% 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_1105__5378338_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:35:55.498

% 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 (64)
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_Oone__class_Oone_001t__Polynomial__Opoly_It__Polynomial__Opoly_Itf__a_J_J, type,
    one_one_poly_poly_a : poly_poly_a).
thf(sy_c_Groups_Oone__class_Oone_001t__Polynomial__Opoly_Itf__a_J, type,
    one_one_poly_a : poly_a).
thf(sy_c_Groups_Oone__class_Oone_001tf__a, type,
    one_one_a : a).
thf(sy_c_Groups_Otimes__class_Otimes_001t__Nat__Onat, type,
    times_times_nat : nat > nat > nat).
thf(sy_c_Groups_Otimes__class_Otimes_001t__Polynomial__Opoly_It__Nat__Onat_J, type,
    times_times_poly_nat : poly_nat > poly_nat > poly_nat).
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_Itf__a_J, type,
    times_times_poly_a : poly_a > poly_a > poly_a).
thf(sy_c_Groups_Otimes__class_Otimes_001tf__a, type,
    times_times_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_Polynomial_Ocontent_001t__Nat__Onat, type,
    content_nat : poly_nat > 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_Omap__poly_001tf__a_001t__Nat__Onat, type,
    map_poly_a_nat : (a > nat) > poly_a > poly_nat).
thf(sy_c_Polynomial_Omap__poly_001tf__a_001t__Polynomial__Opoly_Itf__a_J, type,
    map_poly_a_poly_a : (a > poly_a) > poly_a > poly_poly_a).
thf(sy_c_Polynomial_Omap__poly_001tf__a_001tf__a, type,
    map_poly_a_a : (a > a) > poly_a > poly_a).
thf(sy_c_Polynomial_OpCons_001t__Nat__Onat, type,
    pCons_nat : nat > poly_nat > poly_nat).
thf(sy_c_Polynomial_OpCons_001t__Polynomial__Opoly_It__Nat__Onat_J, type,
    pCons_poly_nat : poly_nat > poly_poly_nat > poly_poly_nat).
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_Itf__a_J, type,
    pCons_poly_a : poly_a > poly_poly_a > poly_poly_a).
thf(sy_c_Polynomial_OpCons_001tf__a, type,
    pCons_a : a > poly_a > poly_a).
thf(sy_c_Polynomial_Opcompose_001t__Nat__Onat, type,
    pcompose_nat : poly_nat > poly_nat > poly_nat).
thf(sy_c_Polynomial_Opcompose_001t__Polynomial__Opoly_It__Nat__Onat_J, type,
    pcompose_poly_nat : poly_poly_nat > poly_poly_nat > poly_poly_nat).
thf(sy_c_Polynomial_Opcompose_001t__Polynomial__Opoly_It__Polynomial__Opoly_Itf__a_J_J, type,
    pcompose_poly_poly_a : poly_poly_poly_a > poly_poly_poly_a > poly_poly_poly_a).
thf(sy_c_Polynomial_Opcompose_001t__Polynomial__Opoly_Itf__a_J, type,
    pcompose_poly_a : poly_poly_a > poly_poly_a > poly_poly_a).
thf(sy_c_Polynomial_Opcompose_001tf__a, type,
    pcompose_a : poly_a > poly_a > poly_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_Power_Opower__class_Opower_001t__Polynomial__Opoly_It__Nat__Onat_J, type,
    power_power_poly_nat : poly_nat > nat > poly_nat).
thf(sy_c_Power_Opower__class_Opower_001t__Polynomial__Opoly_It__Polynomial__Opoly_Itf__a_J_J, type,
    power_276493840poly_a : poly_poly_a > nat > poly_poly_a).
thf(sy_c_Power_Opower__class_Opower_001t__Polynomial__Opoly_Itf__a_J, type,
    power_power_poly_a : poly_a > nat > 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_c_Rings_Odvd__class_Odvd_001t__Polynomial__Opoly_It__Polynomial__Opoly_Itf__a_J_J, type,
    dvd_dvd_poly_poly_a : poly_poly_a > poly_poly_a > $o).
thf(sy_c_Rings_Odvd__class_Odvd_001t__Polynomial__Opoly_Itf__a_J, type,
    dvd_dvd_poly_a : poly_a > poly_a > $o).
thf(sy_c_Rings_Odvd__class_Odvd_001tf__a, type,
    dvd_dvd_a : a > a > $o).
thf(sy_v_p, type,
    p : poly_a).
thf(sy_v_q, type,
    q : poly_a).

% Relevant facts (247)
thf(fact_0__092_060open_062q_Advd_ApCons_A_I0_058_058_Ha_J_Aq_092_060close_062, axiom,
    ((dvd_dvd_poly_a @ q @ (pCons_a @ zero_zero_a @ q)))). % \<open>q dvd pCons (0::'a) q\<close>
thf(fact_1_pq, axiom,
    ((dvd_dvd_poly_a @ p @ q))). % pq
thf(fact_2_pCons__0__0, axiom,
    (((pCons_poly_nat @ zero_zero_poly_nat @ zero_z1059985641ly_nat) = zero_z1059985641ly_nat))). % pCons_0_0
thf(fact_3_pCons__0__0, axiom,
    (((pCons_poly_poly_a @ zero_z2096148049poly_a @ zero_z2064990175poly_a) = zero_z2064990175poly_a))). % pCons_0_0
thf(fact_4_pCons__0__0, axiom,
    (((pCons_a @ zero_zero_a @ zero_zero_poly_a) = zero_zero_poly_a))). % pCons_0_0
thf(fact_5_pCons__0__0, axiom,
    (((pCons_poly_a @ zero_zero_poly_a @ zero_z2096148049poly_a) = zero_z2096148049poly_a))). % pCons_0_0
thf(fact_6_pCons__0__0, axiom,
    (((pCons_nat @ zero_zero_nat @ zero_zero_poly_nat) = zero_zero_poly_nat))). % pCons_0_0
thf(fact_7_pCons__eq__0__iff, axiom,
    ((![A : poly_nat, P : poly_poly_nat]: (((pCons_poly_nat @ A @ P) = zero_z1059985641ly_nat) = (((A = zero_zero_poly_nat)) & ((P = zero_z1059985641ly_nat))))))). % pCons_eq_0_iff
thf(fact_8_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_9_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_10_pCons__eq__0__iff, axiom,
    ((![A : nat, P : poly_nat]: (((pCons_nat @ A @ P) = zero_zero_poly_nat) = (((A = zero_zero_nat)) & ((P = zero_zero_poly_nat))))))). % pCons_eq_0_iff
thf(fact_11_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_12_dvd__0__right, axiom,
    ((![A : poly_nat]: (dvd_dvd_poly_nat @ A @ zero_zero_poly_nat)))). % dvd_0_right
thf(fact_13_dvd__0__right, axiom,
    ((![A : poly_poly_a]: (dvd_dvd_poly_poly_a @ A @ zero_z2096148049poly_a)))). % dvd_0_right
thf(fact_14_dvd__0__right, axiom,
    ((![A : a]: (dvd_dvd_a @ A @ zero_zero_a)))). % dvd_0_right
thf(fact_15_dvd__0__right, axiom,
    ((![A : poly_a]: (dvd_dvd_poly_a @ A @ zero_zero_poly_a)))). % dvd_0_right
thf(fact_16_dvd__0__right, axiom,
    ((![A : nat]: (dvd_dvd_nat @ A @ zero_zero_nat)))). % dvd_0_right
thf(fact_17_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_18_dvd__0__left__iff, axiom,
    ((![A : poly_poly_a]: ((dvd_dvd_poly_poly_a @ zero_z2096148049poly_a @ A) = (A = zero_z2096148049poly_a))))). % dvd_0_left_iff
thf(fact_19_dvd__0__left__iff, axiom,
    ((![A : a]: ((dvd_dvd_a @ zero_zero_a @ A) = (A = zero_zero_a))))). % dvd_0_left_iff
thf(fact_20_dvd__0__left__iff, axiom,
    ((![A : poly_a]: ((dvd_dvd_poly_a @ zero_zero_poly_a @ A) = (A = zero_zero_poly_a))))). % dvd_0_left_iff
thf(fact_21_dvd__0__left__iff, axiom,
    ((![A : nat]: ((dvd_dvd_nat @ zero_zero_nat @ A) = (A = zero_zero_nat))))). % dvd_0_left_iff
thf(fact_22_pCons__eq__iff, axiom,
    ((![A : nat, P : poly_nat, B : nat, Q : poly_nat]: (((pCons_nat @ A @ P) = (pCons_nat @ B @ Q)) = (((A = B)) & ((P = Q))))))). % pCons_eq_iff
thf(fact_23_pCons__eq__iff, axiom,
    ((![A : poly_a, P : poly_poly_a, B : poly_a, Q : poly_poly_a]: (((pCons_poly_a @ A @ P) = (pCons_poly_a @ B @ Q)) = (((A = B)) & ((P = Q))))))). % pCons_eq_iff
thf(fact_24_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_25_pCons__induct, axiom,
    ((![P2 : poly_poly_nat > $o, P : poly_poly_nat]: ((P2 @ zero_z1059985641ly_nat) => ((![A2 : poly_nat, P3 : poly_poly_nat]: (((~ ((A2 = zero_zero_poly_nat))) | (~ ((P3 = zero_z1059985641ly_nat)))) => ((P2 @ P3) => (P2 @ (pCons_poly_nat @ A2 @ P3))))) => (P2 @ P)))))). % pCons_induct
thf(fact_26_pCons__induct, axiom,
    ((![P2 : poly_poly_poly_a > $o, P : poly_poly_poly_a]: ((P2 @ zero_z2064990175poly_a) => ((![A2 : poly_poly_a, P3 : poly_poly_poly_a]: (((~ ((A2 = zero_z2096148049poly_a))) | (~ ((P3 = zero_z2064990175poly_a)))) => ((P2 @ P3) => (P2 @ (pCons_poly_poly_a @ A2 @ P3))))) => (P2 @ P)))))). % pCons_induct
thf(fact_27_pCons__induct, axiom,
    ((![P2 : poly_poly_a > $o, P : poly_poly_a]: ((P2 @ zero_z2096148049poly_a) => ((![A2 : poly_a, P3 : poly_poly_a]: (((~ ((A2 = zero_zero_poly_a))) | (~ ((P3 = zero_z2096148049poly_a)))) => ((P2 @ P3) => (P2 @ (pCons_poly_a @ A2 @ P3))))) => (P2 @ P)))))). % pCons_induct
thf(fact_28_pCons__induct, axiom,
    ((![P2 : poly_nat > $o, P : poly_nat]: ((P2 @ zero_zero_poly_nat) => ((![A2 : nat, P3 : poly_nat]: (((~ ((A2 = zero_zero_nat))) | (~ ((P3 = zero_zero_poly_nat)))) => ((P2 @ P3) => (P2 @ (pCons_nat @ A2 @ P3))))) => (P2 @ P)))))). % pCons_induct
thf(fact_29_pCons__induct, axiom,
    ((![P2 : poly_a > $o, P : poly_a]: ((P2 @ zero_zero_poly_a) => ((![A2 : a, P3 : poly_a]: (((~ ((A2 = zero_zero_a))) | (~ ((P3 = zero_zero_poly_a)))) => ((P2 @ P3) => (P2 @ (pCons_a @ A2 @ P3))))) => (P2 @ P)))))). % pCons_induct
thf(fact_30_dvd__0__left, axiom,
    ((![A : a]: ((dvd_dvd_a @ zero_zero_a @ A) => (A = zero_zero_a))))). % dvd_0_left
thf(fact_31_dvd__0__left, axiom,
    ((![A : poly_a]: ((dvd_dvd_poly_a @ zero_zero_poly_a @ A) => (A = zero_zero_poly_a))))). % dvd_0_left
thf(fact_32_dvd__0__left, axiom,
    ((![A : nat]: ((dvd_dvd_nat @ zero_zero_nat @ A) => (A = zero_zero_nat))))). % dvd_0_left
thf(fact_33_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_34_dvd__0__left, axiom,
    ((![A : poly_poly_a]: ((dvd_dvd_poly_poly_a @ zero_z2096148049poly_a @ A) => (A = zero_z2096148049poly_a))))). % dvd_0_left
thf(fact_35_pCons__cases, axiom,
    ((![P : poly_a]: (~ ((![A2 : a, Q2 : poly_a]: (~ ((P = (pCons_a @ A2 @ Q2)))))))))). % pCons_cases
thf(fact_36_pCons__cases, axiom,
    ((![P : poly_nat]: (~ ((![A2 : nat, Q2 : poly_nat]: (~ ((P = (pCons_nat @ A2 @ Q2)))))))))). % pCons_cases
thf(fact_37_pCons__cases, axiom,
    ((![P : poly_poly_a]: (~ ((![A2 : poly_a, Q2 : poly_poly_a]: (~ ((P = (pCons_poly_a @ A2 @ Q2)))))))))). % pCons_cases
thf(fact_38_pderiv_Ocases, axiom,
    ((![X : poly_nat]: (~ ((![A2 : nat, P3 : poly_nat]: (~ ((X = (pCons_nat @ A2 @ P3)))))))))). % pderiv.cases
thf(fact_39_dvd__refl, axiom,
    ((![A : poly_a]: (dvd_dvd_poly_a @ A @ A)))). % dvd_refl
thf(fact_40_dvd__refl, axiom,
    ((![A : nat]: (dvd_dvd_nat @ A @ A)))). % dvd_refl
thf(fact_41_dvd__refl, axiom,
    ((![A : a]: (dvd_dvd_a @ A @ A)))). % dvd_refl
thf(fact_42_const__poly__dvd__const__poly__iff, axiom,
    ((![A : nat, B : nat]: ((dvd_dvd_poly_nat @ (pCons_nat @ A @ zero_zero_poly_nat) @ (pCons_nat @ B @ zero_zero_poly_nat)) = (dvd_dvd_nat @ A @ B))))). % const_poly_dvd_const_poly_iff
thf(fact_43_pderiv_Oinduct, axiom,
    ((![P2 : poly_nat > $o, A0 : poly_nat]: ((![A2 : nat, P3 : poly_nat]: (((~ ((P3 = zero_zero_poly_nat))) => (P2 @ P3)) => (P2 @ (pCons_nat @ A2 @ P3)))) => (P2 @ A0))))). % pderiv.induct
thf(fact_44_poly__induct2, axiom,
    ((![P2 : poly_a > poly_a > $o, P : poly_a, Q : poly_a]: ((P2 @ zero_zero_poly_a @ zero_zero_poly_a) => ((![A2 : a, P3 : poly_a, B2 : a, Q2 : poly_a]: ((P2 @ P3 @ Q2) => (P2 @ (pCons_a @ A2 @ P3) @ (pCons_a @ B2 @ Q2)))) => (P2 @ P @ Q)))))). % poly_induct2
thf(fact_45_poly__induct2, axiom,
    ((![P2 : poly_a > poly_nat > $o, P : poly_a, Q : poly_nat]: ((P2 @ zero_zero_poly_a @ zero_zero_poly_nat) => ((![A2 : a, P3 : poly_a, B2 : nat, Q2 : poly_nat]: ((P2 @ P3 @ Q2) => (P2 @ (pCons_a @ A2 @ P3) @ (pCons_nat @ B2 @ Q2)))) => (P2 @ P @ Q)))))). % poly_induct2
thf(fact_46_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) => ((![A2 : a, P3 : poly_a, B2 : poly_a, Q2 : poly_poly_a]: ((P2 @ P3 @ Q2) => (P2 @ (pCons_a @ A2 @ P3) @ (pCons_poly_a @ B2 @ Q2)))) => (P2 @ P @ Q)))))). % poly_induct2
thf(fact_47_poly__induct2, axiom,
    ((![P2 : poly_nat > poly_a > $o, P : poly_nat, Q : poly_a]: ((P2 @ zero_zero_poly_nat @ zero_zero_poly_a) => ((![A2 : nat, P3 : poly_nat, B2 : a, Q2 : poly_a]: ((P2 @ P3 @ Q2) => (P2 @ (pCons_nat @ A2 @ P3) @ (pCons_a @ B2 @ Q2)))) => (P2 @ P @ Q)))))). % poly_induct2
thf(fact_48_poly__induct2, axiom,
    ((![P2 : poly_nat > poly_nat > $o, P : poly_nat, Q : poly_nat]: ((P2 @ zero_zero_poly_nat @ zero_zero_poly_nat) => ((![A2 : nat, P3 : poly_nat, B2 : nat, Q2 : poly_nat]: ((P2 @ P3 @ Q2) => (P2 @ (pCons_nat @ A2 @ P3) @ (pCons_nat @ B2 @ Q2)))) => (P2 @ P @ Q)))))). % poly_induct2
thf(fact_49_poly__induct2, axiom,
    ((![P2 : poly_nat > poly_poly_a > $o, P : poly_nat, Q : poly_poly_a]: ((P2 @ zero_zero_poly_nat @ zero_z2096148049poly_a) => ((![A2 : nat, P3 : poly_nat, B2 : poly_a, Q2 : poly_poly_a]: ((P2 @ P3 @ Q2) => (P2 @ (pCons_nat @ A2 @ P3) @ (pCons_poly_a @ B2 @ Q2)))) => (P2 @ P @ Q)))))). % poly_induct2
thf(fact_50_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) => ((![A2 : poly_a, P3 : poly_poly_a, B2 : a, Q2 : poly_a]: ((P2 @ P3 @ Q2) => (P2 @ (pCons_poly_a @ A2 @ P3) @ (pCons_a @ B2 @ Q2)))) => (P2 @ P @ Q)))))). % poly_induct2
thf(fact_51_poly__induct2, axiom,
    ((![P2 : poly_poly_a > poly_nat > $o, P : poly_poly_a, Q : poly_nat]: ((P2 @ zero_z2096148049poly_a @ zero_zero_poly_nat) => ((![A2 : poly_a, P3 : poly_poly_a, B2 : nat, Q2 : poly_nat]: ((P2 @ P3 @ Q2) => (P2 @ (pCons_poly_a @ A2 @ P3) @ (pCons_nat @ B2 @ Q2)))) => (P2 @ P @ Q)))))). % poly_induct2
thf(fact_52_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) => ((![A2 : poly_a, P3 : poly_poly_a, B2 : poly_a, Q2 : poly_poly_a]: ((P2 @ P3 @ Q2) => (P2 @ (pCons_poly_a @ A2 @ P3) @ (pCons_poly_a @ B2 @ Q2)))) => (P2 @ P @ Q)))))). % poly_induct2
thf(fact_53_zero__reorient, axiom,
    ((![X : a]: ((zero_zero_a = X) = (X = zero_zero_a))))). % zero_reorient
thf(fact_54_zero__reorient, axiom,
    ((![X : poly_a]: ((zero_zero_poly_a = X) = (X = zero_zero_poly_a))))). % zero_reorient
thf(fact_55_zero__reorient, axiom,
    ((![X : nat]: ((zero_zero_nat = X) = (X = zero_zero_nat))))). % zero_reorient
thf(fact_56_zero__reorient, axiom,
    ((![X : poly_nat]: ((zero_zero_poly_nat = X) = (X = zero_zero_poly_nat))))). % zero_reorient
thf(fact_57_zero__reorient, axiom,
    ((![X : poly_poly_a]: ((zero_z2096148049poly_a = X) = (X = zero_z2096148049poly_a))))). % zero_reorient
thf(fact_58_dvd__trans, axiom,
    ((![A : poly_a, B : poly_a, C : poly_a]: ((dvd_dvd_poly_a @ A @ B) => ((dvd_dvd_poly_a @ B @ C) => (dvd_dvd_poly_a @ A @ C)))))). % dvd_trans
thf(fact_59_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_60_dvd__trans, axiom,
    ((![A : a, B : a, C : a]: ((dvd_dvd_a @ A @ B) => ((dvd_dvd_a @ B @ C) => (dvd_dvd_a @ A @ C)))))). % dvd_trans
thf(fact_61_const__poly__dvd__iff__dvd__content, axiom,
    ((![C : nat, P : poly_nat]: ((dvd_dvd_poly_nat @ (pCons_nat @ C @ zero_zero_poly_nat) @ P) = (dvd_dvd_nat @ C @ (content_nat @ P)))))). % const_poly_dvd_iff_dvd_content
thf(fact_62_is__zero__null, axiom,
    ((is_zero_a = (^[P4 : poly_a]: (P4 = zero_zero_poly_a))))). % is_zero_null
thf(fact_63_is__zero__null, axiom,
    ((is_zero_nat = (^[P4 : poly_nat]: (P4 = zero_zero_poly_nat))))). % is_zero_null
thf(fact_64_is__zero__null, axiom,
    ((is_zero_poly_a = (^[P4 : poly_poly_a]: (P4 = zero_z2096148049poly_a))))). % is_zero_null
thf(fact_65_poly__cutoff__0, axiom,
    ((![N : nat]: ((poly_cutoff_a @ N @ zero_zero_poly_a) = zero_zero_poly_a)))). % poly_cutoff_0
thf(fact_66_poly__cutoff__0, axiom,
    ((![N : nat]: ((poly_cutoff_nat @ N @ zero_zero_poly_nat) = zero_zero_poly_nat)))). % poly_cutoff_0
thf(fact_67_poly__cutoff__0, axiom,
    ((![N : nat]: ((poly_cutoff_poly_a @ N @ zero_z2096148049poly_a) = zero_z2096148049poly_a)))). % poly_cutoff_0
thf(fact_68__092_060open_062pCons_A_I0_058_058_Ha_J_Aq_A_061_Aq_A_K_A_091_0580_058_058_Ha_M_A1_058_058_Ha_058_093_092_060close_062, axiom,
    (((pCons_a @ zero_zero_a @ q) = (times_times_poly_a @ q @ (pCons_a @ zero_zero_a @ (pCons_a @ one_one_a @ zero_zero_poly_a)))))). % \<open>pCons (0::'a) q = q * [:0::'a, 1::'a:]\<close>
thf(fact_69_offset__poly__single, axiom,
    ((![A : a, H : a]: ((fundam1358810038poly_a @ (pCons_a @ A @ zero_zero_poly_a) @ H) = (pCons_a @ A @ zero_zero_poly_a))))). % offset_poly_single
thf(fact_70_offset__poly__single, axiom,
    ((![A : nat, H : nat]: ((fundam170929432ly_nat @ (pCons_nat @ A @ zero_zero_poly_nat) @ H) = (pCons_nat @ A @ zero_zero_poly_nat))))). % offset_poly_single
thf(fact_71_offset__poly__single, axiom,
    ((![A : poly_a, H : poly_a]: ((fundam1343031620poly_a @ (pCons_poly_a @ A @ zero_z2096148049poly_a) @ H) = (pCons_poly_a @ A @ zero_z2096148049poly_a))))). % offset_poly_single
thf(fact_72_const__poly__dvd__iff, axiom,
    ((![C : nat, P : poly_nat]: ((dvd_dvd_poly_nat @ (pCons_nat @ C @ zero_zero_poly_nat) @ P) = (![N2 : nat]: (dvd_dvd_nat @ C @ (coeff_nat @ P @ N2))))))). % const_poly_dvd_iff
thf(fact_73_content__dvd, axiom,
    ((![P : poly_nat]: (dvd_dvd_poly_nat @ (pCons_nat @ (content_nat @ P) @ zero_zero_poly_nat) @ P)))). % content_dvd
thf(fact_74_poly__shift__0, axiom,
    ((![N : nat]: ((poly_shift_a @ N @ zero_zero_poly_a) = zero_zero_poly_a)))). % poly_shift_0
thf(fact_75_poly__shift__0, axiom,
    ((![N : nat]: ((poly_shift_nat @ N @ zero_zero_poly_nat) = zero_zero_poly_nat)))). % poly_shift_0
thf(fact_76_poly__shift__0, axiom,
    ((![N : nat]: ((poly_shift_poly_a @ N @ zero_z2096148049poly_a) = zero_z2096148049poly_a)))). % poly_shift_0
thf(fact_77_mult__zero__left, axiom,
    ((![A : a]: ((times_times_a @ zero_zero_a @ A) = zero_zero_a)))). % mult_zero_left
thf(fact_78_mult__zero__left, axiom,
    ((![A : nat]: ((times_times_nat @ zero_zero_nat @ A) = zero_zero_nat)))). % mult_zero_left
thf(fact_79_mult__zero__left, axiom,
    ((![A : poly_nat]: ((times_times_poly_nat @ zero_zero_poly_nat @ A) = zero_zero_poly_nat)))). % mult_zero_left
thf(fact_80_mult__zero__left, axiom,
    ((![A : poly_poly_a]: ((times_545135445poly_a @ zero_z2096148049poly_a @ A) = zero_z2096148049poly_a)))). % mult_zero_left
thf(fact_81_mult__zero__left, axiom,
    ((![A : poly_a]: ((times_times_poly_a @ zero_zero_poly_a @ A) = zero_zero_poly_a)))). % mult_zero_left
thf(fact_82_mult__zero__right, axiom,
    ((![A : a]: ((times_times_a @ A @ zero_zero_a) = zero_zero_a)))). % mult_zero_right
thf(fact_83_mult__zero__right, axiom,
    ((![A : nat]: ((times_times_nat @ A @ zero_zero_nat) = zero_zero_nat)))). % mult_zero_right
thf(fact_84_mult__zero__right, axiom,
    ((![A : poly_nat]: ((times_times_poly_nat @ A @ zero_zero_poly_nat) = zero_zero_poly_nat)))). % mult_zero_right
thf(fact_85_mult__zero__right, axiom,
    ((![A : poly_poly_a]: ((times_545135445poly_a @ A @ zero_z2096148049poly_a) = zero_z2096148049poly_a)))). % mult_zero_right
thf(fact_86_mult__zero__right, axiom,
    ((![A : poly_a]: ((times_times_poly_a @ A @ zero_zero_poly_a) = zero_zero_poly_a)))). % mult_zero_right
thf(fact_87_mult__eq__0__iff, axiom,
    ((![A : nat, B : nat]: (((times_times_nat @ A @ B) = zero_zero_nat) = (((A = zero_zero_nat)) | ((B = zero_zero_nat))))))). % mult_eq_0_iff
thf(fact_88_mult__eq__0__iff, axiom,
    ((![A : poly_nat, B : poly_nat]: (((times_times_poly_nat @ A @ B) = zero_zero_poly_nat) = (((A = zero_zero_poly_nat)) | ((B = zero_zero_poly_nat))))))). % mult_eq_0_iff
thf(fact_89_mult__cancel__left, axiom,
    ((![C : nat, A : nat, B : nat]: (((times_times_nat @ C @ A) = (times_times_nat @ C @ B)) = (((C = zero_zero_nat)) | ((A = B))))))). % mult_cancel_left
thf(fact_90_mult__cancel__right, axiom,
    ((![A : nat, C : nat, B : nat]: (((times_times_nat @ A @ C) = (times_times_nat @ B @ C)) = (((C = zero_zero_nat)) | ((A = B))))))). % mult_cancel_right
thf(fact_91_mult_Oleft__neutral, axiom,
    ((![A : a]: ((times_times_a @ one_one_a @ A) = A)))). % mult.left_neutral
thf(fact_92_mult_Oleft__neutral, axiom,
    ((![A : poly_a]: ((times_times_poly_a @ one_one_poly_a @ A) = A)))). % mult.left_neutral
thf(fact_93_mult_Oright__neutral, axiom,
    ((![A : a]: ((times_times_a @ A @ one_one_a) = A)))). % mult.right_neutral
thf(fact_94_mult_Oright__neutral, axiom,
    ((![A : poly_a]: ((times_times_poly_a @ A @ one_one_poly_a) = A)))). % mult.right_neutral
thf(fact_95_coeff__pCons__0, axiom,
    ((![A : a, P : poly_a]: ((coeff_a @ (pCons_a @ A @ P) @ zero_zero_nat) = A)))). % coeff_pCons_0
thf(fact_96_coeff__pCons__0, axiom,
    ((![A : nat, P : poly_nat]: ((coeff_nat @ (pCons_nat @ A @ P) @ zero_zero_nat) = A)))). % coeff_pCons_0
thf(fact_97_coeff__pCons__0, axiom,
    ((![A : poly_a, P : poly_poly_a]: ((coeff_poly_a @ (pCons_poly_a @ A @ P) @ zero_zero_nat) = A)))). % coeff_pCons_0
thf(fact_98_dvd__times__left__cancel__iff, axiom,
    ((![A : nat, B : nat, C : nat]: ((~ ((A = zero_zero_nat))) => ((dvd_dvd_nat @ (times_times_nat @ A @ B) @ (times_times_nat @ A @ C)) = (dvd_dvd_nat @ B @ C)))))). % dvd_times_left_cancel_iff
thf(fact_99_dvd__times__right__cancel__iff, axiom,
    ((![A : nat, B : nat, C : nat]: ((~ ((A = zero_zero_nat))) => ((dvd_dvd_nat @ (times_times_nat @ B @ A) @ (times_times_nat @ C @ A)) = (dvd_dvd_nat @ B @ C)))))). % dvd_times_right_cancel_iff
thf(fact_100_unit__prod, axiom,
    ((![A : nat, B : nat]: ((dvd_dvd_nat @ A @ one_one_nat) => ((dvd_dvd_nat @ B @ one_one_nat) => (dvd_dvd_nat @ (times_times_nat @ A @ B) @ one_one_nat)))))). % unit_prod
thf(fact_101_coeff__0, axiom,
    ((![N : nat]: ((coeff_poly_nat @ zero_z1059985641ly_nat @ N) = zero_zero_poly_nat)))). % coeff_0
thf(fact_102_coeff__0, axiom,
    ((![N : nat]: ((coeff_poly_poly_a @ zero_z2064990175poly_a @ N) = zero_z2096148049poly_a)))). % coeff_0
thf(fact_103_coeff__0, axiom,
    ((![N : nat]: ((coeff_a @ zero_zero_poly_a @ N) = zero_zero_a)))). % coeff_0
thf(fact_104_coeff__0, axiom,
    ((![N : nat]: ((coeff_nat @ zero_zero_poly_nat @ N) = zero_zero_nat)))). % coeff_0
thf(fact_105_coeff__0, axiom,
    ((![N : nat]: ((coeff_poly_a @ zero_z2096148049poly_a @ N) = zero_zero_poly_a)))). % coeff_0
thf(fact_106_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_107_content__0, axiom,
    (((content_nat @ zero_zero_poly_nat) = zero_zero_nat))). % content_0
thf(fact_108_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_109_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_110_poly__cutoff__1, axiom,
    ((![N : nat]: (((N = zero_zero_nat) => ((poly_cutoff_a @ N @ one_one_poly_a) = zero_zero_poly_a)) & ((~ ((N = zero_zero_nat))) => ((poly_cutoff_a @ N @ one_one_poly_a) = one_one_poly_a)))))). % poly_cutoff_1
thf(fact_111_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_112_poly__cutoff__1, axiom,
    ((![N : nat]: (((N = zero_zero_nat) => ((poly_cutoff_poly_a @ N @ one_one_poly_poly_a) = zero_z2096148049poly_a)) & ((~ ((N = zero_zero_nat))) => ((poly_cutoff_poly_a @ N @ one_one_poly_poly_a) = one_one_poly_poly_a)))))). % poly_cutoff_1
thf(fact_113_one__poly__eq__simps_I1_J, axiom,
    ((one_one_poly_a = (pCons_a @ one_one_a @ zero_zero_poly_a)))). % one_poly_eq_simps(1)
thf(fact_114_one__poly__eq__simps_I1_J, axiom,
    ((one_one_poly_nat = (pCons_nat @ one_one_nat @ zero_zero_poly_nat)))). % one_poly_eq_simps(1)
thf(fact_115_one__poly__eq__simps_I1_J, axiom,
    ((one_one_poly_poly_a = (pCons_poly_a @ one_one_poly_a @ zero_z2096148049poly_a)))). % one_poly_eq_simps(1)
thf(fact_116_one__poly__eq__simps_I2_J, axiom,
    (((pCons_a @ one_one_a @ zero_zero_poly_a) = one_one_poly_a))). % one_poly_eq_simps(2)
thf(fact_117_one__poly__eq__simps_I2_J, axiom,
    (((pCons_nat @ one_one_nat @ zero_zero_poly_nat) = one_one_poly_nat))). % one_poly_eq_simps(2)
thf(fact_118_one__poly__eq__simps_I2_J, axiom,
    (((pCons_poly_a @ one_one_poly_a @ zero_z2096148049poly_a) = one_one_poly_poly_a))). % one_poly_eq_simps(2)
thf(fact_119_ab__semigroup__mult__class_Omult__ac_I1_J, axiom,
    ((![A : poly_a, B : poly_a, C : poly_a]: ((times_times_poly_a @ (times_times_poly_a @ A @ B) @ C) = (times_times_poly_a @ A @ (times_times_poly_a @ B @ C)))))). % ab_semigroup_mult_class.mult_ac(1)
thf(fact_120_one__reorient, axiom,
    ((![X : a]: ((one_one_a = X) = (X = one_one_a))))). % one_reorient
thf(fact_121_content__dvd__coeff, axiom,
    ((![P : poly_nat, N : nat]: (dvd_dvd_nat @ (content_nat @ P) @ (coeff_nat @ P @ N))))). % content_dvd_coeff
thf(fact_122_comm__monoid__mult__class_Omult__1, axiom,
    ((![A : a]: ((times_times_a @ one_one_a @ A) = A)))). % comm_monoid_mult_class.mult_1
thf(fact_123_comm__monoid__mult__class_Omult__1, axiom,
    ((![A : poly_a]: ((times_times_poly_a @ one_one_poly_a @ A) = A)))). % comm_monoid_mult_class.mult_1
thf(fact_124_mult_Oassoc, axiom,
    ((![A : poly_a, B : poly_a, C : poly_a]: ((times_times_poly_a @ (times_times_poly_a @ A @ B) @ C) = (times_times_poly_a @ A @ (times_times_poly_a @ B @ C)))))). % mult.assoc
thf(fact_125_mult_Ocommute, axiom,
    ((times_times_poly_a = (^[A3 : poly_a]: (^[B3 : poly_a]: (times_times_poly_a @ B3 @ A3)))))). % mult.commute
thf(fact_126_is__unit__mult__iff, axiom,
    ((![A : nat, B : nat]: ((dvd_dvd_nat @ (times_times_nat @ A @ B) @ one_one_nat) = (((dvd_dvd_nat @ A @ one_one_nat)) & ((dvd_dvd_nat @ B @ one_one_nat))))))). % is_unit_mult_iff
thf(fact_127_mult_Ocomm__neutral, axiom,
    ((![A : a]: ((times_times_a @ A @ one_one_a) = A)))). % mult.comm_neutral
thf(fact_128_mult_Ocomm__neutral, axiom,
    ((![A : poly_a]: ((times_times_poly_a @ A @ one_one_poly_a) = A)))). % mult.comm_neutral
thf(fact_129_dvd__mult__unit__iff, axiom,
    ((![B : nat, A : nat, C : nat]: ((dvd_dvd_nat @ B @ one_one_nat) => ((dvd_dvd_nat @ A @ (times_times_nat @ C @ B)) = (dvd_dvd_nat @ A @ C)))))). % dvd_mult_unit_iff
thf(fact_130_mult__unit__dvd__iff, axiom,
    ((![B : nat, A : nat, C : nat]: ((dvd_dvd_nat @ B @ one_one_nat) => ((dvd_dvd_nat @ (times_times_nat @ A @ B) @ C) = (dvd_dvd_nat @ A @ C)))))). % mult_unit_dvd_iff
thf(fact_131_mult_Oleft__commute, axiom,
    ((![B : poly_a, A : poly_a, C : poly_a]: ((times_times_poly_a @ B @ (times_times_poly_a @ A @ C)) = (times_times_poly_a @ A @ (times_times_poly_a @ B @ C)))))). % mult.left_commute
thf(fact_132_dvd__mult__unit__iff_H, axiom,
    ((![B : nat, A : nat, C : nat]: ((dvd_dvd_nat @ B @ one_one_nat) => ((dvd_dvd_nat @ A @ (times_times_nat @ B @ C)) = (dvd_dvd_nat @ A @ C)))))). % dvd_mult_unit_iff'
thf(fact_133_mult__unit__dvd__iff_H, axiom,
    ((![A : nat, B : nat, C : nat]: ((dvd_dvd_nat @ A @ one_one_nat) => ((dvd_dvd_nat @ (times_times_nat @ A @ B) @ C) = (dvd_dvd_nat @ B @ C)))))). % mult_unit_dvd_iff'
thf(fact_134_unit__mult__left__cancel, axiom,
    ((![A : nat, B : nat, C : nat]: ((dvd_dvd_nat @ A @ one_one_nat) => (((times_times_nat @ A @ B) = (times_times_nat @ A @ C)) = (B = C)))))). % unit_mult_left_cancel
thf(fact_135_unit__mult__right__cancel, axiom,
    ((![A : nat, B : nat, C : nat]: ((dvd_dvd_nat @ A @ one_one_nat) => (((times_times_nat @ B @ A) = (times_times_nat @ C @ A)) = (B = C)))))). % unit_mult_right_cancel
thf(fact_136_poly__shift__1, axiom,
    ((![N : nat]: (((N = zero_zero_nat) => ((poly_shift_a @ N @ one_one_poly_a) = one_one_poly_a)) & ((~ ((N = zero_zero_nat))) => ((poly_shift_a @ N @ one_one_poly_a) = zero_zero_poly_a)))))). % poly_shift_1
thf(fact_137_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_138_poly__shift__1, axiom,
    ((![N : nat]: (((N = zero_zero_nat) => ((poly_shift_poly_a @ N @ one_one_poly_poly_a) = one_one_poly_poly_a)) & ((~ ((N = zero_zero_nat))) => ((poly_shift_poly_a @ N @ one_one_poly_poly_a) = zero_z2096148049poly_a)))))). % poly_shift_1
thf(fact_139_unit__dvdE, axiom,
    ((![A : nat, B : nat]: ((dvd_dvd_nat @ A @ one_one_nat) => (~ (((~ ((A = zero_zero_nat))) => (![C2 : nat]: (~ ((B = (times_times_nat @ A @ C2)))))))))))). % unit_dvdE
thf(fact_140_pCons__one, axiom,
    (((pCons_a @ one_one_a @ zero_zero_poly_a) = one_one_poly_a))). % pCons_one
thf(fact_141_pCons__one, axiom,
    (((pCons_nat @ one_one_nat @ zero_zero_poly_nat) = one_one_poly_nat))). % pCons_one
thf(fact_142_pCons__one, axiom,
    (((pCons_poly_a @ one_one_poly_a @ zero_z2096148049poly_a) = one_one_poly_poly_a))). % pCons_one
thf(fact_143_mult__not__zero, axiom,
    ((![A : a, B : a]: ((~ (((times_times_a @ A @ B) = zero_zero_a))) => ((~ ((A = zero_zero_a))) & (~ ((B = zero_zero_a)))))))). % mult_not_zero
thf(fact_144_mult__not__zero, axiom,
    ((![A : nat, B : nat]: ((~ (((times_times_nat @ A @ B) = zero_zero_nat))) => ((~ ((A = zero_zero_nat))) & (~ ((B = zero_zero_nat)))))))). % mult_not_zero
thf(fact_145_mult__not__zero, axiom,
    ((![A : poly_nat, B : poly_nat]: ((~ (((times_times_poly_nat @ A @ B) = zero_zero_poly_nat))) => ((~ ((A = zero_zero_poly_nat))) & (~ ((B = zero_zero_poly_nat)))))))). % mult_not_zero
thf(fact_146_mult__not__zero, axiom,
    ((![A : poly_poly_a, B : poly_poly_a]: ((~ (((times_545135445poly_a @ A @ B) = zero_z2096148049poly_a))) => ((~ ((A = zero_z2096148049poly_a))) & (~ ((B = zero_z2096148049poly_a)))))))). % mult_not_zero
thf(fact_147_mult__not__zero, axiom,
    ((![A : poly_a, B : poly_a]: ((~ (((times_times_poly_a @ A @ B) = zero_zero_poly_a))) => ((~ ((A = zero_zero_poly_a))) & (~ ((B = zero_zero_poly_a)))))))). % mult_not_zero
thf(fact_148_divisors__zero, axiom,
    ((![A : nat, B : nat]: (((times_times_nat @ A @ B) = zero_zero_nat) => ((A = zero_zero_nat) | (B = zero_zero_nat)))))). % divisors_zero
thf(fact_149_divisors__zero, axiom,
    ((![A : poly_nat, B : poly_nat]: (((times_times_poly_nat @ A @ B) = zero_zero_poly_nat) => ((A = zero_zero_poly_nat) | (B = zero_zero_poly_nat)))))). % divisors_zero
thf(fact_150_no__zero__divisors, axiom,
    ((![A : nat, B : nat]: ((~ ((A = zero_zero_nat))) => ((~ ((B = zero_zero_nat))) => (~ (((times_times_nat @ A @ B) = zero_zero_nat)))))))). % no_zero_divisors
thf(fact_151_no__zero__divisors, axiom,
    ((![A : poly_nat, B : poly_nat]: ((~ ((A = zero_zero_poly_nat))) => ((~ ((B = zero_zero_poly_nat))) => (~ (((times_times_poly_nat @ A @ B) = zero_zero_poly_nat)))))))). % no_zero_divisors
thf(fact_152_mult__left__cancel, axiom,
    ((![C : nat, A : nat, B : nat]: ((~ ((C = zero_zero_nat))) => (((times_times_nat @ C @ A) = (times_times_nat @ C @ B)) = (A = B)))))). % mult_left_cancel
thf(fact_153_mult__right__cancel, axiom,
    ((![C : nat, A : nat, B : nat]: ((~ ((C = zero_zero_nat))) => (((times_times_nat @ A @ C) = (times_times_nat @ B @ C)) = (A = B)))))). % mult_right_cancel
thf(fact_154_dvdE, axiom,
    ((![B : nat, A : nat]: ((dvd_dvd_nat @ B @ A) => (~ ((![K : nat]: (~ ((A = (times_times_nat @ B @ K))))))))))). % dvdE
thf(fact_155_dvdE, axiom,
    ((![B : a, A : a]: ((dvd_dvd_a @ B @ A) => (~ ((![K : a]: (~ ((A = (times_times_a @ B @ K))))))))))). % dvdE
thf(fact_156_dvdE, axiom,
    ((![B : poly_a, A : poly_a]: ((dvd_dvd_poly_a @ B @ A) => (~ ((![K : poly_a]: (~ ((A = (times_times_poly_a @ B @ K))))))))))). % dvdE
thf(fact_157_dvdI, axiom,
    ((![A : nat, B : nat, K2 : nat]: ((A = (times_times_nat @ B @ K2)) => (dvd_dvd_nat @ B @ A))))). % dvdI
thf(fact_158_dvdI, axiom,
    ((![A : a, B : a, K2 : a]: ((A = (times_times_a @ B @ K2)) => (dvd_dvd_a @ B @ A))))). % dvdI
thf(fact_159_dvdI, axiom,
    ((![A : poly_a, B : poly_a, K2 : poly_a]: ((A = (times_times_poly_a @ B @ K2)) => (dvd_dvd_poly_a @ B @ A))))). % dvdI
thf(fact_160_dvd__def, axiom,
    ((dvd_dvd_nat = (^[B3 : nat]: (^[A3 : nat]: (?[K3 : nat]: (A3 = (times_times_nat @ B3 @ K3)))))))). % dvd_def
thf(fact_161_dvd__def, axiom,
    ((dvd_dvd_a = (^[B3 : a]: (^[A3 : a]: (?[K3 : a]: (A3 = (times_times_a @ B3 @ K3)))))))). % dvd_def
thf(fact_162_dvd__def, axiom,
    ((dvd_dvd_poly_a = (^[B3 : poly_a]: (^[A3 : poly_a]: (?[K3 : poly_a]: (A3 = (times_times_poly_a @ B3 @ K3)))))))). % dvd_def
thf(fact_163_dvd__mult, axiom,
    ((![A : nat, C : nat, B : nat]: ((dvd_dvd_nat @ A @ C) => (dvd_dvd_nat @ A @ (times_times_nat @ B @ C)))))). % dvd_mult
thf(fact_164_dvd__mult, axiom,
    ((![A : a, C : a, B : a]: ((dvd_dvd_a @ A @ C) => (dvd_dvd_a @ A @ (times_times_a @ B @ C)))))). % dvd_mult
thf(fact_165_dvd__mult, axiom,
    ((![A : poly_a, C : poly_a, B : poly_a]: ((dvd_dvd_poly_a @ A @ C) => (dvd_dvd_poly_a @ A @ (times_times_poly_a @ B @ C)))))). % dvd_mult
thf(fact_166_dvd__mult2, axiom,
    ((![A : nat, B : nat, C : nat]: ((dvd_dvd_nat @ A @ B) => (dvd_dvd_nat @ A @ (times_times_nat @ B @ C)))))). % dvd_mult2
thf(fact_167_dvd__mult2, axiom,
    ((![A : a, B : a, C : a]: ((dvd_dvd_a @ A @ B) => (dvd_dvd_a @ A @ (times_times_a @ B @ C)))))). % dvd_mult2
thf(fact_168_dvd__mult2, axiom,
    ((![A : poly_a, B : poly_a, C : poly_a]: ((dvd_dvd_poly_a @ A @ B) => (dvd_dvd_poly_a @ A @ (times_times_poly_a @ B @ C)))))). % dvd_mult2
thf(fact_169_dvd__mult__left, axiom,
    ((![A : nat, B : nat, C : nat]: ((dvd_dvd_nat @ (times_times_nat @ A @ B) @ C) => (dvd_dvd_nat @ A @ C))))). % dvd_mult_left
thf(fact_170_dvd__mult__left, axiom,
    ((![A : a, B : a, C : a]: ((dvd_dvd_a @ (times_times_a @ A @ B) @ C) => (dvd_dvd_a @ A @ C))))). % dvd_mult_left
thf(fact_171_dvd__mult__left, axiom,
    ((![A : poly_a, B : poly_a, C : poly_a]: ((dvd_dvd_poly_a @ (times_times_poly_a @ A @ B) @ C) => (dvd_dvd_poly_a @ A @ C))))). % dvd_mult_left
thf(fact_172_dvd__triv__left, axiom,
    ((![A : nat, B : nat]: (dvd_dvd_nat @ A @ (times_times_nat @ A @ B))))). % dvd_triv_left
thf(fact_173_dvd__triv__left, axiom,
    ((![A : a, B : a]: (dvd_dvd_a @ A @ (times_times_a @ A @ B))))). % dvd_triv_left
thf(fact_174_dvd__triv__left, axiom,
    ((![A : poly_a, B : poly_a]: (dvd_dvd_poly_a @ A @ (times_times_poly_a @ A @ B))))). % dvd_triv_left
thf(fact_175_mult__dvd__mono, axiom,
    ((![A : nat, B : nat, C : nat, D : nat]: ((dvd_dvd_nat @ A @ B) => ((dvd_dvd_nat @ C @ D) => (dvd_dvd_nat @ (times_times_nat @ A @ C) @ (times_times_nat @ B @ D))))))). % mult_dvd_mono
thf(fact_176_mult__dvd__mono, axiom,
    ((![A : a, B : a, C : a, D : a]: ((dvd_dvd_a @ A @ B) => ((dvd_dvd_a @ C @ D) => (dvd_dvd_a @ (times_times_a @ A @ C) @ (times_times_a @ B @ D))))))). % mult_dvd_mono
thf(fact_177_mult__dvd__mono, axiom,
    ((![A : poly_a, B : poly_a, C : poly_a, D : poly_a]: ((dvd_dvd_poly_a @ A @ B) => ((dvd_dvd_poly_a @ C @ D) => (dvd_dvd_poly_a @ (times_times_poly_a @ A @ C) @ (times_times_poly_a @ B @ D))))))). % mult_dvd_mono
thf(fact_178_dvd__mult__right, axiom,
    ((![A : nat, B : nat, C : nat]: ((dvd_dvd_nat @ (times_times_nat @ A @ B) @ C) => (dvd_dvd_nat @ B @ C))))). % dvd_mult_right
thf(fact_179_dvd__mult__right, axiom,
    ((![A : a, B : a, C : a]: ((dvd_dvd_a @ (times_times_a @ A @ B) @ C) => (dvd_dvd_a @ B @ C))))). % dvd_mult_right
thf(fact_180_dvd__mult__right, axiom,
    ((![A : poly_a, B : poly_a, C : poly_a]: ((dvd_dvd_poly_a @ (times_times_poly_a @ A @ B) @ C) => (dvd_dvd_poly_a @ B @ C))))). % dvd_mult_right
thf(fact_181_dvd__triv__right, axiom,
    ((![A : nat, B : nat]: (dvd_dvd_nat @ A @ (times_times_nat @ B @ A))))). % dvd_triv_right
thf(fact_182_dvd__triv__right, axiom,
    ((![A : a, B : a]: (dvd_dvd_a @ A @ (times_times_a @ B @ A))))). % dvd_triv_right
thf(fact_183_dvd__triv__right, axiom,
    ((![A : poly_a, B : poly_a]: (dvd_dvd_poly_a @ A @ (times_times_poly_a @ B @ A))))). % dvd_triv_right
thf(fact_184_zero__neq__one, axiom,
    ((~ ((zero_zero_a = one_one_a))))). % zero_neq_one
thf(fact_185_zero__neq__one, axiom,
    ((~ ((zero_zero_poly_a = one_one_poly_a))))). % zero_neq_one
thf(fact_186_zero__neq__one, axiom,
    ((~ ((zero_zero_nat = one_one_nat))))). % zero_neq_one
thf(fact_187_zero__neq__one, axiom,
    ((~ ((zero_zero_poly_nat = one_one_poly_nat))))). % zero_neq_one
thf(fact_188_zero__neq__one, axiom,
    ((~ ((zero_z2096148049poly_a = one_one_poly_poly_a))))). % zero_neq_one
thf(fact_189_mult__poly__0__right, axiom,
    ((![P : poly_nat]: ((times_times_poly_nat @ P @ zero_zero_poly_nat) = zero_zero_poly_nat)))). % mult_poly_0_right
thf(fact_190_mult__poly__0__right, axiom,
    ((![P : poly_poly_a]: ((times_545135445poly_a @ P @ zero_z2096148049poly_a) = zero_z2096148049poly_a)))). % mult_poly_0_right
thf(fact_191_mult__poly__0__right, axiom,
    ((![P : poly_a]: ((times_times_poly_a @ P @ zero_zero_poly_a) = zero_zero_poly_a)))). % mult_poly_0_right
thf(fact_192_mult__poly__0__left, axiom,
    ((![Q : poly_nat]: ((times_times_poly_nat @ zero_zero_poly_nat @ Q) = zero_zero_poly_nat)))). % mult_poly_0_left
thf(fact_193_mult__poly__0__left, axiom,
    ((![Q : poly_poly_a]: ((times_545135445poly_a @ zero_z2096148049poly_a @ Q) = zero_z2096148049poly_a)))). % mult_poly_0_left
thf(fact_194_mult__poly__0__left, axiom,
    ((![Q : poly_a]: ((times_times_poly_a @ zero_zero_poly_a @ Q) = zero_zero_poly_a)))). % mult_poly_0_left
thf(fact_195_one__dvd, axiom,
    ((![A : poly_a]: (dvd_dvd_poly_a @ one_one_poly_a @ A)))). % one_dvd
thf(fact_196_one__dvd, axiom,
    ((![A : nat]: (dvd_dvd_nat @ one_one_nat @ A)))). % one_dvd
thf(fact_197_one__dvd, axiom,
    ((![A : a]: (dvd_dvd_a @ one_one_a @ A)))). % one_dvd
thf(fact_198_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_199_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_200_zero__poly_Orep__eq, axiom,
    (((coeff_poly_nat @ zero_z1059985641ly_nat) = (^[Uu : nat]: zero_zero_poly_nat)))). % zero_poly.rep_eq
thf(fact_201_zero__poly_Orep__eq, axiom,
    (((coeff_poly_poly_a @ zero_z2064990175poly_a) = (^[Uu : nat]: zero_z2096148049poly_a)))). % zero_poly.rep_eq
thf(fact_202_zero__poly_Orep__eq, axiom,
    (((coeff_a @ zero_zero_poly_a) = (^[Uu : nat]: zero_zero_a)))). % zero_poly.rep_eq
thf(fact_203_zero__poly_Orep__eq, axiom,
    (((coeff_nat @ zero_zero_poly_nat) = (^[Uu : nat]: zero_zero_nat)))). % zero_poly.rep_eq
thf(fact_204_zero__poly_Orep__eq, axiom,
    (((coeff_poly_a @ zero_z2096148049poly_a) = (^[Uu : nat]: zero_zero_poly_a)))). % zero_poly.rep_eq
thf(fact_205_is__unit__polyE, axiom,
    ((![P : poly_nat]: ((dvd_dvd_poly_nat @ P @ one_one_poly_nat) => (~ ((![C2 : nat]: ((P = (pCons_nat @ C2 @ zero_zero_poly_nat)) => (~ ((dvd_dvd_nat @ C2 @ one_one_nat))))))))))). % is_unit_polyE
thf(fact_206_is__unit__poly__iff, axiom,
    ((![P : poly_nat]: ((dvd_dvd_poly_nat @ P @ one_one_poly_nat) = (?[C3 : nat]: (((P = (pCons_nat @ C3 @ zero_zero_poly_nat))) & ((dvd_dvd_nat @ C3 @ one_one_nat)))))))). % is_unit_poly_iff
thf(fact_207_is__unit__const__poly__iff, axiom,
    ((![C : nat]: ((dvd_dvd_poly_nat @ (pCons_nat @ C @ zero_zero_poly_nat) @ one_one_poly_nat) = (dvd_dvd_nat @ C @ one_one_nat))))). % is_unit_const_poly_iff
thf(fact_208_not__is__unit__0, axiom,
    ((~ ((dvd_dvd_nat @ zero_zero_nat @ one_one_nat))))). % not_is_unit_0
thf(fact_209_offset__poly__eq__0__iff, axiom,
    ((![P : poly_a, H : a]: (((fundam1358810038poly_a @ P @ H) = zero_zero_poly_a) = (P = zero_zero_poly_a))))). % offset_poly_eq_0_iff
thf(fact_210_offset__poly__eq__0__iff, axiom,
    ((![P : poly_nat, H : nat]: (((fundam170929432ly_nat @ P @ H) = zero_zero_poly_nat) = (P = zero_zero_poly_nat))))). % offset_poly_eq_0_iff
thf(fact_211_offset__poly__eq__0__iff, axiom,
    ((![P : poly_poly_a, H : poly_a]: (((fundam1343031620poly_a @ P @ H) = zero_z2096148049poly_a) = (P = zero_z2096148049poly_a))))). % offset_poly_eq_0_iff
thf(fact_212_offset__poly__0, axiom,
    ((![H : a]: ((fundam1358810038poly_a @ zero_zero_poly_a @ H) = zero_zero_poly_a)))). % offset_poly_0
thf(fact_213_offset__poly__0, axiom,
    ((![H : nat]: ((fundam170929432ly_nat @ zero_zero_poly_nat @ H) = zero_zero_poly_nat)))). % offset_poly_0
thf(fact_214_offset__poly__0, axiom,
    ((![H : poly_a]: ((fundam1343031620poly_a @ zero_z2096148049poly_a @ H) = zero_z2096148049poly_a)))). % offset_poly_0
thf(fact_215_dvd__productE, axiom,
    ((![P : nat, A : nat, B : nat]: ((dvd_dvd_nat @ P @ (times_times_nat @ A @ B)) => (~ ((![X2 : nat, Y : nat]: ((P = (times_times_nat @ X2 @ Y)) => ((dvd_dvd_nat @ X2 @ A) => (~ ((dvd_dvd_nat @ Y @ B)))))))))))). % dvd_productE
thf(fact_216_division__decomp, axiom,
    ((![A : nat, B : nat, C : nat]: ((dvd_dvd_nat @ A @ (times_times_nat @ B @ C)) => (?[B4 : nat, C4 : nat]: ((A = (times_times_nat @ B4 @ C4)) & ((dvd_dvd_nat @ B4 @ B) & (dvd_dvd_nat @ C4 @ C)))))))). % division_decomp
thf(fact_217_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_218_pcompose__idR, axiom,
    ((![P : poly_a]: ((pcompose_a @ P @ (pCons_a @ zero_zero_a @ (pCons_a @ one_one_a @ zero_zero_poly_a))) = P)))). % pcompose_idR
thf(fact_219_pcompose__idR, axiom,
    ((![P : poly_poly_a]: ((pcompose_poly_a @ P @ (pCons_poly_a @ zero_zero_poly_a @ (pCons_poly_a @ one_one_poly_a @ zero_z2096148049poly_a))) = P)))). % pcompose_idR
thf(fact_220_pcompose__idR, axiom,
    ((![P : poly_nat]: ((pcompose_nat @ P @ (pCons_nat @ zero_zero_nat @ (pCons_nat @ one_one_nat @ zero_zero_poly_nat))) = P)))). % pcompose_idR
thf(fact_221_pcompose__idR, axiom,
    ((![P : poly_poly_nat]: ((pcompose_poly_nat @ P @ (pCons_poly_nat @ zero_zero_poly_nat @ (pCons_poly_nat @ one_one_poly_nat @ zero_z1059985641ly_nat))) = P)))). % pcompose_idR
thf(fact_222_pcompose__idR, axiom,
    ((![P : poly_poly_poly_a]: ((pcompose_poly_poly_a @ P @ (pCons_poly_poly_a @ zero_z2096148049poly_a @ (pCons_poly_poly_a @ one_one_poly_poly_a @ zero_z2064990175poly_a))) = P)))). % pcompose_idR
thf(fact_223_map__poly__1, axiom,
    ((![F : a > a]: ((map_poly_a_a @ F @ one_one_poly_a) = (pCons_a @ (F @ one_one_a) @ zero_zero_poly_a))))). % map_poly_1
thf(fact_224_map__poly__1, axiom,
    ((![F : a > nat]: ((map_poly_a_nat @ F @ one_one_poly_a) = (pCons_nat @ (F @ one_one_a) @ zero_zero_poly_nat))))). % map_poly_1
thf(fact_225_map__poly__1, axiom,
    ((![F : a > poly_a]: ((map_poly_a_poly_a @ F @ one_one_poly_a) = (pCons_poly_a @ (F @ one_one_a) @ zero_z2096148049poly_a))))). % map_poly_1
thf(fact_226_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_227_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_228_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_229_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_230_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_231_coeff__linear__power, axiom,
    ((![A : a, N : nat]: ((coeff_a @ (power_power_poly_a @ (pCons_a @ A @ (pCons_a @ one_one_a @ zero_zero_poly_a)) @ N) @ N) = one_one_a)))). % coeff_linear_power
thf(fact_232_coeff__linear__power, axiom,
    ((![A : nat, N : nat]: ((coeff_nat @ (power_power_poly_nat @ (pCons_nat @ A @ (pCons_nat @ one_one_nat @ zero_zero_poly_nat)) @ N) @ N) = one_one_nat)))). % coeff_linear_power
thf(fact_233_coeff__linear__power, axiom,
    ((![A : poly_a, N : nat]: ((coeff_poly_a @ (power_276493840poly_a @ (pCons_poly_a @ A @ (pCons_poly_a @ one_one_poly_a @ zero_z2096148049poly_a)) @ N) @ N) = one_one_poly_a)))). % coeff_linear_power
thf(fact_234_pcompose__0, axiom,
    ((![Q : poly_a]: ((pcompose_a @ zero_zero_poly_a @ Q) = zero_zero_poly_a)))). % pcompose_0
thf(fact_235_pcompose__0, axiom,
    ((![Q : poly_nat]: ((pcompose_nat @ zero_zero_poly_nat @ Q) = zero_zero_poly_nat)))). % pcompose_0
thf(fact_236_pcompose__0, axiom,
    ((![Q : poly_poly_a]: ((pcompose_poly_a @ zero_z2096148049poly_a @ Q) = zero_z2096148049poly_a)))). % pcompose_0
thf(fact_237_reflect__poly__0, axiom,
    (((reflect_poly_nat @ zero_zero_poly_nat) = zero_zero_poly_nat))). % reflect_poly_0
thf(fact_238_reflect__poly__0, axiom,
    (((reflect_poly_poly_a @ zero_z2096148049poly_a) = zero_z2096148049poly_a))). % reflect_poly_0
thf(fact_239_gcd__nat_Oextremum, axiom,
    ((![A : nat]: (dvd_dvd_nat @ A @ zero_zero_nat)))). % gcd_nat.extremum
thf(fact_240_gcd__nat_Oextremum__strict, axiom,
    ((![A : nat]: (~ (((dvd_dvd_nat @ zero_zero_nat @ A) & (~ ((zero_zero_nat = A))))))))). % gcd_nat.extremum_strict
thf(fact_241_gcd__nat_Oextremum__unique, axiom,
    ((![A : nat]: ((dvd_dvd_nat @ zero_zero_nat @ A) = (A = zero_zero_nat))))). % gcd_nat.extremum_unique
thf(fact_242_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_243_gcd__nat_Oextremum__uniqueI, axiom,
    ((![A : nat]: ((dvd_dvd_nat @ zero_zero_nat @ A) => (A = zero_zero_nat))))). % gcd_nat.extremum_uniqueI
thf(fact_244_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_245_gcd__nat_Orefl, axiom,
    ((![A : nat]: (dvd_dvd_nat @ A @ A)))). % gcd_nat.refl
thf(fact_246_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

% Conjectures (1)
thf(conj_0, conjecture,
    ((dvd_dvd_poly_a @ p @ (pCons_a @ zero_zero_a @ q)))).
