% 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_59__5367314_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:26:37.757

% 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 (75)
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_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__Nat__Onat, type,
    if_nat : $o > nat > nat > nat).
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_If_001t__Polynomial__Opoly_Itf__a_J, type,
    if_poly_a : $o > poly_a > poly_a > poly_a).
thf(sy_c_If_001tf__a, type,
    if_a : $o > a > a > a).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat, type,
    ord_less_eq_nat : nat > nat > $o).
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_001t__Nat__Onat_001t__Nat__Onat, type,
    map_poly_nat_nat : (nat > nat) > poly_nat > poly_nat).
thf(sy_c_Polynomial_Omap__poly_001t__Nat__Onat_001t__Polynomial__Opoly_It__Nat__Onat_J, type,
    map_po495548498ly_nat : (nat > poly_nat) > poly_nat > poly_poly_nat).
thf(sy_c_Polynomial_Omap__poly_001t__Nat__Onat_001t__Polynomial__Opoly_Itf__a_J, type,
    map_poly_nat_poly_a : (nat > poly_a) > poly_nat > poly_poly_a).
thf(sy_c_Polynomial_Omap__poly_001t__Nat__Onat_001tf__a, type,
    map_poly_nat_a : (nat > a) > poly_nat > poly_a).
thf(sy_c_Polynomial_Omap__poly_001t__Polynomial__Opoly_It__Nat__Onat_J_001t__Nat__Onat, type,
    map_po1111670354at_nat : (poly_nat > nat) > poly_poly_nat > poly_nat).
thf(sy_c_Polynomial_Omap__poly_001t__Polynomial__Opoly_It__Nat__Onat_J_001tf__a, type,
    map_poly_poly_nat_a : (poly_nat > a) > poly_poly_nat > poly_a).
thf(sy_c_Polynomial_Omap__poly_001t__Polynomial__Opoly_Itf__a_J_001t__Nat__Onat, type,
    map_poly_poly_a_nat : (poly_a > nat) > poly_poly_a > poly_nat).
thf(sy_c_Polynomial_Omap__poly_001t__Polynomial__Opoly_Itf__a_J_001t__Polynomial__Opoly_Itf__a_J, type,
    map_po495521320poly_a : (poly_a > poly_a) > poly_poly_a > poly_poly_a).
thf(sy_c_Polynomial_Omap__poly_001t__Polynomial__Opoly_Itf__a_J_001tf__a, type,
    map_poly_poly_a_a : (poly_a > a) > poly_poly_a > poly_a).
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_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_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_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_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_c_Rings_Ounit__factor__class_Ounit__factor_001t__Nat__Onat, type,
    unit_f109256226or_nat : nat > nat).
thf(sy_v_h, type,
    h : a).

% Relevant facts (246)
thf(fact_0_zero__reorient, axiom,
    ((![X : poly_nat]: ((zero_zero_poly_nat = X) = (X = zero_zero_poly_nat))))). % zero_reorient
thf(fact_1_zero__reorient, axiom,
    ((![X : a]: ((zero_zero_a = X) = (X = zero_zero_a))))). % zero_reorient
thf(fact_2_zero__reorient, axiom,
    ((![X : poly_poly_a]: ((zero_z2096148049poly_a = X) = (X = zero_z2096148049poly_a))))). % zero_reorient
thf(fact_3_zero__reorient, axiom,
    ((![X : poly_a]: ((zero_zero_poly_a = X) = (X = zero_zero_poly_a))))). % zero_reorient
thf(fact_4_zero__reorient, axiom,
    ((![X : nat]: ((zero_zero_nat = X) = (X = zero_zero_nat))))). % zero_reorient
thf(fact_5_content__0, axiom,
    (((content_nat @ zero_zero_poly_nat) = zero_zero_nat))). % content_0
thf(fact_6_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_7_is__zero__null, axiom,
    ((is_zero_nat = (^[P2 : poly_nat]: (P2 = zero_zero_poly_nat))))). % is_zero_null
thf(fact_8_is__zero__null, axiom,
    ((is_zero_poly_a = (^[P2 : poly_poly_a]: (P2 = zero_z2096148049poly_a))))). % is_zero_null
thf(fact_9_is__zero__null, axiom,
    ((is_zero_a = (^[P2 : poly_a]: (P2 = zero_zero_poly_a))))). % is_zero_null
thf(fact_10_poly__cutoff__0, axiom,
    ((![N : nat]: ((poly_cutoff_nat @ N @ zero_zero_poly_nat) = zero_zero_poly_nat)))). % poly_cutoff_0
thf(fact_11_poly__cutoff__0, axiom,
    ((![N : nat]: ((poly_cutoff_poly_a @ N @ zero_z2096148049poly_a) = zero_z2096148049poly_a)))). % poly_cutoff_0
thf(fact_12_poly__cutoff__0, axiom,
    ((![N : nat]: ((poly_cutoff_a @ N @ zero_zero_poly_a) = zero_zero_poly_a)))). % poly_cutoff_0
thf(fact_13_poly__0, axiom,
    ((![X : poly_nat]: ((poly_poly_nat2 @ zero_z1059985641ly_nat @ X) = zero_zero_poly_nat)))). % poly_0
thf(fact_14_poly__0, axiom,
    ((![X : poly_poly_a]: ((poly_poly_poly_a2 @ zero_z2064990175poly_a @ X) = zero_z2096148049poly_a)))). % poly_0
thf(fact_15_poly__0, axiom,
    ((![X : poly_a]: ((poly_poly_a2 @ zero_z2096148049poly_a @ X) = zero_zero_poly_a)))). % poly_0
thf(fact_16_poly__0, axiom,
    ((![X : nat]: ((poly_nat2 @ zero_zero_poly_nat @ X) = zero_zero_nat)))). % poly_0
thf(fact_17_poly__0, axiom,
    ((![X : a]: ((poly_a2 @ zero_zero_poly_a @ X) = zero_zero_a)))). % poly_0
thf(fact_18_monom__eq__0, axiom,
    ((![N : nat]: ((monom_poly_a @ zero_zero_poly_a @ N) = zero_z2096148049poly_a)))). % monom_eq_0
thf(fact_19_monom__eq__0, axiom,
    ((![N : nat]: ((monom_nat @ zero_zero_nat @ N) = zero_zero_poly_nat)))). % monom_eq_0
thf(fact_20_monom__eq__0, axiom,
    ((![N : nat]: ((monom_poly_nat @ zero_zero_poly_nat @ N) = zero_z1059985641ly_nat)))). % monom_eq_0
thf(fact_21_monom__eq__0, axiom,
    ((![N : nat]: ((monom_a @ zero_zero_a @ N) = zero_zero_poly_a)))). % monom_eq_0
thf(fact_22_monom__eq__0, axiom,
    ((![N : nat]: ((monom_poly_poly_a @ zero_z2096148049poly_a @ N) = zero_z2064990175poly_a)))). % monom_eq_0
thf(fact_23_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_24_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_25_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_26_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_27_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_28_monom__eq__iff_H, axiom,
    ((![C : poly_a, N : nat, D : poly_a, M : nat]: (((monom_poly_a @ C @ N) = (monom_poly_a @ D @ M)) = (((C = D)) & ((((C = zero_zero_poly_a)) | ((N = M))))))))). % monom_eq_iff'
thf(fact_29_monom__eq__iff_H, axiom,
    ((![C : nat, N : nat, D : nat, M : nat]: (((monom_nat @ C @ N) = (monom_nat @ D @ M)) = (((C = D)) & ((((C = zero_zero_nat)) | ((N = M))))))))). % monom_eq_iff'
thf(fact_30_monom__eq__iff_H, axiom,
    ((![C : poly_nat, N : nat, D : poly_nat, M : nat]: (((monom_poly_nat @ C @ N) = (monom_poly_nat @ D @ M)) = (((C = D)) & ((((C = zero_zero_poly_nat)) | ((N = M))))))))). % monom_eq_iff'
thf(fact_31_monom__eq__iff_H, axiom,
    ((![C : a, N : nat, D : a, M : nat]: (((monom_a @ C @ N) = (monom_a @ D @ M)) = (((C = D)) & ((((C = zero_zero_a)) | ((N = M))))))))). % monom_eq_iff'
thf(fact_32_monom__eq__iff_H, axiom,
    ((![C : poly_poly_a, N : nat, D : poly_poly_a, M : nat]: (((monom_poly_poly_a @ C @ N) = (monom_poly_poly_a @ D @ M)) = (((C = D)) & ((((C = zero_z2096148049poly_a)) | ((N = M))))))))). % monom_eq_iff'
thf(fact_33_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_34_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_35_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_36_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_37_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_38_poly__shift__0, axiom,
    ((![N : nat]: ((poly_shift_a @ N @ zero_zero_poly_a) = zero_zero_poly_a)))). % poly_shift_0
thf(fact_39_poly__shift__0, axiom,
    ((![N : nat]: ((poly_shift_nat @ N @ zero_zero_poly_nat) = zero_zero_poly_nat)))). % poly_shift_0
thf(fact_40_poly__shift__0, axiom,
    ((![N : nat]: ((poly_shift_poly_a @ N @ zero_z2096148049poly_a) = zero_z2096148049poly_a)))). % poly_shift_0
thf(fact_41_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_42_synthetic__div__0, axiom,
    ((![C : a]: ((synthetic_div_a @ zero_zero_poly_a @ C) = zero_zero_poly_a)))). % synthetic_div_0
thf(fact_43_synthetic__div__0, axiom,
    ((![C : nat]: ((synthetic_div_nat @ zero_zero_poly_nat @ C) = zero_zero_poly_nat)))). % synthetic_div_0
thf(fact_44_synthetic__div__0, axiom,
    ((![C : poly_a]: ((synthetic_div_poly_a @ zero_z2096148049poly_a @ C) = zero_z2096148049poly_a)))). % synthetic_div_0
thf(fact_45_monom__eq__const__iff, axiom,
    ((![C : poly_nat, N : nat, D : poly_nat]: (((monom_poly_nat @ C @ N) = (pCons_poly_nat @ D @ zero_z1059985641ly_nat)) = (((C = D)) & ((((C = zero_zero_poly_nat)) | ((N = zero_zero_nat))))))))). % monom_eq_const_iff
thf(fact_46_monom__eq__const__iff, axiom,
    ((![C : poly_poly_a, N : nat, D : poly_poly_a]: (((monom_poly_poly_a @ C @ N) = (pCons_poly_poly_a @ D @ zero_z2064990175poly_a)) = (((C = D)) & ((((C = zero_z2096148049poly_a)) | ((N = zero_zero_nat))))))))). % monom_eq_const_iff
thf(fact_47_monom__eq__const__iff, axiom,
    ((![C : a, N : nat, D : a]: (((monom_a @ C @ N) = (pCons_a @ D @ zero_zero_poly_a)) = (((C = D)) & ((((C = zero_zero_a)) | ((N = zero_zero_nat))))))))). % monom_eq_const_iff
thf(fact_48_monom__eq__const__iff, axiom,
    ((![C : nat, N : nat, D : nat]: (((monom_nat @ C @ N) = (pCons_nat @ D @ zero_zero_poly_nat)) = (((C = D)) & ((((C = zero_zero_nat)) | ((N = zero_zero_nat))))))))). % monom_eq_const_iff
thf(fact_49_monom__eq__const__iff, axiom,
    ((![C : poly_a, N : nat, D : poly_a]: (((monom_poly_a @ C @ N) = (pCons_poly_a @ D @ zero_z2096148049poly_a)) = (((C = D)) & ((((C = zero_zero_poly_a)) | ((N = zero_zero_nat))))))))). % monom_eq_const_iff
thf(fact_50_map__poly__monom, axiom,
    ((![F : nat > nat, C : nat, N : nat]: (((F @ zero_zero_nat) = zero_zero_nat) => ((map_poly_nat_nat @ F @ (monom_nat @ C @ N)) = (monom_nat @ (F @ C) @ N)))))). % map_poly_monom
thf(fact_51_map__poly__monom, axiom,
    ((![F : nat > a, C : nat, N : nat]: (((F @ zero_zero_nat) = zero_zero_a) => ((map_poly_nat_a @ F @ (monom_nat @ C @ N)) = (monom_a @ (F @ C) @ N)))))). % map_poly_monom
thf(fact_52_map__poly__monom, axiom,
    ((![F : a > nat, C : a, N : nat]: (((F @ zero_zero_a) = zero_zero_nat) => ((map_poly_a_nat @ F @ (monom_a @ C @ N)) = (monom_nat @ (F @ C) @ N)))))). % map_poly_monom
thf(fact_53_map__poly__monom, axiom,
    ((![F : a > a, C : a, N : nat]: (((F @ zero_zero_a) = zero_zero_a) => ((map_poly_a_a @ F @ (monom_a @ C @ N)) = (monom_a @ (F @ C) @ N)))))). % map_poly_monom
thf(fact_54_map__poly__monom, axiom,
    ((![F : poly_a > nat, C : poly_a, N : nat]: (((F @ zero_zero_poly_a) = zero_zero_nat) => ((map_poly_poly_a_nat @ F @ (monom_poly_a @ C @ N)) = (monom_nat @ (F @ C) @ N)))))). % map_poly_monom
thf(fact_55_map__poly__monom, axiom,
    ((![F : poly_a > a, C : poly_a, N : nat]: (((F @ zero_zero_poly_a) = zero_zero_a) => ((map_poly_poly_a_a @ F @ (monom_poly_a @ C @ N)) = (monom_a @ (F @ C) @ N)))))). % map_poly_monom
thf(fact_56_map__poly__monom, axiom,
    ((![F : nat > poly_a, C : nat, N : nat]: (((F @ zero_zero_nat) = zero_zero_poly_a) => ((map_poly_nat_poly_a @ F @ (monom_nat @ C @ N)) = (monom_poly_a @ (F @ C) @ N)))))). % map_poly_monom
thf(fact_57_map__poly__monom, axiom,
    ((![F : nat > poly_nat, C : nat, N : nat]: (((F @ zero_zero_nat) = zero_zero_poly_nat) => ((map_po495548498ly_nat @ F @ (monom_nat @ C @ N)) = (monom_poly_nat @ (F @ C) @ N)))))). % map_poly_monom
thf(fact_58_map__poly__monom, axiom,
    ((![F : poly_nat > nat, C : poly_nat, N : nat]: (((F @ zero_zero_poly_nat) = zero_zero_nat) => ((map_po1111670354at_nat @ F @ (monom_poly_nat @ C @ N)) = (monom_nat @ (F @ C) @ N)))))). % map_poly_monom
thf(fact_59_map__poly__monom, axiom,
    ((![F : poly_nat > a, C : poly_nat, N : nat]: (((F @ zero_zero_poly_nat) = zero_zero_a) => ((map_poly_poly_nat_a @ F @ (monom_poly_nat @ C @ N)) = (monom_a @ (F @ C) @ N)))))). % map_poly_monom
thf(fact_60_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_61_reflect__poly__0, axiom,
    (((reflect_poly_a @ zero_zero_poly_a) = zero_zero_poly_a))). % reflect_poly_0
thf(fact_62_reflect__poly__0, axiom,
    (((reflect_poly_nat @ zero_zero_poly_nat) = zero_zero_poly_nat))). % reflect_poly_0
thf(fact_63_reflect__poly__0, axiom,
    (((reflect_poly_poly_a @ zero_z2096148049poly_a) = zero_z2096148049poly_a))). % reflect_poly_0
thf(fact_64_map__poly__0, axiom,
    ((![F : a > a]: ((map_poly_a_a @ F @ zero_zero_poly_a) = zero_zero_poly_a)))). % map_poly_0
thf(fact_65_map__poly__0, axiom,
    ((![F : a > nat]: ((map_poly_a_nat @ F @ zero_zero_poly_a) = zero_zero_poly_nat)))). % map_poly_0
thf(fact_66_map__poly__0, axiom,
    ((![F : a > poly_a]: ((map_poly_a_poly_a @ F @ zero_zero_poly_a) = zero_z2096148049poly_a)))). % map_poly_0
thf(fact_67_map__poly__0, axiom,
    ((![F : nat > a]: ((map_poly_nat_a @ F @ zero_zero_poly_nat) = zero_zero_poly_a)))). % map_poly_0
thf(fact_68_map__poly__0, axiom,
    ((![F : nat > nat]: ((map_poly_nat_nat @ F @ zero_zero_poly_nat) = zero_zero_poly_nat)))). % map_poly_0
thf(fact_69_map__poly__0, axiom,
    ((![F : nat > poly_a]: ((map_poly_nat_poly_a @ F @ zero_zero_poly_nat) = zero_z2096148049poly_a)))). % map_poly_0
thf(fact_70_map__poly__0, axiom,
    ((![F : poly_a > a]: ((map_poly_poly_a_a @ F @ zero_z2096148049poly_a) = zero_zero_poly_a)))). % map_poly_0
thf(fact_71_map__poly__0, axiom,
    ((![F : poly_a > nat]: ((map_poly_poly_a_nat @ F @ zero_z2096148049poly_a) = zero_zero_poly_nat)))). % map_poly_0
thf(fact_72_map__poly__0, axiom,
    ((![F : poly_a > poly_a]: ((map_po495521320poly_a @ F @ zero_z2096148049poly_a) = zero_z2096148049poly_a)))). % map_poly_0
thf(fact_73_primitive__part__0, axiom,
    (((primitive_part_nat @ zero_zero_poly_nat) = zero_zero_poly_nat))). % primitive_part_0
thf(fact_74_pCons__0__0, axiom,
    (((pCons_poly_a @ zero_zero_poly_a @ zero_z2096148049poly_a) = zero_z2096148049poly_a))). % pCons_0_0
thf(fact_75_pCons__0__0, axiom,
    (((pCons_nat @ zero_zero_nat @ zero_zero_poly_nat) = zero_zero_poly_nat))). % pCons_0_0
thf(fact_76_pCons__0__0, axiom,
    (((pCons_poly_nat @ zero_zero_poly_nat @ zero_z1059985641ly_nat) = zero_z1059985641ly_nat))). % pCons_0_0
thf(fact_77_pCons__0__0, axiom,
    (((pCons_a @ zero_zero_a @ zero_zero_poly_a) = zero_zero_poly_a))). % pCons_0_0
thf(fact_78_pCons__0__0, axiom,
    (((pCons_poly_poly_a @ zero_z2096148049poly_a @ zero_z2064990175poly_a) = zero_z2064990175poly_a))). % pCons_0_0
thf(fact_79_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_80_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_81_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_82_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_83_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_84_poly__1, axiom,
    ((![X : nat]: ((poly_nat2 @ one_one_poly_nat @ X) = one_one_nat)))). % poly_1
thf(fact_85_reflect__poly__const, axiom,
    ((![A : a]: ((reflect_poly_a @ (pCons_a @ A @ zero_zero_poly_a)) = (pCons_a @ A @ zero_zero_poly_a))))). % reflect_poly_const
thf(fact_86_reflect__poly__const, axiom,
    ((![A : nat]: ((reflect_poly_nat @ (pCons_nat @ A @ zero_zero_poly_nat)) = (pCons_nat @ A @ zero_zero_poly_nat))))). % reflect_poly_const
thf(fact_87_reflect__poly__const, axiom,
    ((![A : poly_a]: ((reflect_poly_poly_a @ (pCons_poly_a @ A @ zero_z2096148049poly_a)) = (pCons_poly_a @ A @ zero_z2096148049poly_a))))). % reflect_poly_const
thf(fact_88_content__1, axiom,
    (((content_nat @ one_one_poly_nat) = one_one_nat))). % content_1
thf(fact_89_map__poly__1_H, axiom,
    ((![F : nat > nat]: (((F @ one_one_nat) = one_one_nat) => ((map_poly_nat_nat @ F @ one_one_poly_nat) = one_one_poly_nat))))). % map_poly_1'
thf(fact_90_synthetic__div__pCons, axiom,
    ((![A : a, P : poly_a, C : a]: ((synthetic_div_a @ (pCons_a @ A @ P) @ C) = (pCons_a @ (poly_a2 @ P @ C) @ (synthetic_div_a @ P @ C)))))). % synthetic_div_pCons
thf(fact_91_synthetic__div__pCons, axiom,
    ((![A : nat, P : poly_nat, C : nat]: ((synthetic_div_nat @ (pCons_nat @ A @ P) @ C) = (pCons_nat @ (poly_nat2 @ P @ C) @ (synthetic_div_nat @ P @ C)))))). % synthetic_div_pCons
thf(fact_92_synthetic__div__pCons, axiom,
    ((![A : poly_a, P : poly_poly_a, C : poly_a]: ((synthetic_div_poly_a @ (pCons_poly_a @ A @ P) @ C) = (pCons_poly_a @ (poly_poly_a2 @ P @ C) @ (synthetic_div_poly_a @ P @ C)))))). % synthetic_div_pCons
thf(fact_93_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_94_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_95_monom__eq__1, axiom,
    (((monom_nat @ one_one_nat @ zero_zero_nat) = one_one_poly_nat))). % monom_eq_1
thf(fact_96_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_97_one__reorient, axiom,
    ((![X : nat]: ((one_one_nat = X) = (X = one_one_nat))))). % one_reorient
thf(fact_98_pCons__one, axiom,
    (((pCons_nat @ one_one_nat @ zero_zero_poly_nat) = one_one_poly_nat))). % pCons_one
thf(fact_99_map__poly__1, axiom,
    ((![F : nat > a]: ((map_poly_nat_a @ F @ one_one_poly_nat) = (pCons_a @ (F @ one_one_nat) @ zero_zero_poly_a))))). % map_poly_1
thf(fact_100_map__poly__1, axiom,
    ((![F : nat > nat]: ((map_poly_nat_nat @ F @ one_one_poly_nat) = (pCons_nat @ (F @ one_one_nat) @ zero_zero_poly_nat))))). % map_poly_1
thf(fact_101_map__poly__1, axiom,
    ((![F : nat > poly_a]: ((map_poly_nat_poly_a @ F @ one_one_poly_nat) = (pCons_poly_a @ (F @ one_one_nat) @ zero_z2096148049poly_a))))). % map_poly_1
thf(fact_102_map__poly__pCons, axiom,
    ((![F : nat > nat, C : nat, P : poly_nat]: (((F @ zero_zero_nat) = zero_zero_nat) => ((map_poly_nat_nat @ F @ (pCons_nat @ C @ P)) = (pCons_nat @ (F @ C) @ (map_poly_nat_nat @ F @ P))))))). % map_poly_pCons
thf(fact_103_map__poly__pCons, axiom,
    ((![F : nat > a, C : nat, P : poly_nat]: (((F @ zero_zero_nat) = zero_zero_a) => ((map_poly_nat_a @ F @ (pCons_nat @ C @ P)) = (pCons_a @ (F @ C) @ (map_poly_nat_a @ F @ P))))))). % map_poly_pCons
thf(fact_104_map__poly__pCons, axiom,
    ((![F : a > nat, C : a, P : poly_a]: (((F @ zero_zero_a) = zero_zero_nat) => ((map_poly_a_nat @ F @ (pCons_a @ C @ P)) = (pCons_nat @ (F @ C) @ (map_poly_a_nat @ F @ P))))))). % map_poly_pCons
thf(fact_105_map__poly__pCons, axiom,
    ((![F : a > a, C : a, P : poly_a]: (((F @ zero_zero_a) = zero_zero_a) => ((map_poly_a_a @ F @ (pCons_a @ C @ P)) = (pCons_a @ (F @ C) @ (map_poly_a_a @ F @ P))))))). % map_poly_pCons
thf(fact_106_map__poly__pCons, axiom,
    ((![F : poly_a > nat, C : poly_a, P : poly_poly_a]: (((F @ zero_zero_poly_a) = zero_zero_nat) => ((map_poly_poly_a_nat @ F @ (pCons_poly_a @ C @ P)) = (pCons_nat @ (F @ C) @ (map_poly_poly_a_nat @ F @ P))))))). % map_poly_pCons
thf(fact_107_map__poly__pCons, axiom,
    ((![F : poly_a > a, C : poly_a, P : poly_poly_a]: (((F @ zero_zero_poly_a) = zero_zero_a) => ((map_poly_poly_a_a @ F @ (pCons_poly_a @ C @ P)) = (pCons_a @ (F @ C) @ (map_poly_poly_a_a @ F @ P))))))). % map_poly_pCons
thf(fact_108_map__poly__pCons, axiom,
    ((![F : nat > poly_a, C : nat, P : poly_nat]: (((F @ zero_zero_nat) = zero_zero_poly_a) => ((map_poly_nat_poly_a @ F @ (pCons_nat @ C @ P)) = (pCons_poly_a @ (F @ C) @ (map_poly_nat_poly_a @ F @ P))))))). % map_poly_pCons
thf(fact_109_map__poly__pCons, axiom,
    ((![F : nat > poly_nat, C : nat, P : poly_nat]: (((F @ zero_zero_nat) = zero_zero_poly_nat) => ((map_po495548498ly_nat @ F @ (pCons_nat @ C @ P)) = (pCons_poly_nat @ (F @ C) @ (map_po495548498ly_nat @ F @ P))))))). % map_poly_pCons
thf(fact_110_map__poly__pCons, axiom,
    ((![F : poly_nat > nat, C : poly_nat, P : poly_poly_nat]: (((F @ zero_zero_poly_nat) = zero_zero_nat) => ((map_po1111670354at_nat @ F @ (pCons_poly_nat @ C @ P)) = (pCons_nat @ (F @ C) @ (map_po1111670354at_nat @ F @ P))))))). % map_poly_pCons
thf(fact_111_map__poly__pCons, axiom,
    ((![F : poly_nat > a, C : poly_nat, P : poly_poly_nat]: (((F @ zero_zero_poly_nat) = zero_zero_a) => ((map_poly_poly_nat_a @ F @ (pCons_poly_nat @ C @ P)) = (pCons_a @ (F @ C) @ (map_poly_poly_nat_a @ F @ P))))))). % map_poly_pCons
thf(fact_112_monom__eq__1__iff, axiom,
    ((![C : nat, N : nat]: (((monom_nat @ C @ N) = one_one_poly_nat) = (((C = one_one_nat)) & ((N = zero_zero_nat))))))). % monom_eq_1_iff
thf(fact_113_primitive__part__prim, axiom,
    ((![P : poly_nat]: (((content_nat @ P) = one_one_nat) => ((primitive_part_nat @ P) = P))))). % primitive_part_prim
thf(fact_114_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_115_poly__induct2, axiom,
    ((![P3 : poly_a > poly_a > $o, P : poly_a, Q : poly_a]: ((P3 @ zero_zero_poly_a @ zero_zero_poly_a) => ((![A2 : a, P4 : poly_a, B : a, Q2 : poly_a]: ((P3 @ P4 @ Q2) => (P3 @ (pCons_a @ A2 @ P4) @ (pCons_a @ B @ Q2)))) => (P3 @ P @ Q)))))). % poly_induct2
thf(fact_116_poly__induct2, axiom,
    ((![P3 : poly_a > poly_nat > $o, P : poly_a, Q : poly_nat]: ((P3 @ zero_zero_poly_a @ zero_zero_poly_nat) => ((![A2 : a, P4 : poly_a, B : nat, Q2 : poly_nat]: ((P3 @ P4 @ Q2) => (P3 @ (pCons_a @ A2 @ P4) @ (pCons_nat @ B @ Q2)))) => (P3 @ P @ Q)))))). % poly_induct2
thf(fact_117_poly__induct2, axiom,
    ((![P3 : poly_a > poly_poly_a > $o, P : poly_a, Q : poly_poly_a]: ((P3 @ zero_zero_poly_a @ zero_z2096148049poly_a) => ((![A2 : a, P4 : poly_a, B : poly_a, Q2 : poly_poly_a]: ((P3 @ P4 @ Q2) => (P3 @ (pCons_a @ A2 @ P4) @ (pCons_poly_a @ B @ Q2)))) => (P3 @ P @ Q)))))). % poly_induct2
thf(fact_118_poly__induct2, axiom,
    ((![P3 : poly_nat > poly_a > $o, P : poly_nat, Q : poly_a]: ((P3 @ zero_zero_poly_nat @ zero_zero_poly_a) => ((![A2 : nat, P4 : poly_nat, B : a, Q2 : poly_a]: ((P3 @ P4 @ Q2) => (P3 @ (pCons_nat @ A2 @ P4) @ (pCons_a @ B @ Q2)))) => (P3 @ P @ Q)))))). % poly_induct2
thf(fact_119_poly__induct2, axiom,
    ((![P3 : poly_nat > poly_nat > $o, P : poly_nat, Q : poly_nat]: ((P3 @ zero_zero_poly_nat @ zero_zero_poly_nat) => ((![A2 : nat, P4 : poly_nat, B : nat, Q2 : poly_nat]: ((P3 @ P4 @ Q2) => (P3 @ (pCons_nat @ A2 @ P4) @ (pCons_nat @ B @ Q2)))) => (P3 @ P @ Q)))))). % poly_induct2
thf(fact_120_poly__induct2, axiom,
    ((![P3 : poly_nat > poly_poly_a > $o, P : poly_nat, Q : poly_poly_a]: ((P3 @ zero_zero_poly_nat @ zero_z2096148049poly_a) => ((![A2 : nat, P4 : poly_nat, B : poly_a, Q2 : poly_poly_a]: ((P3 @ P4 @ Q2) => (P3 @ (pCons_nat @ A2 @ P4) @ (pCons_poly_a @ B @ Q2)))) => (P3 @ P @ Q)))))). % poly_induct2
thf(fact_121_poly__induct2, axiom,
    ((![P3 : poly_poly_a > poly_a > $o, P : poly_poly_a, Q : poly_a]: ((P3 @ zero_z2096148049poly_a @ zero_zero_poly_a) => ((![A2 : poly_a, P4 : poly_poly_a, B : a, Q2 : poly_a]: ((P3 @ P4 @ Q2) => (P3 @ (pCons_poly_a @ A2 @ P4) @ (pCons_a @ B @ Q2)))) => (P3 @ P @ Q)))))). % poly_induct2
thf(fact_122_poly__induct2, axiom,
    ((![P3 : poly_poly_a > poly_nat > $o, P : poly_poly_a, Q : poly_nat]: ((P3 @ zero_z2096148049poly_a @ zero_zero_poly_nat) => ((![A2 : poly_a, P4 : poly_poly_a, B : nat, Q2 : poly_nat]: ((P3 @ P4 @ Q2) => (P3 @ (pCons_poly_a @ A2 @ P4) @ (pCons_nat @ B @ Q2)))) => (P3 @ P @ Q)))))). % poly_induct2
thf(fact_123_poly__induct2, axiom,
    ((![P3 : poly_poly_a > poly_poly_a > $o, P : poly_poly_a, Q : poly_poly_a]: ((P3 @ zero_z2096148049poly_a @ zero_z2096148049poly_a) => ((![A2 : poly_a, P4 : poly_poly_a, B : poly_a, Q2 : poly_poly_a]: ((P3 @ P4 @ Q2) => (P3 @ (pCons_poly_a @ A2 @ P4) @ (pCons_poly_a @ B @ Q2)))) => (P3 @ P @ Q)))))). % poly_induct2
thf(fact_124_pderiv_Oinduct, axiom,
    ((![P3 : poly_nat > $o, A0 : poly_nat]: ((![A2 : nat, P4 : poly_nat]: (((~ ((P4 = zero_zero_poly_nat))) => (P3 @ P4)) => (P3 @ (pCons_nat @ A2 @ P4)))) => (P3 @ A0))))). % pderiv.induct
thf(fact_125_pCons__induct, axiom,
    ((![P3 : poly_poly_nat > $o, P : poly_poly_nat]: ((P3 @ zero_z1059985641ly_nat) => ((![A2 : poly_nat, P4 : poly_poly_nat]: (((~ ((A2 = zero_zero_poly_nat))) | (~ ((P4 = zero_z1059985641ly_nat)))) => ((P3 @ P4) => (P3 @ (pCons_poly_nat @ A2 @ P4))))) => (P3 @ P)))))). % pCons_induct
thf(fact_126_pCons__induct, axiom,
    ((![P3 : poly_poly_poly_a > $o, P : poly_poly_poly_a]: ((P3 @ zero_z2064990175poly_a) => ((![A2 : poly_poly_a, P4 : poly_poly_poly_a]: (((~ ((A2 = zero_z2096148049poly_a))) | (~ ((P4 = zero_z2064990175poly_a)))) => ((P3 @ P4) => (P3 @ (pCons_poly_poly_a @ A2 @ P4))))) => (P3 @ P)))))). % pCons_induct
thf(fact_127_pCons__induct, axiom,
    ((![P3 : poly_a > $o, P : poly_a]: ((P3 @ zero_zero_poly_a) => ((![A2 : a, P4 : poly_a]: (((~ ((A2 = zero_zero_a))) | (~ ((P4 = zero_zero_poly_a)))) => ((P3 @ P4) => (P3 @ (pCons_a @ A2 @ P4))))) => (P3 @ P)))))). % pCons_induct
thf(fact_128_pCons__induct, axiom,
    ((![P3 : poly_nat > $o, P : poly_nat]: ((P3 @ zero_zero_poly_nat) => ((![A2 : nat, P4 : poly_nat]: (((~ ((A2 = zero_zero_nat))) | (~ ((P4 = zero_zero_poly_nat)))) => ((P3 @ P4) => (P3 @ (pCons_nat @ A2 @ P4))))) => (P3 @ P)))))). % pCons_induct
thf(fact_129_pCons__induct, axiom,
    ((![P3 : poly_poly_a > $o, P : poly_poly_a]: ((P3 @ zero_z2096148049poly_a) => ((![A2 : poly_a, P4 : poly_poly_a]: (((~ ((A2 = zero_zero_poly_a))) | (~ ((P4 = zero_z2096148049poly_a)))) => ((P3 @ P4) => (P3 @ (pCons_poly_a @ A2 @ P4))))) => (P3 @ P)))))). % pCons_induct
thf(fact_130_monom__0, axiom,
    ((![A : a]: ((monom_a @ A @ zero_zero_nat) = (pCons_a @ A @ zero_zero_poly_a))))). % monom_0
thf(fact_131_monom__0, axiom,
    ((![A : nat]: ((monom_nat @ A @ zero_zero_nat) = (pCons_nat @ A @ zero_zero_poly_nat))))). % monom_0
thf(fact_132_monom__0, axiom,
    ((![A : poly_a]: ((monom_poly_a @ A @ zero_zero_nat) = (pCons_poly_a @ A @ zero_z2096148049poly_a))))). % monom_0
thf(fact_133_zero__neq__one, axiom,
    ((~ ((zero_zero_nat = one_one_nat))))). % zero_neq_one
thf(fact_134_zero__neq__one, axiom,
    ((~ ((zero_zero_poly_nat = one_one_poly_nat))))). % zero_neq_one
thf(fact_135_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_136_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_137_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_138_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_139_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_140_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_141_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_142_primitive__part__const__poly, axiom,
    ((![X : nat]: ((primitive_part_nat @ (pCons_nat @ X @ zero_zero_poly_nat)) = (pCons_nat @ (unit_f109256226or_nat @ X) @ zero_zero_poly_nat))))). % primitive_part_const_poly
thf(fact_143_unit__factor__idem, axiom,
    ((![A : nat]: ((unit_f109256226or_nat @ (unit_f109256226or_nat @ A)) = (unit_f109256226or_nat @ A))))). % unit_factor_idem
thf(fact_144_dvd__0__right, axiom,
    ((![A : nat]: (dvd_dvd_nat @ A @ zero_zero_nat)))). % dvd_0_right
thf(fact_145_dvd__0__right, axiom,
    ((![A : poly_nat]: (dvd_dvd_poly_nat @ A @ zero_zero_poly_nat)))). % dvd_0_right
thf(fact_146_dvd__0__left__iff, axiom,
    ((![A : nat]: ((dvd_dvd_nat @ zero_zero_nat @ A) = (A = zero_zero_nat))))). % dvd_0_left_iff
thf(fact_147_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_148_unit__factor__0, axiom,
    (((unit_f109256226or_nat @ zero_zero_nat) = zero_zero_nat))). % unit_factor_0
thf(fact_149_unit__factor__eq__0__iff, axiom,
    ((![A : nat]: (((unit_f109256226or_nat @ A) = zero_zero_nat) = (A = zero_zero_nat))))). % unit_factor_eq_0_iff
thf(fact_150_unit__factor__1, axiom,
    (((unit_f109256226or_nat @ one_one_nat) = one_one_nat))). % unit_factor_1
thf(fact_151_pcompose__0, axiom,
    ((![Q : poly_a]: ((pcompose_a @ zero_zero_poly_a @ Q) = zero_zero_poly_a)))). % pcompose_0
thf(fact_152_pcompose__0, axiom,
    ((![Q : poly_nat]: ((pcompose_nat @ zero_zero_poly_nat @ Q) = zero_zero_poly_nat)))). % pcompose_0
thf(fact_153_pcompose__0, axiom,
    ((![Q : poly_poly_a]: ((pcompose_poly_a @ zero_z2096148049poly_a @ Q) = zero_z2096148049poly_a)))). % pcompose_0
thf(fact_154_coeff__0, axiom,
    ((![N : nat]: ((coeff_poly_nat @ zero_z1059985641ly_nat @ N) = zero_zero_poly_nat)))). % coeff_0
thf(fact_155_coeff__0, axiom,
    ((![N : nat]: ((coeff_poly_poly_a @ zero_z2064990175poly_a @ N) = zero_z2096148049poly_a)))). % coeff_0
thf(fact_156_coeff__0, axiom,
    ((![N : nat]: ((coeff_a @ zero_zero_poly_a @ N) = zero_zero_a)))). % coeff_0
thf(fact_157_coeff__0, axiom,
    ((![N : nat]: ((coeff_nat @ zero_zero_poly_nat @ N) = zero_zero_nat)))). % coeff_0
thf(fact_158_coeff__0, axiom,
    ((![N : nat]: ((coeff_poly_a @ zero_z2096148049poly_a @ N) = zero_zero_poly_a)))). % coeff_0
thf(fact_159_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_160_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_161_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_162_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_163_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_164_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_165_pcompose__const, axiom,
    ((![A : a, Q : poly_a]: ((pcompose_a @ (pCons_a @ A @ zero_zero_poly_a) @ Q) = (pCons_a @ A @ zero_zero_poly_a))))). % pcompose_const
thf(fact_166_pcompose__const, axiom,
    ((![A : nat, Q : poly_nat]: ((pcompose_nat @ (pCons_nat @ A @ zero_zero_poly_nat) @ Q) = (pCons_nat @ A @ zero_zero_poly_nat))))). % pcompose_const
thf(fact_167_pcompose__const, axiom,
    ((![A : poly_a, Q : poly_poly_a]: ((pcompose_poly_a @ (pCons_poly_a @ A @ zero_z2096148049poly_a) @ Q) = (pCons_poly_a @ A @ zero_z2096148049poly_a))))). % pcompose_const
thf(fact_168_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_169_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_170_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_171_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_172_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_173_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_174_const__poly__dvd__const__poly__iff, axiom,
    ((![A : nat, B2 : nat]: ((dvd_dvd_poly_nat @ (pCons_nat @ A @ zero_zero_poly_nat) @ (pCons_nat @ B2 @ zero_zero_poly_nat)) = (dvd_dvd_nat @ A @ B2))))). % const_poly_dvd_const_poly_iff
thf(fact_175_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_176_unit__factor__dvd, axiom,
    ((![A : nat, B2 : nat]: ((~ ((A = zero_zero_nat))) => (dvd_dvd_nat @ (unit_f109256226or_nat @ A) @ B2))))). % unit_factor_dvd
thf(fact_177_unit__factor__is__unit, axiom,
    ((![A : nat]: ((~ ((A = zero_zero_nat))) => (dvd_dvd_nat @ (unit_f109256226or_nat @ A) @ one_one_nat))))). % unit_factor_is_unit
thf(fact_178_is__unit__unit__factor, axiom,
    ((![A : nat]: ((dvd_dvd_nat @ A @ one_one_nat) => ((unit_f109256226or_nat @ A) = A))))). % is_unit_unit_factor
thf(fact_179_dvd__unit__imp__unit, axiom,
    ((![A : nat, B2 : nat]: ((dvd_dvd_nat @ A @ B2) => ((dvd_dvd_nat @ B2 @ one_one_nat) => (dvd_dvd_nat @ A @ one_one_nat)))))). % dvd_unit_imp_unit
thf(fact_180_unit__imp__dvd, axiom,
    ((![B2 : nat, A : nat]: ((dvd_dvd_nat @ B2 @ one_one_nat) => (dvd_dvd_nat @ B2 @ A))))). % unit_imp_dvd
thf(fact_181_one__dvd, axiom,
    ((![A : nat]: (dvd_dvd_nat @ one_one_nat @ A)))). % one_dvd
thf(fact_182_dvd__0__left, axiom,
    ((![A : nat]: ((dvd_dvd_nat @ zero_zero_nat @ A) => (A = zero_zero_nat))))). % dvd_0_left
thf(fact_183_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_184_content__dvd__coeff, axiom,
    ((![P : poly_nat, N : nat]: (dvd_dvd_nat @ (content_nat @ P) @ (coeff_nat @ P @ N))))). % content_dvd_coeff
thf(fact_185_dvd__refl, axiom,
    ((![A : nat]: (dvd_dvd_nat @ A @ A)))). % dvd_refl
thf(fact_186_dvd__trans, axiom,
    ((![A : nat, B2 : nat, C : nat]: ((dvd_dvd_nat @ A @ B2) => ((dvd_dvd_nat @ B2 @ C) => (dvd_dvd_nat @ A @ C)))))). % dvd_trans
thf(fact_187_unit__factor__self, axiom,
    ((![A : nat]: (dvd_dvd_nat @ (unit_f109256226or_nat @ A) @ A)))). % unit_factor_self
thf(fact_188_not__is__unit__0, axiom,
    ((~ ((dvd_dvd_nat @ zero_zero_nat @ one_one_nat))))). % not_is_unit_0
thf(fact_189_poly__pcompose, axiom,
    ((![P : poly_a, Q : poly_a, X : a]: ((poly_a2 @ (pcompose_a @ P @ Q) @ X) = (poly_a2 @ P @ (poly_a2 @ Q @ X)))))). % poly_pcompose
thf(fact_190_poly__pcompose, axiom,
    ((![P : poly_nat, Q : poly_nat, X : nat]: ((poly_nat2 @ (pcompose_nat @ P @ Q) @ X) = (poly_nat2 @ P @ (poly_nat2 @ Q @ X)))))). % poly_pcompose
thf(fact_191_poly__pcompose, axiom,
    ((![P : poly_poly_a, Q : poly_poly_a, X : poly_a]: ((poly_poly_a2 @ (pcompose_poly_a @ P @ Q) @ X) = (poly_poly_a2 @ P @ (poly_poly_a2 @ Q @ X)))))). % poly_pcompose
thf(fact_192_pcompose__0_H, axiom,
    ((![P : poly_a]: ((pcompose_a @ P @ zero_zero_poly_a) = (pCons_a @ (coeff_a @ P @ zero_zero_nat) @ zero_zero_poly_a))))). % pcompose_0'
thf(fact_193_pcompose__0_H, axiom,
    ((![P : poly_nat]: ((pcompose_nat @ P @ zero_zero_poly_nat) = (pCons_nat @ (coeff_nat @ P @ zero_zero_nat) @ zero_zero_poly_nat))))). % pcompose_0'
thf(fact_194_pcompose__0_H, axiom,
    ((![P : poly_poly_a]: ((pcompose_poly_a @ P @ zero_z2096148049poly_a) = (pCons_poly_a @ (coeff_poly_a @ P @ zero_zero_nat) @ zero_z2096148049poly_a))))). % pcompose_0'
thf(fact_195_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_196_zero__poly_Orep__eq, axiom,
    (((coeff_poly_nat @ zero_z1059985641ly_nat) = (^[Uu : nat]: zero_zero_poly_nat)))). % zero_poly.rep_eq
thf(fact_197_zero__poly_Orep__eq, axiom,
    (((coeff_poly_poly_a @ zero_z2064990175poly_a) = (^[Uu : nat]: zero_z2096148049poly_a)))). % zero_poly.rep_eq
thf(fact_198_zero__poly_Orep__eq, axiom,
    (((coeff_a @ zero_zero_poly_a) = (^[Uu : nat]: zero_zero_a)))). % zero_poly.rep_eq
thf(fact_199_zero__poly_Orep__eq, axiom,
    (((coeff_nat @ zero_zero_poly_nat) = (^[Uu : nat]: zero_zero_nat)))). % zero_poly.rep_eq
thf(fact_200_zero__poly_Orep__eq, axiom,
    (((coeff_poly_a @ zero_z2096148049poly_a) = (^[Uu : nat]: zero_zero_poly_a)))). % zero_poly.rep_eq
thf(fact_201_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_202_is__unit__poly__iff, 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_poly_iff
thf(fact_203_is__unit__polyE, 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_polyE
thf(fact_204_monom_Orep__eq, axiom,
    ((![X : poly_a, Xa : nat]: ((coeff_poly_a @ (monom_poly_a @ X @ Xa)) = (^[N2 : nat]: (if_poly_a @ (Xa = N2) @ X @ zero_zero_poly_a)))))). % monom.rep_eq
thf(fact_205_monom_Orep__eq, axiom,
    ((![X : nat, Xa : nat]: ((coeff_nat @ (monom_nat @ X @ Xa)) = (^[N2 : nat]: (if_nat @ (Xa = N2) @ X @ zero_zero_nat)))))). % monom.rep_eq
thf(fact_206_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_207_monom_Orep__eq, axiom,
    ((![X : a, Xa : nat]: ((coeff_a @ (monom_a @ X @ Xa)) = (^[N2 : nat]: (if_a @ (Xa = N2) @ X @ zero_zero_a)))))). % monom.rep_eq
thf(fact_208_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
thf(fact_209_coeff__map__poly, axiom,
    ((![F : nat > nat, P : poly_nat, N : nat]: (((F @ zero_zero_nat) = zero_zero_nat) => ((coeff_nat @ (map_poly_nat_nat @ F @ P) @ N) = (F @ (coeff_nat @ P @ N))))))). % coeff_map_poly
thf(fact_210_coeff__map__poly, axiom,
    ((![F : nat > a, P : poly_nat, N : nat]: (((F @ zero_zero_nat) = zero_zero_a) => ((coeff_a @ (map_poly_nat_a @ F @ P) @ N) = (F @ (coeff_nat @ P @ N))))))). % coeff_map_poly
thf(fact_211_coeff__map__poly, axiom,
    ((![F : a > nat, P : poly_a, N : nat]: (((F @ zero_zero_a) = zero_zero_nat) => ((coeff_nat @ (map_poly_a_nat @ F @ P) @ N) = (F @ (coeff_a @ P @ N))))))). % coeff_map_poly
thf(fact_212_coeff__map__poly, axiom,
    ((![F : a > a, P : poly_a, N : nat]: (((F @ zero_zero_a) = zero_zero_a) => ((coeff_a @ (map_poly_a_a @ F @ P) @ N) = (F @ (coeff_a @ P @ N))))))). % coeff_map_poly
thf(fact_213_coeff__map__poly, axiom,
    ((![F : poly_a > nat, P : poly_poly_a, N : nat]: (((F @ zero_zero_poly_a) = zero_zero_nat) => ((coeff_nat @ (map_poly_poly_a_nat @ F @ P) @ N) = (F @ (coeff_poly_a @ P @ N))))))). % coeff_map_poly
thf(fact_214_coeff__map__poly, axiom,
    ((![F : poly_a > a, P : poly_poly_a, N : nat]: (((F @ zero_zero_poly_a) = zero_zero_a) => ((coeff_a @ (map_poly_poly_a_a @ F @ P) @ N) = (F @ (coeff_poly_a @ P @ N))))))). % coeff_map_poly
thf(fact_215_coeff__map__poly, axiom,
    ((![F : nat > poly_a, P : poly_nat, N : nat]: (((F @ zero_zero_nat) = zero_zero_poly_a) => ((coeff_poly_a @ (map_poly_nat_poly_a @ F @ P) @ N) = (F @ (coeff_nat @ P @ N))))))). % coeff_map_poly
thf(fact_216_coeff__map__poly, axiom,
    ((![F : nat > poly_nat, P : poly_nat, N : nat]: (((F @ zero_zero_nat) = zero_zero_poly_nat) => ((coeff_poly_nat @ (map_po495548498ly_nat @ F @ P) @ N) = (F @ (coeff_nat @ P @ N))))))). % coeff_map_poly
thf(fact_217_coeff__map__poly, axiom,
    ((![F : poly_nat > nat, P : poly_poly_nat, N : nat]: (((F @ zero_zero_poly_nat) = zero_zero_nat) => ((coeff_nat @ (map_po1111670354at_nat @ F @ P) @ N) = (F @ (coeff_poly_nat @ P @ N))))))). % coeff_map_poly
thf(fact_218_coeff__map__poly, axiom,
    ((![F : poly_nat > a, P : poly_poly_nat, N : nat]: (((F @ zero_zero_poly_nat) = zero_zero_a) => ((coeff_a @ (map_poly_poly_nat_a @ F @ P) @ N) = (F @ (coeff_poly_nat @ P @ N))))))). % coeff_map_poly
thf(fact_219_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_220_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_221_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_222_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_223_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_224_content__dvd, axiom,
    ((![P : poly_nat]: (dvd_dvd_poly_nat @ (pCons_nat @ (content_nat @ P) @ zero_zero_poly_nat) @ P)))). % content_dvd
thf(fact_225_unit__factor__simps_I1_J, axiom,
    (((unit_f109256226or_nat @ zero_zero_nat) = zero_zero_nat))). % unit_factor_simps(1)
thf(fact_226_le__zero__eq, axiom,
    ((![N : nat]: ((ord_less_eq_nat @ N @ zero_zero_nat) = (N = zero_zero_nat))))). % le_zero_eq
thf(fact_227_zero__le, axiom,
    ((![X : nat]: (ord_less_eq_nat @ zero_zero_nat @ X)))). % zero_le
thf(fact_228_zero__le__one, axiom,
    ((ord_less_eq_nat @ zero_zero_nat @ one_one_nat))). % zero_le_one
thf(fact_229_not__one__le__zero, axiom,
    ((~ ((ord_less_eq_nat @ one_one_nat @ zero_zero_nat))))). % not_one_le_zero
thf(fact_230_unit__factor__nat__def, axiom,
    ((unit_f109256226or_nat = (^[N2 : nat]: (if_nat @ (N2 = zero_zero_nat) @ zero_zero_nat @ one_one_nat))))). % unit_factor_nat_def
thf(fact_231_bot__nat__0_Oextremum, axiom,
    ((![A : nat]: (ord_less_eq_nat @ zero_zero_nat @ A)))). % bot_nat_0.extremum
thf(fact_232_le0, axiom,
    ((![N : nat]: (ord_less_eq_nat @ zero_zero_nat @ N)))). % le0
thf(fact_233_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_234_le__refl, axiom,
    ((![N : nat]: (ord_less_eq_nat @ N @ N)))). % le_refl
thf(fact_235_le__trans, axiom,
    ((![I : nat, J : nat, K : nat]: ((ord_less_eq_nat @ I @ J) => ((ord_less_eq_nat @ J @ K) => (ord_less_eq_nat @ I @ K)))))). % le_trans
thf(fact_236_eq__imp__le, axiom,
    ((![M : nat, N : nat]: ((M = N) => (ord_less_eq_nat @ M @ N))))). % eq_imp_le
thf(fact_237_le__antisym, axiom,
    ((![M : nat, N : nat]: ((ord_less_eq_nat @ M @ N) => ((ord_less_eq_nat @ N @ M) => (M = N)))))). % le_antisym
thf(fact_238_nat__le__linear, axiom,
    ((![M : nat, N : nat]: ((ord_less_eq_nat @ M @ N) | (ord_less_eq_nat @ N @ M))))). % nat_le_linear
thf(fact_239_Nat_Oex__has__greatest__nat, axiom,
    ((![P3 : nat > $o, K : nat, B2 : nat]: ((P3 @ K) => ((![Y : nat]: ((P3 @ Y) => (ord_less_eq_nat @ Y @ B2))) => (?[X2 : nat]: ((P3 @ X2) & (![Y2 : nat]: ((P3 @ Y2) => (ord_less_eq_nat @ Y2 @ X2)))))))))). % Nat.ex_has_greatest_nat
thf(fact_240_less__eq__nat_Osimps_I1_J, axiom,
    ((![N : nat]: (ord_less_eq_nat @ zero_zero_nat @ N)))). % less_eq_nat.simps(1)
thf(fact_241_le__0__eq, axiom,
    ((![N : nat]: ((ord_less_eq_nat @ N @ zero_zero_nat) = (N = zero_zero_nat))))). % le_0_eq
thf(fact_242_bot__nat__0_Oextremum__unique, axiom,
    ((![A : nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) = (A = zero_zero_nat))))). % bot_nat_0.extremum_unique
thf(fact_243_bot__nat__0_Oextremum__uniqueI, axiom,
    ((![A : nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) => (A = zero_zero_nat))))). % bot_nat_0.extremum_uniqueI
thf(fact_244_order__refl, axiom,
    ((![X : nat]: (ord_less_eq_nat @ X @ X)))). % order_refl
thf(fact_245_dvd__antisym, axiom,
    ((![M : nat, N : nat]: ((dvd_dvd_nat @ M @ N) => ((dvd_dvd_nat @ N @ M) => (M = N)))))). % dvd_antisym

% Helper facts (11)
thf(help_If_2_1_If_001tf__a_T, axiom,
    ((![X : a, Y3 : a]: ((if_a @ $false @ X @ Y3) = Y3)))).
thf(help_If_1_1_If_001tf__a_T, axiom,
    ((![X : a, Y3 : a]: ((if_a @ $true @ X @ Y3) = X)))).
thf(help_If_2_1_If_001t__Nat__Onat_T, axiom,
    ((![X : nat, Y3 : nat]: ((if_nat @ $false @ X @ Y3) = Y3)))).
thf(help_If_1_1_If_001t__Nat__Onat_T, axiom,
    ((![X : nat, Y3 : nat]: ((if_nat @ $true @ X @ Y3) = X)))).
thf(help_If_2_1_If_001t__Polynomial__Opoly_Itf__a_J_T, axiom,
    ((![X : poly_a, Y3 : poly_a]: ((if_poly_a @ $false @ X @ Y3) = Y3)))).
thf(help_If_1_1_If_001t__Polynomial__Opoly_Itf__a_J_T, axiom,
    ((![X : poly_a, Y3 : poly_a]: ((if_poly_a @ $true @ X @ Y3) = X)))).
thf(help_If_2_1_If_001t__Polynomial__Opoly_It__Nat__Onat_J_T, axiom,
    ((![X : poly_nat, Y3 : poly_nat]: ((if_poly_nat @ $false @ X @ Y3) = Y3)))).
thf(help_If_1_1_If_001t__Polynomial__Opoly_It__Nat__Onat_J_T, axiom,
    ((![X : poly_nat, Y3 : poly_nat]: ((if_poly_nat @ $true @ X @ Y3) = 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, Y3 : poly_poly_a]: ((if_poly_poly_a @ $false @ X @ Y3) = Y3)))).
thf(help_If_1_1_If_001t__Polynomial__Opoly_It__Polynomial__Opoly_Itf__a_J_J_T, axiom,
    ((![X : poly_poly_a, Y3 : poly_poly_a]: ((if_poly_poly_a @ $true @ X @ Y3) = X)))).

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