% 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_1035__5377660_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:35:26.554

% Could-be-implicit typings (7)
thf(ty_n_t__Polynomial__Opoly_It__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J_J, type,
    poly_p1267267526omplex : $tType).
thf(ty_n_t__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
    poly_poly_complex : $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__Complex__Ocomplex_J, type,
    poly_complex : $tType).
thf(ty_n_t__Polynomial__Opoly_It__Nat__Onat_J, type,
    poly_nat : $tType).
thf(ty_n_t__Complex__Ocomplex, type,
    complex : $tType).
thf(ty_n_t__Nat__Onat, type,
    nat : $tType).

% Explicit typings (76)
thf(sy_c_Fundamental__Theorem__Algebra__Mirabelle__sywschxjbb_Oconstant_001t__Complex__Ocomplex_001t__Complex__Ocomplex, type,
    fundam1158420650omplex : (complex > complex) > $o).
thf(sy_c_Fundamental__Theorem__Algebra__Mirabelle__sywschxjbb_Ooffset__poly_001t__Complex__Ocomplex, type,
    fundam1201687030omplex : poly_complex > complex > poly_complex).
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_It__Complex__Ocomplex_J, type,
    fundam1307691262omplex : poly_poly_complex > poly_complex > poly_poly_complex).
thf(sy_c_Fundamental__Theorem__Algebra__Mirabelle__sywschxjbb_Opsize_001t__Complex__Ocomplex, type,
    fundam1709708056omplex : poly_complex > nat).
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_It__Complex__Ocomplex_J, type,
    fundam1956464160omplex : poly_poly_complex > nat).
thf(sy_c_Groups_Oone__class_Oone_001t__Complex__Ocomplex, type,
    one_one_complex : complex).
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__Complex__Ocomplex_J, type,
    one_one_poly_complex : poly_complex).
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_It__Complex__Ocomplex_J_J, type,
    one_on1331105667omplex : poly_poly_complex).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Complex__Ocomplex, type,
    zero_zero_complex : complex).
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__Complex__Ocomplex_J, type,
    zero_z1746442943omplex : poly_complex).
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__Complex__Ocomplex_J_J, type,
    zero_z1040703943omplex : poly_poly_complex).
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_It__Complex__Ocomplex_J_J_J, type,
    zero_z1200043727omplex : poly_p1267267526omplex).
thf(sy_c_If_001t__Nat__Onat, type,
    if_nat : $o > nat > nat > nat).
thf(sy_c_Nat_OSuc, type,
    suc : nat > nat).
thf(sy_c_Polynomial_Ocontent_001t__Nat__Onat, type,
    content_nat : poly_nat > nat).
thf(sy_c_Polynomial_Odegree_001t__Complex__Ocomplex, type,
    degree_complex : poly_complex > nat).
thf(sy_c_Polynomial_Odegree_001t__Nat__Onat, type,
    degree_nat : poly_nat > nat).
thf(sy_c_Polynomial_Odegree_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    degree_poly_complex : poly_poly_complex > 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_It__Complex__Ocomplex_J_J, type,
    degree2006505739omplex : poly_p1267267526omplex > nat).
thf(sy_c_Polynomial_Odivide__poly__main_001t__Complex__Ocomplex, type,
    divide23485933omplex : complex > poly_complex > poly_complex > poly_complex > nat > nat > poly_complex).
thf(sy_c_Polynomial_Odivide__poly__main_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    divide219992821omplex : poly_complex > poly_poly_complex > poly_poly_complex > poly_poly_complex > nat > nat > poly_poly_complex).
thf(sy_c_Polynomial_Odivide__poly__main_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
    divide713971197omplex : poly_poly_complex > poly_p1267267526omplex > poly_p1267267526omplex > poly_p1267267526omplex > nat > nat > poly_p1267267526omplex).
thf(sy_c_Polynomial_Ois__zero_001t__Complex__Ocomplex, type,
    is_zero_complex : poly_complex > $o).
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_It__Complex__Ocomplex_J, type,
    is_zero_poly_complex : poly_poly_complex > $o).
thf(sy_c_Polynomial_OpCons_001t__Complex__Ocomplex, type,
    pCons_complex : complex > poly_complex > poly_complex).
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__Complex__Ocomplex_J, type,
    pCons_poly_complex : poly_complex > poly_poly_complex > poly_poly_complex).
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_It__Complex__Ocomplex_J_J, type,
    pCons_1087637536omplex : poly_poly_complex > poly_p1267267526omplex > poly_p1267267526omplex).
thf(sy_c_Polynomial_Opoly_001t__Complex__Ocomplex, type,
    poly_complex2 : poly_complex > complex > complex).
thf(sy_c_Polynomial_Opoly_001t__Nat__Onat, type,
    poly_nat2 : poly_nat > nat > nat).
thf(sy_c_Polynomial_Opoly_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    poly_poly_complex2 : poly_poly_complex > poly_complex > poly_complex).
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_It__Complex__Ocomplex_J_J, type,
    poly_p282434315omplex : poly_p1267267526omplex > poly_poly_complex > poly_poly_complex).
thf(sy_c_Polynomial_Opoly_Ocoeff_001t__Complex__Ocomplex, type,
    coeff_complex : poly_complex > nat > complex).
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__Complex__Ocomplex_J, type,
    coeff_poly_complex : poly_poly_complex > nat > poly_complex).
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_It__Complex__Ocomplex_J_J, type,
    coeff_1429652124omplex : poly_p1267267526omplex > nat > poly_poly_complex).
thf(sy_c_Polynomial_Opoly__cutoff_001t__Complex__Ocomplex, type,
    poly_cutoff_complex : nat > poly_complex > poly_complex).
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_It__Complex__Ocomplex_J, type,
    poly_c622223248omplex : nat > poly_poly_complex > poly_poly_complex).
thf(sy_c_Polynomial_Opoly__shift_001t__Complex__Ocomplex, type,
    poly_shift_complex : nat > poly_complex > poly_complex).
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_It__Complex__Ocomplex_J, type,
    poly_s558570093omplex : nat > poly_poly_complex > poly_poly_complex).
thf(sy_c_Polynomial_Oreflect__poly_001t__Complex__Ocomplex, type,
    reflect_poly_complex : poly_complex > poly_complex).
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__Complex__Ocomplex_J, type,
    reflec309385472omplex : poly_poly_complex > poly_poly_complex).
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_It__Complex__Ocomplex_J_J, type,
    reflec1997789704omplex : poly_p1267267526omplex > poly_p1267267526omplex).
thf(sy_c_Polynomial_Osynthetic__div_001t__Complex__Ocomplex, type,
    synthe151143547omplex : poly_complex > complex > poly_complex).
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_It__Complex__Ocomplex_J, type,
    synthe1985144195omplex : poly_poly_complex > poly_complex > poly_poly_complex).
thf(sy_c_Power_Opower__class_Opower_001t__Complex__Ocomplex, type,
    power_power_complex : complex > nat > complex).
thf(sy_c_Power_Opower__class_Opower_001t__Nat__Onat, type,
    power_power_nat : nat > nat > nat).
thf(sy_c_Power_Opower__class_Opower_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    power_184595776omplex : poly_complex > nat > poly_complex).
thf(sy_c_Power_Opower__class_Opower_001t__Polynomial__Opoly_It__Nat__Onat_J, type,
    power_power_poly_nat : poly_nat > nat > poly_nat).
thf(sy_c_Power_Opower__class_Opower_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
    power_432682568omplex : poly_poly_complex > nat > poly_poly_complex).
thf(sy_c_Rings_Odvd__class_Odvd_001t__Complex__Ocomplex, type,
    dvd_dvd_complex : complex > complex > $o).
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__Complex__Ocomplex_J, type,
    dvd_dvd_poly_complex : poly_complex > poly_complex > $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_It__Complex__Ocomplex_J_J, type,
    dvd_dv598755940omplex : poly_poly_complex > poly_poly_complex > $o).
thf(sy_v_n____, type,
    n : nat).
thf(sy_v_p, type,
    p : poly_complex).
thf(sy_v_q, type,
    q : poly_complex).
thf(sy_v_x____, type,
    x : complex).

% Relevant facts (243)
thf(fact_0_constant__def, axiom,
    ((fundam1158420650omplex = (^[F : complex > complex]: (![X : complex]: (![Y : complex]: ((F @ X) = (F @ Y)))))))). % constant_def
thf(fact_1_dp_I1_J, axiom,
    ((~ ((p = zero_z1746442943omplex))))). % dp(1)
thf(fact_2_zero__reorient, axiom,
    ((![X2 : poly_poly_complex]: ((zero_z1040703943omplex = X2) = (X2 = zero_z1040703943omplex))))). % zero_reorient
thf(fact_3_zero__reorient, axiom,
    ((![X2 : poly_nat]: ((zero_zero_poly_nat = X2) = (X2 = zero_zero_poly_nat))))). % zero_reorient
thf(fact_4_zero__reorient, axiom,
    ((![X2 : poly_complex]: ((zero_z1746442943omplex = X2) = (X2 = zero_z1746442943omplex))))). % zero_reorient
thf(fact_5_zero__reorient, axiom,
    ((![X2 : complex]: ((zero_zero_complex = X2) = (X2 = zero_zero_complex))))). % zero_reorient
thf(fact_6_zero__reorient, axiom,
    ((![X2 : nat]: ((zero_zero_nat = X2) = (X2 = zero_zero_nat))))). % zero_reorient
thf(fact_7_offset__poly__0, axiom,
    ((![H : poly_complex]: ((fundam1307691262omplex @ zero_z1040703943omplex @ H) = zero_z1040703943omplex)))). % offset_poly_0
thf(fact_8_offset__poly__0, axiom,
    ((![H : nat]: ((fundam170929432ly_nat @ zero_zero_poly_nat @ H) = zero_zero_poly_nat)))). % offset_poly_0
thf(fact_9_offset__poly__0, axiom,
    ((![H : complex]: ((fundam1201687030omplex @ zero_z1746442943omplex @ H) = zero_z1746442943omplex)))). % offset_poly_0
thf(fact_10_offset__poly__eq__0__iff, axiom,
    ((![P : poly_poly_complex, H : poly_complex]: (((fundam1307691262omplex @ P @ H) = zero_z1040703943omplex) = (P = zero_z1040703943omplex))))). % offset_poly_eq_0_iff
thf(fact_11_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_12_offset__poly__eq__0__iff, axiom,
    ((![P : poly_complex, H : complex]: (((fundam1201687030omplex @ P @ H) = zero_z1746442943omplex) = (P = zero_z1746442943omplex))))). % offset_poly_eq_0_iff
thf(fact_13_divide__poly__main__0, axiom,
    ((![R : poly_p1267267526omplex, D : poly_p1267267526omplex, Dr : nat, N : nat]: ((divide713971197omplex @ zero_z1040703943omplex @ zero_z1200043727omplex @ R @ D @ Dr @ N) = zero_z1200043727omplex)))). % divide_poly_main_0
thf(fact_14_divide__poly__main__0, axiom,
    ((![R : poly_poly_complex, D : poly_poly_complex, Dr : nat, N : nat]: ((divide219992821omplex @ zero_z1746442943omplex @ zero_z1040703943omplex @ R @ D @ Dr @ N) = zero_z1040703943omplex)))). % divide_poly_main_0
thf(fact_15_divide__poly__main__0, axiom,
    ((![R : poly_complex, D : poly_complex, Dr : nat, N : nat]: ((divide23485933omplex @ zero_zero_complex @ zero_z1746442943omplex @ R @ D @ Dr @ N) = zero_z1746442943omplex)))). % divide_poly_main_0
thf(fact_16_content__0, axiom,
    (((content_nat @ zero_zero_poly_nat) = zero_zero_nat))). % content_0
thf(fact_17_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_18_that_I2_J, axiom,
    (((poly_complex2 @ p @ x) = zero_zero_complex))). % that(2)
thf(fact_19_dp_I2_J, axiom,
    (((degree_complex @ p) = (suc @ n)))). % dp(2)
thf(fact_20_is__zero__null, axiom,
    ((is_zero_complex = (^[P2 : poly_complex]: (P2 = zero_z1746442943omplex))))). % is_zero_null
thf(fact_21_is__zero__null, axiom,
    ((is_zero_poly_complex = (^[P2 : poly_poly_complex]: (P2 = zero_z1040703943omplex))))). % is_zero_null
thf(fact_22_is__zero__null, axiom,
    ((is_zero_nat = (^[P2 : poly_nat]: (P2 = zero_zero_poly_nat))))). % is_zero_null
thf(fact_23_that_I3_J, axiom,
    ((~ (((poly_complex2 @ q @ x) = zero_zero_complex))))). % that(3)
thf(fact_24__092_060open_062_092_060And_062thesis_O_A_092_060lbrakk_062p_A_061_A0_A_092_060Longrightarrow_062_Athesis_059_A_092_060lbrakk_062p_A_092_060noteq_062_A0_059_Adegree_Ap_A_061_A0_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_059_A_092_060And_062n_O_A_092_060lbrakk_062p_A_092_060noteq_062_A0_059_Adegree_Ap_A_061_ASuc_An_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom,
    (((~ ((p = zero_z1746442943omplex))) => (((~ ((p = zero_z1746442943omplex))) => (~ (((degree_complex @ p) = zero_zero_nat)))) => (~ (((~ ((p = zero_z1746442943omplex))) => (![N2 : nat]: (~ (((degree_complex @ p) = (suc @ N2)))))))))))). % \<open>\<And>thesis. \<lbrakk>p = 0 \<Longrightarrow> thesis; \<lbrakk>p \<noteq> 0; degree p = 0\<rbrakk> \<Longrightarrow> thesis; \<And>n. \<lbrakk>p \<noteq> 0; degree p = Suc n\<rbrakk> \<Longrightarrow> thesis\<rbrakk> \<Longrightarrow> thesis\<close>
thf(fact_25_degree__0, axiom,
    (((degree_complex @ zero_z1746442943omplex) = zero_zero_nat))). % degree_0
thf(fact_26_degree__0, axiom,
    (((degree_poly_complex @ zero_z1040703943omplex) = zero_zero_nat))). % degree_0
thf(fact_27_degree__0, axiom,
    (((degree_nat @ zero_zero_poly_nat) = zero_zero_nat))). % degree_0
thf(fact_28_poly__0, axiom,
    ((![X2 : poly_poly_complex]: ((poly_p282434315omplex @ zero_z1200043727omplex @ X2) = zero_z1040703943omplex)))). % poly_0
thf(fact_29_poly__0, axiom,
    ((![X2 : poly_nat]: ((poly_poly_nat2 @ zero_z1059985641ly_nat @ X2) = zero_zero_poly_nat)))). % poly_0
thf(fact_30_poly__0, axiom,
    ((![X2 : complex]: ((poly_complex2 @ zero_z1746442943omplex @ X2) = zero_zero_complex)))). % poly_0
thf(fact_31_poly__0, axiom,
    ((![X2 : poly_complex]: ((poly_poly_complex2 @ zero_z1040703943omplex @ X2) = zero_z1746442943omplex)))). % poly_0
thf(fact_32_poly__0, axiom,
    ((![X2 : nat]: ((poly_nat2 @ zero_zero_poly_nat @ X2) = zero_zero_nat)))). % poly_0
thf(fact_33_divide__poly__main_Osimps_I2_J, axiom,
    ((![Lc : complex, Q : poly_complex, R : poly_complex, D : poly_complex, Dr : nat]: ((divide23485933omplex @ Lc @ Q @ R @ D @ Dr @ zero_zero_nat) = Q)))). % divide_poly_main.simps(2)
thf(fact_34_divide__poly__main_Osimps_I2_J, axiom,
    ((![Lc : poly_complex, Q : poly_poly_complex, R : poly_poly_complex, D : poly_poly_complex, Dr : nat]: ((divide219992821omplex @ Lc @ Q @ R @ D @ Dr @ zero_zero_nat) = Q)))). % divide_poly_main.simps(2)
thf(fact_35_fundamental__theorem__of__algebra, axiom,
    ((![P : poly_complex]: ((~ ((fundam1158420650omplex @ (poly_complex2 @ P)))) => (?[Z : complex]: ((poly_complex2 @ P @ Z) = zero_zero_complex)))))). % fundamental_theorem_of_algebra
thf(fact_36_degree__offset__poly, axiom,
    ((![P : poly_complex, H : complex]: ((degree_complex @ (fundam1201687030omplex @ P @ H)) = (degree_complex @ P))))). % degree_offset_poly
thf(fact_37_poly__eq__poly__eq__iff, axiom,
    ((![P : poly_complex, Q : poly_complex]: (((poly_complex2 @ P) = (poly_complex2 @ Q)) = (P = Q))))). % poly_eq_poly_eq_iff
thf(fact_38_poly__all__0__iff__0, axiom,
    ((![P : poly_poly_complex]: ((![X : poly_complex]: ((poly_poly_complex2 @ P @ X) = zero_z1746442943omplex)) = (P = zero_z1040703943omplex))))). % poly_all_0_iff_0
thf(fact_39_poly__all__0__iff__0, axiom,
    ((![P : poly_complex]: ((![X : complex]: ((poly_complex2 @ P @ X) = zero_zero_complex)) = (P = zero_z1746442943omplex))))). % poly_all_0_iff_0
thf(fact_40_poly__all__0__iff__0, axiom,
    ((![P : poly_p1267267526omplex]: ((![X : poly_poly_complex]: ((poly_p282434315omplex @ P @ X) = zero_z1040703943omplex)) = (P = zero_z1200043727omplex))))). % poly_all_0_iff_0
thf(fact_41_old_Onat_Oinject, axiom,
    ((![Nat : nat, Nat2 : nat]: (((suc @ Nat) = (suc @ Nat2)) = (Nat = Nat2))))). % old.nat.inject
thf(fact_42_nat_Oinject, axiom,
    ((![X22 : nat, Y2 : nat]: (((suc @ X22) = (suc @ Y2)) = (X22 = Y2))))). % nat.inject
thf(fact_43_psize__def, axiom,
    ((fundam1709708056omplex = (^[P2 : poly_complex]: (if_nat @ (P2 = zero_z1746442943omplex) @ zero_zero_nat @ (suc @ (degree_complex @ P2))))))). % psize_def
thf(fact_44_psize__def, axiom,
    ((fundam1956464160omplex = (^[P2 : poly_poly_complex]: (if_nat @ (P2 = zero_z1040703943omplex) @ zero_zero_nat @ (suc @ (degree_poly_complex @ P2))))))). % psize_def
thf(fact_45_psize__def, axiom,
    ((fundam1567013434ze_nat = (^[P2 : poly_nat]: (if_nat @ (P2 = zero_zero_poly_nat) @ zero_zero_nat @ (suc @ (degree_nat @ P2))))))). % psize_def
thf(fact_46_dvd, axiom,
    ((dvd_dvd_poly_complex @ p @ (power_184595776omplex @ q @ (suc @ n))))). % dvd
thf(fact_47_poly__cutoff__0, axiom,
    ((![N : nat]: ((poly_cutoff_complex @ N @ zero_z1746442943omplex) = zero_z1746442943omplex)))). % poly_cutoff_0
thf(fact_48_poly__cutoff__0, axiom,
    ((![N : nat]: ((poly_c622223248omplex @ N @ zero_z1040703943omplex) = zero_z1040703943omplex)))). % poly_cutoff_0
thf(fact_49_poly__cutoff__0, axiom,
    ((![N : nat]: ((poly_cutoff_nat @ N @ zero_zero_poly_nat) = zero_zero_poly_nat)))). % poly_cutoff_0
thf(fact_50_reflect__poly__at__0__eq__0__iff, axiom,
    ((![P : poly_poly_complex]: (((poly_poly_complex2 @ (reflec309385472omplex @ P) @ zero_z1746442943omplex) = zero_z1746442943omplex) = (P = zero_z1040703943omplex))))). % reflect_poly_at_0_eq_0_iff
thf(fact_51_reflect__poly__at__0__eq__0__iff, axiom,
    ((![P : poly_complex]: (((poly_complex2 @ (reflect_poly_complex @ P) @ zero_zero_complex) = zero_zero_complex) = (P = zero_z1746442943omplex))))). % reflect_poly_at_0_eq_0_iff
thf(fact_52_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_53_reflect__poly__at__0__eq__0__iff, axiom,
    ((![P : poly_p1267267526omplex]: (((poly_p282434315omplex @ (reflec1997789704omplex @ P) @ zero_z1040703943omplex) = zero_z1040703943omplex) = (P = zero_z1200043727omplex))))). % reflect_poly_at_0_eq_0_iff
thf(fact_54_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_55_fundamental__theorem__of__algebra__alt, axiom,
    ((![P : poly_complex]: ((~ ((?[A : complex, L : poly_complex]: ((~ ((A = zero_zero_complex))) & ((L = zero_z1746442943omplex) & (P = (pCons_complex @ A @ L))))))) => (?[Z : complex]: ((poly_complex2 @ P @ Z) = zero_zero_complex)))))). % fundamental_theorem_of_algebra_alt
thf(fact_56_synthetic__div__eq__0__iff, axiom,
    ((![P : poly_complex, C : complex]: (((synthe151143547omplex @ P @ C) = zero_z1746442943omplex) = ((degree_complex @ P) = zero_zero_nat))))). % synthetic_div_eq_0_iff
thf(fact_57_synthetic__div__eq__0__iff, axiom,
    ((![P : poly_poly_complex, C : poly_complex]: (((synthe1985144195omplex @ P @ C) = zero_z1040703943omplex) = ((degree_poly_complex @ P) = zero_zero_nat))))). % synthetic_div_eq_0_iff
thf(fact_58_synthetic__div__eq__0__iff, axiom,
    ((![P : poly_nat, C : nat]: (((synthetic_div_nat @ P @ C) = zero_zero_poly_nat) = ((degree_nat @ P) = zero_zero_nat))))). % synthetic_div_eq_0_iff
thf(fact_59_poly__shift__0, axiom,
    ((![N : nat]: ((poly_shift_complex @ N @ zero_z1746442943omplex) = zero_z1746442943omplex)))). % poly_shift_0
thf(fact_60_poly__shift__0, axiom,
    ((![N : nat]: ((poly_s558570093omplex @ N @ zero_z1040703943omplex) = zero_z1040703943omplex)))). % poly_shift_0
thf(fact_61_poly__shift__0, axiom,
    ((![N : nat]: ((poly_shift_nat @ N @ zero_zero_poly_nat) = zero_zero_poly_nat)))). % poly_shift_0
thf(fact_62_pCons__eq__iff, axiom,
    ((![A2 : complex, P : poly_complex, B : complex, Q : poly_complex]: (((pCons_complex @ A2 @ P) = (pCons_complex @ B @ Q)) = (((A2 = B)) & ((P = Q))))))). % pCons_eq_iff
thf(fact_63_reflect__poly__0, axiom,
    (((reflect_poly_complex @ zero_z1746442943omplex) = zero_z1746442943omplex))). % reflect_poly_0
thf(fact_64_reflect__poly__0, axiom,
    (((reflec309385472omplex @ zero_z1040703943omplex) = zero_z1040703943omplex))). % reflect_poly_0
thf(fact_65_reflect__poly__0, axiom,
    (((reflect_poly_nat @ zero_zero_poly_nat) = zero_zero_poly_nat))). % reflect_poly_0
thf(fact_66_synthetic__div__0, axiom,
    ((![C : complex]: ((synthe151143547omplex @ zero_z1746442943omplex @ C) = zero_z1746442943omplex)))). % synthetic_div_0
thf(fact_67_synthetic__div__0, axiom,
    ((![C : poly_complex]: ((synthe1985144195omplex @ zero_z1040703943omplex @ C) = zero_z1040703943omplex)))). % synthetic_div_0
thf(fact_68_synthetic__div__0, axiom,
    ((![C : nat]: ((synthetic_div_nat @ zero_zero_poly_nat @ C) = zero_zero_poly_nat)))). % synthetic_div_0
thf(fact_69_pCons__0__0, axiom,
    (((pCons_poly_complex @ zero_z1746442943omplex @ zero_z1040703943omplex) = zero_z1040703943omplex))). % pCons_0_0
thf(fact_70_pCons__0__0, axiom,
    (((pCons_complex @ zero_zero_complex @ zero_z1746442943omplex) = zero_z1746442943omplex))). % pCons_0_0
thf(fact_71_pCons__0__0, axiom,
    (((pCons_nat @ zero_zero_nat @ zero_zero_poly_nat) = zero_zero_poly_nat))). % pCons_0_0
thf(fact_72_pCons__0__0, axiom,
    (((pCons_1087637536omplex @ zero_z1040703943omplex @ zero_z1200043727omplex) = zero_z1200043727omplex))). % pCons_0_0
thf(fact_73_pCons__0__0, axiom,
    (((pCons_poly_nat @ zero_zero_poly_nat @ zero_z1059985641ly_nat) = zero_z1059985641ly_nat))). % pCons_0_0
thf(fact_74_pCons__eq__0__iff, axiom,
    ((![A2 : poly_poly_complex, P : poly_p1267267526omplex]: (((pCons_1087637536omplex @ A2 @ P) = zero_z1200043727omplex) = (((A2 = zero_z1040703943omplex)) & ((P = zero_z1200043727omplex))))))). % pCons_eq_0_iff
thf(fact_75_pCons__eq__0__iff, axiom,
    ((![A2 : poly_nat, P : poly_poly_nat]: (((pCons_poly_nat @ A2 @ P) = zero_z1059985641ly_nat) = (((A2 = zero_zero_poly_nat)) & ((P = zero_z1059985641ly_nat))))))). % pCons_eq_0_iff
thf(fact_76_pCons__eq__0__iff, axiom,
    ((![A2 : complex, P : poly_complex]: (((pCons_complex @ A2 @ P) = zero_z1746442943omplex) = (((A2 = zero_zero_complex)) & ((P = zero_z1746442943omplex))))))). % pCons_eq_0_iff
thf(fact_77_pCons__eq__0__iff, axiom,
    ((![A2 : poly_complex, P : poly_poly_complex]: (((pCons_poly_complex @ A2 @ P) = zero_z1040703943omplex) = (((A2 = zero_z1746442943omplex)) & ((P = zero_z1040703943omplex))))))). % pCons_eq_0_iff
thf(fact_78_pCons__eq__0__iff, axiom,
    ((![A2 : nat, P : poly_nat]: (((pCons_nat @ A2 @ P) = zero_zero_poly_nat) = (((A2 = zero_zero_nat)) & ((P = zero_zero_poly_nat))))))). % pCons_eq_0_iff
thf(fact_79_poly__power, axiom,
    ((![P : poly_poly_complex, N : nat, X2 : poly_complex]: ((poly_poly_complex2 @ (power_432682568omplex @ P @ N) @ X2) = (power_184595776omplex @ (poly_poly_complex2 @ P @ X2) @ N))))). % poly_power
thf(fact_80_poly__power, axiom,
    ((![P : poly_nat, N : nat, X2 : nat]: ((poly_nat2 @ (power_power_poly_nat @ P @ N) @ X2) = (power_power_nat @ (poly_nat2 @ P @ X2) @ N))))). % poly_power
thf(fact_81_poly__power, axiom,
    ((![P : poly_complex, N : nat, X2 : complex]: ((poly_complex2 @ (power_184595776omplex @ P @ N) @ X2) = (power_power_complex @ (poly_complex2 @ P @ X2) @ N))))). % poly_power
thf(fact_82_reflect__poly__const, axiom,
    ((![A2 : complex]: ((reflect_poly_complex @ (pCons_complex @ A2 @ zero_z1746442943omplex)) = (pCons_complex @ A2 @ zero_z1746442943omplex))))). % reflect_poly_const
thf(fact_83_reflect__poly__const, axiom,
    ((![A2 : poly_complex]: ((reflec309385472omplex @ (pCons_poly_complex @ A2 @ zero_z1040703943omplex)) = (pCons_poly_complex @ A2 @ zero_z1040703943omplex))))). % reflect_poly_const
thf(fact_84_reflect__poly__const, axiom,
    ((![A2 : nat]: ((reflect_poly_nat @ (pCons_nat @ A2 @ zero_zero_poly_nat)) = (pCons_nat @ A2 @ zero_zero_poly_nat))))). % reflect_poly_const
thf(fact_85_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_86_psize__eq__0__iff, axiom,
    ((![P : poly_complex]: (((fundam1709708056omplex @ P) = zero_zero_nat) = (P = zero_z1746442943omplex))))). % psize_eq_0_iff
thf(fact_87_psize__eq__0__iff, axiom,
    ((![P : poly_poly_complex]: (((fundam1956464160omplex @ P) = zero_zero_nat) = (P = zero_z1040703943omplex))))). % psize_eq_0_iff
thf(fact_88_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_89_synthetic__div__pCons, axiom,
    ((![A2 : complex, P : poly_complex, C : complex]: ((synthe151143547omplex @ (pCons_complex @ A2 @ P) @ C) = (pCons_complex @ (poly_complex2 @ P @ C) @ (synthe151143547omplex @ P @ C)))))). % synthetic_div_pCons
thf(fact_90_const__poly__dvd__const__poly__iff, axiom,
    ((![A2 : complex, B : complex]: ((dvd_dvd_poly_complex @ (pCons_complex @ A2 @ zero_z1746442943omplex) @ (pCons_complex @ B @ zero_z1746442943omplex)) = (dvd_dvd_complex @ A2 @ B))))). % const_poly_dvd_const_poly_iff
thf(fact_91_const__poly__dvd__const__poly__iff, axiom,
    ((![A2 : poly_complex, B : poly_complex]: ((dvd_dv598755940omplex @ (pCons_poly_complex @ A2 @ zero_z1040703943omplex) @ (pCons_poly_complex @ B @ zero_z1040703943omplex)) = (dvd_dvd_poly_complex @ A2 @ B))))). % const_poly_dvd_const_poly_iff
thf(fact_92_const__poly__dvd__const__poly__iff, axiom,
    ((![A2 : nat, B : nat]: ((dvd_dvd_poly_nat @ (pCons_nat @ A2 @ zero_zero_poly_nat) @ (pCons_nat @ B @ zero_zero_poly_nat)) = (dvd_dvd_nat @ A2 @ B))))). % const_poly_dvd_const_poly_iff
thf(fact_93_degree__pCons__eq__if, axiom,
    ((![P : poly_complex, A2 : complex]: (((P = zero_z1746442943omplex) => ((degree_complex @ (pCons_complex @ A2 @ P)) = zero_zero_nat)) & ((~ ((P = zero_z1746442943omplex))) => ((degree_complex @ (pCons_complex @ A2 @ P)) = (suc @ (degree_complex @ P)))))))). % degree_pCons_eq_if
thf(fact_94_degree__pCons__eq__if, axiom,
    ((![P : poly_poly_complex, A2 : poly_complex]: (((P = zero_z1040703943omplex) => ((degree_poly_complex @ (pCons_poly_complex @ A2 @ P)) = zero_zero_nat)) & ((~ ((P = zero_z1040703943omplex))) => ((degree_poly_complex @ (pCons_poly_complex @ A2 @ P)) = (suc @ (degree_poly_complex @ P)))))))). % degree_pCons_eq_if
thf(fact_95_degree__pCons__eq__if, axiom,
    ((![P : poly_nat, A2 : nat]: (((P = zero_zero_poly_nat) => ((degree_nat @ (pCons_nat @ A2 @ P)) = zero_zero_nat)) & ((~ ((P = zero_zero_poly_nat))) => ((degree_nat @ (pCons_nat @ A2 @ P)) = (suc @ (degree_nat @ P)))))))). % degree_pCons_eq_if
thf(fact_96_reflect__poly__power, axiom,
    ((![P : poly_complex, N : nat]: ((reflect_poly_complex @ (power_184595776omplex @ P @ N)) = (power_184595776omplex @ (reflect_poly_complex @ P) @ N))))). % reflect_poly_power
thf(fact_97_pderiv_Ocases, axiom,
    ((![X2 : poly_complex]: (~ ((![A : complex, P3 : poly_complex]: (~ ((X2 = (pCons_complex @ A @ P3)))))))))). % pderiv.cases
thf(fact_98_pCons__cases, axiom,
    ((![P : poly_complex]: (~ ((![A : complex, Q2 : poly_complex]: (~ ((P = (pCons_complex @ A @ Q2)))))))))). % pCons_cases
thf(fact_99_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_100_content__dvd, axiom,
    ((![P : poly_nat]: (dvd_dvd_poly_nat @ (pCons_nat @ (content_nat @ P) @ zero_zero_poly_nat) @ P)))). % content_dvd
thf(fact_101_poly__induct2, axiom,
    ((![P4 : poly_complex > poly_complex > $o, P : poly_complex, Q : poly_complex]: ((P4 @ zero_z1746442943omplex @ zero_z1746442943omplex) => ((![A : complex, P3 : poly_complex, B2 : complex, Q2 : poly_complex]: ((P4 @ P3 @ Q2) => (P4 @ (pCons_complex @ A @ P3) @ (pCons_complex @ B2 @ Q2)))) => (P4 @ P @ Q)))))). % poly_induct2
thf(fact_102_poly__induct2, axiom,
    ((![P4 : poly_complex > poly_poly_complex > $o, P : poly_complex, Q : poly_poly_complex]: ((P4 @ zero_z1746442943omplex @ zero_z1040703943omplex) => ((![A : complex, P3 : poly_complex, B2 : poly_complex, Q2 : poly_poly_complex]: ((P4 @ P3 @ Q2) => (P4 @ (pCons_complex @ A @ P3) @ (pCons_poly_complex @ B2 @ Q2)))) => (P4 @ P @ Q)))))). % poly_induct2
thf(fact_103_poly__induct2, axiom,
    ((![P4 : poly_complex > poly_nat > $o, P : poly_complex, Q : poly_nat]: ((P4 @ zero_z1746442943omplex @ zero_zero_poly_nat) => ((![A : complex, P3 : poly_complex, B2 : nat, Q2 : poly_nat]: ((P4 @ P3 @ Q2) => (P4 @ (pCons_complex @ A @ P3) @ (pCons_nat @ B2 @ Q2)))) => (P4 @ P @ Q)))))). % poly_induct2
thf(fact_104_poly__induct2, axiom,
    ((![P4 : poly_poly_complex > poly_complex > $o, P : poly_poly_complex, Q : poly_complex]: ((P4 @ zero_z1040703943omplex @ zero_z1746442943omplex) => ((![A : poly_complex, P3 : poly_poly_complex, B2 : complex, Q2 : poly_complex]: ((P4 @ P3 @ Q2) => (P4 @ (pCons_poly_complex @ A @ P3) @ (pCons_complex @ B2 @ Q2)))) => (P4 @ P @ Q)))))). % poly_induct2
thf(fact_105_poly__induct2, axiom,
    ((![P4 : poly_poly_complex > poly_poly_complex > $o, P : poly_poly_complex, Q : poly_poly_complex]: ((P4 @ zero_z1040703943omplex @ zero_z1040703943omplex) => ((![A : poly_complex, P3 : poly_poly_complex, B2 : poly_complex, Q2 : poly_poly_complex]: ((P4 @ P3 @ Q2) => (P4 @ (pCons_poly_complex @ A @ P3) @ (pCons_poly_complex @ B2 @ Q2)))) => (P4 @ P @ Q)))))). % poly_induct2
thf(fact_106_poly__induct2, axiom,
    ((![P4 : poly_poly_complex > poly_nat > $o, P : poly_poly_complex, Q : poly_nat]: ((P4 @ zero_z1040703943omplex @ zero_zero_poly_nat) => ((![A : poly_complex, P3 : poly_poly_complex, B2 : nat, Q2 : poly_nat]: ((P4 @ P3 @ Q2) => (P4 @ (pCons_poly_complex @ A @ P3) @ (pCons_nat @ B2 @ Q2)))) => (P4 @ P @ Q)))))). % poly_induct2
thf(fact_107_poly__induct2, axiom,
    ((![P4 : poly_nat > poly_complex > $o, P : poly_nat, Q : poly_complex]: ((P4 @ zero_zero_poly_nat @ zero_z1746442943omplex) => ((![A : nat, P3 : poly_nat, B2 : complex, Q2 : poly_complex]: ((P4 @ P3 @ Q2) => (P4 @ (pCons_nat @ A @ P3) @ (pCons_complex @ B2 @ Q2)))) => (P4 @ P @ Q)))))). % poly_induct2
thf(fact_108_poly__induct2, axiom,
    ((![P4 : poly_nat > poly_poly_complex > $o, P : poly_nat, Q : poly_poly_complex]: ((P4 @ zero_zero_poly_nat @ zero_z1040703943omplex) => ((![A : nat, P3 : poly_nat, B2 : poly_complex, Q2 : poly_poly_complex]: ((P4 @ P3 @ Q2) => (P4 @ (pCons_nat @ A @ P3) @ (pCons_poly_complex @ B2 @ Q2)))) => (P4 @ P @ Q)))))). % poly_induct2
thf(fact_109_poly__induct2, axiom,
    ((![P4 : poly_nat > poly_nat > $o, P : poly_nat, Q : poly_nat]: ((P4 @ zero_zero_poly_nat @ zero_zero_poly_nat) => ((![A : nat, P3 : poly_nat, B2 : nat, Q2 : poly_nat]: ((P4 @ P3 @ Q2) => (P4 @ (pCons_nat @ A @ P3) @ (pCons_nat @ B2 @ Q2)))) => (P4 @ P @ Q)))))). % poly_induct2
thf(fact_110_pderiv_Oinduct, axiom,
    ((![P4 : poly_complex > $o, A0 : poly_complex]: ((![A : complex, P3 : poly_complex]: (((~ ((P3 = zero_z1746442943omplex))) => (P4 @ P3)) => (P4 @ (pCons_complex @ A @ P3)))) => (P4 @ A0))))). % pderiv.induct
thf(fact_111_pderiv_Oinduct, axiom,
    ((![P4 : poly_poly_complex > $o, A0 : poly_poly_complex]: ((![A : poly_complex, P3 : poly_poly_complex]: (((~ ((P3 = zero_z1040703943omplex))) => (P4 @ P3)) => (P4 @ (pCons_poly_complex @ A @ P3)))) => (P4 @ A0))))). % pderiv.induct
thf(fact_112_pderiv_Oinduct, axiom,
    ((![P4 : poly_nat > $o, A0 : poly_nat]: ((![A : nat, P3 : poly_nat]: (((~ ((P3 = zero_zero_poly_nat))) => (P4 @ P3)) => (P4 @ (pCons_nat @ A @ P3)))) => (P4 @ A0))))). % pderiv.induct
thf(fact_113_pCons__induct, axiom,
    ((![P4 : poly_p1267267526omplex > $o, P : poly_p1267267526omplex]: ((P4 @ zero_z1200043727omplex) => ((![A : poly_poly_complex, P3 : poly_p1267267526omplex]: (((~ ((A = zero_z1040703943omplex))) | (~ ((P3 = zero_z1200043727omplex)))) => ((P4 @ P3) => (P4 @ (pCons_1087637536omplex @ A @ P3))))) => (P4 @ P)))))). % pCons_induct
thf(fact_114_pCons__induct, axiom,
    ((![P4 : poly_poly_nat > $o, P : poly_poly_nat]: ((P4 @ zero_z1059985641ly_nat) => ((![A : poly_nat, P3 : poly_poly_nat]: (((~ ((A = zero_zero_poly_nat))) | (~ ((P3 = zero_z1059985641ly_nat)))) => ((P4 @ P3) => (P4 @ (pCons_poly_nat @ A @ P3))))) => (P4 @ P)))))). % pCons_induct
thf(fact_115_pCons__induct, axiom,
    ((![P4 : poly_complex > $o, P : poly_complex]: ((P4 @ zero_z1746442943omplex) => ((![A : complex, P3 : poly_complex]: (((~ ((A = zero_zero_complex))) | (~ ((P3 = zero_z1746442943omplex)))) => ((P4 @ P3) => (P4 @ (pCons_complex @ A @ P3))))) => (P4 @ P)))))). % pCons_induct
thf(fact_116_pCons__induct, axiom,
    ((![P4 : poly_poly_complex > $o, P : poly_poly_complex]: ((P4 @ zero_z1040703943omplex) => ((![A : poly_complex, P3 : poly_poly_complex]: (((~ ((A = zero_z1746442943omplex))) | (~ ((P3 = zero_z1040703943omplex)))) => ((P4 @ P3) => (P4 @ (pCons_poly_complex @ A @ P3))))) => (P4 @ P)))))). % pCons_induct
thf(fact_117_pCons__induct, axiom,
    ((![P4 : poly_nat > $o, P : poly_nat]: ((P4 @ zero_zero_poly_nat) => ((![A : nat, P3 : poly_nat]: (((~ ((A = zero_zero_nat))) | (~ ((P3 = zero_zero_poly_nat)))) => ((P4 @ P3) => (P4 @ (pCons_nat @ A @ P3))))) => (P4 @ P)))))). % pCons_induct
thf(fact_118_degree__eq__zeroE, axiom,
    ((![P : poly_complex]: (((degree_complex @ P) = zero_zero_nat) => (~ ((![A : complex]: (~ ((P = (pCons_complex @ A @ zero_z1746442943omplex))))))))))). % degree_eq_zeroE
thf(fact_119_degree__eq__zeroE, axiom,
    ((![P : poly_poly_complex]: (((degree_poly_complex @ P) = zero_zero_nat) => (~ ((![A : poly_complex]: (~ ((P = (pCons_poly_complex @ A @ zero_z1040703943omplex))))))))))). % degree_eq_zeroE
thf(fact_120_degree__eq__zeroE, axiom,
    ((![P : poly_nat]: (((degree_nat @ P) = zero_zero_nat) => (~ ((![A : nat]: (~ ((P = (pCons_nat @ A @ zero_zero_poly_nat))))))))))). % degree_eq_zeroE
thf(fact_121_degree__pCons__0, axiom,
    ((![A2 : complex]: ((degree_complex @ (pCons_complex @ A2 @ zero_z1746442943omplex)) = zero_zero_nat)))). % degree_pCons_0
thf(fact_122_degree__pCons__0, axiom,
    ((![A2 : poly_complex]: ((degree_poly_complex @ (pCons_poly_complex @ A2 @ zero_z1040703943omplex)) = zero_zero_nat)))). % degree_pCons_0
thf(fact_123_degree__pCons__0, axiom,
    ((![A2 : nat]: ((degree_nat @ (pCons_nat @ A2 @ zero_zero_poly_nat)) = zero_zero_nat)))). % degree_pCons_0
thf(fact_124_nullstellensatz__lemma, axiom,
    ((![P : poly_complex, Q : poly_complex, N : nat]: ((![X3 : complex]: (((poly_complex2 @ P @ X3) = zero_zero_complex) => ((poly_complex2 @ Q @ X3) = zero_zero_complex))) => (((degree_complex @ P) = N) => ((~ ((N = zero_zero_nat))) => (dvd_dvd_poly_complex @ P @ (power_184595776omplex @ Q @ N)))))))). % nullstellensatz_lemma
thf(fact_125_offset__poly__single, axiom,
    ((![A2 : poly_complex, H : poly_complex]: ((fundam1307691262omplex @ (pCons_poly_complex @ A2 @ zero_z1040703943omplex) @ H) = (pCons_poly_complex @ A2 @ zero_z1040703943omplex))))). % offset_poly_single
thf(fact_126_offset__poly__single, axiom,
    ((![A2 : nat, H : nat]: ((fundam170929432ly_nat @ (pCons_nat @ A2 @ zero_zero_poly_nat) @ H) = (pCons_nat @ A2 @ zero_zero_poly_nat))))). % offset_poly_single
thf(fact_127_offset__poly__single, axiom,
    ((![A2 : complex, H : complex]: ((fundam1201687030omplex @ (pCons_complex @ A2 @ zero_z1746442943omplex) @ H) = (pCons_complex @ A2 @ zero_z1746442943omplex))))). % offset_poly_single
thf(fact_128_degree__pCons__eq, axiom,
    ((![P : poly_complex, A2 : complex]: ((~ ((P = zero_z1746442943omplex))) => ((degree_complex @ (pCons_complex @ A2 @ P)) = (suc @ (degree_complex @ P))))))). % degree_pCons_eq
thf(fact_129_degree__pCons__eq, axiom,
    ((![P : poly_poly_complex, A2 : poly_complex]: ((~ ((P = zero_z1040703943omplex))) => ((degree_poly_complex @ (pCons_poly_complex @ A2 @ P)) = (suc @ (degree_poly_complex @ P))))))). % degree_pCons_eq
thf(fact_130_degree__pCons__eq, axiom,
    ((![P : poly_nat, A2 : nat]: ((~ ((P = zero_zero_poly_nat))) => ((degree_nat @ (pCons_nat @ A2 @ P)) = (suc @ (degree_nat @ P))))))). % degree_pCons_eq
thf(fact_131_Suc__inject, axiom,
    ((![X2 : nat, Y3 : nat]: (((suc @ X2) = (suc @ Y3)) => (X2 = Y3))))). % Suc_inject
thf(fact_132_n__not__Suc__n, axiom,
    ((![N : nat]: (~ ((N = (suc @ N))))))). % n_not_Suc_n
thf(fact_133_not0__implies__Suc, axiom,
    ((![N : nat]: ((~ ((N = zero_zero_nat))) => (?[M : nat]: (N = (suc @ M))))))). % not0_implies_Suc
thf(fact_134_old_Onat_Oinducts, axiom,
    ((![P4 : nat > $o, Nat : nat]: ((P4 @ zero_zero_nat) => ((![Nat3 : nat]: ((P4 @ Nat3) => (P4 @ (suc @ Nat3)))) => (P4 @ Nat)))))). % old.nat.inducts
thf(fact_135_old_Onat_Oexhaust, axiom,
    ((![Y3 : nat]: ((~ ((Y3 = zero_zero_nat))) => (~ ((![Nat3 : nat]: (~ ((Y3 = (suc @ Nat3))))))))))). % old.nat.exhaust
thf(fact_136_Zero__not__Suc, axiom,
    ((![M2 : nat]: (~ ((zero_zero_nat = (suc @ M2))))))). % Zero_not_Suc
thf(fact_137_Zero__neq__Suc, axiom,
    ((![M2 : nat]: (~ ((zero_zero_nat = (suc @ M2))))))). % Zero_neq_Suc
thf(fact_138_Suc__neq__Zero, axiom,
    ((![M2 : nat]: (~ (((suc @ M2) = zero_zero_nat)))))). % Suc_neq_Zero
thf(fact_139_zero__induct, axiom,
    ((![P4 : nat > $o, K : nat]: ((P4 @ K) => ((![N2 : nat]: ((P4 @ (suc @ N2)) => (P4 @ N2))) => (P4 @ zero_zero_nat)))))). % zero_induct
thf(fact_140_diff__induct, axiom,
    ((![P4 : nat > nat > $o, M2 : nat, N : nat]: ((![X3 : nat]: (P4 @ X3 @ zero_zero_nat)) => ((![Y4 : nat]: (P4 @ zero_zero_nat @ (suc @ Y4))) => ((![X3 : nat, Y4 : nat]: ((P4 @ X3 @ Y4) => (P4 @ (suc @ X3) @ (suc @ Y4)))) => (P4 @ M2 @ N))))))). % diff_induct
thf(fact_141_nat__induct, axiom,
    ((![P4 : nat > $o, N : nat]: ((P4 @ zero_zero_nat) => ((![N2 : nat]: ((P4 @ N2) => (P4 @ (suc @ N2)))) => (P4 @ N)))))). % nat_induct
thf(fact_142_nat_OdiscI, axiom,
    ((![Nat : nat, X22 : nat]: ((Nat = (suc @ X22)) => (~ ((Nat = zero_zero_nat))))))). % nat.discI
thf(fact_143_old_Onat_Odistinct_I1_J, axiom,
    ((![Nat2 : nat]: (~ ((zero_zero_nat = (suc @ Nat2))))))). % old.nat.distinct(1)
thf(fact_144_old_Onat_Odistinct_I2_J, axiom,
    ((![Nat2 : nat]: (~ (((suc @ Nat2) = zero_zero_nat)))))). % old.nat.distinct(2)
thf(fact_145_nat_Odistinct_I1_J, axiom,
    ((![X22 : nat]: (~ ((zero_zero_nat = (suc @ X22))))))). % nat.distinct(1)
thf(fact_146_power__Suc0__right, axiom,
    ((![A2 : poly_complex]: ((power_184595776omplex @ A2 @ (suc @ zero_zero_nat)) = A2)))). % power_Suc0_right
thf(fact_147_power__Suc0__right, axiom,
    ((![A2 : nat]: ((power_power_nat @ A2 @ (suc @ zero_zero_nat)) = A2)))). % power_Suc0_right
thf(fact_148_power__0__Suc, axiom,
    ((![N : nat]: ((power_power_complex @ zero_zero_complex @ (suc @ N)) = zero_zero_complex)))). % power_0_Suc
thf(fact_149_power__0__Suc, axiom,
    ((![N : nat]: ((power_432682568omplex @ zero_z1040703943omplex @ (suc @ N)) = zero_z1040703943omplex)))). % power_0_Suc
thf(fact_150_power__0__Suc, axiom,
    ((![N : nat]: ((power_power_poly_nat @ zero_zero_poly_nat @ (suc @ N)) = zero_zero_poly_nat)))). % power_0_Suc
thf(fact_151_power__0__Suc, axiom,
    ((![N : nat]: ((power_184595776omplex @ zero_z1746442943omplex @ (suc @ N)) = zero_z1746442943omplex)))). % power_0_Suc
thf(fact_152_power__0__Suc, axiom,
    ((![N : nat]: ((power_power_nat @ zero_zero_nat @ (suc @ N)) = zero_zero_nat)))). % power_0_Suc
thf(fact_153_dvd__0__right, axiom,
    ((![A2 : poly_complex]: (dvd_dvd_poly_complex @ A2 @ zero_z1746442943omplex)))). % dvd_0_right
thf(fact_154_dvd__0__right, axiom,
    ((![A2 : complex]: (dvd_dvd_complex @ A2 @ zero_zero_complex)))). % dvd_0_right
thf(fact_155_dvd__0__right, axiom,
    ((![A2 : nat]: (dvd_dvd_nat @ A2 @ zero_zero_nat)))). % dvd_0_right
thf(fact_156_dvd__0__right, axiom,
    ((![A2 : poly_poly_complex]: (dvd_dv598755940omplex @ A2 @ zero_z1040703943omplex)))). % dvd_0_right
thf(fact_157_dvd__0__right, axiom,
    ((![A2 : poly_nat]: (dvd_dvd_poly_nat @ A2 @ zero_zero_poly_nat)))). % dvd_0_right
thf(fact_158_dvd__0__left__iff, axiom,
    ((![A2 : poly_complex]: ((dvd_dvd_poly_complex @ zero_z1746442943omplex @ A2) = (A2 = zero_z1746442943omplex))))). % dvd_0_left_iff
thf(fact_159_dvd__0__left__iff, axiom,
    ((![A2 : complex]: ((dvd_dvd_complex @ zero_zero_complex @ A2) = (A2 = zero_zero_complex))))). % dvd_0_left_iff
thf(fact_160_dvd__0__left__iff, axiom,
    ((![A2 : nat]: ((dvd_dvd_nat @ zero_zero_nat @ A2) = (A2 = zero_zero_nat))))). % dvd_0_left_iff
thf(fact_161_dvd__0__left__iff, axiom,
    ((![A2 : poly_poly_complex]: ((dvd_dv598755940omplex @ zero_z1040703943omplex @ A2) = (A2 = zero_z1040703943omplex))))). % dvd_0_left_iff
thf(fact_162_dvd__0__left__iff, axiom,
    ((![A2 : poly_nat]: ((dvd_dvd_poly_nat @ zero_zero_poly_nat @ A2) = (A2 = zero_zero_poly_nat))))). % dvd_0_left_iff
thf(fact_163_exists__least__lemma, axiom,
    ((![P4 : nat > $o]: ((~ ((P4 @ zero_zero_nat))) => ((?[X_1 : nat]: (P4 @ X_1)) => (?[N2 : nat]: ((~ ((P4 @ N2))) & (P4 @ (suc @ N2))))))))). % exists_least_lemma
thf(fact_164_power__Suc__0, axiom,
    ((![N : nat]: ((power_power_nat @ (suc @ zero_zero_nat) @ N) = (suc @ zero_zero_nat))))). % power_Suc_0
thf(fact_165_nat__power__eq__Suc__0__iff, axiom,
    ((![X2 : nat, M2 : nat]: (((power_power_nat @ X2 @ M2) = (suc @ zero_zero_nat)) = (((M2 = zero_zero_nat)) | ((X2 = (suc @ zero_zero_nat)))))))). % nat_power_eq_Suc_0_iff
thf(fact_166_dvd__1__left, axiom,
    ((![K : nat]: (dvd_dvd_nat @ (suc @ zero_zero_nat) @ K)))). % dvd_1_left
thf(fact_167_dvd__1__iff__1, axiom,
    ((![M2 : nat]: ((dvd_dvd_nat @ M2 @ (suc @ zero_zero_nat)) = (M2 = (suc @ zero_zero_nat)))))). % dvd_1_iff_1
thf(fact_168_dvd__trans, axiom,
    ((![A2 : poly_complex, B : poly_complex, C : poly_complex]: ((dvd_dvd_poly_complex @ A2 @ B) => ((dvd_dvd_poly_complex @ B @ C) => (dvd_dvd_poly_complex @ A2 @ C)))))). % dvd_trans
thf(fact_169_dvd__trans, axiom,
    ((![A2 : nat, B : nat, C : nat]: ((dvd_dvd_nat @ A2 @ B) => ((dvd_dvd_nat @ B @ C) => (dvd_dvd_nat @ A2 @ C)))))). % dvd_trans
thf(fact_170_dvd__refl, axiom,
    ((![A2 : poly_complex]: (dvd_dvd_poly_complex @ A2 @ A2)))). % dvd_refl
thf(fact_171_dvd__refl, axiom,
    ((![A2 : nat]: (dvd_dvd_nat @ A2 @ A2)))). % dvd_refl
thf(fact_172_power__not__zero, axiom,
    ((![A2 : complex, N : nat]: ((~ ((A2 = zero_zero_complex))) => (~ (((power_power_complex @ A2 @ N) = zero_zero_complex))))))). % power_not_zero
thf(fact_173_power__not__zero, axiom,
    ((![A2 : poly_poly_complex, N : nat]: ((~ ((A2 = zero_z1040703943omplex))) => (~ (((power_432682568omplex @ A2 @ N) = zero_z1040703943omplex))))))). % power_not_zero
thf(fact_174_power__not__zero, axiom,
    ((![A2 : poly_nat, N : nat]: ((~ ((A2 = zero_zero_poly_nat))) => (~ (((power_power_poly_nat @ A2 @ N) = zero_zero_poly_nat))))))). % power_not_zero
thf(fact_175_power__not__zero, axiom,
    ((![A2 : poly_complex, N : nat]: ((~ ((A2 = zero_z1746442943omplex))) => (~ (((power_184595776omplex @ A2 @ N) = zero_z1746442943omplex))))))). % power_not_zero
thf(fact_176_power__not__zero, axiom,
    ((![A2 : nat, N : nat]: ((~ ((A2 = zero_zero_nat))) => (~ (((power_power_nat @ A2 @ N) = zero_zero_nat))))))). % power_not_zero
thf(fact_177_dvd__0__left, axiom,
    ((![A2 : poly_complex]: ((dvd_dvd_poly_complex @ zero_z1746442943omplex @ A2) => (A2 = zero_z1746442943omplex))))). % dvd_0_left
thf(fact_178_dvd__0__left, axiom,
    ((![A2 : complex]: ((dvd_dvd_complex @ zero_zero_complex @ A2) => (A2 = zero_zero_complex))))). % dvd_0_left
thf(fact_179_dvd__0__left, axiom,
    ((![A2 : nat]: ((dvd_dvd_nat @ zero_zero_nat @ A2) => (A2 = zero_zero_nat))))). % dvd_0_left
thf(fact_180_dvd__0__left, axiom,
    ((![A2 : poly_poly_complex]: ((dvd_dv598755940omplex @ zero_z1040703943omplex @ A2) => (A2 = zero_z1040703943omplex))))). % dvd_0_left
thf(fact_181_dvd__0__left, axiom,
    ((![A2 : poly_nat]: ((dvd_dvd_poly_nat @ zero_zero_poly_nat @ A2) => (A2 = zero_zero_poly_nat))))). % dvd_0_left
thf(fact_182_dvd__power__same, axiom,
    ((![X2 : poly_complex, Y3 : poly_complex, N : nat]: ((dvd_dvd_poly_complex @ X2 @ Y3) => (dvd_dvd_poly_complex @ (power_184595776omplex @ X2 @ N) @ (power_184595776omplex @ Y3 @ N)))))). % dvd_power_same
thf(fact_183_dvd__power__same, axiom,
    ((![X2 : nat, Y3 : nat, N : nat]: ((dvd_dvd_nat @ X2 @ Y3) => (dvd_dvd_nat @ (power_power_nat @ X2 @ N) @ (power_power_nat @ Y3 @ N)))))). % dvd_power_same
thf(fact_184_dvd__field__iff, axiom,
    ((dvd_dvd_complex = (^[A3 : complex]: (^[B3 : complex]: (((A3 = zero_zero_complex)) => ((B3 = zero_zero_complex)))))))). % dvd_field_iff
thf(fact_185_poly__reflect__poly__0, axiom,
    ((![P : poly_poly_complex]: ((poly_poly_complex2 @ (reflec309385472omplex @ P) @ zero_z1746442943omplex) = (coeff_poly_complex @ P @ (degree_poly_complex @ P)))))). % poly_reflect_poly_0
thf(fact_186_poly__reflect__poly__0, axiom,
    ((![P : poly_complex]: ((poly_complex2 @ (reflect_poly_complex @ P) @ zero_zero_complex) = (coeff_complex @ P @ (degree_complex @ P)))))). % poly_reflect_poly_0
thf(fact_187_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_188_poly__reflect__poly__0, axiom,
    ((![P : poly_p1267267526omplex]: ((poly_p282434315omplex @ (reflec1997789704omplex @ P) @ zero_z1040703943omplex) = (coeff_1429652124omplex @ P @ (degree2006505739omplex @ P)))))). % poly_reflect_poly_0
thf(fact_189_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_190_poly__cutoff__1, axiom,
    ((![N : nat]: (((N = zero_zero_nat) => ((poly_cutoff_complex @ N @ one_one_poly_complex) = zero_z1746442943omplex)) & ((~ ((N = zero_zero_nat))) => ((poly_cutoff_complex @ N @ one_one_poly_complex) = one_one_poly_complex)))))). % poly_cutoff_1
thf(fact_191_poly__cutoff__1, axiom,
    ((![N : nat]: (((N = zero_zero_nat) => ((poly_c622223248omplex @ N @ one_on1331105667omplex) = zero_z1040703943omplex)) & ((~ ((N = zero_zero_nat))) => ((poly_c622223248omplex @ N @ one_on1331105667omplex) = one_on1331105667omplex)))))). % poly_cutoff_1
thf(fact_192_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_193_degree__reflect__poly__eq, axiom,
    ((![P : poly_poly_complex]: ((~ (((coeff_poly_complex @ P @ zero_zero_nat) = zero_z1746442943omplex))) => ((degree_poly_complex @ (reflec309385472omplex @ P)) = (degree_poly_complex @ P)))))). % degree_reflect_poly_eq
thf(fact_194_degree__reflect__poly__eq, axiom,
    ((![P : poly_complex]: ((~ (((coeff_complex @ P @ zero_zero_nat) = zero_zero_complex))) => ((degree_complex @ (reflect_poly_complex @ P)) = (degree_complex @ P)))))). % degree_reflect_poly_eq
thf(fact_195_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_196_degree__reflect__poly__eq, axiom,
    ((![P : poly_p1267267526omplex]: ((~ (((coeff_1429652124omplex @ P @ zero_zero_nat) = zero_z1040703943omplex))) => ((degree2006505739omplex @ (reflec1997789704omplex @ P)) = (degree2006505739omplex @ P)))))). % degree_reflect_poly_eq
thf(fact_197_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_198_power__one, axiom,
    ((![N : nat]: ((power_184595776omplex @ one_one_poly_complex @ N) = one_one_poly_complex)))). % power_one
thf(fact_199_power__one, axiom,
    ((![N : nat]: ((power_power_nat @ one_one_nat @ N) = one_one_nat)))). % power_one
thf(fact_200_coeff__0, axiom,
    ((![N : nat]: ((coeff_1429652124omplex @ zero_z1200043727omplex @ N) = zero_z1040703943omplex)))). % coeff_0
thf(fact_201_coeff__0, axiom,
    ((![N : nat]: ((coeff_poly_nat @ zero_z1059985641ly_nat @ N) = zero_zero_poly_nat)))). % coeff_0
thf(fact_202_coeff__0, axiom,
    ((![N : nat]: ((coeff_complex @ zero_z1746442943omplex @ N) = zero_zero_complex)))). % coeff_0
thf(fact_203_coeff__0, axiom,
    ((![N : nat]: ((coeff_poly_complex @ zero_z1040703943omplex @ N) = zero_z1746442943omplex)))). % coeff_0
thf(fact_204_coeff__0, axiom,
    ((![N : nat]: ((coeff_nat @ zero_zero_poly_nat @ N) = zero_zero_nat)))). % coeff_0
thf(fact_205_coeff__pCons__0, axiom,
    ((![A2 : complex, P : poly_complex]: ((coeff_complex @ (pCons_complex @ A2 @ P) @ zero_zero_nat) = A2)))). % coeff_pCons_0
thf(fact_206_coeff__pCons__Suc, axiom,
    ((![A2 : complex, P : poly_complex, N : nat]: ((coeff_complex @ (pCons_complex @ A2 @ P) @ (suc @ N)) = (coeff_complex @ P @ N))))). % coeff_pCons_Suc
thf(fact_207_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_208_degree__1, axiom,
    (((degree_complex @ one_one_poly_complex) = zero_zero_nat))). % degree_1
thf(fact_209_poly__1, axiom,
    ((![X2 : complex]: ((poly_complex2 @ one_one_poly_complex @ X2) = one_one_complex)))). % poly_1
thf(fact_210_poly__1, axiom,
    ((![X2 : nat]: ((poly_nat2 @ one_one_poly_nat @ X2) = one_one_nat)))). % poly_1
thf(fact_211_content__1, axiom,
    (((content_nat @ one_one_poly_nat) = one_one_nat))). % content_1
thf(fact_212_leading__coeff__0__iff, axiom,
    ((![P : poly_poly_complex]: (((coeff_poly_complex @ P @ (degree_poly_complex @ P)) = zero_z1746442943omplex) = (P = zero_z1040703943omplex))))). % leading_coeff_0_iff
thf(fact_213_leading__coeff__0__iff, axiom,
    ((![P : poly_complex]: (((coeff_complex @ P @ (degree_complex @ P)) = zero_zero_complex) = (P = zero_z1746442943omplex))))). % leading_coeff_0_iff
thf(fact_214_leading__coeff__0__iff, axiom,
    ((![P : poly_nat]: (((coeff_nat @ P @ (degree_nat @ P)) = zero_zero_nat) = (P = zero_zero_poly_nat))))). % leading_coeff_0_iff
thf(fact_215_leading__coeff__0__iff, axiom,
    ((![P : poly_p1267267526omplex]: (((coeff_1429652124omplex @ P @ (degree2006505739omplex @ P)) = zero_z1040703943omplex) = (P = zero_z1200043727omplex))))). % leading_coeff_0_iff
thf(fact_216_leading__coeff__0__iff, axiom,
    ((![P : poly_poly_nat]: (((coeff_poly_nat @ P @ (degree_poly_nat @ P)) = zero_zero_poly_nat) = (P = zero_z1059985641ly_nat))))). % leading_coeff_0_iff
thf(fact_217_lead__coeff__pCons_I1_J, axiom,
    ((![P : poly_complex, A2 : complex]: ((~ ((P = zero_z1746442943omplex))) => ((coeff_complex @ (pCons_complex @ A2 @ P) @ (degree_complex @ (pCons_complex @ A2 @ P))) = (coeff_complex @ P @ (degree_complex @ P))))))). % lead_coeff_pCons(1)
thf(fact_218_lead__coeff__pCons_I1_J, axiom,
    ((![P : poly_poly_complex, A2 : poly_complex]: ((~ ((P = zero_z1040703943omplex))) => ((coeff_poly_complex @ (pCons_poly_complex @ A2 @ P) @ (degree_poly_complex @ (pCons_poly_complex @ A2 @ P))) = (coeff_poly_complex @ P @ (degree_poly_complex @ P))))))). % lead_coeff_pCons(1)
thf(fact_219_lead__coeff__pCons_I1_J, axiom,
    ((![P : poly_nat, A2 : nat]: ((~ ((P = zero_zero_poly_nat))) => ((coeff_nat @ (pCons_nat @ A2 @ P) @ (degree_nat @ (pCons_nat @ A2 @ P))) = (coeff_nat @ P @ (degree_nat @ P))))))). % lead_coeff_pCons(1)
thf(fact_220_lead__coeff__pCons_I2_J, axiom,
    ((![P : poly_complex, A2 : complex]: ((P = zero_z1746442943omplex) => ((coeff_complex @ (pCons_complex @ A2 @ P) @ (degree_complex @ (pCons_complex @ A2 @ P))) = A2))))). % lead_coeff_pCons(2)
thf(fact_221_lead__coeff__pCons_I2_J, axiom,
    ((![P : poly_poly_complex, A2 : poly_complex]: ((P = zero_z1040703943omplex) => ((coeff_poly_complex @ (pCons_poly_complex @ A2 @ P) @ (degree_poly_complex @ (pCons_poly_complex @ A2 @ P))) = A2))))). % lead_coeff_pCons(2)
thf(fact_222_lead__coeff__pCons_I2_J, axiom,
    ((![P : poly_nat, A2 : nat]: ((P = zero_zero_poly_nat) => ((coeff_nat @ (pCons_nat @ A2 @ P) @ (degree_nat @ (pCons_nat @ A2 @ P))) = A2))))). % lead_coeff_pCons(2)
thf(fact_223_reflect__poly__reflect__poly, axiom,
    ((![P : poly_poly_complex]: ((~ (((coeff_poly_complex @ P @ zero_zero_nat) = zero_z1746442943omplex))) => ((reflec309385472omplex @ (reflec309385472omplex @ P)) = P))))). % reflect_poly_reflect_poly
thf(fact_224_reflect__poly__reflect__poly, axiom,
    ((![P : poly_complex]: ((~ (((coeff_complex @ P @ zero_zero_nat) = zero_zero_complex))) => ((reflect_poly_complex @ (reflect_poly_complex @ P)) = P))))). % reflect_poly_reflect_poly
thf(fact_225_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_226_reflect__poly__reflect__poly, axiom,
    ((![P : poly_p1267267526omplex]: ((~ (((coeff_1429652124omplex @ P @ zero_zero_nat) = zero_z1040703943omplex))) => ((reflec1997789704omplex @ (reflec1997789704omplex @ P)) = P))))). % reflect_poly_reflect_poly
thf(fact_227_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_228_one__poly__eq__simps_I1_J, axiom,
    ((one_one_poly_complex = (pCons_complex @ one_one_complex @ zero_z1746442943omplex)))). % one_poly_eq_simps(1)
thf(fact_229_one__poly__eq__simps_I1_J, axiom,
    ((one_on1331105667omplex = (pCons_poly_complex @ one_one_poly_complex @ zero_z1040703943omplex)))). % one_poly_eq_simps(1)
thf(fact_230_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_231_one__poly__eq__simps_I2_J, axiom,
    (((pCons_complex @ one_one_complex @ zero_z1746442943omplex) = one_one_poly_complex))). % one_poly_eq_simps(2)
thf(fact_232_one__poly__eq__simps_I2_J, axiom,
    (((pCons_poly_complex @ one_one_poly_complex @ zero_z1040703943omplex) = one_on1331105667omplex))). % one_poly_eq_simps(2)
thf(fact_233_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_234_lead__coeff__1, axiom,
    (((coeff_complex @ one_one_poly_complex @ (degree_complex @ one_one_poly_complex)) = one_one_complex))). % lead_coeff_1
thf(fact_235_lead__coeff__1, axiom,
    (((coeff_nat @ one_one_poly_nat @ (degree_nat @ one_one_poly_nat)) = one_one_nat))). % lead_coeff_1
thf(fact_236_coeff__0__reflect__poly, axiom,
    ((![P : poly_complex]: ((coeff_complex @ (reflect_poly_complex @ P) @ zero_zero_nat) = (coeff_complex @ P @ (degree_complex @ P)))))). % coeff_0_reflect_poly
thf(fact_237_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_238_coeff__0__reflect__poly__0__iff, axiom,
    ((![P : poly_p1267267526omplex]: (((coeff_1429652124omplex @ (reflec1997789704omplex @ P) @ zero_zero_nat) = zero_z1040703943omplex) = (P = zero_z1200043727omplex))))). % coeff_0_reflect_poly_0_iff
thf(fact_239_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_240_dvd__antisym, axiom,
    ((![M2 : nat, N : nat]: ((dvd_dvd_nat @ M2 @ N) => ((dvd_dvd_nat @ N @ M2) => (M2 = N)))))). % dvd_antisym
thf(fact_241_gcd__nat_Oextremum__uniqueI, axiom,
    ((![A2 : nat]: ((dvd_dvd_nat @ zero_zero_nat @ A2) => (A2 = zero_zero_nat))))). % gcd_nat.extremum_uniqueI
thf(fact_242_nat__dvd__1__iff__1, axiom,
    ((![M2 : nat]: ((dvd_dvd_nat @ M2 @ one_one_nat) = (M2 = one_one_nat))))). % nat_dvd_1_iff_1

% Helper facts (3)
thf(help_If_3_1_If_001t__Nat__Onat_T, axiom,
    ((![P4 : $o]: ((P4 = $true) | (P4 = $false))))).
thf(help_If_2_1_If_001t__Nat__Onat_T, axiom,
    ((![X2 : nat, Y3 : nat]: ((if_nat @ $false @ X2 @ Y3) = Y3)))).
thf(help_If_1_1_If_001t__Nat__Onat_T, axiom,
    ((![X2 : nat, Y3 : nat]: ((if_nat @ $true @ X2 @ Y3) = X2)))).

% Conjectures (1)
thf(conj_0, conjecture,
    ($false)).
