axiom,
    ((![A : nat]: (dvd_dvd_nat @ A @ zero_zero_nat)))). % gcd_nat.extremum
thf(fact_208_monom__eq__0, axiom,
    ((![N : nat]: ((monom_poly_a @ zero_zero_poly_a @ N) = zero_z2096148049poly_a)))). % monom_eq_0
thf(fact_209_monom__eq__0, axiom,
    ((![N : nat]: ((monom_nat @ zero_zero_nat @ N) = zero_zero_poly_nat)))). % monom_eq_0
thf(fact_210_monom__eq__0, axiom,
    ((![N : nat]: ((monom_a @ zero_zero_a @ N) = zero_zero_poly_a)))). % monom_eq_0
thf(fact_211_monom__eq__0, axiom,
    ((![N : nat]: ((monom_poly_nat @ zero_zero_poly_nat @ N) = zero_z1059985641ly_nat)))). % monom_eq_0
thf(fact_212_monom__eq__0, axiom,
    ((![N : nat]: ((monom_poly_poly_a @ zero_z2096148049poly_a @ N) = zero_z2064990175poly_a)))). % monom_eq_0
thf(fact_213_monom__eq__0__iff, axiom,
    ((![A : poly_nat, N : nat]: (((monom_poly_nat @ A @ N) = zero_z1059985641ly_nat) = (A = zero_zero_poly_nat))))). % monom_eq_0_iff
thf(fact_214_monom__eq__0__iff, axiom,
    ((![A : poly_poly_a, N : nat]: (((monom_poly_poly_a @ A @ N) = zero_z2064990175poly_a) = (A = zero_z2096148049poly_a))))). % monom_eq_0_iff
thf(fact_215_monom__eq__0__iff, axiom,
    ((![A : a, N : nat]: (((monom_a @ A @ N) = zero_zero_poly_a) = (A = zero_zero_a))))). % monom_eq_0_iff
thf(fact_216_monom__eq__0__iff, axiom,
    ((![A : nat, N : nat]: (((monom_nat @ A @ N) = zero_zero_poly_nat) = (A = zero_zero_nat))))). % monom_eq_0_iff
thf(fact_217_monom__eq__0__iff, axiom,
    ((![A : poly_a, N : nat]: (((monom_poly_a @ A @ N) = zero_z2096148049poly_a) = (A = zero_zero_poly_a))))). % monom_eq_0_iff
thf(fact_218_coeff__monom, axiom,
    ((![M : nat, N : nat, A : poly_a]: (((M = N) => ((coeff_poly_a @ (monom_poly_a @ A @ M) @ N) = A)) & ((~ ((M = N))) => ((coeff_poly_a @ (monom_poly_a @ A @ M) @ N) = zero_zero_poly_a)))))). % coeff_monom
thf(fact_219_coeff__monom, axiom,
    ((![M : nat, N : nat, A : nat]: (((M = N) => ((coeff_nat @ (monom_nat @ A @ M) @ N) = A)) & ((~ ((M = N))) => ((coeff_nat @ (monom_nat @ A @ M) @ N) = zero_zero_nat)))))). % coeff_monom
thf(fact_220_coeff__monom, axiom,
    ((![M : nat, N : nat, A : a]: (((M = N) => ((coeff_a @ (monom_a @ A @ M) @ N) = A)) & ((~ ((M = N))) => ((coeff_a @ (monom_a @ A @ M) @ N) = zero_zero_a)))))). % coeff_monom
thf(fact_221_coeff__monom, axiom,
    ((![M : nat, N : nat, A : poly_nat]: (((M = N) => ((coeff_poly_nat @ (monom_poly_nat @ A @ M) @ N) = A)) & ((~ ((M = N))) => ((coeff_poly_nat @ (monom_poly_nat @ A @ M) @ N) = zero_zero_poly_nat)))))). % coeff_monom
thf(fact_222_coeff__monom, axiom,
    ((![M : nat, N : nat, A : poly_poly_a]: (((M = N) => ((coeff_poly_poly_a @ (monom_poly_poly_a @ A @ M) @ N) = A)) & ((~ ((M = N))) => ((coeff_poly_poly_a @ (monom_poly_poly_a @ A @ M) @ N) = zero_z2096148049poly_a)))))). % coeff_monom
thf(fact_223_monom__eq__1, axiom,
    (((monom_nat @ one_one_nat @ zero_zero_nat) = one_one_poly_nat))). % monom_eq_1
thf(fact_224_gcd__nat_Onot__eq__order__implies__strict, axiom,
    ((![A : nat, B : nat]: ((~ ((A = B))) => ((dvd_dvd_nat @ A @ B) => ((dvd_dvd_nat @ A @ B) & (~ ((A = B))))))))). % gcd_nat.not_eq_order_implies_strict
thf(fact_225_gcd__nat_Ostrict__implies__not__eq, axiom,
    ((![A : nat, B : nat]: (((dvd_dvd_nat @ A @ B) & (~ ((A = B)))) => (~ ((A = B))))))). % gcd_nat.strict_implies_not_eq
thf(fact_226_gcd__nat_Ostrict__implies__order, axiom,
    ((![A : nat, B : nat]: (((dvd_dvd_nat @ A @ B) & (~ ((A = B)))) => (dvd_dvd_nat @ A @ B))))). % gcd_nat.strict_implies_order
thf(fact_227_gcd__nat_Ostrict__iff__order, axiom,
    ((![A : nat, B : nat]: ((((dvd_dvd_nat @ A @ B)) & ((~ ((A = B))))) = (((dvd_dvd_nat @ A @ B)) & ((~ ((A = B))))))))). % gcd_nat.strict_iff_order
thf(fact_228_gcd__nat_Oorder__iff__strict, axiom,
    ((dvd_dvd_nat = (^[A2 : nat]: (^[B2 : nat]: (((((dvd_dvd_nat @ A2 @ B2)) & ((~ ((A2 = B2)))))) | ((A2 = B2)))))))). % gcd_nat.order_iff_strict
thf(fact_229_gcd__nat_Ostrict__trans2, axiom,
    ((![A : nat, B : nat, C : nat]: (((dvd_dvd_nat @ A @ B) & (~ ((A = B)))) => ((dvd_dvd_nat @ B @ C) => ((dvd_dvd_nat @ A @ C) & (~ ((A = C))))))))). % gcd_nat.strict_trans2
thf(fact_230_gcd__nat_Ostrict__trans1, axiom,
    ((![A : nat, B : nat, C : nat]: ((dvd_dvd_nat @ A @ B) => (((dvd_dvd_nat @ B @ C) & (~ ((B = C)))) => ((dvd_dvd_nat @ A @ C) & (~ ((A = C))))))))). % gcd_nat.strict_trans1
thf(fact_231_gcd__nat_Ostrict__trans, axiom,
    ((![A : nat, B : nat, C : nat]: (((dvd_dvd_nat @ A @ B) & (~ ((A = B)))) => (((dvd_dvd_nat @ B @ C) & (~ ((B = C)))) => ((dvd_dvd_nat @ A @ C) & (~ ((A = C))))))))). % gcd_nat.strict_trans
thf(fact_232_gcd__nat_Oantisym, axiom,
    ((![A : nat, B : nat]: ((dvd_dvd_nat @ A @ B) => ((dvd_dvd_nat @ B @ A) => (A = B)))))). % gcd_nat.antisym
thf(fact_233_gcd__nat_Oirrefl, axiom,
    ((![A : nat]: (~ (((dvd_dvd_nat @ A @ A) & (~ ((A = A))))))))). % gcd_nat.irrefl
thf(fact_234_gcd__nat_Oeq__iff, axiom,
    (((^[Y2 : nat]: (^[Z : nat]: (Y2 = Z))) = (^[A2 : nat]: (^[B2 : nat]: (((dvd_dvd_nat @ A2 @ B2)) & ((dvd_dvd_nat @ B2 @ A2)))))))). % gcd_nat.eq_iff
thf(fact_235_gcd__nat_Otrans, axiom,
    ((![A : nat, B : nat, C : nat]: ((dvd_dvd_nat @ A @ B) => ((dvd_dvd_nat @ B @ C) => (dvd_dvd_nat @ A @ C)))))). % gcd_nat.trans
thf(fact_236_gcd__nat_Orefl, axiom,
    ((![A : nat]: (dvd_dvd_nat @ A @ A)))). % gcd_nat.refl
thf(fact_237_gcd__nat_Oasym, axiom,
    ((![A : nat, B : nat]: (((dvd_dvd_nat @ A @ B) & (~ ((A = B)))) => (~ (((dvd_dvd_nat @ B @ A) & (~ ((B = A)))))))))). % gcd_nat.asym
thf(fact_238_dvd__antisym, axiom,
    ((![M : nat, N : nat]: ((dvd_dvd_nat @ M @ N) => ((dvd_dvd_nat @ N @ M) => (M = N)))))). % dvd_antisym
thf(fact_239_degree__monom__eq, axiom,
    ((![A : poly_a, N : nat]: ((~ ((A = zero_zero_poly_a))) => ((degree_poly_a @ (monom_poly_a @ A @ N)) = N))))). % degree_monom_eq
thf(fact_240_degree__monom__eq, axiom,
    ((![A : nat, N : nat]: ((~ ((A = zero_zero_nat))) => ((degree_nat @ (monom_nat @ A @ N)) = N))))). % degree_monom_eq
thf(fact_241_degree__monom__eq, axiom,
    ((![A : a, N : nat]: ((~ ((A = zero_zero_a))) => ((degree_a @ (monom_a @ A @ N)) = N))))). % degree_monom_eq
thf(fact_242_degree__monom__eq, axiom,
    ((![A : poly_nat, N : nat]: ((~ ((A = zero_zero_poly_nat))) => ((degree_poly_nat @ (monom_poly_nat @ A @ N)) = N))))). % degree_monom_eq
thf(fact_243_degree__monom__eq, axiom,
    ((![A : poly_poly_a, N : nat]: ((~ ((A = zero_z2096148049poly_a))) => ((degree_poly_poly_a @ (monom_poly_poly_a @ A @ N)) = N))))). % degree_monom_eq
thf(fact_244_monom_Orep__eq, axiom,
    ((![X : poly_nat, Xa : nat]: ((coeff_poly_nat @ (monom_poly_nat @ X @ Xa)) = (^[N2 : nat]: (if_poly_nat @ (Xa = N2) @ X @ zero_zero_poly_nat)))))). % monom.rep_eq
thf(fact_245_monom_Orep__eq, axiom,
    ((![X : poly_poly_a, Xa : nat]: ((coeff_poly_poly_a @ (monom_poly_poly_a @ X @ Xa)) = (^[N2 : nat]: (if_poly_poly_a @ (Xa = N2) @ X @ zero_z2096148049poly_a)))))). % monom.rep_eq

% Helper facts (5)
thf(help_If_2_1_If_001t__Polynomial__Opoly_It__Nat__Onat_J_T, axiom,
    ((![X : poly_nat, Y : poly_nat]: ((if_poly_nat @ $false @ X @ Y) = Y)))).
thf(help_If_1_1_If_001t__Polynomial__Opoly_It__Nat__Onat_J_T, axiom,
    ((![X : poly_nat, Y : poly_nat]: ((if_poly_nat @ $true @ X @ Y) = X)))).
thf(help_If_3_1_If_001t__Polynomial__Opoly_It__Polynomial__Opoly_Itf__a_J_J_T, axiom,
    ((![P3 : $o]: ((P3 = $true) | (P3 = $false))))).
thf(help_If_2_1_If_001t__Polynomial__Opoly_It__Polynomial__Opoly_Itf__a_J_J_T, axiom,
    ((![X : poly_poly_a, Y : poly_poly_a]: ((if_poly_poly_a @ $false @ X @ Y) = Y)))).
thf(help_If_1_1_If_001t__Polynomial__Opoly_It__Polynomial__Opoly_Itf__a_J_J_T, axiom,
    ((![X : poly_poly_a, Y : poly_poly_a]: ((if_poly_poly_a @ $true @ X @ Y) = X)))).

% Conjectures (1)
thf(conj_0, conjecture,
    (((poly_a2 @ (fundam1358810038poly_a @ zero_zero_poly_a @ h) @ x) = (poly_a2 @ zero_zero_poly_a @ (plus_plus_a @ h @ x))))).
