% 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_1020__5377502_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:35:19.384

% 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 (70)
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_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_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_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_Oorder_001t__Complex__Ocomplex, type,
    order_complex : complex > poly_complex > nat).
thf(sy_c_Polynomial_Oorder_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    order_poly_complex : poly_complex > poly_poly_complex > nat).
thf(sy_c_Polynomial_Oorder_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
    order_1735763309omplex : poly_poly_complex > poly_p1267267526omplex > nat).
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_Opderiv_001t__Complex__Ocomplex, type,
    pderiv_complex : poly_complex > poly_complex).
thf(sy_c_Polynomial_Opderiv_001t__Nat__Onat, type,
    pderiv_nat : poly_nat > poly_nat).
thf(sy_c_Polynomial_Opderiv_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    pderiv_poly_complex : poly_poly_complex > poly_poly_complex).
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__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_Orsquarefree_001t__Complex__Ocomplex, type,
    rsquarefree_complex : poly_complex > $o).
thf(sy_c_Polynomial_Orsquarefree_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    rsquar936197586omplex : poly_poly_complex > $o).
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_Power_Opower__class_Opower_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Nat__Onat_J_J, type,
    power_1336127338ly_nat : poly_poly_nat > nat > poly_poly_nat).
thf(sy_c_Power_Opower__class_Opower_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J_J, type,
    power_2001192272omplex : poly_p1267267526omplex > nat > poly_p1267267526omplex).
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_p, type,
    p : poly_complex).
thf(sy_v_q, type,
    q : poly_complex).

% Relevant facts (243)
thf(fact_0_p, axiom,
    ((p = zero_z1746442943omplex))). % p
thf(fact_1_eq, axiom,
    (((![X : complex]: ((((poly_complex2 @ p @ X) = zero_zero_complex)) => (((poly_complex2 @ q @ X) = zero_zero_complex)))) = (q = zero_z1746442943omplex)))). % eq
thf(fact_2__092_060open_062p_Advd_Aq_A_094_Adegree_Ap_A_092_060Longrightarrow_062_AFalse_092_060close_062, axiom,
    ((~ ((dvd_dvd_poly_complex @ p @ (power_184595776omplex @ q @ (degree_complex @ p))))))). % \<open>p dvd q ^ degree p \<Longrightarrow> False\<close>
thf(fact_3_poly__power, axiom,
    ((![P : poly_poly_nat, N : nat, X2 : poly_nat]: ((poly_poly_nat2 @ (power_1336127338ly_nat @ P @ N) @ X2) = (power_power_poly_nat @ (poly_poly_nat2 @ P @ X2) @ N))))). % poly_power
thf(fact_4_poly__power, axiom,
    ((![P : poly_p1267267526omplex, N : nat, X2 : poly_poly_complex]: ((poly_p282434315omplex @ (power_2001192272omplex @ P @ N) @ X2) = (power_432682568omplex @ (poly_p282434315omplex @ P @ X2) @ N))))). % poly_power
thf(fact_5_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_6_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_7_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_8_poly__0, axiom,
    ((![X2 : poly_nat]: ((poly_poly_nat2 @ zero_z1059985641ly_nat @ X2) = zero_zero_poly_nat)))). % poly_0
thf(fact_9_poly__0, axiom,
    ((![X2 : poly_poly_complex]: ((poly_p282434315omplex @ zero_z1200043727omplex @ X2) = zero_z1040703943omplex)))). % poly_0
thf(fact_10_poly__0, axiom,
    ((![X2 : poly_complex]: ((poly_poly_complex2 @ zero_z1040703943omplex @ X2) = zero_z1746442943omplex)))). % poly_0
thf(fact_11_poly__0, axiom,
    ((![X2 : nat]: ((poly_nat2 @ zero_zero_poly_nat @ X2) = zero_zero_nat)))). % poly_0
thf(fact_12_poly__0, axiom,
    ((![X2 : complex]: ((poly_complex2 @ zero_z1746442943omplex @ X2) = zero_zero_complex)))). % poly_0
thf(fact_13_dvd__0__right, axiom,
    ((![A : poly_nat]: (dvd_dvd_poly_nat @ A @ zero_zero_poly_nat)))). % dvd_0_right
thf(fact_14_dvd__0__right, axiom,
    ((![A : poly_poly_complex]: (dvd_dv598755940omplex @ A @ zero_z1040703943omplex)))). % dvd_0_right
thf(fact_15_dvd__0__right, axiom,
    ((![A : complex]: (dvd_dvd_complex @ A @ zero_zero_complex)))). % dvd_0_right
thf(fact_16_dvd__0__right, axiom,
    ((![A : poly_complex]: (dvd_dvd_poly_complex @ A @ zero_z1746442943omplex)))). % dvd_0_right
thf(fact_17_dvd__0__right, axiom,
    ((![A : nat]: (dvd_dvd_nat @ A @ zero_zero_nat)))). % dvd_0_right
thf(fact_18_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_19_dvd__0__left__iff, axiom,
    ((![A : poly_poly_complex]: ((dvd_dv598755940omplex @ zero_z1040703943omplex @ A) = (A = zero_z1040703943omplex))))). % dvd_0_left_iff
thf(fact_20_dvd__0__left__iff, axiom,
    ((![A : complex]: ((dvd_dvd_complex @ zero_zero_complex @ A) = (A = zero_zero_complex))))). % dvd_0_left_iff
thf(fact_21_dvd__0__left__iff, axiom,
    ((![A : poly_complex]: ((dvd_dvd_poly_complex @ zero_z1746442943omplex @ A) = (A = zero_z1746442943omplex))))). % dvd_0_left_iff
thf(fact_22_dvd__0__left__iff, axiom,
    ((![A : nat]: ((dvd_dvd_nat @ zero_zero_nat @ A) = (A = zero_zero_nat))))). % dvd_0_left_iff
thf(fact_23_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_24_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_25_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_26_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_27_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_28_dvd__power__same, axiom,
    ((![X2 : poly_complex, Y : poly_complex, N : nat]: ((dvd_dvd_poly_complex @ X2 @ Y) => (dvd_dvd_poly_complex @ (power_184595776omplex @ X2 @ N) @ (power_184595776omplex @ Y @ N)))))). % dvd_power_same
thf(fact_29_dvd__power__same, axiom,
    ((![X2 : nat, Y : nat, N : nat]: ((dvd_dvd_nat @ X2 @ Y) => (dvd_dvd_nat @ (power_power_nat @ X2 @ N) @ (power_power_nat @ Y @ N)))))). % dvd_power_same
thf(fact_30_dvd__power__same, axiom,
    ((![X2 : complex, Y : complex, N : nat]: ((dvd_dvd_complex @ X2 @ Y) => (dvd_dvd_complex @ (power_power_complex @ X2 @ N) @ (power_power_complex @ Y @ N)))))). % dvd_power_same
thf(fact_31_dvd__power__same, axiom,
    ((![X2 : poly_nat, Y : poly_nat, N : nat]: ((dvd_dvd_poly_nat @ X2 @ Y) => (dvd_dvd_poly_nat @ (power_power_poly_nat @ X2 @ N) @ (power_power_poly_nat @ Y @ N)))))). % dvd_power_same
thf(fact_32_dvd__power__same, axiom,
    ((![X2 : poly_poly_complex, Y : poly_poly_complex, N : nat]: ((dvd_dv598755940omplex @ X2 @ Y) => (dvd_dv598755940omplex @ (power_432682568omplex @ X2 @ N) @ (power_432682568omplex @ Y @ N)))))). % dvd_power_same
thf(fact_33_dvd__field__iff, axiom,
    ((dvd_dvd_complex = (^[A2 : complex]: (^[B : complex]: (((A2 = zero_zero_complex)) => ((B = zero_zero_complex)))))))). % dvd_field_iff
thf(fact_34_dvd__0__left, axiom,
    ((![A : complex]: ((dvd_dvd_complex @ zero_zero_complex @ A) => (A = zero_zero_complex))))). % dvd_0_left
thf(fact_35_dvd__0__left, axiom,
    ((![A : poly_complex]: ((dvd_dvd_poly_complex @ zero_z1746442943omplex @ A) => (A = zero_z1746442943omplex))))). % dvd_0_left
thf(fact_36_dvd__0__left, axiom,
    ((![A : nat]: ((dvd_dvd_nat @ zero_zero_nat @ A) => (A = zero_zero_nat))))). % dvd_0_left
thf(fact_37_dvd__0__left, axiom,
    ((![A : poly_nat]: ((dvd_dvd_poly_nat @ zero_zero_poly_nat @ A) => (A = zero_zero_poly_nat))))). % dvd_0_left
thf(fact_38_dvd__0__left, axiom,
    ((![A : poly_poly_complex]: ((dvd_dv598755940omplex @ zero_z1040703943omplex @ A) => (A = zero_z1040703943omplex))))). % dvd_0_left
thf(fact_39_power__not__zero, axiom,
    ((![A : poly_complex, N : nat]: ((~ ((A = zero_z1746442943omplex))) => (~ (((power_184595776omplex @ A @ N) = zero_z1746442943omplex))))))). % power_not_zero
thf(fact_40_power__not__zero, axiom,
    ((![A : nat, N : nat]: ((~ ((A = zero_zero_nat))) => (~ (((power_power_nat @ A @ N) = zero_zero_nat))))))). % power_not_zero
thf(fact_41_power__not__zero, axiom,
    ((![A : complex, N : nat]: ((~ ((A = zero_zero_complex))) => (~ (((power_power_complex @ A @ N) = zero_zero_complex))))))). % power_not_zero
thf(fact_42_power__not__zero, axiom,
    ((![A : poly_nat, N : nat]: ((~ ((A = zero_zero_poly_nat))) => (~ (((power_power_poly_nat @ A @ N) = zero_zero_poly_nat))))))). % power_not_zero
thf(fact_43_power__not__zero, axiom,
    ((![A : poly_poly_complex, N : nat]: ((~ ((A = zero_z1040703943omplex))) => (~ (((power_432682568omplex @ A @ N) = zero_z1040703943omplex))))))). % power_not_zero
thf(fact_44_degree__0, axiom,
    (((degree_complex @ zero_z1746442943omplex) = zero_zero_nat))). % degree_0
thf(fact_45_degree__0, axiom,
    (((degree_nat @ zero_zero_poly_nat) = zero_zero_nat))). % degree_0
thf(fact_46_degree__0, axiom,
    (((degree_poly_complex @ zero_z1040703943omplex) = zero_zero_nat))). % degree_0
thf(fact_47_constant__def, axiom,
    ((fundam1158420650omplex = (^[F : complex > complex]: (![X : complex]: (![Y2 : complex]: ((F @ X) = (F @ Y2)))))))). % constant_def
thf(fact_48_zero__reorient, axiom,
    ((![X2 : complex]: ((zero_zero_complex = X2) = (X2 = zero_zero_complex))))). % zero_reorient
thf(fact_49_zero__reorient, axiom,
    ((![X2 : poly_complex]: ((zero_z1746442943omplex = X2) = (X2 = zero_z1746442943omplex))))). % zero_reorient
thf(fact_50_zero__reorient, axiom,
    ((![X2 : nat]: ((zero_zero_nat = X2) = (X2 = zero_zero_nat))))). % zero_reorient
thf(fact_51_zero__reorient, axiom,
    ((![X2 : poly_nat]: ((zero_zero_poly_nat = X2) = (X2 = zero_zero_poly_nat))))). % zero_reorient
thf(fact_52_zero__reorient, axiom,
    ((![X2 : poly_poly_complex]: ((zero_z1040703943omplex = X2) = (X2 = zero_z1040703943omplex))))). % zero_reorient
thf(fact_53_dvd__trans, axiom,
    ((![A : poly_complex, B2 : poly_complex, C : poly_complex]: ((dvd_dvd_poly_complex @ A @ B2) => ((dvd_dvd_poly_complex @ B2 @ C) => (dvd_dvd_poly_complex @ A @ C)))))). % dvd_trans
thf(fact_54_dvd__trans, axiom,
    ((![A : nat, B2 : nat, C : nat]: ((dvd_dvd_nat @ A @ B2) => ((dvd_dvd_nat @ B2 @ C) => (dvd_dvd_nat @ A @ C)))))). % dvd_trans
thf(fact_55_dvd__trans, axiom,
    ((![A : complex, B2 : complex, C : complex]: ((dvd_dvd_complex @ A @ B2) => ((dvd_dvd_complex @ B2 @ C) => (dvd_dvd_complex @ A @ C)))))). % dvd_trans
thf(fact_56_dvd__refl, axiom,
    ((![A : poly_complex]: (dvd_dvd_poly_complex @ A @ A)))). % dvd_refl
thf(fact_57_dvd__refl, axiom,
    ((![A : nat]: (dvd_dvd_nat @ A @ A)))). % dvd_refl
thf(fact_58_dvd__refl, axiom,
    ((![A : complex]: (dvd_dvd_complex @ A @ A)))). % dvd_refl
thf(fact_59_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_60_poly__eq__poly__eq__iff, axiom,
    ((![P : poly_poly_complex, Q : poly_poly_complex]: (((poly_poly_complex2 @ P) = (poly_poly_complex2 @ Q)) = (P = Q))))). % poly_eq_poly_eq_iff
thf(fact_61__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_62_psize__eq__0__iff, axiom,
    ((![P : poly_complex]: (((fundam1709708056omplex @ P) = zero_zero_nat) = (P = zero_z1746442943omplex))))). % psize_eq_0_iff
thf(fact_63_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_64_psize__eq__0__iff, axiom,
    ((![P : poly_poly_complex]: (((fundam1956464160omplex @ P) = zero_zero_nat) = (P = zero_z1040703943omplex))))). % psize_eq_0_iff
thf(fact_65_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_66_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_67_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_68_is__zero__null, axiom,
    ((is_zero_complex = (^[P2 : poly_complex]: (P2 = zero_z1746442943omplex))))). % is_zero_null
thf(fact_69_is__zero__null, axiom,
    ((is_zero_nat = (^[P2 : poly_nat]: (P2 = zero_zero_poly_nat))))). % is_zero_null
thf(fact_70_is__zero__null, axiom,
    ((is_zero_poly_complex = (^[P2 : poly_poly_complex]: (P2 = zero_z1040703943omplex))))). % is_zero_null
thf(fact_71_poly__cutoff__0, axiom,
    ((![N : nat]: ((poly_cutoff_complex @ N @ zero_z1746442943omplex) = zero_z1746442943omplex)))). % poly_cutoff_0
thf(fact_72_poly__cutoff__0, axiom,
    ((![N : nat]: ((poly_cutoff_nat @ N @ zero_zero_poly_nat) = zero_zero_poly_nat)))). % poly_cutoff_0
thf(fact_73_poly__cutoff__0, axiom,
    ((![N : nat]: ((poly_c622223248omplex @ N @ zero_z1040703943omplex) = zero_z1040703943omplex)))). % poly_cutoff_0
thf(fact_74_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_75_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_76_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_77_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_78_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_79_order__root, axiom,
    ((![P : poly_complex, A : complex]: (((poly_complex2 @ P @ A) = zero_zero_complex) = (((P = zero_z1746442943omplex)) | ((~ (((order_complex @ A @ P) = zero_zero_nat))))))))). % order_root
thf(fact_80_order__root, axiom,
    ((![P : poly_poly_complex, A : poly_complex]: (((poly_poly_complex2 @ P @ A) = zero_z1746442943omplex) = (((P = zero_z1040703943omplex)) | ((~ (((order_poly_complex @ A @ P) = zero_zero_nat))))))))). % order_root
thf(fact_81_order__root, axiom,
    ((![P : poly_p1267267526omplex, A : poly_poly_complex]: (((poly_p282434315omplex @ P @ A) = zero_z1040703943omplex) = (((P = zero_z1200043727omplex)) | ((~ (((order_1735763309omplex @ A @ P) = zero_zero_nat))))))))). % order_root
thf(fact_82_is__unit__iff__degree, axiom,
    ((![P : poly_complex]: ((~ ((P = zero_z1746442943omplex))) => ((dvd_dvd_poly_complex @ P @ one_one_poly_complex) = ((degree_complex @ P) = zero_zero_nat)))))). % is_unit_iff_degree
thf(fact_83_dvd__pderiv__iff, axiom,
    ((![P : poly_complex]: ((dvd_dvd_poly_complex @ P @ (pderiv_complex @ P)) = ((degree_complex @ P) = zero_zero_nat))))). % dvd_pderiv_iff
thf(fact_84_poly__shift__0, axiom,
    ((![N : nat]: ((poly_shift_complex @ N @ zero_z1746442943omplex) = zero_z1746442943omplex)))). % poly_shift_0
thf(fact_85_poly__shift__0, axiom,
    ((![N : nat]: ((poly_shift_nat @ N @ zero_zero_poly_nat) = zero_zero_poly_nat)))). % poly_shift_0
thf(fact_86_poly__shift__0, axiom,
    ((![N : nat]: ((poly_s558570093omplex @ N @ zero_z1040703943omplex) = zero_z1040703943omplex)))). % poly_shift_0
thf(fact_87_power__one, axiom,
    ((![N : nat]: ((power_184595776omplex @ one_one_poly_complex @ N) = one_one_poly_complex)))). % power_one
thf(fact_88_power__one, axiom,
    ((![N : nat]: ((power_power_nat @ one_one_nat @ N) = one_one_nat)))). % power_one
thf(fact_89_power__one, axiom,
    ((![N : nat]: ((power_power_complex @ one_one_complex @ N) = one_one_complex)))). % power_one
thf(fact_90_power__one, axiom,
    ((![N : nat]: ((power_power_poly_nat @ one_one_poly_nat @ N) = one_one_poly_nat)))). % power_one
thf(fact_91_power__one, axiom,
    ((![N : nat]: ((power_432682568omplex @ one_on1331105667omplex @ N) = one_on1331105667omplex)))). % power_one
thf(fact_92_nat__power__eq__Suc__0__iff, axiom,
    ((![X2 : nat, M : nat]: (((power_power_nat @ X2 @ M) = (suc @ zero_zero_nat)) = (((M = zero_zero_nat)) | ((X2 = (suc @ zero_zero_nat)))))))). % nat_power_eq_Suc_0_iff
thf(fact_93_power__Suc__0, axiom,
    ((![N : nat]: ((power_power_nat @ (suc @ zero_zero_nat) @ N) = (suc @ zero_zero_nat))))). % power_Suc_0
thf(fact_94_pderiv__0, axiom,
    (((pderiv_complex @ zero_z1746442943omplex) = zero_z1746442943omplex))). % pderiv_0
thf(fact_95_pderiv__0, axiom,
    (((pderiv_nat @ zero_zero_poly_nat) = zero_zero_poly_nat))). % pderiv_0
thf(fact_96_pderiv__0, axiom,
    (((pderiv_poly_complex @ zero_z1040703943omplex) = zero_z1040703943omplex))). % pderiv_0
thf(fact_97_reflect__poly__0, axiom,
    (((reflect_poly_complex @ zero_z1746442943omplex) = zero_z1746442943omplex))). % reflect_poly_0
thf(fact_98_reflect__poly__0, axiom,
    (((reflect_poly_nat @ zero_zero_poly_nat) = zero_zero_poly_nat))). % reflect_poly_0
thf(fact_99_reflect__poly__0, axiom,
    (((reflec309385472omplex @ zero_z1040703943omplex) = zero_z1040703943omplex))). % reflect_poly_0
thf(fact_100_synthetic__div__0, axiom,
    ((![C : complex]: ((synthe151143547omplex @ zero_z1746442943omplex @ C) = zero_z1746442943omplex)))). % synthetic_div_0
thf(fact_101_synthetic__div__0, axiom,
    ((![C : nat]: ((synthetic_div_nat @ zero_zero_poly_nat @ C) = zero_zero_poly_nat)))). % synthetic_div_0
thf(fact_102_synthetic__div__0, axiom,
    ((![C : poly_complex]: ((synthe1985144195omplex @ zero_z1040703943omplex @ C) = zero_z1040703943omplex)))). % synthetic_div_0
thf(fact_103_power__0__Suc, axiom,
    ((![N : nat]: ((power_184595776omplex @ zero_z1746442943omplex @ (suc @ N)) = zero_z1746442943omplex)))). % power_0_Suc
thf(fact_104_power__0__Suc, axiom,
    ((![N : nat]: ((power_power_nat @ zero_zero_nat @ (suc @ N)) = zero_zero_nat)))). % power_0_Suc
thf(fact_105_power__0__Suc, axiom,
    ((![N : nat]: ((power_power_complex @ zero_zero_complex @ (suc @ N)) = zero_zero_complex)))). % power_0_Suc
thf(fact_106_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_107_power__0__Suc, axiom,
    ((![N : nat]: ((power_432682568omplex @ zero_z1040703943omplex @ (suc @ N)) = zero_z1040703943omplex)))). % power_0_Suc
thf(fact_108_power__Suc0__right, axiom,
    ((![A : poly_complex]: ((power_184595776omplex @ A @ (suc @ zero_zero_nat)) = A)))). % power_Suc0_right
thf(fact_109_power__Suc0__right, axiom,
    ((![A : nat]: ((power_power_nat @ A @ (suc @ zero_zero_nat)) = A)))). % power_Suc0_right
thf(fact_110_power__Suc0__right, axiom,
    ((![A : complex]: ((power_power_complex @ A @ (suc @ zero_zero_nat)) = A)))). % power_Suc0_right
thf(fact_111_power__Suc0__right, axiom,
    ((![A : poly_nat]: ((power_power_poly_nat @ A @ (suc @ zero_zero_nat)) = A)))). % power_Suc0_right
thf(fact_112_power__Suc0__right, axiom,
    ((![A : poly_poly_complex]: ((power_432682568omplex @ A @ (suc @ zero_zero_nat)) = A)))). % power_Suc0_right
thf(fact_113_degree__1, axiom,
    (((degree_complex @ one_one_poly_complex) = zero_zero_nat))). % degree_1
thf(fact_114_poly__1, axiom,
    ((![X2 : complex]: ((poly_complex2 @ one_one_poly_complex @ X2) = one_one_complex)))). % poly_1
thf(fact_115_poly__1, axiom,
    ((![X2 : poly_complex]: ((poly_poly_complex2 @ one_on1331105667omplex @ X2) = one_one_poly_complex)))). % poly_1
thf(fact_116_poly__1, axiom,
    ((![X2 : nat]: ((poly_nat2 @ one_one_poly_nat @ X2) = one_one_nat)))). % poly_1
thf(fact_117_pderiv__1, axiom,
    (((pderiv_complex @ one_one_poly_complex) = zero_z1746442943omplex))). % pderiv_1
thf(fact_118_pderiv__1, axiom,
    (((pderiv_nat @ one_one_poly_nat) = zero_zero_poly_nat))). % pderiv_1
thf(fact_119_pderiv__1, axiom,
    (((pderiv_poly_complex @ one_on1331105667omplex) = zero_z1040703943omplex))). % pderiv_1
thf(fact_120_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_121_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_122_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_123_one__reorient, axiom,
    ((![X2 : nat]: ((one_one_nat = X2) = (X2 = one_one_nat))))). % one_reorient
thf(fact_124_order__pderiv2, axiom,
    ((![P : poly_complex, A : complex, N : nat]: ((~ (((pderiv_complex @ P) = zero_z1746442943omplex))) => ((~ (((order_complex @ A @ P) = zero_zero_nat))) => (((order_complex @ A @ (pderiv_complex @ P)) = N) = ((order_complex @ A @ P) = (suc @ N)))))))). % order_pderiv2
thf(fact_125_order__pderiv, axiom,
    ((![P : poly_complex, A : complex]: ((~ (((pderiv_complex @ P) = zero_z1746442943omplex))) => ((~ (((order_complex @ A @ P) = zero_zero_nat))) => ((order_complex @ A @ P) = (suc @ (order_complex @ A @ (pderiv_complex @ P))))))))). % order_pderiv
thf(fact_126_zero__neq__one, axiom,
    ((~ ((zero_zero_complex = one_one_complex))))). % zero_neq_one
thf(fact_127_zero__neq__one, axiom,
    ((~ ((zero_z1746442943omplex = one_one_poly_complex))))). % zero_neq_one
thf(fact_128_zero__neq__one, axiom,
    ((~ ((zero_zero_nat = one_one_nat))))). % zero_neq_one
thf(fact_129_zero__neq__one, axiom,
    ((~ ((zero_zero_poly_nat = one_one_poly_nat))))). % zero_neq_one
thf(fact_130_zero__neq__one, axiom,
    ((~ ((zero_z1040703943omplex = one_on1331105667omplex))))). % zero_neq_one
thf(fact_131_one__dvd, axiom,
    ((![A : poly_complex]: (dvd_dvd_poly_complex @ one_one_poly_complex @ A)))). % one_dvd
thf(fact_132_one__dvd, axiom,
    ((![A : complex]: (dvd_dvd_complex @ one_one_complex @ A)))). % one_dvd
thf(fact_133_one__dvd, axiom,
    ((![A : nat]: (dvd_dvd_nat @ one_one_nat @ A)))). % one_dvd
thf(fact_134_unit__imp__dvd, axiom,
    ((![B2 : poly_complex, A : poly_complex]: ((dvd_dvd_poly_complex @ B2 @ one_one_poly_complex) => (dvd_dvd_poly_complex @ B2 @ A))))). % unit_imp_dvd
thf(fact_135_unit__imp__dvd, axiom,
    ((![B2 : nat, A : nat]: ((dvd_dvd_nat @ B2 @ one_one_nat) => (dvd_dvd_nat @ B2 @ A))))). % unit_imp_dvd
thf(fact_136_dvd__unit__imp__unit, axiom,
    ((![A : poly_complex, B2 : poly_complex]: ((dvd_dvd_poly_complex @ A @ B2) => ((dvd_dvd_poly_complex @ B2 @ one_one_poly_complex) => (dvd_dvd_poly_complex @ A @ one_one_poly_complex)))))). % dvd_unit_imp_unit
thf(fact_137_dvd__unit__imp__unit, axiom,
    ((![A : nat, B2 : nat]: ((dvd_dvd_nat @ A @ B2) => ((dvd_dvd_nat @ B2 @ one_one_nat) => (dvd_dvd_nat @ A @ one_one_nat)))))). % dvd_unit_imp_unit
thf(fact_138_poly__shift__1, axiom,
    ((![N : nat]: (((N = zero_zero_nat) => ((poly_shift_complex @ N @ one_one_poly_complex) = one_one_poly_complex)) & ((~ ((N = zero_zero_nat))) => ((poly_shift_complex @ N @ one_one_poly_complex) = zero_z1746442943omplex)))))). % poly_shift_1
thf(fact_139_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_140_poly__shift__1, axiom,
    ((![N : nat]: (((N = zero_zero_nat) => ((poly_s558570093omplex @ N @ one_on1331105667omplex) = one_on1331105667omplex)) & ((~ ((N = zero_zero_nat))) => ((poly_s558570093omplex @ N @ one_on1331105667omplex) = zero_z1040703943omplex)))))). % poly_shift_1
thf(fact_141_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_142_reflect__poly__power, axiom,
    ((![P : poly_nat, N : nat]: ((reflect_poly_nat @ (power_power_poly_nat @ P @ N)) = (power_power_poly_nat @ (reflect_poly_nat @ P) @ N))))). % reflect_poly_power
thf(fact_143_reflect__poly__power, axiom,
    ((![P : poly_poly_complex, N : nat]: ((reflec309385472omplex @ (power_432682568omplex @ P @ N)) = (power_432682568omplex @ (reflec309385472omplex @ P) @ N))))). % reflect_poly_power
thf(fact_144_psize__def, axiom,
    ((fundam1709708056omplex = (^[P2 : poly_complex]: (if_nat @ (P2 = zero_z1746442943omplex) @ zero_zero_nat @ (suc @ (degree_complex @ P2))))))). % psize_def
thf(fact_145_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_146_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_147_not__is__unit__0, axiom,
    ((~ ((dvd_dvd_poly_complex @ zero_z1746442943omplex @ one_one_poly_complex))))). % not_is_unit_0
thf(fact_148_not__is__unit__0, axiom,
    ((~ ((dvd_dvd_nat @ zero_zero_nat @ one_one_nat))))). % not_is_unit_0
thf(fact_149_not__is__unit__0, axiom,
    ((~ ((dvd_dv598755940omplex @ zero_z1040703943omplex @ one_on1331105667omplex))))). % not_is_unit_0
thf(fact_150_power__0, axiom,
    ((![A : poly_complex]: ((power_184595776omplex @ A @ zero_zero_nat) = one_one_poly_complex)))). % power_0
thf(fact_151_power__0, axiom,
    ((![A : nat]: ((power_power_nat @ A @ zero_zero_nat) = one_one_nat)))). % power_0
thf(fact_152_power__0, axiom,
    ((![A : complex]: ((power_power_complex @ A @ zero_zero_nat) = one_one_complex)))). % power_0
thf(fact_153_power__0, axiom,
    ((![A : poly_nat]: ((power_power_poly_nat @ A @ zero_zero_nat) = one_one_poly_nat)))). % power_0
thf(fact_154_power__0, axiom,
    ((![A : poly_poly_complex]: ((power_432682568omplex @ A @ zero_zero_nat) = one_on1331105667omplex)))). % power_0
thf(fact_155_pderiv__eq__0__iff, axiom,
    ((![P : poly_complex]: (((pderiv_complex @ P) = zero_z1746442943omplex) = ((degree_complex @ P) = zero_zero_nat))))). % pderiv_eq_0_iff
thf(fact_156_pderiv__eq__0__iff, axiom,
    ((![P : poly_nat]: (((pderiv_nat @ P) = zero_zero_poly_nat) = ((degree_nat @ P) = zero_zero_nat))))). % pderiv_eq_0_iff
thf(fact_157_pderiv__eq__0__iff, axiom,
    ((![P : poly_poly_complex]: (((pderiv_poly_complex @ P) = zero_z1040703943omplex) = ((degree_poly_complex @ P) = zero_zero_nat))))). % pderiv_eq_0_iff
thf(fact_158_power__0__left, axiom,
    ((![N : nat]: (((N = zero_zero_nat) => ((power_184595776omplex @ zero_z1746442943omplex @ N) = one_one_poly_complex)) & ((~ ((N = zero_zero_nat))) => ((power_184595776omplex @ zero_z1746442943omplex @ N) = zero_z1746442943omplex)))))). % power_0_left
thf(fact_159_power__0__left, axiom,
    ((![N : nat]: (((N = zero_zero_nat) => ((power_power_nat @ zero_zero_nat @ N) = one_one_nat)) & ((~ ((N = zero_zero_nat))) => ((power_power_nat @ zero_zero_nat @ N) = zero_zero_nat)))))). % power_0_left
thf(fact_160_power__0__left, axiom,
    ((![N : nat]: (((N = zero_zero_nat) => ((power_power_complex @ zero_zero_complex @ N) = one_one_complex)) & ((~ ((N = zero_zero_nat))) => ((power_power_complex @ zero_zero_complex @ N) = zero_zero_complex)))))). % power_0_left
thf(fact_161_power__0__left, axiom,
    ((![N : nat]: (((N = zero_zero_nat) => ((power_power_poly_nat @ zero_zero_poly_nat @ N) = one_one_poly_nat)) & ((~ ((N = zero_zero_nat))) => ((power_power_poly_nat @ zero_zero_poly_nat @ N) = zero_zero_poly_nat)))))). % power_0_left
thf(fact_162_power__0__left, axiom,
    ((![N : nat]: (((N = zero_zero_nat) => ((power_432682568omplex @ zero_z1040703943omplex @ N) = one_on1331105667omplex)) & ((~ ((N = zero_zero_nat))) => ((power_432682568omplex @ zero_z1040703943omplex @ N) = zero_z1040703943omplex)))))). % power_0_left
thf(fact_163_is__unit__power__iff, axiom,
    ((![A : poly_complex, N : nat]: ((dvd_dvd_poly_complex @ (power_184595776omplex @ A @ N) @ one_one_poly_complex) = (((dvd_dvd_poly_complex @ A @ one_one_poly_complex)) | ((N = zero_zero_nat))))))). % is_unit_power_iff
thf(fact_164_is__unit__power__iff, axiom,
    ((![A : nat, N : nat]: ((dvd_dvd_nat @ (power_power_nat @ A @ N) @ one_one_nat) = (((dvd_dvd_nat @ A @ one_one_nat)) | ((N = zero_zero_nat))))))). % is_unit_power_iff
thf(fact_165_is__unit__power__iff, axiom,
    ((![A : poly_poly_complex, N : nat]: ((dvd_dv598755940omplex @ (power_432682568omplex @ A @ N) @ one_on1331105667omplex) = (((dvd_dv598755940omplex @ A @ one_on1331105667omplex)) | ((N = zero_zero_nat))))))). % is_unit_power_iff
thf(fact_166_not__dvd__pderiv, axiom,
    ((![P : poly_complex]: ((~ (((degree_complex @ P) = zero_zero_nat))) => (~ ((dvd_dvd_poly_complex @ P @ (pderiv_complex @ P)))))))). % not_dvd_pderiv
thf(fact_167_order__0I, axiom,
    ((![P : poly_complex, A : complex]: ((~ (((poly_complex2 @ P @ A) = zero_zero_complex))) => ((order_complex @ A @ P) = zero_zero_nat))))). % order_0I
thf(fact_168_order__0I, axiom,
    ((![P : poly_poly_complex, A : poly_complex]: ((~ (((poly_poly_complex2 @ P @ A) = zero_z1746442943omplex))) => ((order_poly_complex @ A @ P) = zero_zero_nat))))). % order_0I
thf(fact_169_order__0I, axiom,
    ((![P : poly_p1267267526omplex, A : poly_poly_complex]: ((~ (((poly_p282434315omplex @ P @ A) = zero_z1040703943omplex))) => ((order_1735763309omplex @ A @ P) = zero_zero_nat))))). % order_0I
thf(fact_170_dvd__1__iff__1, axiom,
    ((![M : nat]: ((dvd_dvd_nat @ M @ (suc @ zero_zero_nat)) = (M = (suc @ zero_zero_nat)))))). % dvd_1_iff_1
thf(fact_171_dvd__1__left, axiom,
    ((![K : nat]: (dvd_dvd_nat @ (suc @ zero_zero_nat) @ K)))). % dvd_1_left
thf(fact_172_rsquarefree__roots, axiom,
    ((rsquarefree_complex = (^[P2 : poly_complex]: (![A2 : complex]: (~ (((((poly_complex2 @ P2 @ A2) = zero_zero_complex)) & (((poly_complex2 @ (pderiv_complex @ P2) @ A2) = zero_zero_complex)))))))))). % rsquarefree_roots
thf(fact_173_old_Onat_Oinject, axiom,
    ((![Nat : nat, Nat2 : nat]: (((suc @ Nat) = (suc @ Nat2)) = (Nat = Nat2))))). % old.nat.inject
thf(fact_174_nat_Oinject, axiom,
    ((![X22 : nat, Y22 : nat]: (((suc @ X22) = (suc @ Y22)) = (X22 = Y22))))). % nat.inject
thf(fact_175_exists__least__lemma, axiom,
    ((![P3 : nat > $o]: ((~ ((P3 @ zero_zero_nat))) => ((?[X_1 : nat]: (P3 @ X_1)) => (?[N2 : nat]: ((~ ((P3 @ N2))) & (P3 @ (suc @ N2))))))))). % exists_least_lemma
thf(fact_176_power__one__right, axiom,
    ((![A : poly_complex]: ((power_184595776omplex @ A @ one_one_nat) = A)))). % power_one_right
thf(fact_177_power__one__right, axiom,
    ((![A : nat]: ((power_power_nat @ A @ one_one_nat) = A)))). % power_one_right
thf(fact_178_power__one__right, axiom,
    ((![A : complex]: ((power_power_complex @ A @ one_one_nat) = A)))). % power_one_right
thf(fact_179_power__one__right, axiom,
    ((![A : poly_nat]: ((power_power_poly_nat @ A @ one_one_nat) = A)))). % power_one_right
thf(fact_180_power__one__right, axiom,
    ((![A : poly_poly_complex]: ((power_432682568omplex @ A @ one_one_nat) = A)))). % power_one_right
thf(fact_181_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_182_dvd__antisym, axiom,
    ((![M : nat, N : nat]: ((dvd_dvd_nat @ M @ N) => ((dvd_dvd_nat @ N @ M) => (M = N)))))). % dvd_antisym
thf(fact_183_One__nat__def, axiom,
    ((one_one_nat = (suc @ zero_zero_nat)))). % One_nat_def
thf(fact_184_rsquarefree__def, axiom,
    ((rsquarefree_complex = (^[P2 : poly_complex]: (((~ ((P2 = zero_z1746442943omplex)))) & ((![A2 : complex]: ((((order_complex @ A2 @ P2) = zero_zero_nat)) | (((order_complex @ A2 @ P2) = one_one_nat)))))))))). % rsquarefree_def
thf(fact_185_rsquarefree__def, axiom,
    ((rsquar936197586omplex = (^[P2 : poly_poly_complex]: (((~ ((P2 = zero_z1040703943omplex)))) & ((![A2 : poly_complex]: ((((order_poly_complex @ A2 @ P2) = zero_zero_nat)) | (((order_poly_complex @ A2 @ P2) = one_one_nat)))))))))). % rsquarefree_def
thf(fact_186_Suc__inject, axiom,
    ((![X2 : nat, Y : nat]: (((suc @ X2) = (suc @ Y)) => (X2 = Y))))). % Suc_inject
thf(fact_187_n__not__Suc__n, axiom,
    ((![N : nat]: (~ ((N = (suc @ N))))))). % n_not_Suc_n
thf(fact_188_nat_Odistinct_I1_J, axiom,
    ((![X22 : nat]: (~ ((zero_zero_nat = (suc @ X22))))))). % nat.distinct(1)
thf(fact_189_old_Onat_Odistinct_I2_J, axiom,
    ((![Nat2 : nat]: (~ (((suc @ Nat2) = zero_zero_nat)))))). % old.nat.distinct(2)
thf(fact_190_old_Onat_Odistinct_I1_J, axiom,
    ((![Nat2 : nat]: (~ ((zero_zero_nat = (suc @ Nat2))))))). % old.nat.distinct(1)
thf(fact_191_nat_OdiscI, axiom,
    ((![Nat : nat, X22 : nat]: ((Nat = (suc @ X22)) => (~ ((Nat = zero_zero_nat))))))). % nat.discI
thf(fact_192_nat__induct, axiom,
    ((![P3 : nat > $o, N : nat]: ((P3 @ zero_zero_nat) => ((![N2 : nat]: ((P3 @ N2) => (P3 @ (suc @ N2)))) => (P3 @ N)))))). % nat_induct
thf(fact_193_diff__induct, axiom,
    ((![P3 : nat > nat > $o, M : nat, N : nat]: ((![X3 : nat]: (P3 @ X3 @ zero_zero_nat)) => ((![Y3 : nat]: (P3 @ zero_zero_nat @ (suc @ Y3))) => ((![X3 : nat, Y3 : nat]: ((P3 @ X3 @ Y3) => (P3 @ (suc @ X3) @ (suc @ Y3)))) => (P3 @ M @ N))))))). % diff_induct
thf(fact_194_zero__induct, axiom,
    ((![P3 : nat > $o, K : nat]: ((P3 @ K) => ((![N2 : nat]: ((P3 @ (suc @ N2)) => (P3 @ N2))) => (P3 @ zero_zero_nat)))))). % zero_induct
thf(fact_195_Suc__neq__Zero, axiom,
    ((![M : nat]: (~ (((suc @ M) = zero_zero_nat)))))). % Suc_neq_Zero
thf(fact_196_Zero__neq__Suc, axiom,
    ((![M : nat]: (~ ((zero_zero_nat = (suc @ M))))))). % Zero_neq_Suc
thf(fact_197_Zero__not__Suc, axiom,
    ((![M : nat]: (~ ((zero_zero_nat = (suc @ M))))))). % Zero_not_Suc
thf(fact_198_old_Onat_Oexhaust, axiom,
    ((![Y : nat]: ((~ ((Y = zero_zero_nat))) => (~ ((![Nat3 : nat]: (~ ((Y = (suc @ Nat3))))))))))). % old.nat.exhaust
thf(fact_199_old_Onat_Oinducts, axiom,
    ((![P3 : nat > $o, Nat : nat]: ((P3 @ zero_zero_nat) => ((![Nat3 : nat]: ((P3 @ Nat3) => (P3 @ (suc @ Nat3)))) => (P3 @ Nat)))))). % old.nat.inducts
thf(fact_200_not0__implies__Suc, axiom,
    ((![N : nat]: ((~ ((N = zero_zero_nat))) => (?[M2 : nat]: (N = (suc @ M2))))))). % not0_implies_Suc
thf(fact_201_gcd__nat_Oextremum, axiom,
    ((![A : nat]: (dvd_dvd_nat @ A @ zero_zero_nat)))). % gcd_nat.extremum
thf(fact_202_gcd__nat_Oextremum__strict, axiom,
    ((![A : nat]: (~ (((dvd_dvd_nat @ zero_zero_nat @ A) & (~ ((zero_zero_nat = A))))))))). % gcd_nat.extremum_strict
thf(fact_203_gcd__nat_Oextremum__unique, axiom,
    ((![A : nat]: ((dvd_dvd_nat @ zero_zero_nat @ A) = (A = zero_zero_nat))))). % gcd_nat.extremum_unique
thf(fact_204_gcd__nat_Onot__eq__extremum, axiom,
    ((![A : nat]: ((~ ((A = zero_zero_nat))) = (((dvd_dvd_nat @ A @ zero_zero_nat)) & ((~ ((A = zero_zero_nat))))))))). % gcd_nat.not_eq_extremum
thf(fact_205_gcd__nat_Onot__eq__order__implies__strict, axiom,
    ((![A : nat, B2 : nat]: ((~ ((A = B2))) => ((dvd_dvd_nat @ A @ B2) => ((dvd_dvd_nat @ A @ B2) & (~ ((A = B2))))))))). % gcd_nat.not_eq_order_implies_strict
thf(fact_206_gcd__nat_Ostrict__implies__not__eq, axiom,
    ((![A : nat, B2 : nat]: (((dvd_dvd_nat @ A @ B2) & (~ ((A = B2)))) => (~ ((A = B2))))))). % gcd_nat.strict_implies_not_eq
thf(fact_207_gcd__nat_Ostrict__implies__order, axiom,
    ((![A : nat, B2 : nat]: (((dvd_dvd_nat @ A @ B2) & (~ ((A = B2)))) => (dvd_dvd_nat @ A @ B2))))). % gcd_nat.strict_implies_order
thf(fact_208_gcd__nat_Ostrict__iff__order, axiom,
    ((![A : nat, B2 : nat]: ((((dvd_dvd_nat @ A @ B2)) & ((~ ((A = B2))))) = (((dvd_dvd_nat @ A @ B2)) & ((~ ((A = B2))))))))). % gcd_nat.strict_iff_order
thf(fact_209_gcd__nat_Oorder__iff__strict, axiom,
    ((dvd_dvd_nat = (^[A2 : nat]: (^[B : nat]: (((((dvd_dvd_nat @ A2 @ B)) & ((~ ((A2 = B)))))) | ((A2 = B)))))))). % gcd_nat.order_iff_strict
thf(fact_210_gcd__nat_Ostrict__trans2, axiom,
    ((![A : nat, B2 : nat, C : nat]: (((dvd_dvd_nat @ A @ B2) & (~ ((A = B2)))) => ((dvd_dvd_nat @ B2 @ C) => ((dvd_dvd_nat @ A @ C) & (~ ((A = C))))))))). % gcd_nat.strict_trans2
thf(fact_211_gcd__nat_Ostrict__trans1, axiom,
    ((![A : nat, B2 : nat, C : nat]: ((dvd_dvd_nat @ A @ B2) => (((dvd_dvd_nat @ B2 @ C) & (~ ((B2 = C)))) => ((dvd_dvd_nat @ A @ C) & (~ ((A = C))))))))). % gcd_nat.strict_trans1
thf(fact_212_gcd__nat_Ostrict__trans, axiom,
    ((![A : nat, B2 : nat, C : nat]: (((dvd_dvd_nat @ A @ B2) & (~ ((A = B2)))) => (((dvd_dvd_nat @ B2 @ C) & (~ ((B2 = C)))) => ((dvd_dvd_nat @ A @ C) & (~ ((A = C))))))))). % gcd_nat.strict_trans
thf(fact_213_gcd__nat_Oantisym, axiom,
    ((![A : nat, B2 : nat]: ((dvd_dvd_nat @ A @ B2) => ((dvd_dvd_nat @ B2 @ A) => (A = B2)))))). % gcd_nat.antisym
thf(fact_214_gcd__nat_Oirrefl, axiom,
    ((![A : nat]: (~ (((dvd_dvd_nat @ A @ A) & (~ ((A = A))))))))). % gcd_nat.irrefl
thf(fact_215_gcd__nat_Oeq__iff, axiom,
    (((^[Y4 : nat]: (^[Z2 : nat]: (Y4 = Z2))) = (^[A2 : nat]: (^[B : nat]: (((dvd_dvd_nat @ A2 @ B)) & ((dvd_dvd_nat @ B @ A2)))))))). % gcd_nat.eq_iff
thf(fact_216_gcd__nat_Otrans, axiom,
    ((![A : nat, B2 : nat, C : nat]: ((dvd_dvd_nat @ A @ B2) => ((dvd_dvd_nat @ B2 @ C) => (dvd_dvd_nat @ A @ C)))))). % gcd_nat.trans
thf(fact_217_gcd__nat_Orefl, axiom,
    ((![A : nat]: (dvd_dvd_nat @ A @ A)))). % gcd_nat.refl
thf(fact_218_gcd__nat_Oasym, axiom,
    ((![A : nat, B2 : nat]: (((dvd_dvd_nat @ A @ B2) & (~ ((A = B2)))) => (~ (((dvd_dvd_nat @ B2 @ A) & (~ ((B2 = A)))))))))). % gcd_nat.asym
thf(fact_219_gcd__nat_Oextremum__uniqueI, axiom,
    ((![A : nat]: ((dvd_dvd_nat @ zero_zero_nat @ A) => (A = zero_zero_nat))))). % gcd_nat.extremum_uniqueI
thf(fact_220_is__unit__polyE, axiom,
    ((![P : poly_complex]: ((dvd_dvd_poly_complex @ P @ one_one_poly_complex) => (~ ((![C2 : complex]: ((P = (pCons_complex @ C2 @ zero_z1746442943omplex)) => (~ ((dvd_dvd_complex @ C2 @ one_one_complex))))))))))). % is_unit_polyE
thf(fact_221_is__unit__polyE, axiom,
    ((![P : poly_nat]: ((dvd_dvd_poly_nat @ P @ one_one_poly_nat) => (~ ((![C2 : nat]: ((P = (pCons_nat @ C2 @ zero_zero_poly_nat)) => (~ ((dvd_dvd_nat @ C2 @ one_one_nat))))))))))). % is_unit_polyE
thf(fact_222_is__unit__polyE, axiom,
    ((![P : poly_poly_complex]: ((dvd_dv598755940omplex @ P @ one_on1331105667omplex) => (~ ((![C2 : poly_complex]: ((P = (pCons_poly_complex @ C2 @ zero_z1040703943omplex)) => (~ ((dvd_dvd_poly_complex @ C2 @ one_one_poly_complex))))))))))). % is_unit_polyE
thf(fact_223_pCons__eq__iff, axiom,
    ((![A : complex, P : poly_complex, B2 : complex, Q : poly_complex]: (((pCons_complex @ A @ P) = (pCons_complex @ B2 @ Q)) = (((A = B2)) & ((P = Q))))))). % pCons_eq_iff
thf(fact_224_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_225_pCons__eq__0__iff, axiom,
    ((![A : poly_poly_complex, P : poly_p1267267526omplex]: (((pCons_1087637536omplex @ A @ P) = zero_z1200043727omplex) = (((A = zero_z1040703943omplex)) & ((P = zero_z1200043727omplex))))))). % pCons_eq_0_iff
thf(fact_226_pCons__eq__0__iff, axiom,
    ((![A : complex, P : poly_complex]: (((pCons_complex @ A @ P) = zero_z1746442943omplex) = (((A = zero_zero_complex)) & ((P = zero_z1746442943omplex))))))). % pCons_eq_0_iff
thf(fact_227_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_228_pCons__eq__0__iff, axiom,
    ((![A : poly_complex, P : poly_poly_complex]: (((pCons_poly_complex @ A @ P) = zero_z1040703943omplex) = (((A = zero_z1746442943omplex)) & ((P = zero_z1040703943omplex))))))). % pCons_eq_0_iff
thf(fact_229_pCons__0__0, axiom,
    (((pCons_complex @ zero_zero_complex @ zero_z1746442943omplex) = zero_z1746442943omplex))). % pCons_0_0
thf(fact_230_pCons__0__0, axiom,
    (((pCons_poly_complex @ zero_z1746442943omplex @ zero_z1040703943omplex) = zero_z1040703943omplex))). % pCons_0_0
thf(fact_231_pCons__0__0, axiom,
    (((pCons_nat @ zero_zero_nat @ zero_zero_poly_nat) = zero_zero_poly_nat))). % pCons_0_0
thf(fact_232_pCons__0__0, axiom,
    (((pCons_poly_nat @ zero_zero_poly_nat @ zero_z1059985641ly_nat) = zero_z1059985641ly_nat))). % pCons_0_0
thf(fact_233_pCons__0__0, axiom,
    (((pCons_1087637536omplex @ zero_z1040703943omplex @ zero_z1200043727omplex) = zero_z1200043727omplex))). % pCons_0_0
thf(fact_234_pderiv__singleton, axiom,
    ((![A : complex]: ((pderiv_complex @ (pCons_complex @ A @ zero_z1746442943omplex)) = zero_z1746442943omplex)))). % pderiv_singleton
thf(fact_235_pderiv__singleton, axiom,
    ((![A : nat]: ((pderiv_nat @ (pCons_nat @ A @ zero_zero_poly_nat)) = zero_zero_poly_nat)))). % pderiv_singleton
thf(fact_236_pderiv__singleton, axiom,
    ((![A : poly_complex]: ((pderiv_poly_complex @ (pCons_poly_complex @ A @ zero_z1040703943omplex)) = zero_z1040703943omplex)))). % pderiv_singleton
thf(fact_237_reflect__poly__const, axiom,
    ((![A : complex]: ((reflect_poly_complex @ (pCons_complex @ A @ zero_z1746442943omplex)) = (pCons_complex @ A @ zero_z1746442943omplex))))). % reflect_poly_const
thf(fact_238_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_239_reflect__poly__const, axiom,
    ((![A : poly_complex]: ((reflec309385472omplex @ (pCons_poly_complex @ A @ zero_z1040703943omplex)) = (pCons_poly_complex @ A @ zero_z1040703943omplex))))). % reflect_poly_const
thf(fact_240_synthetic__div__pCons, axiom,
    ((![A : poly_complex, P : poly_poly_complex, C : poly_complex]: ((synthe1985144195omplex @ (pCons_poly_complex @ A @ P) @ C) = (pCons_poly_complex @ (poly_poly_complex2 @ P @ C) @ (synthe1985144195omplex @ P @ C)))))). % synthetic_div_pCons
thf(fact_241_synthetic__div__pCons, axiom,
    ((![A : complex, P : poly_complex, C : complex]: ((synthe151143547omplex @ (pCons_complex @ A @ P) @ C) = (pCons_complex @ (poly_complex2 @ P @ C) @ (synthe151143547omplex @ P @ C)))))). % synthetic_div_pCons
thf(fact_242_fundamental__theorem__of__algebra__alt, axiom,
    ((![P : poly_complex]: ((~ ((?[A3 : complex, L : poly_complex]: ((~ ((A3 = zero_zero_complex))) & ((L = zero_z1746442943omplex) & (P = (pCons_complex @ A3 @ L))))))) => (?[Z : complex]: ((poly_complex2 @ P @ Z) = zero_zero_complex)))))). % fundamental_theorem_of_algebra_alt

% Helper facts (3)
thf(help_If_3_1_If_001t__Nat__Onat_T, axiom,
    ((![P3 : $o]: ((P3 = $true) | (P3 = $false))))).
thf(help_If_2_1_If_001t__Nat__Onat_T, axiom,
    ((![X2 : nat, Y : nat]: ((if_nat @ $false @ X2 @ Y) = Y)))).
thf(help_If_1_1_If_001t__Nat__Onat_T, axiom,
    ((![X2 : nat, Y : nat]: ((if_nat @ $true @ X2 @ Y) = X2)))).

% Conjectures (1)
thf(conj_0, conjecture,
    (((![X : complex]: ((((poly_complex2 @ p @ X) = zero_zero_complex)) => (((poly_complex2 @ q @ X) = zero_zero_complex)))) = (((dvd_dvd_poly_complex @ p @ (power_184595776omplex @ q @ (degree_complex @ p)))) | ((((p = zero_z1746442943omplex)) & ((q = zero_z1746442943omplex)))))))).
