% 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_1199__5379374_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:36:28.358

% Could-be-implicit typings (13)
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__Set__Oset_It__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J_J, type,
    set_po447080308omplex : $tType).
thf(ty_n_t__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
    poly_poly_complex : $tType).
thf(ty_n_t__Set__Oset_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
    set_poly_complex : $tType).
thf(ty_n_t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    poly_complex : $tType).
thf(ty_n_t__Set__Oset_It__Complex__Ocomplex_J, type,
    set_complex : $tType).
thf(ty_n_t__Polynomial__Opoly_It__Nat__Onat_J, type,
    poly_nat : $tType).
thf(ty_n_t__Polynomial__Opoly_It__Int__Oint_J, type,
    poly_int : $tType).
thf(ty_n_t__Set__Oset_It__Int__Oint_J, type,
    set_int : $tType).
thf(ty_n_t__Complex__Ocomplex, type,
    complex : $tType).
thf(ty_n_t__Real__Oreal, type,
    real : $tType).
thf(ty_n_t__Nat__Onat, type,
    nat : $tType).
thf(ty_n_t__Int__Oint, type,
    int : $tType).

% Explicit typings (73)
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_Oconstant_001t__Polynomial__Opoly_It__Complex__Ocomplex_J_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    fundam466968762omplex : (poly_complex > poly_complex) > $o).
thf(sy_c_Fundamental__Theorem__Algebra__Mirabelle__sywschxjbb_Opsize_001t__Complex__Ocomplex, type,
    fundam1709708056omplex : 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__Int__Oint, type,
    one_one_int : int).
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__Int__Oint, type,
    zero_zero_int : int).
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__Real__Oreal, type,
    zero_zero_real : real).
thf(sy_c_Int_Oring__1__class_OInts_001t__Complex__Ocomplex, type,
    ring_1_Ints_complex : set_complex).
thf(sy_c_Int_Oring__1__class_OInts_001t__Int__Oint, type,
    ring_1_Ints_int : set_int).
thf(sy_c_Int_Oring__1__class_OInts_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    ring_1947948997omplex : set_poly_complex).
thf(sy_c_Int_Oring__1__class_OInts_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
    ring_1546648269omplex : set_po447080308omplex).
thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Complex__Ocomplex, type,
    semiri356525583omplex : nat > complex).
thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Int__Oint, type,
    semiri2019852685at_int : nat > int).
thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Nat__Onat, type,
    semiri1382578993at_nat : nat > nat).
thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    semiri1679838999omplex : nat > poly_complex).
thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Polynomial__Opoly_It__Int__Oint_J, type,
    semiri308135317ly_int : nat > poly_int).
thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
    semiri1266910751omplex : nat > poly_poly_complex).
thf(sy_c_Polynomial_Oalgebraic_001t__Complex__Ocomplex, type,
    algebraic_complex : complex > $o).
thf(sy_c_Polynomial_Odegree_001t__Complex__Ocomplex, type,
    degree_complex : poly_complex > nat).
thf(sy_c_Polynomial_Odegree_001t__Int__Oint, type,
    degree_int : poly_int > 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__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
    degree2006505739omplex : 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_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__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__Int__Oint, type,
    coeff_int : poly_int > nat > int).
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__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__shift_001t__Complex__Ocomplex, type,
    poly_shift_complex : nat > poly_complex > 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_Osynthetic__div_001t__Complex__Ocomplex, type,
    synthe151143547omplex : poly_complex > complex > poly_complex).
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__Int__Oint, type,
    power_power_int : int > nat > int).
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__Polynomial__Opoly_It__Complex__Ocomplex_J_J_J, type,
    power_2001192272omplex : poly_p1267267526omplex > nat > poly_p1267267526omplex).
thf(sy_c_Power_Opower__class_Opower_001t__Real__Oreal, type,
    power_power_real : real > nat > real).
thf(sy_c_Rat_Ofield__char__0__class_ORats_001t__Complex__Ocomplex, type,
    field_1668707340omplex : set_complex).
thf(sy_c_Real__Vector__Spaces_OscaleR__class_OscaleR_001t__Complex__Ocomplex, type,
    real_V1560324349omplex : real > complex > 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__Int__Oint, type,
    dvd_dvd_int : int > int > $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__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
    dvd_dv598755940omplex : poly_poly_complex > poly_poly_complex > $o).
thf(sy_c_member_001t__Complex__Ocomplex, type,
    member_complex : complex > set_complex > $o).
thf(sy_c_member_001t__Int__Oint, type,
    member_int : int > set_int > $o).
thf(sy_c_member_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    member_poly_complex : poly_complex > set_poly_complex > $o).
thf(sy_c_member_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
    member1411246933omplex : poly_poly_complex > set_po447080308omplex > $o).
thf(sy_v_n, type,
    n : nat).
thf(sy_v_q, type,
    q : poly_complex).
thf(sy_v_r, type,
    r : poly_complex).

% Relevant facts (246)
thf(fact_0__092_060open_062poly_A_Iq_A_094_An_J_A_061_Apoly_Ar_092_060close_062, axiom,
    (((poly_complex2 @ (power_184595776omplex @ q @ n)) = (poly_complex2 @ r)))). % \<open>poly (q ^ n) = poly r\<close>
thf(fact_1_h, axiom,
    ((![X : complex]: ((poly_complex2 @ (power_184595776omplex @ q @ n) @ X) = (poly_complex2 @ r @ X))))). % h
thf(fact_2_poly__power, axiom,
    ((![P : poly_p1267267526omplex, N : nat, X : poly_poly_complex]: ((poly_p282434315omplex @ (power_2001192272omplex @ P @ N) @ X) = (power_432682568omplex @ (poly_p282434315omplex @ P @ X) @ N))))). % poly_power
thf(fact_3_poly__power, axiom,
    ((![P : poly_nat, N : nat, X : nat]: ((poly_nat2 @ (power_power_poly_nat @ P @ N) @ X) = (power_power_nat @ (poly_nat2 @ P @ X) @ N))))). % poly_power
thf(fact_4_poly__power, axiom,
    ((![P : poly_poly_complex, N : nat, X : poly_complex]: ((poly_poly_complex2 @ (power_432682568omplex @ P @ N) @ X) = (power_184595776omplex @ (poly_poly_complex2 @ P @ X) @ N))))). % poly_power
thf(fact_5_poly__power, axiom,
    ((![P : poly_complex, N : nat, X : complex]: ((poly_complex2 @ (power_184595776omplex @ P @ N) @ X) = (power_power_complex @ (poly_complex2 @ P @ X) @ N))))). % poly_power
thf(fact_6_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_7_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_8_coeff__0__power, axiom,
    ((![P : poly_p1267267526omplex, N : nat]: ((coeff_1429652124omplex @ (power_2001192272omplex @ P @ N) @ zero_zero_nat) = (power_432682568omplex @ (coeff_1429652124omplex @ P @ zero_zero_nat) @ N))))). % coeff_0_power
thf(fact_9_coeff__0__power, axiom,
    ((![P : poly_nat, N : nat]: ((coeff_nat @ (power_power_poly_nat @ P @ N) @ zero_zero_nat) = (power_power_nat @ (coeff_nat @ P @ zero_zero_nat) @ N))))). % coeff_0_power
thf(fact_10_coeff__0__power, axiom,
    ((![P : poly_poly_complex, N : nat]: ((coeff_poly_complex @ (power_432682568omplex @ P @ N) @ zero_zero_nat) = (power_184595776omplex @ (coeff_poly_complex @ P @ zero_zero_nat) @ N))))). % coeff_0_power
thf(fact_11_coeff__0__power, axiom,
    ((![P : poly_complex, N : nat]: ((coeff_complex @ (power_184595776omplex @ P @ N) @ zero_zero_nat) = (power_power_complex @ (coeff_complex @ P @ zero_zero_nat) @ N))))). % coeff_0_power
thf(fact_12_constant__def, axiom,
    ((fundam1158420650omplex = (^[F : complex > complex]: (![X2 : complex]: (![Y : complex]: ((F @ X2) = (F @ Y)))))))). % constant_def
thf(fact_13_power__one__right, axiom,
    ((![A : complex]: ((power_power_complex @ A @ one_one_nat) = A)))). % power_one_right
thf(fact_14_power__one__right, axiom,
    ((![A : poly_poly_complex]: ((power_432682568omplex @ A @ one_one_nat) = A)))). % power_one_right
thf(fact_15_power__one__right, axiom,
    ((![A : nat]: ((power_power_nat @ A @ one_one_nat) = A)))). % power_one_right
thf(fact_16_power__one__right, axiom,
    ((![A : poly_complex]: ((power_184595776omplex @ A @ one_one_nat) = A)))). % power_one_right
thf(fact_17_power__one, axiom,
    ((![N : nat]: ((power_power_complex @ one_one_complex @ N) = one_one_complex)))). % power_one
thf(fact_18_power__one, axiom,
    ((![N : nat]: ((power_432682568omplex @ one_on1331105667omplex @ N) = one_on1331105667omplex)))). % power_one
thf(fact_19_power__one, axiom,
    ((![N : nat]: ((power_power_nat @ one_one_nat @ N) = one_one_nat)))). % power_one
thf(fact_20_power__one, axiom,
    ((![N : nat]: ((power_184595776omplex @ one_one_poly_complex @ N) = one_one_poly_complex)))). % power_one
thf(fact_21_Rats__power, axiom,
    ((![A : complex, N : nat]: ((member_complex @ A @ field_1668707340omplex) => (member_complex @ (power_power_complex @ A @ N) @ field_1668707340omplex))))). % Rats_power
thf(fact_22_lead__coeff__power, axiom,
    ((![P : poly_p1267267526omplex, N : nat]: ((coeff_1429652124omplex @ (power_2001192272omplex @ P @ N) @ (degree2006505739omplex @ (power_2001192272omplex @ P @ N))) = (power_432682568omplex @ (coeff_1429652124omplex @ P @ (degree2006505739omplex @ P)) @ N))))). % lead_coeff_power
thf(fact_23_lead__coeff__power, axiom,
    ((![P : poly_nat, N : nat]: ((coeff_nat @ (power_power_poly_nat @ P @ N) @ (degree_nat @ (power_power_poly_nat @ P @ N))) = (power_power_nat @ (coeff_nat @ P @ (degree_nat @ P)) @ N))))). % lead_coeff_power
thf(fact_24_lead__coeff__power, axiom,
    ((![P : poly_poly_complex, N : nat]: ((coeff_poly_complex @ (power_432682568omplex @ P @ N) @ (degree_poly_complex @ (power_432682568omplex @ P @ N))) = (power_184595776omplex @ (coeff_poly_complex @ P @ (degree_poly_complex @ P)) @ N))))). % lead_coeff_power
thf(fact_25_lead__coeff__power, axiom,
    ((![P : poly_complex, N : nat]: ((coeff_complex @ (power_184595776omplex @ P @ N) @ (degree_complex @ (power_184595776omplex @ P @ N))) = (power_power_complex @ (coeff_complex @ P @ (degree_complex @ P)) @ N))))). % lead_coeff_power
thf(fact_26_of__nat__power, axiom,
    ((![M : nat, N : nat]: ((semiri1679838999omplex @ (power_power_nat @ M @ N)) = (power_184595776omplex @ (semiri1679838999omplex @ M) @ N))))). % of_nat_power
thf(fact_27_of__nat__power, axiom,
    ((![M : nat, N : nat]: ((semiri356525583omplex @ (power_power_nat @ M @ N)) = (power_power_complex @ (semiri356525583omplex @ M) @ N))))). % of_nat_power
thf(fact_28_of__nat__power, axiom,
    ((![M : nat, N : nat]: ((semiri1266910751omplex @ (power_power_nat @ M @ N)) = (power_432682568omplex @ (semiri1266910751omplex @ M) @ N))))). % of_nat_power
thf(fact_29_of__nat__power, axiom,
    ((![M : nat, N : nat]: ((semiri1382578993at_nat @ (power_power_nat @ M @ N)) = (power_power_nat @ (semiri1382578993at_nat @ M) @ N))))). % of_nat_power
thf(fact_30_of__nat__power, axiom,
    ((![M : nat, N : nat]: ((semiri2019852685at_int @ (power_power_nat @ M @ N)) = (power_power_int @ (semiri2019852685at_int @ M) @ N))))). % of_nat_power
thf(fact_31_of__nat__eq__of__nat__power__cancel__iff, axiom,
    ((![B : nat, W : nat, X : nat]: (((power_184595776omplex @ (semiri1679838999omplex @ B) @ W) = (semiri1679838999omplex @ X)) = ((power_power_nat @ B @ W) = X))))). % of_nat_eq_of_nat_power_cancel_iff
thf(fact_32_of__nat__eq__of__nat__power__cancel__iff, axiom,
    ((![B : nat, W : nat, X : nat]: (((power_power_complex @ (semiri356525583omplex @ B) @ W) = (semiri356525583omplex @ X)) = ((power_power_nat @ B @ W) = X))))). % of_nat_eq_of_nat_power_cancel_iff
thf(fact_33_of__nat__eq__of__nat__power__cancel__iff, axiom,
    ((![B : nat, W : nat, X : nat]: (((power_432682568omplex @ (semiri1266910751omplex @ B) @ W) = (semiri1266910751omplex @ X)) = ((power_power_nat @ B @ W) = X))))). % of_nat_eq_of_nat_power_cancel_iff
thf(fact_34_of__nat__eq__of__nat__power__cancel__iff, axiom,
    ((![B : nat, W : nat, X : nat]: (((power_power_nat @ (semiri1382578993at_nat @ B) @ W) = (semiri1382578993at_nat @ X)) = ((power_power_nat @ B @ W) = X))))). % of_nat_eq_of_nat_power_cancel_iff
thf(fact_35_of__nat__eq__of__nat__power__cancel__iff, axiom,
    ((![B : nat, W : nat, X : nat]: (((power_power_int @ (semiri2019852685at_int @ B) @ W) = (semiri2019852685at_int @ X)) = ((power_power_nat @ B @ W) = X))))). % of_nat_eq_of_nat_power_cancel_iff
thf(fact_36_of__nat__power__eq__of__nat__cancel__iff, axiom,
    ((![X : nat, B : nat, W : nat]: (((semiri1679838999omplex @ X) = (power_184595776omplex @ (semiri1679838999omplex @ B) @ W)) = (X = (power_power_nat @ B @ W)))))). % of_nat_power_eq_of_nat_cancel_iff
thf(fact_37_of__nat__power__eq__of__nat__cancel__iff, axiom,
    ((![X : nat, B : nat, W : nat]: (((semiri356525583omplex @ X) = (power_power_complex @ (semiri356525583omplex @ B) @ W)) = (X = (power_power_nat @ B @ W)))))). % of_nat_power_eq_of_nat_cancel_iff
thf(fact_38_of__nat__power__eq__of__nat__cancel__iff, axiom,
    ((![X : nat, B : nat, W : nat]: (((semiri1266910751omplex @ X) = (power_432682568omplex @ (semiri1266910751omplex @ B) @ W)) = (X = (power_power_nat @ B @ W)))))). % of_nat_power_eq_of_nat_cancel_iff
thf(fact_39_of__nat__power__eq__of__nat__cancel__iff, axiom,
    ((![X : nat, B : nat, W : nat]: (((semiri1382578993at_nat @ X) = (power_power_nat @ (semiri1382578993at_nat @ B) @ W)) = (X = (power_power_nat @ B @ W)))))). % of_nat_power_eq_of_nat_cancel_iff
thf(fact_40_of__nat__power__eq__of__nat__cancel__iff, axiom,
    ((![X : nat, B : nat, W : nat]: (((semiri2019852685at_int @ X) = (power_power_int @ (semiri2019852685at_int @ B) @ W)) = (X = (power_power_nat @ B @ W)))))). % of_nat_power_eq_of_nat_cancel_iff
thf(fact_41_scaleR__power, axiom,
    ((![X : real, Y2 : complex, N : nat]: ((power_power_complex @ (real_V1560324349omplex @ X @ Y2) @ N) = (real_V1560324349omplex @ (power_power_real @ X @ N) @ (power_power_complex @ Y2 @ N)))))). % scaleR_power
thf(fact_42_reflect__poly__1, axiom,
    (((reflect_poly_complex @ one_one_poly_complex) = one_one_poly_complex))). % reflect_poly_1
thf(fact_43_scale__eq__0__iff, axiom,
    ((![A : real, X : complex]: (((real_V1560324349omplex @ A @ X) = zero_zero_complex) = (((A = zero_zero_real)) | ((X = zero_zero_complex))))))). % scale_eq_0_iff
thf(fact_44_scale__zero__left, axiom,
    ((![X : complex]: ((real_V1560324349omplex @ zero_zero_real @ X) = zero_zero_complex)))). % scale_zero_left
thf(fact_45_scale__zero__right, axiom,
    ((![A : real]: ((real_V1560324349omplex @ A @ zero_zero_complex) = zero_zero_complex)))). % scale_zero_right
thf(fact_46_scale__cancel__right, axiom,
    ((![A : real, X : complex, B : real]: (((real_V1560324349omplex @ A @ X) = (real_V1560324349omplex @ B @ X)) = (((A = B)) | ((X = zero_zero_complex))))))). % scale_cancel_right
thf(fact_47_coeff__0, axiom,
    ((![N : nat]: ((coeff_poly_complex @ zero_z1040703943omplex @ N) = zero_z1746442943omplex)))). % coeff_0
thf(fact_48_coeff__0, axiom,
    ((![N : nat]: ((coeff_nat @ zero_zero_poly_nat @ N) = zero_zero_nat)))). % coeff_0
thf(fact_49_coeff__0, axiom,
    ((![N : nat]: ((coeff_complex @ zero_z1746442943omplex @ N) = zero_zero_complex)))). % coeff_0
thf(fact_50_poly__0, axiom,
    ((![X : poly_complex]: ((poly_poly_complex2 @ zero_z1040703943omplex @ X) = zero_z1746442943omplex)))). % poly_0
thf(fact_51_poly__0, axiom,
    ((![X : nat]: ((poly_nat2 @ zero_zero_poly_nat @ X) = zero_zero_nat)))). % poly_0
thf(fact_52_poly__0, axiom,
    ((![X : complex]: ((poly_complex2 @ zero_z1746442943omplex @ X) = zero_zero_complex)))). % poly_0
thf(fact_53_degree__1, axiom,
    (((degree_poly_complex @ one_on1331105667omplex) = zero_zero_nat))). % degree_1
thf(fact_54_degree__1, axiom,
    (((degree_complex @ one_one_poly_complex) = zero_zero_nat))). % degree_1
thf(fact_55_degree__of__nat, axiom,
    ((![N : nat]: ((degree_complex @ (semiri1679838999omplex @ N)) = zero_zero_nat)))). % degree_of_nat
thf(fact_56_degree__of__nat, axiom,
    ((![N : nat]: ((degree_poly_complex @ (semiri1266910751omplex @ N)) = zero_zero_nat)))). % degree_of_nat
thf(fact_57_poly__1, axiom,
    ((![X : nat]: ((poly_nat2 @ one_one_poly_nat @ X) = one_one_nat)))). % poly_1
thf(fact_58_poly__1, axiom,
    ((![X : poly_complex]: ((poly_poly_complex2 @ one_on1331105667omplex @ X) = one_one_poly_complex)))). % poly_1
thf(fact_59_poly__1, axiom,
    ((![X : complex]: ((poly_complex2 @ one_one_poly_complex @ X) = one_one_complex)))). % poly_1
thf(fact_60_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_61_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_62_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_63_lead__coeff__1, axiom,
    (((coeff_nat @ one_one_poly_nat @ (degree_nat @ one_one_poly_nat)) = one_one_nat))). % lead_coeff_1
thf(fact_64_lead__coeff__1, axiom,
    (((coeff_complex @ one_one_poly_complex @ (degree_complex @ one_one_poly_complex)) = one_one_complex))). % lead_coeff_1
thf(fact_65_lead__coeff__1, axiom,
    (((coeff_poly_complex @ one_on1331105667omplex @ (degree_poly_complex @ one_on1331105667omplex)) = one_one_poly_complex))). % lead_coeff_1
thf(fact_66_lead__coeff__of__nat, axiom,
    ((![N : nat]: ((coeff_complex @ (semiri1679838999omplex @ N) @ (degree_complex @ (semiri1679838999omplex @ N))) = (semiri356525583omplex @ N))))). % lead_coeff_of_nat
thf(fact_67_lead__coeff__of__nat, axiom,
    ((![N : nat]: ((coeff_poly_complex @ (semiri1266910751omplex @ N) @ (degree_poly_complex @ (semiri1266910751omplex @ N))) = (semiri1679838999omplex @ N))))). % lead_coeff_of_nat
thf(fact_68_lead__coeff__of__nat, axiom,
    ((![N : nat]: ((coeff_int @ (semiri308135317ly_int @ N) @ (degree_int @ (semiri308135317ly_int @ N))) = (semiri2019852685at_int @ N))))). % lead_coeff_of_nat
thf(fact_69_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_70_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_71_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_72_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_73_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_74_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_75_coeff__0__reflect__poly__0__iff, axiom,
    ((![P : poly_poly_complex]: (((coeff_poly_complex @ (reflec309385472omplex @ P) @ zero_zero_nat) = zero_z1746442943omplex) = (P = zero_z1040703943omplex))))). % coeff_0_reflect_poly_0_iff
thf(fact_76_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_77_coeff__0__reflect__poly__0__iff, axiom,
    ((![P : poly_complex]: (((coeff_complex @ (reflect_poly_complex @ P) @ zero_zero_nat) = zero_zero_complex) = (P = zero_z1746442943omplex))))). % coeff_0_reflect_poly_0_iff
thf(fact_78_coeff__0__reflect__poly, axiom,
    ((![P : poly_poly_complex]: ((coeff_poly_complex @ (reflec309385472omplex @ P) @ zero_zero_nat) = (coeff_poly_complex @ P @ (degree_poly_complex @ P)))))). % coeff_0_reflect_poly
thf(fact_79_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_80_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_81_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_82_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_83_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_84_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_85_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_86_basic__cqe__conv1_I4_J, axiom,
    ((?[X3 : poly_complex]: ((poly_poly_complex2 @ zero_z1040703943omplex @ X3) = zero_z1746442943omplex)))). % basic_cqe_conv1(4)
thf(fact_87_basic__cqe__conv1_I4_J, axiom,
    ((?[X3 : nat]: ((poly_nat2 @ zero_zero_poly_nat @ X3) = zero_zero_nat)))). % basic_cqe_conv1(4)
thf(fact_88_basic__cqe__conv1_I4_J, axiom,
    ((?[X3 : complex]: ((poly_complex2 @ zero_z1746442943omplex @ X3) = zero_zero_complex)))). % basic_cqe_conv1(4)
thf(fact_89_basic__cqe__conv1_I2_J, axiom,
    ((~ ((?[X4 : poly_complex]: (~ (((poly_poly_complex2 @ zero_z1040703943omplex @ X4) = zero_z1746442943omplex)))))))). % basic_cqe_conv1(2)
thf(fact_90_basic__cqe__conv1_I2_J, axiom,
    ((~ ((?[X4 : nat]: (~ (((poly_nat2 @ zero_zero_poly_nat @ X4) = zero_zero_nat)))))))). % basic_cqe_conv1(2)
thf(fact_91_basic__cqe__conv1_I2_J, axiom,
    ((~ ((?[X4 : complex]: (~ (((poly_complex2 @ zero_z1746442943omplex @ X4) = zero_zero_complex)))))))). % basic_cqe_conv1(2)
thf(fact_92_basic__cqe__conv1_I1_J, axiom,
    ((![P : poly_complex]: (~ ((?[X4 : complex]: (((poly_complex2 @ P @ X4) = zero_zero_complex) & (~ (((poly_complex2 @ zero_z1746442943omplex @ X4) = zero_zero_complex)))))))))). % basic_cqe_conv1(1)
thf(fact_93_basic__cqe__conv1_I1_J, axiom,
    ((![P : poly_poly_complex]: (~ ((?[X4 : poly_complex]: (((poly_poly_complex2 @ P @ X4) = zero_z1746442943omplex) & (~ (((poly_poly_complex2 @ zero_z1040703943omplex @ X4) = zero_z1746442943omplex)))))))))). % basic_cqe_conv1(1)
thf(fact_94_basic__cqe__conv1_I1_J, axiom,
    ((![P : poly_nat]: (~ ((?[X4 : nat]: (((poly_nat2 @ P @ X4) = zero_zero_nat) & (~ (((poly_nat2 @ zero_zero_poly_nat @ X4) = zero_zero_nat)))))))))). % basic_cqe_conv1(1)
thf(fact_95_mpoly__base__conv_I1_J, axiom,
    ((![X : complex]: (zero_zero_complex = (poly_complex2 @ zero_z1746442943omplex @ X))))). % mpoly_base_conv(1)
thf(fact_96_mpoly__base__conv_I1_J, axiom,
    ((![X : poly_complex]: (zero_z1746442943omplex = (poly_poly_complex2 @ zero_z1040703943omplex @ X))))). % mpoly_base_conv(1)
thf(fact_97_Rats__0, axiom,
    ((member_complex @ zero_zero_complex @ field_1668707340omplex))). % Rats_0
thf(fact_98_poly__eqI, axiom,
    ((![P : poly_complex, Q : poly_complex]: ((![N2 : nat]: ((coeff_complex @ P @ N2) = (coeff_complex @ Q @ N2))) => (P = Q))))). % poly_eqI
thf(fact_99_poly__eqI, axiom,
    ((![P : poly_poly_complex, Q : poly_poly_complex]: ((![N2 : nat]: ((coeff_poly_complex @ P @ N2) = (coeff_poly_complex @ Q @ N2))) => (P = Q))))). % poly_eqI
thf(fact_100_poly__eq__iff, axiom,
    (((^[Y3 : poly_complex]: (^[Z : poly_complex]: (Y3 = Z))) = (^[P2 : poly_complex]: (^[Q2 : poly_complex]: (![N3 : nat]: ((coeff_complex @ P2 @ N3) = (coeff_complex @ Q2 @ N3)))))))). % poly_eq_iff
thf(fact_101_poly__eq__iff, axiom,
    (((^[Y3 : poly_poly_complex]: (^[Z : poly_poly_complex]: (Y3 = Z))) = (^[P2 : poly_poly_complex]: (^[Q2 : poly_poly_complex]: (![N3 : nat]: ((coeff_poly_complex @ P2 @ N3) = (coeff_poly_complex @ Q2 @ N3)))))))). % poly_eq_iff
thf(fact_102_poly__0__coeff__0, axiom,
    ((![P : poly_complex]: ((poly_complex2 @ P @ zero_zero_complex) = (coeff_complex @ P @ zero_zero_nat))))). % poly_0_coeff_0
thf(fact_103_poly__0__coeff__0, axiom,
    ((![P : poly_poly_complex]: ((poly_poly_complex2 @ P @ zero_z1746442943omplex) = (coeff_poly_complex @ P @ zero_zero_nat))))). % poly_0_coeff_0
thf(fact_104_poly__0__coeff__0, axiom,
    ((![P : poly_nat]: ((poly_nat2 @ P @ zero_zero_nat) = (coeff_nat @ P @ zero_zero_nat))))). % poly_0_coeff_0
thf(fact_105_poly__all__0__iff__0, axiom,
    ((![P : poly_complex]: ((![X2 : complex]: ((poly_complex2 @ P @ X2) = zero_zero_complex)) = (P = zero_z1746442943omplex))))). % poly_all_0_iff_0
thf(fact_106_poly__all__0__iff__0, axiom,
    ((![P : poly_poly_complex]: ((![X2 : poly_complex]: ((poly_poly_complex2 @ P @ X2) = zero_z1746442943omplex)) = (P = zero_z1040703943omplex))))). % poly_all_0_iff_0
thf(fact_107_zero__poly_Orep__eq, axiom,
    (((coeff_poly_complex @ zero_z1040703943omplex) = (^[Uu : nat]: zero_z1746442943omplex)))). % zero_poly.rep_eq
thf(fact_108_zero__poly_Orep__eq, axiom,
    (((coeff_nat @ zero_zero_poly_nat) = (^[Uu : nat]: zero_zero_nat)))). % zero_poly.rep_eq
thf(fact_109_zero__poly_Orep__eq, axiom,
    (((coeff_complex @ zero_z1746442943omplex) = (^[Uu : nat]: zero_zero_complex)))). % zero_poly.rep_eq
thf(fact_110_coeff__inject, axiom,
    ((![X : poly_complex, Y2 : poly_complex]: (((coeff_complex @ X) = (coeff_complex @ Y2)) = (X = Y2))))). % coeff_inject
thf(fact_111_coeff__inject, axiom,
    ((![X : poly_poly_complex, Y2 : poly_poly_complex]: (((coeff_poly_complex @ X) = (coeff_poly_complex @ Y2)) = (X = Y2))))). % coeff_inject
thf(fact_112_leading__coeff__neq__0, axiom,
    ((![P : poly_poly_complex]: ((~ ((P = zero_z1040703943omplex))) => (~ (((coeff_poly_complex @ P @ (degree_poly_complex @ P)) = zero_z1746442943omplex))))))). % leading_coeff_neq_0
thf(fact_113_leading__coeff__neq__0, axiom,
    ((![P : poly_nat]: ((~ ((P = zero_zero_poly_nat))) => (~ (((coeff_nat @ P @ (degree_nat @ P)) = zero_zero_nat))))))). % leading_coeff_neq_0
thf(fact_114_leading__coeff__neq__0, axiom,
    ((![P : poly_complex]: ((~ ((P = zero_z1746442943omplex))) => (~ (((coeff_complex @ P @ (degree_complex @ P)) = zero_zero_complex))))))). % leading_coeff_neq_0
thf(fact_115_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_116_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_117_power__0, axiom,
    ((![A : poly_complex]: ((power_184595776omplex @ A @ zero_zero_nat) = one_one_poly_complex)))). % power_0
thf(fact_118_power__0, axiom,
    ((![A : complex]: ((power_power_complex @ A @ zero_zero_nat) = one_one_complex)))). % power_0
thf(fact_119_power__0, axiom,
    ((![A : poly_poly_complex]: ((power_432682568omplex @ A @ zero_zero_nat) = one_on1331105667omplex)))). % power_0
thf(fact_120_power__0, axiom,
    ((![A : nat]: ((power_power_nat @ A @ zero_zero_nat) = one_one_nat)))). % power_0
thf(fact_121_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_122_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_123_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_124_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_125_scale__right__imp__eq, axiom,
    ((![X : complex, A : real, B : real]: ((~ ((X = zero_zero_complex))) => (((real_V1560324349omplex @ A @ X) = (real_V1560324349omplex @ B @ X)) => (A = B)))))). % scale_right_imp_eq
thf(fact_126_constant__degree, axiom,
    ((![P : poly_poly_complex]: ((fundam466968762omplex @ (poly_poly_complex2 @ P)) = ((degree_poly_complex @ P) = zero_zero_nat))))). % constant_degree
thf(fact_127_constant__degree, axiom,
    ((![P : poly_complex]: ((fundam1158420650omplex @ (poly_complex2 @ P)) = ((degree_complex @ P) = zero_zero_nat))))). % constant_degree
thf(fact_128_power__not__zero, axiom,
    ((![A : poly_complex, N : nat]: ((~ ((A = zero_z1746442943omplex))) => (~ (((power_184595776omplex @ A @ N) = zero_z1746442943omplex))))))). % power_not_zero
thf(fact_129_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_130_power__not__zero, axiom,
    ((![A : poly_poly_complex, N : nat]: ((~ ((A = zero_z1040703943omplex))) => (~ (((power_432682568omplex @ A @ N) = zero_z1040703943omplex))))))). % power_not_zero
thf(fact_131_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_132_of__nat__1__eq__iff, axiom,
    ((![N : nat]: ((one_one_nat = (semiri1382578993at_nat @ N)) = (N = one_one_nat))))). % of_nat_1_eq_iff
thf(fact_133_of__nat__1__eq__iff, axiom,
    ((![N : nat]: ((one_one_poly_complex = (semiri1679838999omplex @ N)) = (N = one_one_nat))))). % of_nat_1_eq_iff
thf(fact_134_of__nat__1__eq__iff, axiom,
    ((![N : nat]: ((one_one_int = (semiri2019852685at_int @ N)) = (N = one_one_nat))))). % of_nat_1_eq_iff
thf(fact_135_of__nat__eq__1__iff, axiom,
    ((![N : nat]: (((semiri1382578993at_nat @ N) = one_one_nat) = (N = one_one_nat))))). % of_nat_eq_1_iff
thf(fact_136_of__nat__eq__1__iff, axiom,
    ((![N : nat]: (((semiri1679838999omplex @ N) = one_one_poly_complex) = (N = one_one_nat))))). % of_nat_eq_1_iff
thf(fact_137_of__nat__eq__1__iff, axiom,
    ((![N : nat]: (((semiri2019852685at_int @ N) = one_one_int) = (N = one_one_nat))))). % of_nat_eq_1_iff
thf(fact_138_of__nat__1, axiom,
    (((semiri1382578993at_nat @ one_one_nat) = one_one_nat))). % of_nat_1
thf(fact_139_of__nat__1, axiom,
    (((semiri1679838999omplex @ one_one_nat) = one_one_poly_complex))). % of_nat_1
thf(fact_140_of__nat__1, axiom,
    (((semiri2019852685at_int @ one_one_nat) = one_one_int))). % of_nat_1
thf(fact_141_of__nat__0, axiom,
    (((semiri356525583omplex @ zero_zero_nat) = zero_zero_complex))). % of_nat_0
thf(fact_142_of__nat__0, axiom,
    (((semiri1679838999omplex @ zero_zero_nat) = zero_z1746442943omplex))). % of_nat_0
thf(fact_143_of__nat__0, axiom,
    (((semiri1382578993at_nat @ zero_zero_nat) = zero_zero_nat))). % of_nat_0
thf(fact_144_of__nat__0, axiom,
    (((semiri2019852685at_int @ zero_zero_nat) = zero_zero_int))). % of_nat_0
thf(fact_145_of__nat__0__eq__iff, axiom,
    ((![N : nat]: ((zero_zero_complex = (semiri356525583omplex @ N)) = (zero_zero_nat = N))))). % of_nat_0_eq_iff
thf(fact_146_of__nat__0__eq__iff, axiom,
    ((![N : nat]: ((zero_z1746442943omplex = (semiri1679838999omplex @ N)) = (zero_zero_nat = N))))). % of_nat_0_eq_iff
thf(fact_147_of__nat__0__eq__iff, axiom,
    ((![N : nat]: ((zero_zero_nat = (semiri1382578993at_nat @ N)) = (zero_zero_nat = N))))). % of_nat_0_eq_iff
thf(fact_148_of__nat__0__eq__iff, axiom,
    ((![N : nat]: ((zero_zero_int = (semiri2019852685at_int @ N)) = (zero_zero_nat = N))))). % of_nat_0_eq_iff
thf(fact_149_of__nat__eq__0__iff, axiom,
    ((![M : nat]: (((semiri356525583omplex @ M) = zero_zero_complex) = (M = zero_zero_nat))))). % of_nat_eq_0_iff
thf(fact_150_of__nat__eq__0__iff, axiom,
    ((![M : nat]: (((semiri1679838999omplex @ M) = zero_z1746442943omplex) = (M = zero_zero_nat))))). % of_nat_eq_0_iff
thf(fact_151_of__nat__eq__0__iff, axiom,
    ((![M : nat]: (((semiri1382578993at_nat @ M) = zero_zero_nat) = (M = zero_zero_nat))))). % of_nat_eq_0_iff
thf(fact_152_of__nat__eq__0__iff, axiom,
    ((![M : nat]: (((semiri2019852685at_int @ M) = zero_zero_int) = (M = zero_zero_nat))))). % of_nat_eq_0_iff
thf(fact_153_algebraic__altdef, axiom,
    ((algebraic_complex = (^[X2 : complex]: (?[P2 : poly_complex]: (((![I : nat]: (member_complex @ (coeff_complex @ P2 @ I) @ field_1668707340omplex))) & ((((~ ((P2 = zero_z1746442943omplex)))) & (((poly_complex2 @ P2 @ X2) = zero_zero_complex)))))))))). % algebraic_altdef
thf(fact_154_of__nat__eq__iff, axiom,
    ((![M : nat, N : nat]: (((semiri2019852685at_int @ M) = (semiri2019852685at_int @ N)) = (M = N))))). % of_nat_eq_iff
thf(fact_155_reflect__poly__0, axiom,
    (((reflect_poly_complex @ zero_z1746442943omplex) = zero_z1746442943omplex))). % reflect_poly_0
thf(fact_156_degree__0, axiom,
    (((degree_poly_complex @ zero_z1040703943omplex) = zero_zero_nat))). % degree_0
thf(fact_157_degree__0, axiom,
    (((degree_complex @ zero_z1746442943omplex) = zero_zero_nat))). % degree_0
thf(fact_158_basic__cqe__conv__2b, axiom,
    ((![P : poly_complex]: ((?[X2 : complex]: (~ (((poly_complex2 @ P @ X2) = zero_zero_complex)))) = (~ ((P = zero_z1746442943omplex))))))). % basic_cqe_conv_2b
thf(fact_159_fundamental__theorem__of__algebra, axiom,
    ((![P : poly_complex]: ((~ ((fundam1158420650omplex @ (poly_complex2 @ P)))) => (?[Z2 : complex]: ((poly_complex2 @ P @ Z2) = zero_zero_complex)))))). % fundamental_theorem_of_algebra
thf(fact_160_zero__reorient, axiom,
    ((![X : complex]: ((zero_zero_complex = X) = (X = zero_zero_complex))))). % zero_reorient
thf(fact_161_zero__reorient, axiom,
    ((![X : poly_complex]: ((zero_z1746442943omplex = X) = (X = zero_z1746442943omplex))))). % zero_reorient
thf(fact_162_zero__reorient, axiom,
    ((![X : nat]: ((zero_zero_nat = X) = (X = zero_zero_nat))))). % zero_reorient
thf(fact_163_one__reorient, axiom,
    ((![X : nat]: ((one_one_nat = X) = (X = one_one_nat))))). % one_reorient
thf(fact_164_one__reorient, axiom,
    ((![X : poly_complex]: ((one_one_poly_complex = X) = (X = one_one_poly_complex))))). % one_reorient
thf(fact_165_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_166_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_167_zero__neq__one, axiom,
    ((~ ((zero_zero_complex = one_one_complex))))). % zero_neq_one
thf(fact_168_zero__neq__one, axiom,
    ((~ ((zero_z1746442943omplex = one_one_poly_complex))))). % zero_neq_one
thf(fact_169_zero__neq__one, axiom,
    ((~ ((zero_zero_nat = one_one_nat))))). % zero_neq_one
thf(fact_170_algebraic__def, axiom,
    ((algebraic_complex = (^[X2 : complex]: (?[P2 : poly_complex]: (((![I : nat]: (member_complex @ (coeff_complex @ P2 @ I) @ ring_1_Ints_complex))) & ((((~ ((P2 = zero_z1746442943omplex)))) & (((poly_complex2 @ P2 @ X2) = zero_zero_complex)))))))))). % algebraic_def
thf(fact_171_poly__shift__0, axiom,
    ((![N : nat]: ((poly_shift_complex @ N @ zero_z1746442943omplex) = zero_z1746442943omplex)))). % poly_shift_0
thf(fact_172_poly__cutoff__0, axiom,
    ((![N : nat]: ((poly_cutoff_complex @ N @ zero_z1746442943omplex) = zero_z1746442943omplex)))). % poly_cutoff_0
thf(fact_173_algebraicE, axiom,
    ((![X : complex]: ((algebraic_complex @ X) => (~ ((![P3 : poly_complex]: ((![I2 : nat]: (member_complex @ (coeff_complex @ P3 @ I2) @ ring_1_Ints_complex)) => ((~ ((P3 = zero_z1746442943omplex))) => (~ (((poly_complex2 @ P3 @ X) = zero_zero_complex)))))))))))). % algebraicE
thf(fact_174_algebraicI, axiom,
    ((![P : poly_complex, X : complex]: ((![I3 : nat]: (member_complex @ (coeff_complex @ P @ I3) @ ring_1_Ints_complex)) => ((~ ((P = zero_z1746442943omplex))) => (((poly_complex2 @ P @ X) = zero_zero_complex) => (algebraic_complex @ X))))))). % algebraicI
thf(fact_175_Ints__of__nat, axiom,
    ((![N : nat]: (member_int @ (semiri2019852685at_int @ N) @ ring_1_Ints_int)))). % Ints_of_nat
thf(fact_176_Ints__power, axiom,
    ((![A : poly_complex, N : nat]: ((member_poly_complex @ A @ ring_1947948997omplex) => (member_poly_complex @ (power_184595776omplex @ A @ N) @ ring_1947948997omplex))))). % Ints_power
thf(fact_177_Ints__power, axiom,
    ((![A : complex, N : nat]: ((member_complex @ A @ ring_1_Ints_complex) => (member_complex @ (power_power_complex @ A @ N) @ ring_1_Ints_complex))))). % Ints_power
thf(fact_178_Ints__power, axiom,
    ((![A : poly_poly_complex, N : nat]: ((member1411246933omplex @ A @ ring_1546648269omplex) => (member1411246933omplex @ (power_432682568omplex @ A @ N) @ ring_1546648269omplex))))). % Ints_power
thf(fact_179_Ints__1, axiom,
    ((member_poly_complex @ one_one_poly_complex @ ring_1947948997omplex))). % Ints_1
thf(fact_180_Ints__0, axiom,
    ((member_complex @ zero_zero_complex @ ring_1_Ints_complex))). % Ints_0
thf(fact_181_Ints__0, axiom,
    ((member_poly_complex @ zero_z1746442943omplex @ ring_1947948997omplex))). % Ints_0
thf(fact_182_psize__eq__0__iff, axiom,
    ((![P : poly_complex]: (((fundam1709708056omplex @ P) = zero_zero_nat) = (P = zero_z1746442943omplex))))). % psize_eq_0_iff
thf(fact_183_nullstellensatz__univariate, axiom,
    ((![P : poly_complex, Q : poly_complex]: ((![X2 : complex]: ((((poly_complex2 @ P @ X2) = zero_zero_complex)) => (((poly_complex2 @ Q @ X2) = zero_zero_complex)))) = (((dvd_dvd_poly_complex @ P @ (power_184595776omplex @ Q @ (degree_complex @ P)))) | ((((P = zero_z1746442943omplex)) & ((Q = zero_z1746442943omplex))))))))). % nullstellensatz_univariate
thf(fact_184_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_185_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_186_dvd__0__right, axiom,
    ((![A : int]: (dvd_dvd_int @ A @ zero_zero_int)))). % dvd_0_right
thf(fact_187_dvd__0__right, axiom,
    ((![A : complex]: (dvd_dvd_complex @ A @ zero_zero_complex)))). % dvd_0_right
thf(fact_188_dvd__0__right, axiom,
    ((![A : poly_complex]: (dvd_dvd_poly_complex @ A @ zero_z1746442943omplex)))). % dvd_0_right
thf(fact_189_dvd__0__right, axiom,
    ((![A : nat]: (dvd_dvd_nat @ A @ zero_zero_nat)))). % dvd_0_right
thf(fact_190_dvd__0__left__iff, axiom,
    ((![A : int]: ((dvd_dvd_int @ zero_zero_int @ A) = (A = zero_zero_int))))). % dvd_0_left_iff
thf(fact_191_dvd__0__left__iff, axiom,
    ((![A : complex]: ((dvd_dvd_complex @ zero_zero_complex @ A) = (A = zero_zero_complex))))). % dvd_0_left_iff
thf(fact_192_dvd__0__left__iff, axiom,
    ((![A : poly_complex]: ((dvd_dvd_poly_complex @ zero_z1746442943omplex @ A) = (A = zero_z1746442943omplex))))). % dvd_0_left_iff
thf(fact_193_dvd__0__left__iff, axiom,
    ((![A : nat]: ((dvd_dvd_nat @ zero_zero_nat @ A) = (A = zero_zero_nat))))). % dvd_0_left_iff
thf(fact_194_synthetic__div__0, axiom,
    ((![C : complex]: ((synthe151143547omplex @ zero_z1746442943omplex @ C) = zero_z1746442943omplex)))). % synthetic_div_0
thf(fact_195_dvd__power__same, axiom,
    ((![X : int, Y2 : int, N : nat]: ((dvd_dvd_int @ X @ Y2) => (dvd_dvd_int @ (power_power_int @ X @ N) @ (power_power_int @ Y2 @ N)))))). % dvd_power_same
thf(fact_196_dvd__power__same, axiom,
    ((![X : poly_complex, Y2 : poly_complex, N : nat]: ((dvd_dvd_poly_complex @ X @ Y2) => (dvd_dvd_poly_complex @ (power_184595776omplex @ X @ N) @ (power_184595776omplex @ Y2 @ N)))))). % dvd_power_same
thf(fact_197_dvd__power__same, axiom,
    ((![X : complex, Y2 : complex, N : nat]: ((dvd_dvd_complex @ X @ Y2) => (dvd_dvd_complex @ (power_power_complex @ X @ N) @ (power_power_complex @ Y2 @ N)))))). % dvd_power_same
thf(fact_198_dvd__power__same, axiom,
    ((![X : poly_poly_complex, Y2 : poly_poly_complex, N : nat]: ((dvd_dv598755940omplex @ X @ Y2) => (dvd_dv598755940omplex @ (power_432682568omplex @ X @ N) @ (power_432682568omplex @ Y2 @ N)))))). % dvd_power_same
thf(fact_199_dvd__power__same, axiom,
    ((![X : nat, Y2 : nat, N : nat]: ((dvd_dvd_nat @ X @ Y2) => (dvd_dvd_nat @ (power_power_nat @ X @ N) @ (power_power_nat @ Y2 @ N)))))). % dvd_power_same
thf(fact_200_dvd__trans, axiom,
    ((![A : poly_complex, B : poly_complex, C : poly_complex]: ((dvd_dvd_poly_complex @ A @ B) => ((dvd_dvd_poly_complex @ B @ C) => (dvd_dvd_poly_complex @ A @ C)))))). % dvd_trans
thf(fact_201_dvd__trans, axiom,
    ((![A : int, B : int, C : int]: ((dvd_dvd_int @ A @ B) => ((dvd_dvd_int @ B @ C) => (dvd_dvd_int @ A @ C)))))). % dvd_trans
thf(fact_202_dvd__trans, axiom,
    ((![A : nat, B : nat, C : nat]: ((dvd_dvd_nat @ A @ B) => ((dvd_dvd_nat @ B @ C) => (dvd_dvd_nat @ A @ C)))))). % dvd_trans
thf(fact_203_dvd__refl, axiom,
    ((![A : poly_complex]: (dvd_dvd_poly_complex @ A @ A)))). % dvd_refl
thf(fact_204_dvd__refl, axiom,
    ((![A : int]: (dvd_dvd_int @ A @ A)))). % dvd_refl
thf(fact_205_dvd__refl, axiom,
    ((![A : nat]: (dvd_dvd_nat @ A @ A)))). % dvd_refl
thf(fact_206_one__dvd, axiom,
    ((![A : int]: (dvd_dvd_int @ one_one_int @ A)))). % one_dvd
thf(fact_207_one__dvd, axiom,
    ((![A : nat]: (dvd_dvd_nat @ one_one_nat @ A)))). % one_dvd
thf(fact_208_one__dvd, axiom,
    ((![A : poly_complex]: (dvd_dvd_poly_complex @ one_one_poly_complex @ A)))). % one_dvd
thf(fact_209_unit__imp__dvd, axiom,
    ((![B : int, A : int]: ((dvd_dvd_int @ B @ one_one_int) => (dvd_dvd_int @ B @ A))))). % unit_imp_dvd
thf(fact_210_unit__imp__dvd, axiom,
    ((![B : nat, A : nat]: ((dvd_dvd_nat @ B @ one_one_nat) => (dvd_dvd_nat @ B @ A))))). % unit_imp_dvd
thf(fact_211_unit__imp__dvd, axiom,
    ((![B : poly_complex, A : poly_complex]: ((dvd_dvd_poly_complex @ B @ one_one_poly_complex) => (dvd_dvd_poly_complex @ B @ A))))). % unit_imp_dvd
thf(fact_212_dvd__unit__imp__unit, axiom,
    ((![A : int, B : int]: ((dvd_dvd_int @ A @ B) => ((dvd_dvd_int @ B @ one_one_int) => (dvd_dvd_int @ A @ one_one_int)))))). % dvd_unit_imp_unit
thf(fact_213_dvd__unit__imp__unit, axiom,
    ((![A : nat, B : nat]: ((dvd_dvd_nat @ A @ B) => ((dvd_dvd_nat @ B @ one_one_nat) => (dvd_dvd_nat @ A @ one_one_nat)))))). % dvd_unit_imp_unit
thf(fact_214_dvd__unit__imp__unit, axiom,
    ((![A : poly_complex, B : poly_complex]: ((dvd_dvd_poly_complex @ A @ B) => ((dvd_dvd_poly_complex @ B @ one_one_poly_complex) => (dvd_dvd_poly_complex @ A @ one_one_poly_complex)))))). % dvd_unit_imp_unit
thf(fact_215_dvd__0__left, axiom,
    ((![A : int]: ((dvd_dvd_int @ zero_zero_int @ A) => (A = zero_zero_int))))). % dvd_0_left
thf(fact_216_dvd__0__left, axiom,
    ((![A : complex]: ((dvd_dvd_complex @ zero_zero_complex @ A) => (A = zero_zero_complex))))). % dvd_0_left
thf(fact_217_dvd__0__left, axiom,
    ((![A : poly_complex]: ((dvd_dvd_poly_complex @ zero_z1746442943omplex @ A) => (A = zero_z1746442943omplex))))). % dvd_0_left
thf(fact_218_dvd__0__left, axiom,
    ((![A : nat]: ((dvd_dvd_nat @ zero_zero_nat @ A) => (A = zero_zero_nat))))). % dvd_0_left
thf(fact_219_not__is__unit__0, axiom,
    ((~ ((dvd_dvd_int @ zero_zero_int @ one_one_int))))). % not_is_unit_0
thf(fact_220_not__is__unit__0, axiom,
    ((~ ((dvd_dvd_poly_complex @ zero_z1746442943omplex @ one_one_poly_complex))))). % not_is_unit_0
thf(fact_221_not__is__unit__0, axiom,
    ((~ ((dvd_dvd_nat @ zero_zero_nat @ one_one_nat))))). % not_is_unit_0
thf(fact_222_is__unit__power__iff, axiom,
    ((![A : int, N : nat]: ((dvd_dvd_int @ (power_power_int @ A @ N) @ one_one_int) = (((dvd_dvd_int @ A @ one_one_int)) | ((N = zero_zero_nat))))))). % is_unit_power_iff
thf(fact_223_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_224_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_225_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_226_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_227_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_228_basic__cqe__conv3, axiom,
    ((![P : poly_complex, A : complex, Q : poly_complex]: ((~ ((P = zero_z1746442943omplex))) => ((?[X2 : complex]: ((((poly_complex2 @ (pCons_complex @ A @ P) @ X2) = zero_zero_complex)) & ((~ (((poly_complex2 @ Q @ X2) = zero_zero_complex)))))) = (~ ((dvd_dvd_poly_complex @ (pCons_complex @ A @ P) @ (power_184595776omplex @ Q @ (fundam1709708056omplex @ P)))))))))). % basic_cqe_conv3
thf(fact_229_of__nat__dvd__iff, axiom,
    ((![M : nat, N : nat]: ((dvd_dvd_nat @ (semiri1382578993at_nat @ M) @ (semiri1382578993at_nat @ N)) = (dvd_dvd_nat @ M @ N))))). % of_nat_dvd_iff
thf(fact_230_of__nat__dvd__iff, axiom,
    ((![M : nat, N : nat]: ((dvd_dvd_int @ (semiri2019852685at_int @ M) @ (semiri2019852685at_int @ N)) = (dvd_dvd_nat @ M @ N))))). % of_nat_dvd_iff
thf(fact_231_dvd__field__iff, axiom,
    ((dvd_dvd_complex = (^[A2 : complex]: (^[B2 : complex]: (((A2 = zero_zero_complex)) => ((B2 = zero_zero_complex)))))))). % dvd_field_iff
thf(fact_232_int__dvd__int__iff, axiom,
    ((![M : nat, N : nat]: ((dvd_dvd_int @ (semiri2019852685at_int @ M) @ (semiri2019852685at_int @ N)) = (dvd_dvd_nat @ M @ N))))). % int_dvd_int_iff
thf(fact_233_pCons__eq__iff, axiom,
    ((![A : complex, P : poly_complex, B : complex, Q : poly_complex]: (((pCons_complex @ A @ P) = (pCons_complex @ B @ Q)) = (((A = B)) & ((P = Q))))))). % pCons_eq_iff
thf(fact_234_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_235_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_236_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_237_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_238_pCons__0__0, axiom,
    (((pCons_complex @ zero_zero_complex @ zero_z1746442943omplex) = zero_z1746442943omplex))). % pCons_0_0
thf(fact_239_pCons__0__0, axiom,
    (((pCons_poly_complex @ zero_z1746442943omplex @ zero_z1040703943omplex) = zero_z1040703943omplex))). % pCons_0_0
thf(fact_240_pCons__0__0, axiom,
    (((pCons_nat @ zero_zero_nat @ zero_zero_poly_nat) = zero_zero_poly_nat))). % pCons_0_0
thf(fact_241_coeff__pCons__0, axiom,
    ((![A : complex, P : poly_complex]: ((coeff_complex @ (pCons_complex @ A @ P) @ zero_zero_nat) = A)))). % coeff_pCons_0
thf(fact_242_coeff__pCons__0, axiom,
    ((![A : poly_complex, P : poly_poly_complex]: ((coeff_poly_complex @ (pCons_poly_complex @ A @ P) @ zero_zero_nat) = A)))). % coeff_pCons_0
thf(fact_243_dvd__antisym, axiom,
    ((![M : nat, N : nat]: ((dvd_dvd_nat @ M @ N) => ((dvd_dvd_nat @ N @ M) => (M = N)))))). % dvd_antisym
thf(fact_244_basic__cqe__conv2, axiom,
    ((![P : poly_complex, A : complex, B : complex]: ((~ ((P = zero_z1746442943omplex))) => (?[X3 : complex]: ((poly_complex2 @ (pCons_complex @ A @ (pCons_complex @ B @ P)) @ X3) = zero_zero_complex)))))). % basic_cqe_conv2
thf(fact_245_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))))))) => (?[Z2 : complex]: ((poly_complex2 @ P @ Z2) = zero_zero_complex)))))). % fundamental_theorem_of_algebra_alt

% Conjectures (1)
thf(conj_0, conjecture,
    (((power_184595776omplex @ q @ n) = r))).
