% 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_1197__5379362_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:36:26.925

% Could-be-implicit typings (9)
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__Complex__Ocomplex, type,
    complex : $tType).
thf(ty_n_t__Nat__Onat, type,
    nat : $tType).

% Explicit typings (67)
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_Ooffset__poly_001t__Complex__Ocomplex, type,
    fundam1201687030omplex : poly_complex > complex > poly_complex).
thf(sy_c_Fundamental__Theorem__Algebra__Mirabelle__sywschxjbb_Ooffset__poly_001t__Nat__Onat, type,
    fundam170929432ly_nat : poly_nat > nat > poly_nat).
thf(sy_c_Fundamental__Theorem__Algebra__Mirabelle__sywschxjbb_Ooffset__poly_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    fundam1307691262omplex : poly_poly_complex > poly_complex > poly_poly_complex).
thf(sy_c_Fundamental__Theorem__Algebra__Mirabelle__sywschxjbb_Opsize_001t__Complex__Ocomplex, type,
    fundam1709708056omplex : poly_complex > nat).
thf(sy_c_Fundamental__Theorem__Algebra__Mirabelle__sywschxjbb_Opsize_001t__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_Oplus__class_Oplus_001t__Complex__Ocomplex, type,
    plus_plus_complex : complex > complex > complex).
thf(sy_c_Groups_Oplus__class_Oplus_001t__Nat__Onat, type,
    plus_plus_nat : nat > nat > nat).
thf(sy_c_Groups_Oplus__class_Oplus_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    plus_p1547158847omplex : poly_complex > poly_complex > poly_complex).
thf(sy_c_Groups_Oplus__class_Oplus_001t__Polynomial__Opoly_It__Nat__Onat_J, type,
    plus_plus_poly_nat : poly_nat > poly_nat > poly_nat).
thf(sy_c_Groups_Oplus__class_Oplus_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
    plus_p138939463omplex : poly_poly_complex > poly_poly_complex > 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_Int_Oring__1__class_OInts_001t__Complex__Ocomplex, type,
    ring_1_Ints_complex : set_complex).
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_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__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_Ois__zero_001t__Complex__Ocomplex, type,
    is_zero_complex : poly_complex > $o).
thf(sy_c_Polynomial_OpCons_001t__Complex__Ocomplex, type,
    pCons_complex : complex > poly_complex > poly_complex).
thf(sy_c_Polynomial_Opcompose_001t__Complex__Ocomplex, type,
    pcompose_complex : poly_complex > poly_complex > poly_complex).
thf(sy_c_Polynomial_Opcompose_001t__Nat__Onat, type,
    pcompose_nat : poly_nat > poly_nat > poly_nat).
thf(sy_c_Polynomial_Opcompose_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    pcompo1411605209omplex : poly_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__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_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_Osynthetic__div_001t__Complex__Ocomplex, type,
    synthe151143547omplex : poly_complex > complex > 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__Polynomial__Opoly_It__Complex__Ocomplex_J_J_J, type,
    power_2001192272omplex : poly_p1267267526omplex > nat > poly_p1267267526omplex).
thf(sy_c_Rat_Ofield__char__0__class_ORats_001t__Complex__Ocomplex, type,
    field_1668707340omplex : set_complex).
thf(sy_c_Rings_Odvd__class_Odvd_001t__Complex__Ocomplex, type,
    dvd_dvd_complex : complex > complex > $o).
thf(sy_c_Rings_Odvd__class_Odvd_001t__Nat__Onat, type,
    dvd_dvd_nat : nat > nat > $o).
thf(sy_c_Rings_Odvd__class_Odvd_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    dvd_dvd_poly_complex : poly_complex > poly_complex > $o).
thf(sy_c_Rings_Odvd__class_Odvd_001t__Polynomial__Opoly_It__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__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_h, axiom,
    ((![X : complex]: ((poly_complex2 @ (power_184595776omplex @ q @ n) @ X) = (poly_complex2 @ r @ X))))). % h
thf(fact_1_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_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_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_4_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_5_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_6_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_7_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_8_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_9_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_10_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_11_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_12_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_13_poly__offset, axiom,
    ((![P : poly_poly_complex, A : poly_complex]: (?[Q2 : poly_poly_complex]: (((fundam1956464160omplex @ Q2) = (fundam1956464160omplex @ P)) & (![X2 : poly_complex]: ((poly_poly_complex2 @ Q2 @ X2) = (poly_poly_complex2 @ P @ (plus_p1547158847omplex @ A @ X2))))))))). % poly_offset
thf(fact_14_poly__offset, axiom,
    ((![P : poly_complex, A : complex]: (?[Q2 : poly_complex]: (((fundam1709708056omplex @ Q2) = (fundam1709708056omplex @ P)) & (![X2 : complex]: ((poly_complex2 @ Q2 @ X2) = (poly_complex2 @ P @ (plus_plus_complex @ A @ X2))))))))). % poly_offset
thf(fact_15_poly__offset__poly, axiom,
    ((![P : poly_poly_complex, H : poly_complex, X : poly_complex]: ((poly_poly_complex2 @ (fundam1307691262omplex @ P @ H) @ X) = (poly_poly_complex2 @ P @ (plus_p1547158847omplex @ H @ X)))))). % poly_offset_poly
thf(fact_16_poly__offset__poly, axiom,
    ((![P : poly_complex, H : complex, X : complex]: ((poly_complex2 @ (fundam1201687030omplex @ P @ H) @ X) = (poly_complex2 @ P @ (plus_plus_complex @ H @ X)))))). % poly_offset_poly
thf(fact_17_poly__offset__poly, axiom,
    ((![P : poly_nat, H : nat, X : nat]: ((poly_nat2 @ (fundam170929432ly_nat @ P @ H) @ X) = (poly_nat2 @ P @ (plus_plus_nat @ H @ X)))))). % poly_offset_poly
thf(fact_18_constant__def, axiom,
    ((fundam1158420650omplex = (^[F : complex > complex]: (![X3 : complex]: (![Y : complex]: ((F @ X3) = (F @ Y)))))))). % constant_def
thf(fact_19_poly__pcompose, axiom,
    ((![P : poly_poly_complex, Q : poly_poly_complex, X : poly_complex]: ((poly_poly_complex2 @ (pcompo1411605209omplex @ P @ Q) @ X) = (poly_poly_complex2 @ P @ (poly_poly_complex2 @ Q @ X)))))). % poly_pcompose
thf(fact_20_poly__pcompose, axiom,
    ((![P : poly_nat, Q : poly_nat, X : nat]: ((poly_nat2 @ (pcompose_nat @ P @ Q) @ X) = (poly_nat2 @ P @ (poly_nat2 @ Q @ X)))))). % poly_pcompose
thf(fact_21_poly__pcompose, axiom,
    ((![P : poly_complex, Q : poly_complex, X : complex]: ((poly_complex2 @ (pcompose_complex @ P @ Q) @ X) = (poly_complex2 @ P @ (poly_complex2 @ Q @ X)))))). % poly_pcompose
thf(fact_22_power__one__right, axiom,
    ((![A : poly_complex]: ((power_184595776omplex @ A @ one_one_nat) = A)))). % power_one_right
thf(fact_23_power__one__right, axiom,
    ((![A : complex]: ((power_power_complex @ A @ one_one_nat) = A)))). % power_one_right
thf(fact_24_power__one__right, axiom,
    ((![A : poly_poly_complex]: ((power_432682568omplex @ A @ one_one_nat) = A)))). % power_one_right
thf(fact_25_power__one, axiom,
    ((![N : nat]: ((power_power_nat @ one_one_nat @ N) = one_one_nat)))). % power_one
thf(fact_26_power__one, axiom,
    ((![N : nat]: ((power_184595776omplex @ one_one_poly_complex @ N) = one_one_poly_complex)))). % power_one
thf(fact_27_power__one, axiom,
    ((![N : nat]: ((power_power_complex @ one_one_complex @ N) = one_one_complex)))). % power_one
thf(fact_28_power__one, axiom,
    ((![N : nat]: ((power_432682568omplex @ one_on1331105667omplex @ N) = one_on1331105667omplex)))). % power_one
thf(fact_29_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_30_reflect__poly__1, axiom,
    (((reflect_poly_complex @ one_one_poly_complex) = one_one_poly_complex))). % reflect_poly_1
thf(fact_31_coeff__0, axiom,
    ((![N : nat]: ((coeff_poly_complex @ zero_z1040703943omplex @ N) = zero_z1746442943omplex)))). % coeff_0
thf(fact_32_coeff__0, axiom,
    ((![N : nat]: ((coeff_nat @ zero_zero_poly_nat @ N) = zero_zero_nat)))). % coeff_0
thf(fact_33_coeff__0, axiom,
    ((![N : nat]: ((coeff_complex @ zero_z1746442943omplex @ N) = zero_zero_complex)))). % coeff_0
thf(fact_34_coeff__add, axiom,
    ((![P : poly_poly_complex, Q : poly_poly_complex, N : nat]: ((coeff_poly_complex @ (plus_p138939463omplex @ P @ Q) @ N) = (plus_p1547158847omplex @ (coeff_poly_complex @ P @ N) @ (coeff_poly_complex @ Q @ N)))))). % coeff_add
thf(fact_35_coeff__add, axiom,
    ((![P : poly_nat, Q : poly_nat, N : nat]: ((coeff_nat @ (plus_plus_poly_nat @ P @ Q) @ N) = (plus_plus_nat @ (coeff_nat @ P @ N) @ (coeff_nat @ Q @ N)))))). % coeff_add
thf(fact_36_coeff__add, axiom,
    ((![P : poly_complex, Q : poly_complex, N : nat]: ((coeff_complex @ (plus_p1547158847omplex @ P @ Q) @ N) = (plus_plus_complex @ (coeff_complex @ P @ N) @ (coeff_complex @ Q @ N)))))). % coeff_add
thf(fact_37_poly__0, axiom,
    ((![X : poly_complex]: ((poly_poly_complex2 @ zero_z1040703943omplex @ X) = zero_z1746442943omplex)))). % poly_0
thf(fact_38_poly__0, axiom,
    ((![X : nat]: ((poly_nat2 @ zero_zero_poly_nat @ X) = zero_zero_nat)))). % poly_0
thf(fact_39_poly__0, axiom,
    ((![X : complex]: ((poly_complex2 @ zero_z1746442943omplex @ X) = zero_zero_complex)))). % poly_0
thf(fact_40_poly__add, axiom,
    ((![P : poly_poly_complex, Q : poly_poly_complex, X : poly_complex]: ((poly_poly_complex2 @ (plus_p138939463omplex @ P @ Q) @ X) = (plus_p1547158847omplex @ (poly_poly_complex2 @ P @ X) @ (poly_poly_complex2 @ Q @ X)))))). % poly_add
thf(fact_41_poly__add, axiom,
    ((![P : poly_nat, Q : poly_nat, X : nat]: ((poly_nat2 @ (plus_plus_poly_nat @ P @ Q) @ X) = (plus_plus_nat @ (poly_nat2 @ P @ X) @ (poly_nat2 @ Q @ X)))))). % poly_add
thf(fact_42_poly__add, axiom,
    ((![P : poly_complex, Q : poly_complex, X : complex]: ((poly_complex2 @ (plus_p1547158847omplex @ P @ Q) @ X) = (plus_plus_complex @ (poly_complex2 @ P @ X) @ (poly_complex2 @ Q @ X)))))). % poly_add
thf(fact_43_poly__1, axiom,
    ((![X : complex]: ((poly_complex2 @ one_one_poly_complex @ X) = one_one_complex)))). % poly_1
thf(fact_44_poly__1, axiom,
    ((![X : poly_complex]: ((poly_poly_complex2 @ one_on1331105667omplex @ X) = one_one_poly_complex)))). % poly_1
thf(fact_45_poly__1, axiom,
    ((![X : nat]: ((poly_nat2 @ one_one_poly_nat @ X) = one_one_nat)))). % poly_1
thf(fact_46_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_47_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_48_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_49_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_50_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_51_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_52_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_53_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_54_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_55_Rats__0, axiom,
    ((member_complex @ zero_zero_complex @ field_1668707340omplex))). % Rats_0
thf(fact_56_Rats__add, axiom,
    ((![A : complex, B : complex]: ((member_complex @ A @ field_1668707340omplex) => ((member_complex @ B @ field_1668707340omplex) => (member_complex @ (plus_plus_complex @ A @ B) @ field_1668707340omplex)))))). % Rats_add
thf(fact_57_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_58_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_59_pcompose__1, axiom,
    ((![P : poly_complex]: ((pcompose_complex @ one_one_poly_complex @ P) = one_one_poly_complex)))). % pcompose_1
thf(fact_60_poly__eq__iff, axiom,
    (((^[Y2 : poly_complex]: (^[Z2 : poly_complex]: (Y2 = Z2))) = (^[P2 : poly_complex]: (^[Q3 : poly_complex]: (![N3 : nat]: ((coeff_complex @ P2 @ N3) = (coeff_complex @ Q3 @ N3)))))))). % poly_eq_iff
thf(fact_61_poly__eq__iff, axiom,
    (((^[Y2 : poly_poly_complex]: (^[Z2 : poly_poly_complex]: (Y2 = Z2))) = (^[P2 : poly_poly_complex]: (^[Q3 : poly_poly_complex]: (![N3 : nat]: ((coeff_poly_complex @ P2 @ N3) = (coeff_poly_complex @ Q3 @ N3)))))))). % poly_eq_iff
thf(fact_62_pcompose__add, axiom,
    ((![P : poly_complex, Q : poly_complex, R : poly_complex]: ((pcompose_complex @ (plus_p1547158847omplex @ P @ Q) @ R) = (plus_p1547158847omplex @ (pcompose_complex @ P @ R) @ (pcompose_complex @ Q @ R)))))). % pcompose_add
thf(fact_63_pcompose__assoc, axiom,
    ((![P : poly_complex, Q : poly_complex, R : poly_complex]: ((pcompose_complex @ P @ (pcompose_complex @ Q @ R)) = (pcompose_complex @ (pcompose_complex @ P @ Q) @ R))))). % pcompose_assoc
thf(fact_64_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_65_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_66_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_67_plus__poly_Orep__eq, axiom,
    ((![X : poly_poly_complex, Xa : poly_poly_complex]: ((coeff_poly_complex @ (plus_p138939463omplex @ X @ Xa)) = (^[N3 : nat]: (plus_p1547158847omplex @ (coeff_poly_complex @ X @ N3) @ (coeff_poly_complex @ Xa @ N3))))))). % plus_poly.rep_eq
thf(fact_68_plus__poly_Orep__eq, axiom,
    ((![X : poly_nat, Xa : poly_nat]: ((coeff_nat @ (plus_plus_poly_nat @ X @ Xa)) = (^[N3 : nat]: (plus_plus_nat @ (coeff_nat @ X @ N3) @ (coeff_nat @ Xa @ N3))))))). % plus_poly.rep_eq
thf(fact_69_plus__poly_Orep__eq, axiom,
    ((![X : poly_complex, Xa : poly_complex]: ((coeff_complex @ (plus_p1547158847omplex @ X @ Xa)) = (^[N3 : nat]: (plus_plus_complex @ (coeff_complex @ X @ N3) @ (coeff_complex @ Xa @ N3))))))). % plus_poly.rep_eq
thf(fact_70_poly__all__0__iff__0, axiom,
    ((![P : poly_complex]: ((![X3 : complex]: ((poly_complex2 @ P @ X3) = zero_zero_complex)) = (P = zero_z1746442943omplex))))). % poly_all_0_iff_0
thf(fact_71_poly__all__0__iff__0, axiom,
    ((![P : poly_poly_complex]: ((![X3 : poly_complex]: ((poly_poly_complex2 @ P @ X3) = zero_z1746442943omplex)) = (P = zero_z1040703943omplex))))). % poly_all_0_iff_0
thf(fact_72_zero__poly_Orep__eq, axiom,
    (((coeff_poly_complex @ zero_z1040703943omplex) = (^[Uu : nat]: zero_z1746442943omplex)))). % zero_poly.rep_eq
thf(fact_73_zero__poly_Orep__eq, axiom,
    (((coeff_nat @ zero_zero_poly_nat) = (^[Uu : nat]: zero_zero_nat)))). % zero_poly.rep_eq
thf(fact_74_zero__poly_Orep__eq, axiom,
    (((coeff_complex @ zero_z1746442943omplex) = (^[Uu : nat]: zero_zero_complex)))). % zero_poly.rep_eq
thf(fact_75_coeff__inject, axiom,
    ((![X : poly_complex, Y3 : poly_complex]: (((coeff_complex @ X) = (coeff_complex @ Y3)) = (X = Y3))))). % coeff_inject
thf(fact_76_coeff__inject, axiom,
    ((![X : poly_poly_complex, Y3 : poly_poly_complex]: (((coeff_poly_complex @ X) = (coeff_poly_complex @ Y3)) = (X = Y3))))). % coeff_inject
thf(fact_77_power__0, axiom,
    ((![A : nat]: ((power_power_nat @ A @ zero_zero_nat) = one_one_nat)))). % power_0
thf(fact_78_power__0, axiom,
    ((![A : poly_complex]: ((power_184595776omplex @ A @ zero_zero_nat) = one_one_poly_complex)))). % power_0
thf(fact_79_power__0, axiom,
    ((![A : complex]: ((power_power_complex @ A @ zero_zero_nat) = one_one_complex)))). % power_0
thf(fact_80_power__0, axiom,
    ((![A : poly_poly_complex]: ((power_432682568omplex @ A @ zero_zero_nat) = one_on1331105667omplex)))). % power_0
thf(fact_81_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_82_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_83_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_84_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_85_mpoly__base__conv_I1_J, axiom,
    ((![X : complex]: (zero_zero_complex = (poly_complex2 @ zero_z1746442943omplex @ X))))). % mpoly_base_conv(1)
thf(fact_86_mpoly__base__conv_I1_J, axiom,
    ((![X : poly_complex]: (zero_z1746442943omplex = (poly_poly_complex2 @ zero_z1040703943omplex @ X))))). % mpoly_base_conv(1)
thf(fact_87_basic__cqe__conv1_I1_J, axiom,
    ((![P : poly_complex]: (~ ((?[X2 : complex]: (((poly_complex2 @ P @ X2) = zero_zero_complex) & (~ (((poly_complex2 @ zero_z1746442943omplex @ X2) = zero_zero_complex)))))))))). % basic_cqe_conv1(1)
thf(fact_88_basic__cqe__conv1_I1_J, axiom,
    ((![P : poly_poly_complex]: (~ ((?[X2 : poly_complex]: (((poly_poly_complex2 @ P @ X2) = zero_z1746442943omplex) & (~ (((poly_poly_complex2 @ zero_z1040703943omplex @ X2) = zero_z1746442943omplex)))))))))). % basic_cqe_conv1(1)
thf(fact_89_basic__cqe__conv1_I1_J, axiom,
    ((![P : poly_nat]: (~ ((?[X2 : nat]: (((poly_nat2 @ P @ X2) = zero_zero_nat) & (~ (((poly_nat2 @ zero_zero_poly_nat @ X2) = zero_zero_nat)))))))))). % basic_cqe_conv1(1)
thf(fact_90_basic__cqe__conv1_I2_J, axiom,
    ((~ ((?[X2 : poly_complex]: (~ (((poly_poly_complex2 @ zero_z1040703943omplex @ X2) = zero_z1746442943omplex)))))))). % basic_cqe_conv1(2)
thf(fact_91_basic__cqe__conv1_I2_J, axiom,
    ((~ ((?[X2 : nat]: (~ (((poly_nat2 @ zero_zero_poly_nat @ X2) = zero_zero_nat)))))))). % basic_cqe_conv1(2)
thf(fact_92_basic__cqe__conv1_I2_J, axiom,
    ((~ ((?[X2 : complex]: (~ (((poly_complex2 @ zero_z1746442943omplex @ X2) = zero_zero_complex)))))))). % basic_cqe_conv1(2)
thf(fact_93_basic__cqe__conv1_I4_J, axiom,
    ((?[X4 : poly_complex]: ((poly_poly_complex2 @ zero_z1040703943omplex @ X4) = zero_z1746442943omplex)))). % basic_cqe_conv1(4)
thf(fact_94_basic__cqe__conv1_I4_J, axiom,
    ((?[X4 : nat]: ((poly_nat2 @ zero_zero_poly_nat @ X4) = zero_zero_nat)))). % basic_cqe_conv1(4)
thf(fact_95_basic__cqe__conv1_I4_J, axiom,
    ((?[X4 : complex]: ((poly_complex2 @ zero_z1746442943omplex @ X4) = zero_zero_complex)))). % basic_cqe_conv1(4)
thf(fact_96_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_97_power__not__zero, axiom,
    ((![A : poly_complex, N : nat]: ((~ ((A = zero_z1746442943omplex))) => (~ (((power_184595776omplex @ A @ N) = zero_z1746442943omplex))))))). % power_not_zero
thf(fact_98_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_99_power__not__zero, axiom,
    ((![A : poly_poly_complex, N : nat]: ((~ ((A = zero_z1040703943omplex))) => (~ (((power_432682568omplex @ A @ N) = zero_z1040703943omplex))))))). % power_not_zero
thf(fact_100_add_Oleft__neutral, axiom,
    ((![A : complex]: ((plus_plus_complex @ zero_zero_complex @ A) = A)))). % add.left_neutral
thf(fact_101_add_Oleft__neutral, axiom,
    ((![A : poly_complex]: ((plus_p1547158847omplex @ zero_z1746442943omplex @ A) = A)))). % add.left_neutral
thf(fact_102_add_Oleft__neutral, axiom,
    ((![A : nat]: ((plus_plus_nat @ zero_zero_nat @ A) = A)))). % add.left_neutral
thf(fact_103_add_Oright__neutral, axiom,
    ((![A : complex]: ((plus_plus_complex @ A @ zero_zero_complex) = A)))). % add.right_neutral
thf(fact_104_add_Oright__neutral, axiom,
    ((![A : poly_complex]: ((plus_p1547158847omplex @ A @ zero_z1746442943omplex) = A)))). % add.right_neutral
thf(fact_105_add_Oright__neutral, axiom,
    ((![A : nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A)))). % add.right_neutral
thf(fact_106_add__cancel__left__left, axiom,
    ((![B : complex, A : complex]: (((plus_plus_complex @ B @ A) = A) = (B = zero_zero_complex))))). % add_cancel_left_left
thf(fact_107_add__cancel__left__left, axiom,
    ((![B : poly_complex, A : poly_complex]: (((plus_p1547158847omplex @ B @ A) = A) = (B = zero_z1746442943omplex))))). % add_cancel_left_left
thf(fact_108_add__cancel__left__left, axiom,
    ((![B : nat, A : nat]: (((plus_plus_nat @ B @ A) = A) = (B = zero_zero_nat))))). % add_cancel_left_left
thf(fact_109_add__cancel__left__right, axiom,
    ((![A : complex, B : complex]: (((plus_plus_complex @ A @ B) = A) = (B = zero_zero_complex))))). % add_cancel_left_right
thf(fact_110_add__cancel__left__right, axiom,
    ((![A : poly_complex, B : poly_complex]: (((plus_p1547158847omplex @ A @ B) = A) = (B = zero_z1746442943omplex))))). % add_cancel_left_right
thf(fact_111_add__cancel__left__right, axiom,
    ((![A : nat, B : nat]: (((plus_plus_nat @ A @ B) = A) = (B = zero_zero_nat))))). % add_cancel_left_right
thf(fact_112_add__cancel__right__left, axiom,
    ((![A : complex, B : complex]: ((A = (plus_plus_complex @ B @ A)) = (B = zero_zero_complex))))). % add_cancel_right_left
thf(fact_113_add__cancel__right__left, axiom,
    ((![A : poly_complex, B : poly_complex]: ((A = (plus_p1547158847omplex @ B @ A)) = (B = zero_z1746442943omplex))))). % add_cancel_right_left
thf(fact_114_add__cancel__right__left, axiom,
    ((![A : nat, B : nat]: ((A = (plus_plus_nat @ B @ A)) = (B = zero_zero_nat))))). % add_cancel_right_left
thf(fact_115_add__cancel__right__right, axiom,
    ((![A : complex, B : complex]: ((A = (plus_plus_complex @ A @ B)) = (B = zero_zero_complex))))). % add_cancel_right_right
thf(fact_116_add__cancel__right__right, axiom,
    ((![A : poly_complex, B : poly_complex]: ((A = (plus_p1547158847omplex @ A @ B)) = (B = zero_z1746442943omplex))))). % add_cancel_right_right
thf(fact_117_add__cancel__right__right, axiom,
    ((![A : nat, B : nat]: ((A = (plus_plus_nat @ A @ B)) = (B = zero_zero_nat))))). % add_cancel_right_right
thf(fact_118_add__eq__0__iff__both__eq__0, axiom,
    ((![X : nat, Y3 : nat]: (((plus_plus_nat @ X @ Y3) = zero_zero_nat) = (((X = zero_zero_nat)) & ((Y3 = zero_zero_nat))))))). % add_eq_0_iff_both_eq_0
thf(fact_119_zero__eq__add__iff__both__eq__0, axiom,
    ((![X : nat, Y3 : nat]: ((zero_zero_nat = (plus_plus_nat @ X @ Y3)) = (((X = zero_zero_nat)) & ((Y3 = zero_zero_nat))))))). % zero_eq_add_iff_both_eq_0
thf(fact_120_add__right__cancel, axiom,
    ((![B : nat, A : nat, C : nat]: (((plus_plus_nat @ B @ A) = (plus_plus_nat @ C @ A)) = (B = C))))). % add_right_cancel
thf(fact_121_add__right__cancel, axiom,
    ((![B : complex, A : complex, C : complex]: (((plus_plus_complex @ B @ A) = (plus_plus_complex @ C @ A)) = (B = C))))). % add_right_cancel
thf(fact_122_add__left__cancel, axiom,
    ((![A : nat, B : nat, C : nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ A @ C)) = (B = C))))). % add_left_cancel
thf(fact_123_add__left__cancel, axiom,
    ((![A : complex, B : complex, C : complex]: (((plus_plus_complex @ A @ B) = (plus_plus_complex @ A @ C)) = (B = C))))). % add_left_cancel
thf(fact_124_pcompose__0, axiom,
    ((![Q : poly_complex]: ((pcompose_complex @ zero_z1746442943omplex @ Q) = zero_z1746442943omplex)))). % pcompose_0
thf(fact_125_reflect__poly__0, axiom,
    (((reflect_poly_complex @ zero_z1746442943omplex) = zero_z1746442943omplex))). % reflect_poly_0
thf(fact_126_psize__eq__0__iff, axiom,
    ((![P : poly_complex]: (((fundam1709708056omplex @ P) = zero_zero_nat) = (P = zero_z1746442943omplex))))). % psize_eq_0_iff
thf(fact_127_offset__poly__eq__0__iff, axiom,
    ((![P : poly_nat, H : nat]: (((fundam170929432ly_nat @ P @ H) = zero_zero_poly_nat) = (P = zero_zero_poly_nat))))). % offset_poly_eq_0_iff
thf(fact_128_offset__poly__eq__0__iff, axiom,
    ((![P : poly_complex, H : complex]: (((fundam1201687030omplex @ P @ H) = zero_z1746442943omplex) = (P = zero_z1746442943omplex))))). % offset_poly_eq_0_iff
thf(fact_129_offset__poly__0, axiom,
    ((![H : nat]: ((fundam170929432ly_nat @ zero_zero_poly_nat @ H) = zero_zero_poly_nat)))). % offset_poly_0
thf(fact_130_offset__poly__0, axiom,
    ((![H : complex]: ((fundam1201687030omplex @ zero_z1746442943omplex @ H) = zero_z1746442943omplex)))). % offset_poly_0
thf(fact_131_basic__cqe__conv__2b, axiom,
    ((![P : poly_complex]: ((?[X3 : complex]: (~ (((poly_complex2 @ P @ X3) = zero_zero_complex)))) = (~ ((P = zero_z1746442943omplex))))))). % basic_cqe_conv_2b
thf(fact_132_zero__reorient, axiom,
    ((![X : complex]: ((zero_zero_complex = X) = (X = zero_zero_complex))))). % zero_reorient
thf(fact_133_zero__reorient, axiom,
    ((![X : poly_complex]: ((zero_z1746442943omplex = X) = (X = zero_z1746442943omplex))))). % zero_reorient
thf(fact_134_zero__reorient, axiom,
    ((![X : nat]: ((zero_zero_nat = X) = (X = zero_zero_nat))))). % zero_reorient
thf(fact_135_add__right__imp__eq, axiom,
    ((![B : nat, A : nat, C : nat]: (((plus_plus_nat @ B @ A) = (plus_plus_nat @ C @ A)) => (B = C))))). % add_right_imp_eq
thf(fact_136_add__right__imp__eq, axiom,
    ((![B : complex, A : complex, C : complex]: (((plus_plus_complex @ B @ A) = (plus_plus_complex @ C @ A)) => (B = C))))). % add_right_imp_eq
thf(fact_137_add__left__imp__eq, axiom,
    ((![A : nat, B : nat, C : nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ A @ C)) => (B = C))))). % add_left_imp_eq
thf(fact_138_add__left__imp__eq, axiom,
    ((![A : complex, B : complex, C : complex]: (((plus_plus_complex @ A @ B) = (plus_plus_complex @ A @ C)) => (B = C))))). % add_left_imp_eq
thf(fact_139_add_Oleft__commute, axiom,
    ((![B : nat, A : nat, C : nat]: ((plus_plus_nat @ B @ (plus_plus_nat @ A @ C)) = (plus_plus_nat @ A @ (plus_plus_nat @ B @ C)))))). % add.left_commute
thf(fact_140_add_Oleft__commute, axiom,
    ((![B : complex, A : complex, C : complex]: ((plus_plus_complex @ B @ (plus_plus_complex @ A @ C)) = (plus_plus_complex @ A @ (plus_plus_complex @ B @ C)))))). % add.left_commute
thf(fact_141_add_Ocommute, axiom,
    ((plus_plus_nat = (^[A2 : nat]: (^[B2 : nat]: (plus_plus_nat @ B2 @ A2)))))). % add.commute
thf(fact_142_add_Ocommute, axiom,
    ((plus_plus_complex = (^[A2 : complex]: (^[B2 : complex]: (plus_plus_complex @ B2 @ A2)))))). % add.commute
thf(fact_143_add_Oright__cancel, axiom,
    ((![B : complex, A : complex, C : complex]: (((plus_plus_complex @ B @ A) = (plus_plus_complex @ C @ A)) = (B = C))))). % add.right_cancel
thf(fact_144_add_Oleft__cancel, axiom,
    ((![A : complex, B : complex, C : complex]: (((plus_plus_complex @ A @ B) = (plus_plus_complex @ A @ C)) = (B = C))))). % add.left_cancel
thf(fact_145_add_Oassoc, axiom,
    ((![A : nat, B : nat, C : nat]: ((plus_plus_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ A @ (plus_plus_nat @ B @ C)))))). % add.assoc
thf(fact_146_add_Oassoc, axiom,
    ((![A : complex, B : complex, C : complex]: ((plus_plus_complex @ (plus_plus_complex @ A @ B) @ C) = (plus_plus_complex @ A @ (plus_plus_complex @ B @ C)))))). % add.assoc
thf(fact_147_group__cancel_Oadd2, axiom,
    ((![B3 : nat, K : nat, B : nat, A : nat]: ((B3 = (plus_plus_nat @ K @ B)) => ((plus_plus_nat @ A @ B3) = (plus_plus_nat @ K @ (plus_plus_nat @ A @ B))))))). % group_cancel.add2
thf(fact_148_group__cancel_Oadd2, axiom,
    ((![B3 : complex, K : complex, B : complex, A : complex]: ((B3 = (plus_plus_complex @ K @ B)) => ((plus_plus_complex @ A @ B3) = (plus_plus_complex @ K @ (plus_plus_complex @ A @ B))))))). % group_cancel.add2
thf(fact_149_group__cancel_Oadd1, axiom,
    ((![A3 : nat, K : nat, A : nat, B : nat]: ((A3 = (plus_plus_nat @ K @ A)) => ((plus_plus_nat @ A3 @ B) = (plus_plus_nat @ K @ (plus_plus_nat @ A @ B))))))). % group_cancel.add1
thf(fact_150_group__cancel_Oadd1, axiom,
    ((![A3 : complex, K : complex, A : complex, B : complex]: ((A3 = (plus_plus_complex @ K @ A)) => ((plus_plus_complex @ A3 @ B) = (plus_plus_complex @ K @ (plus_plus_complex @ A @ B))))))). % group_cancel.add1
thf(fact_151_add__mono__thms__linordered__semiring_I4_J, axiom,
    ((![I : nat, J : nat, K : nat, L : nat]: (((I = J) & (K = L)) => ((plus_plus_nat @ I @ K) = (plus_plus_nat @ J @ L)))))). % add_mono_thms_linordered_semiring(4)
thf(fact_152_ab__semigroup__add__class_Oadd__ac_I1_J, axiom,
    ((![A : nat, B : nat, C : nat]: ((plus_plus_nat @ (plus_plus_nat @ A @ B) @ C) = (plus_plus_nat @ A @ (plus_plus_nat @ B @ C)))))). % ab_semigroup_add_class.add_ac(1)
thf(fact_153_ab__semigroup__add__class_Oadd__ac_I1_J, axiom,
    ((![A : complex, B : complex, C : complex]: ((plus_plus_complex @ (plus_plus_complex @ A @ B) @ C) = (plus_plus_complex @ A @ (plus_plus_complex @ B @ C)))))). % ab_semigroup_add_class.add_ac(1)
thf(fact_154_one__reorient, axiom,
    ((![X : nat]: ((one_one_nat = X) = (X = one_one_nat))))). % one_reorient
thf(fact_155_add_Ogroup__left__neutral, axiom,
    ((![A : complex]: ((plus_plus_complex @ zero_zero_complex @ A) = A)))). % add.group_left_neutral
thf(fact_156_add_Ogroup__left__neutral, axiom,
    ((![A : poly_complex]: ((plus_p1547158847omplex @ zero_z1746442943omplex @ A) = A)))). % add.group_left_neutral
thf(fact_157_add_Ocomm__neutral, axiom,
    ((![A : complex]: ((plus_plus_complex @ A @ zero_zero_complex) = A)))). % add.comm_neutral
thf(fact_158_add_Ocomm__neutral, axiom,
    ((![A : poly_complex]: ((plus_p1547158847omplex @ A @ zero_z1746442943omplex) = A)))). % add.comm_neutral
thf(fact_159_add_Ocomm__neutral, axiom,
    ((![A : nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A)))). % add.comm_neutral
thf(fact_160_comm__monoid__add__class_Oadd__0, axiom,
    ((![A : complex]: ((plus_plus_complex @ zero_zero_complex @ A) = A)))). % comm_monoid_add_class.add_0
thf(fact_161_comm__monoid__add__class_Oadd__0, axiom,
    ((![A : poly_complex]: ((plus_p1547158847omplex @ zero_z1746442943omplex @ A) = A)))). % comm_monoid_add_class.add_0
thf(fact_162_comm__monoid__add__class_Oadd__0, axiom,
    ((![A : nat]: ((plus_plus_nat @ zero_zero_nat @ A) = A)))). % comm_monoid_add_class.add_0
thf(fact_163_algebraic__altdef, axiom,
    ((algebraic_complex = (^[X3 : complex]: (?[P2 : poly_complex]: (((![I2 : nat]: (member_complex @ (coeff_complex @ P2 @ I2) @ field_1668707340omplex))) & ((((~ ((P2 = zero_z1746442943omplex)))) & (((poly_complex2 @ P2 @ X3) = zero_zero_complex)))))))))). % algebraic_altdef
thf(fact_164_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_165_Nat_Oadd__0__right, axiom,
    ((![M : nat]: ((plus_plus_nat @ M @ zero_zero_nat) = M)))). % Nat.add_0_right
thf(fact_166_add__is__0, axiom,
    ((![M : nat, N : nat]: (((plus_plus_nat @ M @ N) = zero_zero_nat) = (((M = zero_zero_nat)) & ((N = zero_zero_nat))))))). % add_is_0
thf(fact_167_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_168_poly__shift__0, axiom,
    ((![N : nat]: ((poly_shift_complex @ N @ zero_z1746442943omplex) = zero_z1746442943omplex)))). % poly_shift_0
thf(fact_169_poly__cutoff__0, axiom,
    ((![N : nat]: ((poly_cutoff_complex @ N @ zero_z1746442943omplex) = zero_z1746442943omplex)))). % poly_cutoff_0
thf(fact_170_coeff__poly__shift, axiom,
    ((![N : nat, P : poly_complex, I : nat]: ((coeff_complex @ (poly_shift_complex @ N @ P) @ I) = (coeff_complex @ P @ (plus_plus_nat @ I @ N)))))). % coeff_poly_shift
thf(fact_171_coeff__poly__shift, axiom,
    ((![N : nat, P : poly_poly_complex, I : nat]: ((coeff_poly_complex @ (poly_s558570093omplex @ N @ P) @ I) = (coeff_poly_complex @ P @ (plus_plus_nat @ I @ N)))))). % coeff_poly_shift
thf(fact_172_plus__nat_Oadd__0, axiom,
    ((![N : nat]: ((plus_plus_nat @ zero_zero_nat @ N) = N)))). % plus_nat.add_0
thf(fact_173_add__eq__self__zero, axiom,
    ((![M : nat, N : nat]: (((plus_plus_nat @ M @ N) = M) => (N = zero_zero_nat))))). % add_eq_self_zero
thf(fact_174_Euclid__induct, axiom,
    ((![P3 : nat > nat > $o, A : nat, B : nat]: ((![A4 : nat, B4 : nat]: ((P3 @ A4 @ B4) = (P3 @ B4 @ A4))) => ((![A4 : nat]: (P3 @ A4 @ zero_zero_nat)) => ((![A4 : nat, B4 : nat]: ((P3 @ A4 @ B4) => (P3 @ A4 @ (plus_plus_nat @ A4 @ B4)))) => (P3 @ A @ B))))))). % Euclid_induct
thf(fact_175_zero__neq__one, axiom,
    ((~ ((zero_zero_complex = one_one_complex))))). % zero_neq_one
thf(fact_176_zero__neq__one, axiom,
    ((~ ((zero_z1746442943omplex = one_one_poly_complex))))). % zero_neq_one
thf(fact_177_zero__neq__one, axiom,
    ((~ ((zero_zero_nat = one_one_nat))))). % zero_neq_one
thf(fact_178_verit__sum__simplify, axiom,
    ((![A : complex]: ((plus_plus_complex @ A @ zero_zero_complex) = A)))). % verit_sum_simplify
thf(fact_179_verit__sum__simplify, axiom,
    ((![A : poly_complex]: ((plus_p1547158847omplex @ A @ zero_z1746442943omplex) = A)))). % verit_sum_simplify
thf(fact_180_verit__sum__simplify, axiom,
    ((![A : nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A)))). % verit_sum_simplify
thf(fact_181_add__0__iff, axiom,
    ((![B : complex, A : complex]: ((B = (plus_plus_complex @ B @ A)) = (A = zero_zero_complex))))). % add_0_iff
thf(fact_182_add__0__iff, axiom,
    ((![B : poly_complex, A : poly_complex]: ((B = (plus_p1547158847omplex @ B @ A)) = (A = zero_z1746442943omplex))))). % add_0_iff
thf(fact_183_add__0__iff, axiom,
    ((![B : nat, A : nat]: ((B = (plus_plus_nat @ B @ A)) = (A = zero_zero_nat))))). % add_0_iff
thf(fact_184_algebraic__def, axiom,
    ((algebraic_complex = (^[X3 : complex]: (?[P2 : poly_complex]: (((![I2 : nat]: (member_complex @ (coeff_complex @ P2 @ I2) @ ring_1_Ints_complex))) & ((((~ ((P2 = zero_z1746442943omplex)))) & (((poly_complex2 @ P2 @ X3) = zero_zero_complex)))))))))). % algebraic_def
thf(fact_185_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_186_algebraicE, axiom,
    ((![X : complex]: ((algebraic_complex @ X) => (~ ((![P4 : poly_complex]: ((![I4 : nat]: (member_complex @ (coeff_complex @ P4 @ I4) @ ring_1_Ints_complex)) => ((~ ((P4 = zero_z1746442943omplex))) => (~ (((poly_complex2 @ P4 @ X) = zero_zero_complex)))))))))))). % algebraicE
thf(fact_187_Ints__odd__nonzero, axiom,
    ((![A : complex]: ((member_complex @ A @ ring_1_Ints_complex) => (~ (((plus_plus_complex @ (plus_plus_complex @ one_one_complex @ A) @ A) = zero_zero_complex))))))). % Ints_odd_nonzero
thf(fact_188_Ints__odd__nonzero, axiom,
    ((![A : poly_complex]: ((member_poly_complex @ A @ ring_1947948997omplex) => (~ (((plus_p1547158847omplex @ (plus_p1547158847omplex @ one_one_poly_complex @ A) @ A) = zero_z1746442943omplex))))))). % Ints_odd_nonzero
thf(fact_189_Ints__double__eq__0__iff, axiom,
    ((![A : complex]: ((member_complex @ A @ ring_1_Ints_complex) => (((plus_plus_complex @ A @ A) = zero_zero_complex) = (A = zero_zero_complex)))))). % Ints_double_eq_0_iff
thf(fact_190_Ints__double__eq__0__iff, axiom,
    ((![A : poly_complex]: ((member_poly_complex @ A @ ring_1947948997omplex) => (((plus_p1547158847omplex @ A @ A) = zero_z1746442943omplex) = (A = zero_z1746442943omplex)))))). % Ints_double_eq_0_iff
thf(fact_191_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_192_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_193_Ints__power, axiom,
    ((![A : poly_poly_complex, N : nat]: ((member1411246933omplex @ A @ ring_1546648269omplex) => (member1411246933omplex @ (power_432682568omplex @ A @ N) @ ring_1546648269omplex))))). % Ints_power
thf(fact_194_Ints__0, axiom,
    ((member_complex @ zero_zero_complex @ ring_1_Ints_complex))). % Ints_0
thf(fact_195_Ints__0, axiom,
    ((member_poly_complex @ zero_z1746442943omplex @ ring_1947948997omplex))). % Ints_0
thf(fact_196_Ints__add, axiom,
    ((![A : complex, B : complex]: ((member_complex @ A @ ring_1_Ints_complex) => ((member_complex @ B @ ring_1_Ints_complex) => (member_complex @ (plus_plus_complex @ A @ B) @ ring_1_Ints_complex)))))). % Ints_add
thf(fact_197_is__zero__null, axiom,
    ((is_zero_complex = (^[P2 : poly_complex]: (P2 = zero_z1746442943omplex))))). % is_zero_null
thf(fact_198_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_199_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_200_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_201_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_202_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_203_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_204_degree__0, axiom,
    (((degree_complex @ zero_z1746442943omplex) = zero_zero_nat))). % degree_0
thf(fact_205_degree__1, axiom,
    (((degree_complex @ one_one_poly_complex) = zero_zero_nat))). % degree_1
thf(fact_206_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_207_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_208_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_209_lead__coeff__1, axiom,
    (((coeff_nat @ one_one_poly_nat @ (degree_nat @ one_one_poly_nat)) = one_one_nat))). % lead_coeff_1
thf(fact_210_lead__coeff__1, axiom,
    (((coeff_complex @ one_one_poly_complex @ (degree_complex @ one_one_poly_complex)) = one_one_complex))). % lead_coeff_1
thf(fact_211_lead__coeff__1, axiom,
    (((coeff_poly_complex @ one_on1331105667omplex @ (degree_poly_complex @ one_on1331105667omplex)) = one_one_poly_complex))). % lead_coeff_1
thf(fact_212_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_213_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_214_degree__offset__poly, axiom,
    ((![P : poly_nat, H : nat]: ((degree_nat @ (fundam170929432ly_nat @ P @ H)) = (degree_nat @ P))))). % degree_offset_poly
thf(fact_215_degree__offset__poly, axiom,
    ((![P : poly_complex, H : complex]: ((degree_complex @ (fundam1201687030omplex @ P @ H)) = (degree_complex @ P))))). % degree_offset_poly
thf(fact_216_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_217_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_218_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_219_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_220_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_221_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_222_constant__degree, axiom,
    ((![P : poly_poly_complex]: ((fundam466968762omplex @ (poly_poly_complex2 @ P)) = ((degree_poly_complex @ P) = zero_zero_nat))))). % constant_degree
thf(fact_223_constant__degree, axiom,
    ((![P : poly_complex]: ((fundam1158420650omplex @ (poly_complex2 @ P)) = ((degree_complex @ P) = zero_zero_nat))))). % constant_degree
thf(fact_224_nullstellensatz__univariate, axiom,
    ((![P : poly_complex, Q : poly_complex]: ((![X3 : complex]: ((((poly_complex2 @ P @ X3) = zero_zero_complex)) => (((poly_complex2 @ Q @ X3) = zero_zero_complex)))) = (((dvd_dvd_poly_complex @ P @ (power_184595776omplex @ Q @ (degree_complex @ P)))) | ((((P = zero_z1746442943omplex)) & ((Q = zero_z1746442943omplex))))))))). % nullstellensatz_univariate
thf(fact_225_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_226_nullstellensatz__lemma, axiom,
    ((![P : poly_complex, Q : poly_complex, N : nat]: ((![X4 : complex]: (((poly_complex2 @ P @ X4) = zero_zero_complex) => ((poly_complex2 @ Q @ X4) = zero_zero_complex))) => (((degree_complex @ P) = N) => ((~ ((N = zero_zero_nat))) => (dvd_dvd_poly_complex @ P @ (power_184595776omplex @ Q @ N)))))))). % nullstellensatz_lemma
thf(fact_227_dvd__0__right, axiom,
    ((![A : complex]: (dvd_dvd_complex @ A @ zero_zero_complex)))). % dvd_0_right
thf(fact_228_dvd__0__right, axiom,
    ((![A : poly_complex]: (dvd_dvd_poly_complex @ A @ zero_z1746442943omplex)))). % dvd_0_right
thf(fact_229_dvd__0__right, axiom,
    ((![A : nat]: (dvd_dvd_nat @ A @ zero_zero_nat)))). % dvd_0_right
thf(fact_230_dvd__0__left__iff, axiom,
    ((![A : complex]: ((dvd_dvd_complex @ zero_zero_complex @ A) = (A = zero_zero_complex))))). % dvd_0_left_iff
thf(fact_231_dvd__0__left__iff, axiom,
    ((![A : poly_complex]: ((dvd_dvd_poly_complex @ zero_z1746442943omplex @ A) = (A = zero_z1746442943omplex))))). % dvd_0_left_iff
thf(fact_232_dvd__0__left__iff, axiom,
    ((![A : nat]: ((dvd_dvd_nat @ zero_zero_nat @ A) = (A = zero_zero_nat))))). % dvd_0_left_iff
thf(fact_233_dvd__add__triv__left__iff, axiom,
    ((![A : poly_complex, B : poly_complex]: ((dvd_dvd_poly_complex @ A @ (plus_p1547158847omplex @ A @ B)) = (dvd_dvd_poly_complex @ A @ B))))). % dvd_add_triv_left_iff
thf(fact_234_dvd__add__triv__left__iff, axiom,
    ((![A : nat, B : nat]: ((dvd_dvd_nat @ A @ (plus_plus_nat @ A @ B)) = (dvd_dvd_nat @ A @ B))))). % dvd_add_triv_left_iff
thf(fact_235_dvd__add__triv__left__iff, axiom,
    ((![A : complex, B : complex]: ((dvd_dvd_complex @ A @ (plus_plus_complex @ A @ B)) = (dvd_dvd_complex @ A @ B))))). % dvd_add_triv_left_iff
thf(fact_236_dvd__add__triv__right__iff, axiom,
    ((![A : poly_complex, B : poly_complex]: ((dvd_dvd_poly_complex @ A @ (plus_p1547158847omplex @ B @ A)) = (dvd_dvd_poly_complex @ A @ B))))). % dvd_add_triv_right_iff
thf(fact_237_dvd__add__triv__right__iff, axiom,
    ((![A : nat, B : nat]: ((dvd_dvd_nat @ A @ (plus_plus_nat @ B @ A)) = (dvd_dvd_nat @ A @ B))))). % dvd_add_triv_right_iff
thf(fact_238_dvd__add__triv__right__iff, axiom,
    ((![A : complex, B : complex]: ((dvd_dvd_complex @ A @ (plus_plus_complex @ B @ A)) = (dvd_dvd_complex @ A @ B))))). % dvd_add_triv_right_iff
thf(fact_239_synthetic__div__0, axiom,
    ((![C : complex]: ((synthe151143547omplex @ zero_z1746442943omplex @ C) = zero_z1746442943omplex)))). % synthetic_div_0
thf(fact_240_dvd__power__same, axiom,
    ((![X : nat, Y3 : nat, N : nat]: ((dvd_dvd_nat @ X @ Y3) => (dvd_dvd_nat @ (power_power_nat @ X @ N) @ (power_power_nat @ Y3 @ N)))))). % dvd_power_same
thf(fact_241_dvd__power__same, axiom,
    ((![X : poly_complex, Y3 : poly_complex, N : nat]: ((dvd_dvd_poly_complex @ X @ Y3) => (dvd_dvd_poly_complex @ (power_184595776omplex @ X @ N) @ (power_184595776omplex @ Y3 @ N)))))). % dvd_power_same
thf(fact_242_dvd__power__same, axiom,
    ((![X : complex, Y3 : complex, N : nat]: ((dvd_dvd_complex @ X @ Y3) => (dvd_dvd_complex @ (power_power_complex @ X @ N) @ (power_power_complex @ Y3 @ N)))))). % dvd_power_same
thf(fact_243_dvd__power__same, axiom,
    ((![X : poly_poly_complex, Y3 : poly_poly_complex, N : nat]: ((dvd_dv598755940omplex @ X @ Y3) => (dvd_dv598755940omplex @ (power_432682568omplex @ X @ N) @ (power_432682568omplex @ Y3 @ N)))))). % dvd_power_same
thf(fact_244_basic__cqe__conv3, axiom,
    ((![P : poly_complex, A : complex, Q : poly_complex]: ((~ ((P = zero_z1746442943omplex))) => ((?[X3 : complex]: ((((poly_complex2 @ (pCons_complex @ A @ P) @ X3) = zero_zero_complex)) & ((~ (((poly_complex2 @ Q @ X3) = zero_zero_complex)))))) = (~ ((dvd_dvd_poly_complex @ (pCons_complex @ A @ P) @ (power_184595776omplex @ Q @ (fundam1709708056omplex @ P)))))))))). % basic_cqe_conv3
thf(fact_245_nat__dvd__1__iff__1, axiom,
    ((![M : nat]: ((dvd_dvd_nat @ M @ one_one_nat) = (M = one_one_nat))))). % nat_dvd_1_iff_1

% Conjectures (1)
thf(conj_0, conjecture,
    (((poly_complex2 @ (power_184595776omplex @ q @ n)) = (poly_complex2 @ r)))).
