% 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_1207__5379464_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:36:31.398

% 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 (79)
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_Fundamental__Theorem__Algebra__Mirabelle__sywschxjbb_Opsize_001t__Nat__Onat, type,
    fundam1567013434ze_nat : poly_nat > nat).
thf(sy_c_Fundamental__Theorem__Algebra__Mirabelle__sywschxjbb_Opsize_001t__Polynomial__Opoly_Itf__a_J, type,
    fundam1032801442poly_a : poly_poly_a > nat).
thf(sy_c_Fundamental__Theorem__Algebra__Mirabelle__sywschxjbb_Opsize_001tf__a, type,
    fundam247907092size_a : poly_a > nat).
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_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_Odegree_001t__Nat__Onat, type,
    degree_nat : poly_nat > nat).
thf(sy_c_Polynomial_Odegree_001t__Polynomial__Opoly_It__Nat__Onat_J, type,
    degree_poly_nat : poly_poly_nat > nat).
thf(sy_c_Polynomial_Odegree_001t__Polynomial__Opoly_It__Polynomial__Opoly_Itf__a_J_J, type,
    degree_poly_poly_a : poly_poly_poly_a > nat).
thf(sy_c_Polynomial_Odegree_001t__Polynomial__Opoly_Itf__a_J, type,
    degree_poly_a : poly_poly_a > nat).
thf(sy_c_Polynomial_Odegree_001tf__a, type,
    degree_a : poly_a > nat).
thf(sy_c_Polynomial_Ois__zero_001t__Nat__Onat, type,
    is_zero_nat : poly_nat > $o).
thf(sy_c_Polynomial_Ois__zero_001t__Polynomial__Opoly_Itf__a_J, type,
    is_zero_poly_a : poly_poly_a > $o).
thf(sy_c_Polynomial_Ois__zero_001tf__a, type,
    is_zero_a : poly_a > $o).
thf(sy_c_Polynomial_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_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_It__Nat__Onat_J, type,
    map_poly_a_poly_nat : (a > poly_nat) > poly_a > poly_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_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_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_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_c, type,
    c : a).
thf(sy_v_x, type,
    x : a).
thf(sy_v_y, type,
    y : a).

% Relevant facts (246)
thf(fact_0_basic__cqe__conv1_I5_J, axiom,
    ((![C : poly_nat]: ((?[X : poly_nat]: ((poly_poly_nat2 @ (pCons_poly_nat @ C @ zero_z1059985641ly_nat) @ X) = zero_zero_poly_nat)) = (C = zero_zero_poly_nat))))). % basic_cqe_conv1(5)
thf(fact_1_basic__cqe__conv1_I5_J, axiom,
    ((![C : poly_poly_a]: ((?[X : poly_poly_a]: ((poly_poly_poly_a2 @ (pCons_poly_poly_a @ C @ zero_z2064990175poly_a) @ X) = zero_z2096148049poly_a)) = (C = zero_z2096148049poly_a))))). % basic_cqe_conv1(5)
thf(fact_2_basic__cqe__conv1_I5_J, axiom,
    ((![C : poly_a]: ((?[X : poly_a]: ((poly_poly_a2 @ (pCons_poly_a @ C @ zero_z2096148049poly_a) @ X) = zero_zero_poly_a)) = (C = zero_zero_poly_a))))). % basic_cqe_conv1(5)
thf(fact_3_basic__cqe__conv1_I5_J, axiom,
    ((![C : nat]: ((?[X : nat]: ((poly_nat2 @ (pCons_nat @ C @ zero_zero_poly_nat) @ X) = zero_zero_nat)) = (C = zero_zero_nat))))). % basic_cqe_conv1(5)
thf(fact_4_basic__cqe__conv1_I5_J, axiom,
    ((![C : a]: ((?[X : a]: ((poly_a2 @ (pCons_a @ C @ zero_zero_poly_a) @ X) = zero_zero_a)) = (C = zero_zero_a))))). % basic_cqe_conv1(5)
thf(fact_5_basic__cqe__conv1_I4_J, axiom,
    ((?[X2 : poly_nat]: ((poly_poly_nat2 @ zero_z1059985641ly_nat @ X2) = zero_zero_poly_nat)))). % basic_cqe_conv1(4)
thf(fact_6_basic__cqe__conv1_I4_J, axiom,
    ((?[X2 : poly_poly_a]: ((poly_poly_poly_a2 @ zero_z2064990175poly_a @ X2) = zero_z2096148049poly_a)))). % basic_cqe_conv1(4)
thf(fact_7_basic__cqe__conv1_I4_J, axiom,
    ((?[X2 : poly_a]: ((poly_poly_a2 @ zero_z2096148049poly_a @ X2) = zero_zero_poly_a)))). % basic_cqe_conv1(4)
thf(fact_8_basic__cqe__conv1_I4_J, axiom,
    ((?[X2 : nat]: ((poly_nat2 @ zero_zero_poly_nat @ X2) = zero_zero_nat)))). % basic_cqe_conv1(4)
thf(fact_9_basic__cqe__conv1_I4_J, axiom,
    ((?[X2 : a]: ((poly_a2 @ zero_zero_poly_a @ X2) = zero_zero_a)))). % basic_cqe_conv1(4)
thf(fact_10_basic__cqe__conv1_I3_J, axiom,
    ((![C : poly_nat]: ((?[X : poly_nat]: (~ (((poly_poly_nat2 @ (pCons_poly_nat @ C @ zero_z1059985641ly_nat) @ X) = zero_zero_poly_nat)))) = (~ ((C = zero_zero_poly_nat))))))). % basic_cqe_conv1(3)
thf(fact_11_basic__cqe__conv1_I3_J, axiom,
    ((![C : poly_poly_a]: ((?[X : poly_poly_a]: (~ (((poly_poly_poly_a2 @ (pCons_poly_poly_a @ C @ zero_z2064990175poly_a) @ X) = zero_z2096148049poly_a)))) = (~ ((C = zero_z2096148049poly_a))))))). % basic_cqe_conv1(3)
thf(fact_12_basic__cqe__conv1_I3_J, axiom,
    ((![C : poly_a]: ((?[X : poly_a]: (~ (((poly_poly_a2 @ (pCons_poly_a @ C @ zero_z2096148049poly_a) @ X) = zero_zero_poly_a)))) = (~ ((C = zero_zero_poly_a))))))). % basic_cqe_conv1(3)
thf(fact_13_basic__cqe__conv1_I3_J, axiom,
    ((![C : nat]: ((?[X : nat]: (~ (((poly_nat2 @ (pCons_nat @ C @ zero_zero_poly_nat) @ X) = zero_zero_nat)))) = (~ ((C = zero_zero_nat))))))). % basic_cqe_conv1(3)
thf(fact_14_basic__cqe__conv1_I3_J, axiom,
    ((![C : a]: ((?[X : a]: (~ (((poly_a2 @ (pCons_a @ C @ zero_zero_poly_a) @ X) = zero_zero_a)))) = (~ ((C = zero_zero_a))))))). % basic_cqe_conv1(3)
thf(fact_15_basic__cqe__conv1_I2_J, axiom,
    ((~ ((?[X3 : poly_nat]: (~ (((poly_poly_nat2 @ zero_z1059985641ly_nat @ X3) = zero_zero_poly_nat)))))))). % basic_cqe_conv1(2)
thf(fact_16_basic__cqe__conv1_I2_J, axiom,
    ((~ ((?[X3 : poly_poly_a]: (~ (((poly_poly_poly_a2 @ zero_z2064990175poly_a @ X3) = zero_z2096148049poly_a)))))))). % basic_cqe_conv1(2)
thf(fact_17_basic__cqe__conv1_I2_J, axiom,
    ((~ ((?[X3 : poly_a]: (~ (((poly_poly_a2 @ zero_z2096148049poly_a @ X3) = zero_zero_poly_a)))))))). % basic_cqe_conv1(2)
thf(fact_18_basic__cqe__conv1_I2_J, axiom,
    ((~ ((?[X3 : nat]: (~ (((poly_nat2 @ zero_zero_poly_nat @ X3) = zero_zero_nat)))))))). % basic_cqe_conv1(2)
thf(fact_19_basic__cqe__conv1_I2_J, axiom,
    ((~ ((?[X3 : a]: (~ (((poly_a2 @ zero_zero_poly_a @ X3) = zero_zero_a)))))))). % basic_cqe_conv1(2)
thf(fact_20_basic__cqe__conv1_I1_J, axiom,
    ((![P : poly_poly_nat]: (~ ((?[X3 : poly_nat]: (((poly_poly_nat2 @ P @ X3) = zero_zero_poly_nat) & (~ (((poly_poly_nat2 @ zero_z1059985641ly_nat @ X3) = zero_zero_poly_nat)))))))))). % basic_cqe_conv1(1)
thf(fact_21_basic__cqe__conv1_I1_J, axiom,
    ((![P : poly_poly_poly_a]: (~ ((?[X3 : poly_poly_a]: (((poly_poly_poly_a2 @ P @ X3) = zero_z2096148049poly_a) & (~ (((poly_poly_poly_a2 @ zero_z2064990175poly_a @ X3) = zero_z2096148049poly_a)))))))))). % basic_cqe_conv1(1)
thf(fact_22_basic__cqe__conv1_I1_J, axiom,
    ((![P : poly_a]: (~ ((?[X3 : a]: (((poly_a2 @ P @ X3) = zero_zero_a) & (~ (((poly_a2 @ zero_zero_poly_a @ X3) = zero_zero_a)))))))))). % basic_cqe_conv1(1)
thf(fact_23_basic__cqe__conv1_I1_J, axiom,
    ((![P : poly_poly_a]: (~ ((?[X3 : poly_a]: (((poly_poly_a2 @ P @ X3) = zero_zero_poly_a) & (~ (((poly_poly_a2 @ zero_z2096148049poly_a @ X3) = zero_zero_poly_a)))))))))). % basic_cqe_conv1(1)
thf(fact_24_basic__cqe__conv1_I1_J, axiom,
    ((![P : poly_nat]: (~ ((?[X3 : nat]: (((poly_nat2 @ P @ X3) = zero_zero_nat) & (~ (((poly_nat2 @ zero_zero_poly_nat @ X3) = zero_zero_nat)))))))))). % basic_cqe_conv1(1)
thf(fact_25_mpoly__base__conv_I2_J, axiom,
    ((![C : poly_a, X4 : poly_a]: (C = (poly_poly_a2 @ (pCons_poly_a @ C @ zero_z2096148049poly_a) @ X4))))). % mpoly_base_conv(2)
thf(fact_26_mpoly__base__conv_I2_J, axiom,
    ((![C : a, X4 : a]: (C = (poly_a2 @ (pCons_a @ C @ zero_zero_poly_a) @ X4))))). % mpoly_base_conv(2)
thf(fact_27_mpoly__base__conv_I1_J, axiom,
    ((![X4 : poly_poly_a]: (zero_z2096148049poly_a = (poly_poly_poly_a2 @ zero_z2064990175poly_a @ X4))))). % mpoly_base_conv(1)
thf(fact_28_mpoly__base__conv_I1_J, axiom,
    ((![X4 : a]: (zero_zero_a = (poly_a2 @ zero_zero_poly_a @ X4))))). % mpoly_base_conv(1)
thf(fact_29_mpoly__base__conv_I1_J, axiom,
    ((![X4 : poly_a]: (zero_zero_poly_a = (poly_poly_a2 @ zero_z2096148049poly_a @ X4))))). % mpoly_base_conv(1)
thf(fact_30_mpoly__norm__conv_I2_J, axiom,
    ((![Y : poly_a, X4 : poly_a]: ((poly_poly_a2 @ (pCons_poly_a @ (poly_poly_a2 @ zero_z2096148049poly_a @ Y) @ zero_z2096148049poly_a) @ X4) = (poly_poly_a2 @ zero_z2096148049poly_a @ X4))))). % mpoly_norm_conv(2)
thf(fact_31_mpoly__norm__conv_I2_J, axiom,
    ((![Y : a, X4 : a]: ((poly_a2 @ (pCons_a @ (poly_a2 @ zero_zero_poly_a @ Y) @ zero_zero_poly_a) @ X4) = (poly_a2 @ zero_zero_poly_a @ X4))))). % mpoly_norm_conv(2)
thf(fact_32_mpoly__norm__conv_I1_J, axiom,
    ((![X4 : poly_poly_a]: ((poly_poly_poly_a2 @ (pCons_poly_poly_a @ zero_z2096148049poly_a @ zero_z2064990175poly_a) @ X4) = (poly_poly_poly_a2 @ zero_z2064990175poly_a @ X4))))). % mpoly_norm_conv(1)
thf(fact_33_mpoly__norm__conv_I1_J, axiom,
    ((![X4 : a]: ((poly_a2 @ (pCons_a @ zero_zero_a @ zero_zero_poly_a) @ X4) = (poly_a2 @ zero_zero_poly_a @ X4))))). % mpoly_norm_conv(1)
thf(fact_34_mpoly__norm__conv_I1_J, axiom,
    ((![X4 : poly_a]: ((poly_poly_a2 @ (pCons_poly_a @ zero_zero_poly_a @ zero_z2096148049poly_a) @ X4) = (poly_poly_a2 @ zero_z2096148049poly_a @ X4))))). % mpoly_norm_conv(1)
thf(fact_35_poly__pad__rule, axiom,
    ((![P : poly_poly_nat, X4 : poly_nat]: (((poly_poly_nat2 @ P @ X4) = zero_zero_poly_nat) => ((poly_poly_nat2 @ (pCons_poly_nat @ zero_zero_poly_nat @ P) @ X4) = zero_zero_poly_nat))))). % poly_pad_rule
thf(fact_36_poly__pad__rule, axiom,
    ((![P : poly_poly_poly_a, X4 : poly_poly_a]: (((poly_poly_poly_a2 @ P @ X4) = zero_z2096148049poly_a) => ((poly_poly_poly_a2 @ (pCons_poly_poly_a @ zero_z2096148049poly_a @ P) @ X4) = zero_z2096148049poly_a))))). % poly_pad_rule
thf(fact_37_poly__pad__rule, axiom,
    ((![P : poly_a, X4 : a]: (((poly_a2 @ P @ X4) = zero_zero_a) => ((poly_a2 @ (pCons_a @ zero_zero_a @ P) @ X4) = zero_zero_a))))). % poly_pad_rule
thf(fact_38_poly__pad__rule, axiom,
    ((![P : poly_poly_a, X4 : poly_a]: (((poly_poly_a2 @ P @ X4) = zero_zero_poly_a) => ((poly_poly_a2 @ (pCons_poly_a @ zero_zero_poly_a @ P) @ X4) = zero_zero_poly_a))))). % poly_pad_rule
thf(fact_39_poly__pad__rule, axiom,
    ((![P : poly_nat, X4 : nat]: (((poly_nat2 @ P @ X4) = zero_zero_nat) => ((poly_nat2 @ (pCons_nat @ zero_zero_nat @ P) @ X4) = zero_zero_nat))))). % poly_pad_rule
thf(fact_40_poly__0, axiom,
    ((![X4 : poly_nat]: ((poly_poly_nat2 @ zero_z1059985641ly_nat @ X4) = zero_zero_poly_nat)))). % poly_0
thf(fact_41_poly__0, axiom,
    ((![X4 : poly_poly_a]: ((poly_poly_poly_a2 @ zero_z2064990175poly_a @ X4) = zero_z2096148049poly_a)))). % poly_0
thf(fact_42_poly__0, axiom,
    ((![X4 : a]: ((poly_a2 @ zero_zero_poly_a @ X4) = zero_zero_a)))). % poly_0
thf(fact_43_poly__0, axiom,
    ((![X4 : nat]: ((poly_nat2 @ zero_zero_poly_nat @ X4) = zero_zero_nat)))). % poly_0
thf(fact_44_poly__0, axiom,
    ((![X4 : poly_a]: ((poly_poly_a2 @ zero_z2096148049poly_a @ X4) = zero_zero_poly_a)))). % poly_0
thf(fact_45_pCons__0__0, axiom,
    (((pCons_poly_a @ zero_zero_poly_a @ zero_z2096148049poly_a) = zero_z2096148049poly_a))). % pCons_0_0
thf(fact_46_pCons__0__0, axiom,
    (((pCons_nat @ zero_zero_nat @ zero_zero_poly_nat) = zero_zero_poly_nat))). % pCons_0_0
thf(fact_47_pCons__0__0, axiom,
    (((pCons_a @ zero_zero_a @ zero_zero_poly_a) = zero_zero_poly_a))). % pCons_0_0
thf(fact_48_pCons__0__0, axiom,
    (((pCons_poly_nat @ zero_zero_poly_nat @ zero_z1059985641ly_nat) = zero_z1059985641ly_nat))). % pCons_0_0
thf(fact_49_pCons__0__0, axiom,
    (((pCons_poly_poly_a @ zero_z2096148049poly_a @ zero_z2064990175poly_a) = zero_z2064990175poly_a))). % pCons_0_0
thf(fact_50_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_51_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_52_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_53_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_54_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_55_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_56_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_57_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_58_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_59_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_60_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_61_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_62_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_63_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_64_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_65_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_66_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_67_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_68_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_69_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_70_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_71_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_72_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_73_mpoly__base__conv_I3_J, axiom,
    ((![X4 : poly_a]: (X4 = (poly_poly_a2 @ (pCons_poly_a @ zero_zero_poly_a @ (pCons_poly_a @ one_one_poly_a @ zero_z2096148049poly_a)) @ X4))))). % mpoly_base_conv(3)
thf(fact_74_mpoly__base__conv_I3_J, axiom,
    ((![X4 : a]: (X4 = (poly_a2 @ (pCons_a @ zero_zero_a @ (pCons_a @ one_one_a @ zero_zero_poly_a)) @ X4))))). % mpoly_base_conv(3)
thf(fact_75_mpoly__base__conv_I3_J, axiom,
    ((![X4 : poly_poly_a]: (X4 = (poly_poly_poly_a2 @ (pCons_poly_poly_a @ zero_z2096148049poly_a @ (pCons_poly_poly_a @ one_one_poly_poly_a @ zero_z2064990175poly_a)) @ X4))))). % mpoly_base_conv(3)
thf(fact_76_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_77_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_78_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_79_poly__1, axiom,
    ((![X4 : a]: ((poly_a2 @ one_one_poly_a @ X4) = one_one_a)))). % poly_1
thf(fact_80_poly__1, axiom,
    ((![X4 : poly_a]: ((poly_poly_a2 @ one_one_poly_poly_a @ X4) = one_one_poly_a)))). % poly_1
thf(fact_81_poly__1, axiom,
    ((![X4 : nat]: ((poly_nat2 @ one_one_poly_nat @ X4) = one_one_nat)))). % poly_1
thf(fact_82_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_83_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_84_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_85_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_86_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_87_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_88_one__reorient, axiom,
    ((![X4 : nat]: ((one_one_nat = X4) = (X4 = one_one_nat))))). % one_reorient
thf(fact_89_pCons__one, axiom,
    (((pCons_a @ one_one_a @ zero_zero_poly_a) = one_one_poly_a))). % pCons_one
thf(fact_90_pCons__one, axiom,
    (((pCons_nat @ one_one_nat @ zero_zero_poly_nat) = one_one_poly_nat))). % pCons_one
thf(fact_91_pCons__one, axiom,
    (((pCons_poly_a @ one_one_poly_a @ zero_z2096148049poly_a) = one_one_poly_poly_a))). % pCons_one
thf(fact_92_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_93_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_94_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_95_offset__poly__0, axiom,
    ((![H : a]: ((fundam1358810038poly_a @ zero_zero_poly_a @ H) = zero_zero_poly_a)))). % offset_poly_0
thf(fact_96_offset__poly__0, axiom,
    ((![H : nat]: ((fundam170929432ly_nat @ zero_zero_poly_nat @ H) = zero_zero_poly_nat)))). % offset_poly_0
thf(fact_97_offset__poly__0, axiom,
    ((![H : poly_a]: ((fundam1343031620poly_a @ zero_z2096148049poly_a @ H) = zero_z2096148049poly_a)))). % offset_poly_0
thf(fact_98_zero__reorient, axiom,
    ((![X4 : poly_a]: ((zero_zero_poly_a = X4) = (X4 = zero_zero_poly_a))))). % zero_reorient
thf(fact_99_zero__reorient, axiom,
    ((![X4 : nat]: ((zero_zero_nat = X4) = (X4 = zero_zero_nat))))). % zero_reorient
thf(fact_100_zero__reorient, axiom,
    ((![X4 : a]: ((zero_zero_a = X4) = (X4 = zero_zero_a))))). % zero_reorient
thf(fact_101_zero__reorient, axiom,
    ((![X4 : poly_nat]: ((zero_zero_poly_nat = X4) = (X4 = zero_zero_poly_nat))))). % zero_reorient
thf(fact_102_zero__reorient, axiom,
    ((![X4 : poly_poly_a]: ((zero_z2096148049poly_a = X4) = (X4 = zero_z2096148049poly_a))))). % zero_reorient
thf(fact_103_pderiv_Ocases, axiom,
    ((![X4 : poly_nat]: (~ ((![A2 : nat, P3 : poly_nat]: (~ ((X4 = (pCons_nat @ A2 @ P3)))))))))). % pderiv.cases
thf(fact_104_pCons__cases, axiom,
    ((![P : poly_a]: (~ ((![A2 : a, Q2 : poly_a]: (~ ((P = (pCons_a @ A2 @ Q2)))))))))). % pCons_cases
thf(fact_105_pCons__cases, axiom,
    ((![P : poly_nat]: (~ ((![A2 : nat, Q2 : poly_nat]: (~ ((P = (pCons_nat @ A2 @ Q2)))))))))). % pCons_cases
thf(fact_106_pCons__cases, axiom,
    ((![P : poly_poly_a]: (~ ((![A2 : poly_a, Q2 : poly_poly_a]: (~ ((P = (pCons_poly_a @ A2 @ Q2)))))))))). % pCons_cases
thf(fact_107_zero__neq__one, axiom,
    ((~ ((zero_zero_poly_a = one_one_poly_a))))). % zero_neq_one
thf(fact_108_zero__neq__one, axiom,
    ((~ ((zero_zero_nat = one_one_nat))))). % zero_neq_one
thf(fact_109_zero__neq__one, axiom,
    ((~ ((zero_zero_a = one_one_a))))). % zero_neq_one
thf(fact_110_zero__neq__one, axiom,
    ((~ ((zero_zero_poly_nat = one_one_poly_nat))))). % zero_neq_one
thf(fact_111_zero__neq__one, axiom,
    ((~ ((zero_z2096148049poly_a = one_one_poly_poly_a))))). % zero_neq_one
thf(fact_112_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_113_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_114_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_115_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_116_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_117_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_118_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_119_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_120_is__zero__null, axiom,
    ((is_zero_a = (^[P4 : poly_a]: (P4 = zero_zero_poly_a))))). % is_zero_null
thf(fact_121_is__zero__null, axiom,
    ((is_zero_nat = (^[P4 : poly_nat]: (P4 = zero_zero_poly_nat))))). % is_zero_null
thf(fact_122_is__zero__null, axiom,
    ((is_zero_poly_a = (^[P4 : poly_poly_a]: (P4 = zero_z2096148049poly_a))))). % is_zero_null
thf(fact_123_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_124_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_125_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_126_poly__cutoff__0, axiom,
    ((![N : nat]: ((poly_cutoff_a @ N @ zero_zero_poly_a) = zero_zero_poly_a)))). % poly_cutoff_0
thf(fact_127_poly__cutoff__0, axiom,
    ((![N : nat]: ((poly_cutoff_nat @ N @ zero_zero_poly_nat) = zero_zero_poly_nat)))). % poly_cutoff_0
thf(fact_128_poly__cutoff__0, axiom,
    ((![N : nat]: ((poly_cutoff_poly_a @ N @ zero_z2096148049poly_a) = zero_z2096148049poly_a)))). % poly_cutoff_0
thf(fact_129_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_130_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_131_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_132_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_133_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_134_poly__shift__0, axiom,
    ((![N : nat]: ((poly_shift_a @ N @ zero_zero_poly_a) = zero_zero_poly_a)))). % poly_shift_0
thf(fact_135_poly__shift__0, axiom,
    ((![N : nat]: ((poly_shift_nat @ N @ zero_zero_poly_nat) = zero_zero_poly_nat)))). % poly_shift_0
thf(fact_136_poly__shift__0, axiom,
    ((![N : nat]: ((poly_shift_poly_a @ N @ zero_z2096148049poly_a) = zero_z2096148049poly_a)))). % poly_shift_0
thf(fact_137_pcompose__0, axiom,
    ((![Q : poly_a]: ((pcompose_a @ zero_zero_poly_a @ Q) = zero_zero_poly_a)))). % pcompose_0
thf(fact_138_pcompose__0, axiom,
    ((![Q : poly_nat]: ((pcompose_nat @ zero_zero_poly_nat @ Q) = zero_zero_poly_nat)))). % pcompose_0
thf(fact_139_pcompose__0, axiom,
    ((![Q : poly_poly_a]: ((pcompose_poly_a @ zero_z2096148049poly_a @ Q) = zero_z2096148049poly_a)))). % pcompose_0
thf(fact_140_reflect__poly__0, axiom,
    (((reflect_poly_a @ zero_zero_poly_a) = zero_zero_poly_a))). % reflect_poly_0
thf(fact_141_reflect__poly__0, axiom,
    (((reflect_poly_nat @ zero_zero_poly_nat) = zero_zero_poly_nat))). % reflect_poly_0
thf(fact_142_reflect__poly__0, axiom,
    (((reflect_poly_poly_a @ zero_z2096148049poly_a) = zero_z2096148049poly_a))). % reflect_poly_0
thf(fact_143_synthetic__div__0, axiom,
    ((![C : a]: ((synthetic_div_a @ zero_zero_poly_a @ C) = zero_zero_poly_a)))). % synthetic_div_0
thf(fact_144_synthetic__div__0, axiom,
    ((![C : nat]: ((synthetic_div_nat @ zero_zero_poly_nat @ C) = zero_zero_poly_nat)))). % synthetic_div_0
thf(fact_145_synthetic__div__0, axiom,
    ((![C : poly_a]: ((synthetic_div_poly_a @ zero_z2096148049poly_a @ C) = zero_z2096148049poly_a)))). % synthetic_div_0
thf(fact_146_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_147_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_148_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_149_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_150_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_151_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_152_poly__pcompose, axiom,
    ((![P : poly_a, Q : poly_a, X4 : a]: ((poly_a2 @ (pcompose_a @ P @ Q) @ X4) = (poly_a2 @ P @ (poly_a2 @ Q @ X4)))))). % poly_pcompose
thf(fact_153_poly__pcompose, axiom,
    ((![P : poly_nat, Q : poly_nat, X4 : nat]: ((poly_nat2 @ (pcompose_nat @ P @ Q) @ X4) = (poly_nat2 @ P @ (poly_nat2 @ Q @ X4)))))). % poly_pcompose
thf(fact_154_poly__pcompose, axiom,
    ((![P : poly_poly_a, Q : poly_poly_a, X4 : poly_a]: ((poly_poly_a2 @ (pcompose_poly_a @ P @ Q) @ X4) = (poly_poly_a2 @ P @ (poly_poly_a2 @ Q @ X4)))))). % poly_pcompose
thf(fact_155_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_156_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_157_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_158_psize__eq__0__iff, axiom,
    ((![P : poly_a]: (((fundam247907092size_a @ P) = zero_zero_nat) = (P = zero_zero_poly_a))))). % psize_eq_0_iff
thf(fact_159_psize__eq__0__iff, axiom,
    ((![P : poly_nat]: (((fundam1567013434ze_nat @ P) = zero_zero_nat) = (P = zero_zero_poly_nat))))). % psize_eq_0_iff
thf(fact_160_psize__eq__0__iff, axiom,
    ((![P : poly_poly_a]: (((fundam1032801442poly_a @ P) = zero_zero_nat) = (P = zero_z2096148049poly_a))))). % psize_eq_0_iff
thf(fact_161_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_162_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_163_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_164_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_165_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_166_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_167_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_168_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_169_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_170_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_171_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_172_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_173_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_174_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_175_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_176_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_177_map__poly__0, axiom,
    ((![F : poly_a > poly_a]: ((map_po495521320poly_a @ F @ zero_z2096148049poly_a) = zero_z2096148049poly_a)))). % map_poly_0
thf(fact_178_coeff__0, axiom,
    ((![N : nat]: ((coeff_poly_nat @ zero_z1059985641ly_nat @ N) = zero_zero_poly_nat)))). % coeff_0
thf(fact_179_coeff__0, axiom,
    ((![N : nat]: ((coeff_poly_poly_a @ zero_z2064990175poly_a @ N) = zero_z2096148049poly_a)))). % coeff_0
thf(fact_180_coeff__0, axiom,
    ((![N : nat]: ((coeff_a @ zero_zero_poly_a @ N) = zero_zero_a)))). % coeff_0
thf(fact_181_coeff__0, axiom,
    ((![N : nat]: ((coeff_nat @ zero_zero_poly_nat @ N) = zero_zero_nat)))). % coeff_0
thf(fact_182_coeff__0, axiom,
    ((![N : nat]: ((coeff_poly_a @ zero_z2096148049poly_a @ N) = zero_zero_poly_a)))). % coeff_0
thf(fact_183_coeff__pCons__0, axiom,
    ((![A : a, P : poly_a]: ((coeff_a @ (pCons_a @ A @ P) @ zero_zero_nat) = A)))). % coeff_pCons_0
thf(fact_184_coeff__pCons__0, axiom,
    ((![A : nat, P : poly_nat]: ((coeff_nat @ (pCons_nat @ A @ P) @ zero_zero_nat) = A)))). % coeff_pCons_0
thf(fact_185_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_186_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_187_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_188_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_189_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_190_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_191_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_192_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_193_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_194_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_195_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_196_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_197_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_198_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_199_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_200_coeff__map__poly, axiom,
    ((![F : a > poly_a, P : poly_a, N : nat]: (((F @ zero_zero_a) = zero_zero_poly_a) => ((coeff_poly_a @ (map_poly_a_poly_a @ F @ P) @ N) = (F @ (coeff_a @ P @ N))))))). % coeff_map_poly
thf(fact_201_coeff__map__poly, axiom,
    ((![F : a > poly_nat, P : poly_a, N : nat]: (((F @ zero_zero_a) = zero_zero_poly_nat) => ((coeff_poly_nat @ (map_poly_a_poly_nat @ F @ P) @ N) = (F @ (coeff_a @ P @ N))))))). % coeff_map_poly
thf(fact_202_zero__poly_Orep__eq, axiom,
    (((coeff_poly_nat @ zero_z1059985641ly_nat) = (^[Uu : nat]: zero_zero_poly_nat)))). % zero_poly.rep_eq
thf(fact_203_zero__poly_Orep__eq, axiom,
    (((coeff_poly_poly_a @ zero_z2064990175poly_a) = (^[Uu : nat]: zero_z2096148049poly_a)))). % zero_poly.rep_eq
thf(fact_204_zero__poly_Orep__eq, axiom,
    (((coeff_a @ zero_zero_poly_a) = (^[Uu : nat]: zero_zero_a)))). % zero_poly.rep_eq
thf(fact_205_zero__poly_Orep__eq, axiom,
    (((coeff_nat @ zero_zero_poly_nat) = (^[Uu : nat]: zero_zero_nat)))). % zero_poly.rep_eq
thf(fact_206_zero__poly_Orep__eq, axiom,
    (((coeff_poly_a @ zero_z2096148049poly_a) = (^[Uu : nat]: zero_zero_poly_a)))). % zero_poly.rep_eq
thf(fact_207_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_208_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_209_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_210_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_211_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_212_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_213_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_214_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_215_map__poly__pCons, axiom,
    ((![F : a > poly_a, C : a, P : poly_a]: (((F @ zero_zero_a) = zero_zero_poly_a) => ((map_poly_a_poly_a @ F @ (pCons_a @ C @ P)) = (pCons_poly_a @ (F @ C) @ (map_poly_a_poly_a @ F @ P))))))). % map_poly_pCons
thf(fact_216_map__poly__pCons, axiom,
    ((![F : a > poly_nat, C : a, P : poly_a]: (((F @ zero_zero_a) = zero_zero_poly_nat) => ((map_poly_a_poly_nat @ F @ (pCons_a @ C @ P)) = (pCons_poly_nat @ (F @ C) @ (map_poly_a_poly_nat @ F @ P))))))). % map_poly_pCons
thf(fact_217_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_218_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_219_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_220_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_221_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_222_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_223_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_224_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_225_poly__reflect__poly__0, axiom,
    ((![P : poly_poly_a]: ((poly_poly_a2 @ (reflect_poly_poly_a @ P) @ zero_zero_poly_a) = (coeff_poly_a @ P @ (degree_poly_a @ P)))))). % poly_reflect_poly_0
thf(fact_226_poly__reflect__poly__0, axiom,
    ((![P : poly_nat]: ((poly_nat2 @ (reflect_poly_nat @ P) @ zero_zero_nat) = (coeff_nat @ P @ (degree_nat @ P)))))). % poly_reflect_poly_0
thf(fact_227_poly__reflect__poly__0, axiom,
    ((![P : poly_a]: ((poly_a2 @ (reflect_poly_a @ P) @ zero_zero_a) = (coeff_a @ P @ (degree_a @ P)))))). % poly_reflect_poly_0
thf(fact_228_poly__reflect__poly__0, axiom,
    ((![P : poly_poly_nat]: ((poly_poly_nat2 @ (reflec781175074ly_nat @ P) @ zero_zero_poly_nat) = (coeff_poly_nat @ P @ (degree_poly_nat @ P)))))). % poly_reflect_poly_0
thf(fact_229_poly__reflect__poly__0, axiom,
    ((![P : poly_poly_poly_a]: ((poly_poly_poly_a2 @ (reflec581648976poly_a @ P) @ zero_z2096148049poly_a) = (coeff_poly_poly_a @ P @ (degree_poly_poly_a @ P)))))). % poly_reflect_poly_0
thf(fact_230_degree__reflect__poly__eq, axiom,
    ((![P : poly_poly_a]: ((~ (((coeff_poly_a @ P @ zero_zero_nat) = zero_zero_poly_a))) => ((degree_poly_a @ (reflect_poly_poly_a @ P)) = (degree_poly_a @ P)))))). % degree_reflect_poly_eq
thf(fact_231_degree__reflect__poly__eq, axiom,
    ((![P : poly_nat]: ((~ (((coeff_nat @ P @ zero_zero_nat) = zero_zero_nat))) => ((degree_nat @ (reflect_poly_nat @ P)) = (degree_nat @ P)))))). % degree_reflect_poly_eq
thf(fact_232_degree__reflect__poly__eq, axiom,
    ((![P : poly_a]: ((~ (((coeff_a @ P @ zero_zero_nat) = zero_zero_a))) => ((degree_a @ (reflect_poly_a @ P)) = (degree_a @ P)))))). % degree_reflect_poly_eq
thf(fact_233_degree__reflect__poly__eq, axiom,
    ((![P : poly_poly_nat]: ((~ (((coeff_poly_nat @ P @ zero_zero_nat) = zero_zero_poly_nat))) => ((degree_poly_nat @ (reflec781175074ly_nat @ P)) = (degree_poly_nat @ P)))))). % degree_reflect_poly_eq
thf(fact_234_degree__reflect__poly__eq, axiom,
    ((![P : poly_poly_poly_a]: ((~ (((coeff_poly_poly_a @ P @ zero_zero_nat) = zero_z2096148049poly_a))) => ((degree_poly_poly_a @ (reflec581648976poly_a @ P)) = (degree_poly_poly_a @ P)))))). % degree_reflect_poly_eq
thf(fact_235_dvd__0__right, axiom,
    ((![A : poly_a]: (dvd_dvd_poly_a @ A @ zero_zero_poly_a)))). % dvd_0_right
thf(fact_236_dvd__0__right, axiom,
    ((![A : nat]: (dvd_dvd_nat @ A @ zero_zero_nat)))). % dvd_0_right
thf(fact_237_dvd__0__right, axiom,
    ((![A : a]: (dvd_dvd_a @ A @ zero_zero_a)))). % dvd_0_right
thf(fact_238_dvd__0__right, axiom,
    ((![A : poly_nat]: (dvd_dvd_poly_nat @ A @ zero_zero_poly_nat)))). % dvd_0_right
thf(fact_239_dvd__0__right, axiom,
    ((![A : poly_poly_a]: (dvd_dvd_poly_poly_a @ A @ zero_z2096148049poly_a)))). % dvd_0_right
thf(fact_240_dvd__0__left__iff, axiom,
    ((![A : nat]: ((dvd_dvd_nat @ zero_zero_nat @ A) = (A = zero_zero_nat))))). % dvd_0_left_iff
thf(fact_241_dvd__0__left__iff, axiom,
    ((![A : a]: ((dvd_dvd_a @ zero_zero_a @ A) = (A = zero_zero_a))))). % dvd_0_left_iff
thf(fact_242_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_243_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_244_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_245_dvd__antisym, axiom,
    ((![M : nat, N : nat]: ((dvd_dvd_nat @ M @ N) => ((dvd_dvd_nat @ N @ M) => (M = N)))))). % dvd_antisym

% Conjectures (1)
thf(conj_0, conjecture,
    ((((poly_a2 @ (pCons_a @ c @ zero_zero_poly_a) @ x) = y) = (c = y)))).
