% 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_1009__5377404_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:35:13.436

% Could-be-implicit typings (5)
thf(ty_n_t__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
    poly_poly_complex : $tType).
thf(ty_n_t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    poly_complex : $tType).
thf(ty_n_t__Polynomial__Opoly_It__Nat__Onat_J, type,
    poly_nat : $tType).
thf(ty_n_t__Complex__Ocomplex, type,
    complex : $tType).
thf(ty_n_t__Nat__Onat, type,
    nat : $tType).

% Explicit typings (50)
thf(sy_c_Fundamental__Theorem__Algebra__Mirabelle__sywschxjbb_Oconstant_001t__Complex__Ocomplex_001t__Complex__Ocomplex, type,
    fundam1158420650omplex : (complex > complex) > $o).
thf(sy_c_Fundamental__Theorem__Algebra__Mirabelle__sywschxjbb_Ooffset__poly_001t__Complex__Ocomplex, type,
    fundam1201687030omplex : poly_complex > complex > poly_complex).
thf(sy_c_Fundamental__Theorem__Algebra__Mirabelle__sywschxjbb_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__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_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_If_001t__Nat__Onat, type,
    if_nat : $o > nat > nat > nat).
thf(sy_c_Nat_OSuc, type,
    suc : nat > nat).
thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat, type,
    ord_less_nat : nat > nat > $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_Ois__zero_001t__Complex__Ocomplex, type,
    is_zero_complex : poly_complex > $o).
thf(sy_c_Polynomial_Omap__poly_001t__Complex__Ocomplex_001t__Complex__Ocomplex, type,
    map_po1637612550omplex : (complex > complex) > poly_complex > poly_complex).
thf(sy_c_Polynomial_Omap__poly_001t__Complex__Ocomplex_001t__Nat__Onat, type,
    map_poly_complex_nat : (complex > nat) > poly_complex > poly_nat).
thf(sy_c_Polynomial_Omap__poly_001t__Complex__Ocomplex_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    map_po366287630omplex : (complex > poly_complex) > poly_complex > poly_poly_complex).
thf(sy_c_Polynomial_Omap__poly_001t__Nat__Onat_001t__Complex__Ocomplex, type,
    map_poly_nat_complex : (nat > complex) > poly_nat > poly_complex).
thf(sy_c_Polynomial_Omap__poly_001t__Nat__Onat_001t__Nat__Onat, type,
    map_poly_nat_nat : (nat > nat) > poly_nat > poly_nat).
thf(sy_c_Polynomial_Omap__poly_001t__Nat__Onat_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    map_po2099259440omplex : (nat > poly_complex) > poly_nat > poly_poly_complex).
thf(sy_c_Polynomial_Omap__poly_001t__Polynomial__Opoly_It__Complex__Ocomplex_J_001t__Complex__Ocomplex, type,
    map_po944112910omplex : (poly_complex > complex) > poly_poly_complex > poly_complex).
thf(sy_c_Polynomial_Omap__poly_001t__Polynomial__Opoly_It__Complex__Ocomplex_J_001t__Nat__Onat, type,
    map_po1895962672ex_nat : (poly_complex > nat) > poly_poly_complex > poly_nat).
thf(sy_c_Polynomial_Omap__poly_001t__Polynomial__Opoly_It__Complex__Ocomplex_J_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    map_po1985147926omplex : (poly_complex > poly_complex) > poly_poly_complex > poly_poly_complex).
thf(sy_c_Polynomial_Oorder_001t__Complex__Ocomplex, type,
    order_complex : complex > poly_complex > nat).
thf(sy_c_Polynomial_Oorder_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    order_poly_complex : poly_complex > poly_poly_complex > nat).
thf(sy_c_Polynomial_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_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_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__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_v_p, type,
    p : poly_complex).
thf(sy_v_thesis____, type,
    thesis : $o).

% Relevant facts (195)
thf(fact_0_that_I1_J, axiom,
    (((p = zero_z1746442943omplex) => thesis))). % that(1)
thf(fact_1_that_I2_J, axiom,
    (((~ ((p = zero_z1746442943omplex))) => (((degree_complex @ p) = zero_zero_nat) => thesis)))). % that(2)
thf(fact_2_that_I3_J, axiom,
    ((![N : nat]: ((~ ((p = zero_z1746442943omplex))) => (((degree_complex @ p) = (suc @ N)) => thesis))))). % that(3)
thf(fact_3_degree__0, axiom,
    (((degree_complex @ zero_z1746442943omplex) = zero_zero_nat))). % degree_0
thf(fact_4_nat_Oinject, axiom,
    ((![X2 : nat, Y2 : nat]: (((suc @ X2) = (suc @ Y2)) = (X2 = Y2))))). % nat.inject
thf(fact_5_old_Onat_Oinject, axiom,
    ((![Nat : nat, Nat2 : nat]: (((suc @ Nat) = (suc @ Nat2)) = (Nat = Nat2))))). % old.nat.inject
thf(fact_6_psize__def, axiom,
    ((fundam1709708056omplex = (^[P : poly_complex]: (if_nat @ (P = zero_z1746442943omplex) @ zero_zero_nat @ (suc @ (degree_complex @ P))))))). % psize_def
thf(fact_7_nat_Odistinct_I1_J, axiom,
    ((![X2 : nat]: (~ ((zero_zero_nat = (suc @ X2))))))). % nat.distinct(1)
thf(fact_8_old_Onat_Odistinct_I2_J, axiom,
    ((![Nat2 : nat]: (~ (((suc @ Nat2) = zero_zero_nat)))))). % old.nat.distinct(2)
thf(fact_9_old_Onat_Odistinct_I1_J, axiom,
    ((![Nat2 : nat]: (~ ((zero_zero_nat = (suc @ Nat2))))))). % old.nat.distinct(1)
thf(fact_10_nat_OdiscI, axiom,
    ((![Nat : nat, X2 : nat]: ((Nat = (suc @ X2)) => (~ ((Nat = zero_zero_nat))))))). % nat.discI
thf(fact_11_nat__induct, axiom,
    ((![P2 : nat > $o, N : nat]: ((P2 @ zero_zero_nat) => ((![N2 : nat]: ((P2 @ N2) => (P2 @ (suc @ N2)))) => (P2 @ N)))))). % nat_induct
thf(fact_12_diff__induct, axiom,
    ((![P2 : nat > nat > $o, M : nat, N : nat]: ((![X : nat]: (P2 @ X @ zero_zero_nat)) => ((![Y : nat]: (P2 @ zero_zero_nat @ (suc @ Y))) => ((![X : nat, Y : nat]: ((P2 @ X @ Y) => (P2 @ (suc @ X) @ (suc @ Y)))) => (P2 @ M @ N))))))). % diff_induct
thf(fact_13_psize__eq__0__iff, axiom,
    ((![P3 : poly_complex]: (((fundam1709708056omplex @ P3) = zero_zero_nat) = (P3 = zero_z1746442943omplex))))). % psize_eq_0_iff
thf(fact_14_zero__reorient, axiom,
    ((![X3 : poly_complex]: ((zero_z1746442943omplex = X3) = (X3 = zero_z1746442943omplex))))). % zero_reorient
thf(fact_15_zero__reorient, axiom,
    ((![X3 : nat]: ((zero_zero_nat = X3) = (X3 = zero_zero_nat))))). % zero_reorient
thf(fact_16_zero__reorient, axiom,
    ((![X3 : complex]: ((zero_zero_complex = X3) = (X3 = zero_zero_complex))))). % zero_reorient
thf(fact_17_n__not__Suc__n, axiom,
    ((![N : nat]: (~ ((N = (suc @ N))))))). % n_not_Suc_n
thf(fact_18_Suc__inject, axiom,
    ((![X3 : nat, Y3 : nat]: (((suc @ X3) = (suc @ Y3)) => (X3 = Y3))))). % Suc_inject
thf(fact_19_not0__implies__Suc, axiom,
    ((![N : nat]: ((~ ((N = zero_zero_nat))) => (?[M2 : nat]: (N = (suc @ M2))))))). % not0_implies_Suc
thf(fact_20_old_Onat_Oinducts, axiom,
    ((![P2 : nat > $o, Nat : nat]: ((P2 @ zero_zero_nat) => ((![Nat3 : nat]: ((P2 @ Nat3) => (P2 @ (suc @ Nat3)))) => (P2 @ Nat)))))). % old.nat.inducts
thf(fact_21_old_Onat_Oexhaust, axiom,
    ((![Y3 : nat]: ((~ ((Y3 = zero_zero_nat))) => (~ ((![Nat3 : nat]: (~ ((Y3 = (suc @ Nat3))))))))))). % old.nat.exhaust
thf(fact_22_Zero__not__Suc, axiom,
    ((![M : nat]: (~ ((zero_zero_nat = (suc @ M))))))). % Zero_not_Suc
thf(fact_23_Zero__neq__Suc, axiom,
    ((![M : nat]: (~ ((zero_zero_nat = (suc @ M))))))). % Zero_neq_Suc
thf(fact_24_Suc__neq__Zero, axiom,
    ((![M : nat]: (~ (((suc @ M) = zero_zero_nat)))))). % Suc_neq_Zero
thf(fact_25_zero__induct, axiom,
    ((![P2 : nat > $o, K : nat]: ((P2 @ K) => ((![N2 : nat]: ((P2 @ (suc @ N2)) => (P2 @ N2))) => (P2 @ zero_zero_nat)))))). % zero_induct
thf(fact_26_exists__least__lemma, axiom,
    ((![P2 : nat > $o]: ((~ ((P2 @ zero_zero_nat))) => ((?[X_1 : nat]: (P2 @ X_1)) => (?[N2 : nat]: ((~ ((P2 @ N2))) & (P2 @ (suc @ N2))))))))). % exists_least_lemma
thf(fact_27_synthetic__div__eq__0__iff, axiom,
    ((![P3 : poly_complex, C : complex]: (((synthe151143547omplex @ P3 @ C) = zero_z1746442943omplex) = ((degree_complex @ P3) = zero_zero_nat))))). % synthetic_div_eq_0_iff
thf(fact_28_is__zero__null, axiom,
    ((is_zero_complex = (^[P : poly_complex]: (P = zero_z1746442943omplex))))). % is_zero_null
thf(fact_29_poly__cutoff__0, axiom,
    ((![N : nat]: ((poly_cutoff_complex @ N @ zero_z1746442943omplex) = zero_z1746442943omplex)))). % poly_cutoff_0
thf(fact_30_degree__pCons__eq__if, axiom,
    ((![P3 : poly_complex, A : complex]: (((P3 = zero_z1746442943omplex) => ((degree_complex @ (pCons_complex @ A @ P3)) = zero_zero_nat)) & ((~ ((P3 = zero_z1746442943omplex))) => ((degree_complex @ (pCons_complex @ A @ P3)) = (suc @ (degree_complex @ P3)))))))). % degree_pCons_eq_if
thf(fact_31_poly__shift__0, axiom,
    ((![N : nat]: ((poly_shift_complex @ N @ zero_z1746442943omplex) = zero_z1746442943omplex)))). % poly_shift_0
thf(fact_32_leading__coeff__0__iff, axiom,
    ((![P3 : poly_poly_complex]: (((coeff_poly_complex @ P3 @ (degree_poly_complex @ P3)) = zero_z1746442943omplex) = (P3 = zero_z1040703943omplex))))). % leading_coeff_0_iff
thf(fact_33_leading__coeff__0__iff, axiom,
    ((![P3 : poly_nat]: (((coeff_nat @ P3 @ (degree_nat @ P3)) = zero_zero_nat) = (P3 = zero_zero_poly_nat))))). % leading_coeff_0_iff
thf(fact_34_leading__coeff__0__iff, axiom,
    ((![P3 : poly_complex]: (((coeff_complex @ P3 @ (degree_complex @ P3)) = zero_zero_complex) = (P3 = zero_z1746442943omplex))))). % leading_coeff_0_iff
thf(fact_35_pCons__eq__iff, axiom,
    ((![A : complex, P3 : poly_complex, B : complex, Q : poly_complex]: (((pCons_complex @ A @ P3) = (pCons_complex @ B @ Q)) = (((A = B)) & ((P3 = Q))))))). % pCons_eq_iff
thf(fact_36_synthetic__div__0, axiom,
    ((![C : complex]: ((synthe151143547omplex @ zero_z1746442943omplex @ C) = zero_z1746442943omplex)))). % synthetic_div_0
thf(fact_37_coeff__0, axiom,
    ((![N : nat]: ((coeff_poly_complex @ zero_z1040703943omplex @ N) = zero_z1746442943omplex)))). % coeff_0
thf(fact_38_coeff__0, axiom,
    ((![N : nat]: ((coeff_nat @ zero_zero_poly_nat @ N) = zero_zero_nat)))). % coeff_0
thf(fact_39_coeff__0, axiom,
    ((![N : nat]: ((coeff_complex @ zero_z1746442943omplex @ N) = zero_zero_complex)))). % coeff_0
thf(fact_40_pCons__0__0, axiom,
    (((pCons_poly_complex @ zero_z1746442943omplex @ zero_z1040703943omplex) = zero_z1040703943omplex))). % pCons_0_0
thf(fact_41_pCons__0__0, axiom,
    (((pCons_nat @ zero_zero_nat @ zero_zero_poly_nat) = zero_zero_poly_nat))). % pCons_0_0
thf(fact_42_pCons__0__0, axiom,
    (((pCons_complex @ zero_zero_complex @ zero_z1746442943omplex) = zero_z1746442943omplex))). % pCons_0_0
thf(fact_43_pCons__eq__0__iff, axiom,
    ((![A : poly_complex, P3 : poly_poly_complex]: (((pCons_poly_complex @ A @ P3) = zero_z1040703943omplex) = (((A = zero_z1746442943omplex)) & ((P3 = zero_z1040703943omplex))))))). % pCons_eq_0_iff
thf(fact_44_pCons__eq__0__iff, axiom,
    ((![A : nat, P3 : poly_nat]: (((pCons_nat @ A @ P3) = zero_zero_poly_nat) = (((A = zero_zero_nat)) & ((P3 = zero_zero_poly_nat))))))). % pCons_eq_0_iff
thf(fact_45_pCons__eq__0__iff, axiom,
    ((![A : complex, P3 : poly_complex]: (((pCons_complex @ A @ P3) = zero_z1746442943omplex) = (((A = zero_zero_complex)) & ((P3 = zero_z1746442943omplex))))))). % pCons_eq_0_iff
thf(fact_46_coeff__pCons__0, axiom,
    ((![A : complex, P3 : poly_complex]: ((coeff_complex @ (pCons_complex @ A @ P3) @ zero_zero_nat) = A)))). % coeff_pCons_0
thf(fact_47_coeff__pCons__Suc, axiom,
    ((![A : complex, P3 : poly_complex, N : nat]: ((coeff_complex @ (pCons_complex @ A @ P3) @ (suc @ N)) = (coeff_complex @ P3 @ N))))). % coeff_pCons_Suc
thf(fact_48_lead__coeff__pCons_I2_J, axiom,
    ((![P3 : poly_complex, A : complex]: ((P3 = zero_z1746442943omplex) => ((coeff_complex @ (pCons_complex @ A @ P3) @ (degree_complex @ (pCons_complex @ A @ P3))) = A))))). % lead_coeff_pCons(2)
thf(fact_49_lead__coeff__pCons_I1_J, axiom,
    ((![P3 : poly_complex, A : complex]: ((~ ((P3 = zero_z1746442943omplex))) => ((coeff_complex @ (pCons_complex @ A @ P3) @ (degree_complex @ (pCons_complex @ A @ P3))) = (coeff_complex @ P3 @ (degree_complex @ P3))))))). % lead_coeff_pCons(1)
thf(fact_50_pCons__cases, axiom,
    ((![P3 : poly_complex]: (~ ((![A2 : complex, Q2 : poly_complex]: (~ ((P3 = (pCons_complex @ A2 @ Q2)))))))))). % pCons_cases
thf(fact_51_pderiv_Ocases, axiom,
    ((![X3 : poly_complex]: (~ ((![A2 : complex, P4 : poly_complex]: (~ ((X3 = (pCons_complex @ A2 @ P4)))))))))). % pderiv.cases
thf(fact_52_poly__induct2, axiom,
    ((![P2 : poly_complex > poly_complex > $o, P3 : poly_complex, Q : poly_complex]: ((P2 @ zero_z1746442943omplex @ zero_z1746442943omplex) => ((![A2 : complex, P4 : poly_complex, B2 : complex, Q2 : poly_complex]: ((P2 @ P4 @ Q2) => (P2 @ (pCons_complex @ A2 @ P4) @ (pCons_complex @ B2 @ Q2)))) => (P2 @ P3 @ Q)))))). % poly_induct2
thf(fact_53_pderiv_Oinduct, axiom,
    ((![P2 : poly_complex > $o, A0 : poly_complex]: ((![A2 : complex, P4 : poly_complex]: (((~ ((P4 = zero_z1746442943omplex))) => (P2 @ P4)) => (P2 @ (pCons_complex @ A2 @ P4)))) => (P2 @ A0))))). % pderiv.induct
thf(fact_54_pCons__induct, axiom,
    ((![P2 : poly_poly_complex > $o, P3 : poly_poly_complex]: ((P2 @ zero_z1040703943omplex) => ((![A2 : poly_complex, P4 : poly_poly_complex]: (((~ ((A2 = zero_z1746442943omplex))) | (~ ((P4 = zero_z1040703943omplex)))) => ((P2 @ P4) => (P2 @ (pCons_poly_complex @ A2 @ P4))))) => (P2 @ P3)))))). % pCons_induct
thf(fact_55_pCons__induct, axiom,
    ((![P2 : poly_nat > $o, P3 : poly_nat]: ((P2 @ zero_zero_poly_nat) => ((![A2 : nat, P4 : poly_nat]: (((~ ((A2 = zero_zero_nat))) | (~ ((P4 = zero_zero_poly_nat)))) => ((P2 @ P4) => (P2 @ (pCons_nat @ A2 @ P4))))) => (P2 @ P3)))))). % pCons_induct
thf(fact_56_pCons__induct, axiom,
    ((![P2 : poly_complex > $o, P3 : poly_complex]: ((P2 @ zero_z1746442943omplex) => ((![A2 : complex, P4 : poly_complex]: (((~ ((A2 = zero_zero_complex))) | (~ ((P4 = zero_z1746442943omplex)))) => ((P2 @ P4) => (P2 @ (pCons_complex @ A2 @ P4))))) => (P2 @ P3)))))). % pCons_induct
thf(fact_57_zero__poly_Orep__eq, axiom,
    (((coeff_poly_complex @ zero_z1040703943omplex) = (^[Uu : nat]: zero_z1746442943omplex)))). % zero_poly.rep_eq
thf(fact_58_zero__poly_Orep__eq, axiom,
    (((coeff_nat @ zero_zero_poly_nat) = (^[Uu : nat]: zero_zero_nat)))). % zero_poly.rep_eq
thf(fact_59_zero__poly_Orep__eq, axiom,
    (((coeff_complex @ zero_z1746442943omplex) = (^[Uu : nat]: zero_zero_complex)))). % zero_poly.rep_eq
thf(fact_60_leading__coeff__neq__0, axiom,
    ((![P3 : poly_poly_complex]: ((~ ((P3 = zero_z1040703943omplex))) => (~ (((coeff_poly_complex @ P3 @ (degree_poly_complex @ P3)) = zero_z1746442943omplex))))))). % leading_coeff_neq_0
thf(fact_61_leading__coeff__neq__0, axiom,
    ((![P3 : poly_nat]: ((~ ((P3 = zero_zero_poly_nat))) => (~ (((coeff_nat @ P3 @ (degree_nat @ P3)) = zero_zero_nat))))))). % leading_coeff_neq_0
thf(fact_62_leading__coeff__neq__0, axiom,
    ((![P3 : poly_complex]: ((~ ((P3 = zero_z1746442943omplex))) => (~ (((coeff_complex @ P3 @ (degree_complex @ P3)) = zero_zero_complex))))))). % leading_coeff_neq_0
thf(fact_63_degree__pCons__0, axiom,
    ((![A : complex]: ((degree_complex @ (pCons_complex @ A @ zero_z1746442943omplex)) = zero_zero_nat)))). % degree_pCons_0
thf(fact_64_degree__eq__zeroE, axiom,
    ((![P3 : poly_complex]: (((degree_complex @ P3) = zero_zero_nat) => (~ ((![A2 : complex]: (~ ((P3 = (pCons_complex @ A2 @ zero_z1746442943omplex))))))))))). % degree_eq_zeroE
thf(fact_65_degree__pCons__eq, axiom,
    ((![P3 : poly_complex, A : complex]: ((~ ((P3 = zero_z1746442943omplex))) => ((degree_complex @ (pCons_complex @ A @ P3)) = (suc @ (degree_complex @ P3))))))). % degree_pCons_eq
thf(fact_66_degree__reflect__poly__eq, axiom,
    ((![P3 : poly_poly_complex]: ((~ (((coeff_poly_complex @ P3 @ zero_zero_nat) = zero_z1746442943omplex))) => ((degree_poly_complex @ (reflec309385472omplex @ P3)) = (degree_poly_complex @ P3)))))). % degree_reflect_poly_eq
thf(fact_67_degree__reflect__poly__eq, axiom,
    ((![P3 : poly_nat]: ((~ (((coeff_nat @ P3 @ zero_zero_nat) = zero_zero_nat))) => ((degree_nat @ (reflect_poly_nat @ P3)) = (degree_nat @ P3)))))). % degree_reflect_poly_eq
thf(fact_68_degree__reflect__poly__eq, axiom,
    ((![P3 : poly_complex]: ((~ (((coeff_complex @ P3 @ zero_zero_nat) = zero_zero_complex))) => ((degree_complex @ (reflect_poly_complex @ P3)) = (degree_complex @ P3)))))). % degree_reflect_poly_eq
thf(fact_69_coeff__0__reflect__poly__0__iff, axiom,
    ((![P3 : poly_poly_complex]: (((coeff_poly_complex @ (reflec309385472omplex @ P3) @ zero_zero_nat) = zero_z1746442943omplex) = (P3 = zero_z1040703943omplex))))). % coeff_0_reflect_poly_0_iff
thf(fact_70_coeff__0__reflect__poly__0__iff, axiom,
    ((![P3 : poly_nat]: (((coeff_nat @ (reflect_poly_nat @ P3) @ zero_zero_nat) = zero_zero_nat) = (P3 = zero_zero_poly_nat))))). % coeff_0_reflect_poly_0_iff
thf(fact_71_coeff__0__reflect__poly__0__iff, axiom,
    ((![P3 : poly_complex]: (((coeff_complex @ (reflect_poly_complex @ P3) @ zero_zero_nat) = zero_zero_complex) = (P3 = zero_z1746442943omplex))))). % coeff_0_reflect_poly_0_iff
thf(fact_72_coeff__0__reflect__poly, axiom,
    ((![P3 : poly_complex]: ((coeff_complex @ (reflect_poly_complex @ P3) @ zero_zero_nat) = (coeff_complex @ P3 @ (degree_complex @ P3)))))). % coeff_0_reflect_poly
thf(fact_73_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_74_pcompose__0_H, axiom,
    ((![P3 : poly_complex]: ((pcompose_complex @ P3 @ zero_z1746442943omplex) = (pCons_complex @ (coeff_complex @ P3 @ zero_zero_nat) @ zero_z1746442943omplex))))). % pcompose_0'
thf(fact_75_reflect__poly__reflect__poly, axiom,
    ((![P3 : poly_poly_complex]: ((~ (((coeff_poly_complex @ P3 @ zero_zero_nat) = zero_z1746442943omplex))) => ((reflec309385472omplex @ (reflec309385472omplex @ P3)) = P3))))). % reflect_poly_reflect_poly
thf(fact_76_reflect__poly__reflect__poly, axiom,
    ((![P3 : poly_nat]: ((~ (((coeff_nat @ P3 @ zero_zero_nat) = zero_zero_nat))) => ((reflect_poly_nat @ (reflect_poly_nat @ P3)) = P3))))). % reflect_poly_reflect_poly
thf(fact_77_reflect__poly__reflect__poly, axiom,
    ((![P3 : poly_complex]: ((~ (((coeff_complex @ P3 @ zero_zero_nat) = zero_zero_complex))) => ((reflect_poly_complex @ (reflect_poly_complex @ P3)) = P3))))). % reflect_poly_reflect_poly
thf(fact_78_offset__poly__single, axiom,
    ((![A : complex, H : complex]: ((fundam1201687030omplex @ (pCons_complex @ A @ zero_z1746442943omplex) @ H) = (pCons_complex @ A @ zero_z1746442943omplex))))). % offset_poly_single
thf(fact_79_pcompose__0, axiom,
    ((![Q : poly_complex]: ((pcompose_complex @ zero_z1746442943omplex @ Q) = zero_z1746442943omplex)))). % pcompose_0
thf(fact_80_reflect__poly__0, axiom,
    (((reflect_poly_complex @ zero_z1746442943omplex) = zero_z1746442943omplex))). % reflect_poly_0
thf(fact_81_degree__1, axiom,
    (((degree_complex @ one_one_poly_complex) = zero_zero_nat))). % degree_1
thf(fact_82_pcompose__const, axiom,
    ((![A : complex, Q : poly_complex]: ((pcompose_complex @ (pCons_complex @ A @ zero_z1746442943omplex) @ Q) = (pCons_complex @ A @ zero_z1746442943omplex))))). % pcompose_const
thf(fact_83_reflect__poly__const, axiom,
    ((![A : complex]: ((reflect_poly_complex @ (pCons_complex @ A @ zero_z1746442943omplex)) = (pCons_complex @ A @ zero_z1746442943omplex))))). % reflect_poly_const
thf(fact_84_one__poly__eq__simps_I1_J, axiom,
    ((one_one_poly_nat = (pCons_nat @ one_one_nat @ zero_zero_poly_nat)))). % one_poly_eq_simps(1)
thf(fact_85_one__poly__eq__simps_I1_J, axiom,
    ((one_one_poly_complex = (pCons_complex @ one_one_complex @ zero_z1746442943omplex)))). % one_poly_eq_simps(1)
thf(fact_86_one__poly__eq__simps_I2_J, axiom,
    (((pCons_nat @ one_one_nat @ zero_zero_poly_nat) = one_one_poly_nat))). % one_poly_eq_simps(2)
thf(fact_87_one__poly__eq__simps_I2_J, axiom,
    (((pCons_complex @ one_one_complex @ zero_z1746442943omplex) = one_one_poly_complex))). % one_poly_eq_simps(2)
thf(fact_88_lead__coeff__1, axiom,
    (((coeff_complex @ one_one_poly_complex @ (degree_complex @ one_one_poly_complex)) = one_one_complex))). % lead_coeff_1
thf(fact_89_lead__coeff__1, axiom,
    (((coeff_nat @ one_one_poly_nat @ (degree_nat @ one_one_poly_nat)) = one_one_nat))). % lead_coeff_1
thf(fact_90_pcompose__idR, axiom,
    ((![P3 : poly_poly_complex]: ((pcompo1411605209omplex @ P3 @ (pCons_poly_complex @ zero_z1746442943omplex @ (pCons_poly_complex @ one_one_poly_complex @ zero_z1040703943omplex))) = P3)))). % pcompose_idR
thf(fact_91_pcompose__idR, axiom,
    ((![P3 : poly_nat]: ((pcompose_nat @ P3 @ (pCons_nat @ zero_zero_nat @ (pCons_nat @ one_one_nat @ zero_zero_poly_nat))) = P3)))). % pcompose_idR
thf(fact_92_pcompose__idR, axiom,
    ((![P3 : poly_complex]: ((pcompose_complex @ P3 @ (pCons_complex @ zero_zero_complex @ (pCons_complex @ one_one_complex @ zero_z1746442943omplex))) = P3)))). % pcompose_idR
thf(fact_93_one__reorient, axiom,
    ((![X3 : nat]: ((one_one_nat = X3) = (X3 = one_one_nat))))). % one_reorient
thf(fact_94_pCons__one, axiom,
    (((pCons_nat @ one_one_nat @ zero_zero_poly_nat) = one_one_poly_nat))). % pCons_one
thf(fact_95_pCons__one, axiom,
    (((pCons_complex @ one_one_complex @ zero_z1746442943omplex) = one_one_poly_complex))). % pCons_one
thf(fact_96_offset__poly__eq__0__iff, axiom,
    ((![P3 : poly_complex, H : complex]: (((fundam1201687030omplex @ P3 @ H) = zero_z1746442943omplex) = (P3 = zero_z1746442943omplex))))). % offset_poly_eq_0_iff
thf(fact_97_offset__poly__0, axiom,
    ((![H : complex]: ((fundam1201687030omplex @ zero_z1746442943omplex @ H) = zero_z1746442943omplex)))). % offset_poly_0
thf(fact_98_degree__offset__poly, axiom,
    ((![P3 : poly_complex, H : complex]: ((degree_complex @ (fundam1201687030omplex @ P3 @ H)) = (degree_complex @ P3))))). % degree_offset_poly
thf(fact_99_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_100_zero__neq__one, axiom,
    ((~ ((zero_z1746442943omplex = one_one_poly_complex))))). % zero_neq_one
thf(fact_101_zero__neq__one, axiom,
    ((~ ((zero_zero_nat = one_one_nat))))). % zero_neq_one
thf(fact_102_zero__neq__one, axiom,
    ((~ ((zero_zero_complex = one_one_complex))))). % zero_neq_one
thf(fact_103_map__poly__1, axiom,
    ((![F : nat > complex]: ((map_poly_nat_complex @ F @ one_one_poly_nat) = (pCons_complex @ (F @ one_one_nat) @ zero_z1746442943omplex))))). % map_poly_1
thf(fact_104_poly__reflect__poly__0, axiom,
    ((![P3 : poly_poly_complex]: ((poly_poly_complex2 @ (reflec309385472omplex @ P3) @ zero_z1746442943omplex) = (coeff_poly_complex @ P3 @ (degree_poly_complex @ P3)))))). % poly_reflect_poly_0
thf(fact_105_poly__reflect__poly__0, axiom,
    ((![P3 : poly_nat]: ((poly_nat2 @ (reflect_poly_nat @ P3) @ zero_zero_nat) = (coeff_nat @ P3 @ (degree_nat @ P3)))))). % poly_reflect_poly_0
thf(fact_106_poly__reflect__poly__0, axiom,
    ((![P3 : poly_complex]: ((poly_complex2 @ (reflect_poly_complex @ P3) @ zero_zero_complex) = (coeff_complex @ P3 @ (degree_complex @ P3)))))). % poly_reflect_poly_0
thf(fact_107_map__poly__0, axiom,
    ((![F : complex > complex]: ((map_po1637612550omplex @ F @ zero_z1746442943omplex) = zero_z1746442943omplex)))). % map_poly_0
thf(fact_108_poly__0, axiom,
    ((![X3 : poly_complex]: ((poly_poly_complex2 @ zero_z1040703943omplex @ X3) = zero_z1746442943omplex)))). % poly_0
thf(fact_109_poly__0, axiom,
    ((![X3 : nat]: ((poly_nat2 @ zero_zero_poly_nat @ X3) = zero_zero_nat)))). % poly_0
thf(fact_110_poly__0, axiom,
    ((![X3 : complex]: ((poly_complex2 @ zero_z1746442943omplex @ X3) = zero_zero_complex)))). % poly_0
thf(fact_111_poly__1, axiom,
    ((![X3 : complex]: ((poly_complex2 @ one_one_poly_complex @ X3) = one_one_complex)))). % poly_1
thf(fact_112_poly__1, axiom,
    ((![X3 : nat]: ((poly_nat2 @ one_one_poly_nat @ X3) = one_one_nat)))). % poly_1
thf(fact_113_map__poly__1_H, axiom,
    ((![F : nat > nat]: (((F @ one_one_nat) = one_one_nat) => ((map_poly_nat_nat @ F @ one_one_poly_nat) = one_one_poly_nat))))). % map_poly_1'
thf(fact_114_synthetic__div__pCons, axiom,
    ((![A : complex, P3 : poly_complex, C : complex]: ((synthe151143547omplex @ (pCons_complex @ A @ P3) @ C) = (pCons_complex @ (poly_complex2 @ P3 @ C) @ (synthe151143547omplex @ P3 @ C)))))). % synthetic_div_pCons
thf(fact_115_reflect__poly__at__0__eq__0__iff, axiom,
    ((![P3 : poly_poly_complex]: (((poly_poly_complex2 @ (reflec309385472omplex @ P3) @ zero_z1746442943omplex) = zero_z1746442943omplex) = (P3 = zero_z1040703943omplex))))). % reflect_poly_at_0_eq_0_iff
thf(fact_116_reflect__poly__at__0__eq__0__iff, axiom,
    ((![P3 : poly_nat]: (((poly_nat2 @ (reflect_poly_nat @ P3) @ zero_zero_nat) = zero_zero_nat) = (P3 = zero_zero_poly_nat))))). % reflect_poly_at_0_eq_0_iff
thf(fact_117_reflect__poly__at__0__eq__0__iff, axiom,
    ((![P3 : poly_complex]: (((poly_complex2 @ (reflect_poly_complex @ P3) @ zero_zero_complex) = zero_zero_complex) = (P3 = zero_z1746442943omplex))))). % reflect_poly_at_0_eq_0_iff
thf(fact_118_poly__pcompose, axiom,
    ((![P3 : poly_complex, Q : poly_complex, X3 : complex]: ((poly_complex2 @ (pcompose_complex @ P3 @ Q) @ X3) = (poly_complex2 @ P3 @ (poly_complex2 @ Q @ X3)))))). % poly_pcompose
thf(fact_119_poly__eq__poly__eq__iff, axiom,
    ((![P3 : poly_complex, Q : poly_complex]: (((poly_complex2 @ P3) = (poly_complex2 @ Q)) = (P3 = Q))))). % poly_eq_poly_eq_iff
thf(fact_120_fundamental__theorem__of__algebra__alt, axiom,
    ((![P3 : poly_complex]: ((~ ((?[A2 : complex, L : poly_complex]: ((~ ((A2 = zero_zero_complex))) & ((L = zero_z1746442943omplex) & (P3 = (pCons_complex @ A2 @ L))))))) => (?[Z : complex]: ((poly_complex2 @ P3 @ Z) = zero_zero_complex)))))). % fundamental_theorem_of_algebra_alt
thf(fact_121_poly__all__0__iff__0, axiom,
    ((![P3 : poly_poly_complex]: ((![X4 : poly_complex]: ((poly_poly_complex2 @ P3 @ X4) = zero_z1746442943omplex)) = (P3 = zero_z1040703943omplex))))). % poly_all_0_iff_0
thf(fact_122_poly__all__0__iff__0, axiom,
    ((![P3 : poly_complex]: ((![X4 : complex]: ((poly_complex2 @ P3 @ X4) = zero_zero_complex)) = (P3 = zero_z1746442943omplex))))). % poly_all_0_iff_0
thf(fact_123_One__nat__def, axiom,
    ((one_one_nat = (suc @ zero_zero_nat)))). % One_nat_def
thf(fact_124_degree__map__poly, axiom,
    ((![F : poly_complex > poly_complex, P3 : poly_poly_complex]: ((![X : poly_complex]: ((~ ((X = zero_z1746442943omplex))) => (~ (((F @ X) = zero_z1746442943omplex))))) => ((degree_poly_complex @ (map_po1985147926omplex @ F @ P3)) = (degree_poly_complex @ P3)))))). % degree_map_poly
thf(fact_125_degree__map__poly, axiom,
    ((![F : poly_complex > nat, P3 : poly_poly_complex]: ((![X : poly_complex]: ((~ ((X = zero_z1746442943omplex))) => (~ (((F @ X) = zero_zero_nat))))) => ((degree_nat @ (map_po1895962672ex_nat @ F @ P3)) = (degree_poly_complex @ P3)))))). % degree_map_poly
thf(fact_126_degree__map__poly, axiom,
    ((![F : poly_complex > complex, P3 : poly_poly_complex]: ((![X : poly_complex]: ((~ ((X = zero_z1746442943omplex))) => (~ (((F @ X) = zero_zero_complex))))) => ((degree_complex @ (map_po944112910omplex @ F @ P3)) = (degree_poly_complex @ P3)))))). % degree_map_poly
thf(fact_127_degree__map__poly, axiom,
    ((![F : nat > poly_complex, P3 : poly_nat]: ((![X : nat]: ((~ ((X = zero_zero_nat))) => (~ (((F @ X) = zero_z1746442943omplex))))) => ((degree_poly_complex @ (map_po2099259440omplex @ F @ P3)) = (degree_nat @ P3)))))). % degree_map_poly
thf(fact_128_degree__map__poly, axiom,
    ((![F : nat > nat, P3 : poly_nat]: ((![X : nat]: ((~ ((X = zero_zero_nat))) => (~ (((F @ X) = zero_zero_nat))))) => ((degree_nat @ (map_poly_nat_nat @ F @ P3)) = (degree_nat @ P3)))))). % degree_map_poly
thf(fact_129_degree__map__poly, axiom,
    ((![F : nat > complex, P3 : poly_nat]: ((![X : nat]: ((~ ((X = zero_zero_nat))) => (~ (((F @ X) = zero_zero_complex))))) => ((degree_complex @ (map_poly_nat_complex @ F @ P3)) = (degree_nat @ P3)))))). % degree_map_poly
thf(fact_130_degree__map__poly, axiom,
    ((![F : complex > poly_complex, P3 : poly_complex]: ((![X : complex]: ((~ ((X = zero_zero_complex))) => (~ (((F @ X) = zero_z1746442943omplex))))) => ((degree_poly_complex @ (map_po366287630omplex @ F @ P3)) = (degree_complex @ P3)))))). % degree_map_poly
thf(fact_131_degree__map__poly, axiom,
    ((![F : complex > nat, P3 : poly_complex]: ((![X : complex]: ((~ ((X = zero_zero_complex))) => (~ (((F @ X) = zero_zero_nat))))) => ((degree_nat @ (map_poly_complex_nat @ F @ P3)) = (degree_complex @ P3)))))). % degree_map_poly
thf(fact_132_degree__map__poly, axiom,
    ((![F : complex > complex, P3 : poly_complex]: ((![X : complex]: ((~ ((X = zero_zero_complex))) => (~ (((F @ X) = zero_zero_complex))))) => ((degree_complex @ (map_po1637612550omplex @ F @ P3)) = (degree_complex @ P3)))))). % degree_map_poly
thf(fact_133_coeff__map__poly, axiom,
    ((![F : poly_complex > poly_complex, P3 : poly_poly_complex, N : nat]: (((F @ zero_z1746442943omplex) = zero_z1746442943omplex) => ((coeff_poly_complex @ (map_po1985147926omplex @ F @ P3) @ N) = (F @ (coeff_poly_complex @ P3 @ N))))))). % coeff_map_poly
thf(fact_134_coeff__map__poly, axiom,
    ((![F : poly_complex > nat, P3 : poly_poly_complex, N : nat]: (((F @ zero_z1746442943omplex) = zero_zero_nat) => ((coeff_nat @ (map_po1895962672ex_nat @ F @ P3) @ N) = (F @ (coeff_poly_complex @ P3 @ N))))))). % coeff_map_poly
thf(fact_135_coeff__map__poly, axiom,
    ((![F : poly_complex > complex, P3 : poly_poly_complex, N : nat]: (((F @ zero_z1746442943omplex) = zero_zero_complex) => ((coeff_complex @ (map_po944112910omplex @ F @ P3) @ N) = (F @ (coeff_poly_complex @ P3 @ N))))))). % coeff_map_poly
thf(fact_136_coeff__map__poly, axiom,
    ((![F : nat > poly_complex, P3 : poly_nat, N : nat]: (((F @ zero_zero_nat) = zero_z1746442943omplex) => ((coeff_poly_complex @ (map_po2099259440omplex @ F @ P3) @ N) = (F @ (coeff_nat @ P3 @ N))))))). % coeff_map_poly
thf(fact_137_coeff__map__poly, axiom,
    ((![F : nat > nat, P3 : poly_nat, N : nat]: (((F @ zero_zero_nat) = zero_zero_nat) => ((coeff_nat @ (map_poly_nat_nat @ F @ P3) @ N) = (F @ (coeff_nat @ P3 @ N))))))). % coeff_map_poly
thf(fact_138_coeff__map__poly, axiom,
    ((![F : nat > complex, P3 : poly_nat, N : nat]: (((F @ zero_zero_nat) = zero_zero_complex) => ((coeff_complex @ (map_poly_nat_complex @ F @ P3) @ N) = (F @ (coeff_nat @ P3 @ N))))))). % coeff_map_poly
thf(fact_139_coeff__map__poly, axiom,
    ((![F : complex > poly_complex, P3 : poly_complex, N : nat]: (((F @ zero_zero_complex) = zero_z1746442943omplex) => ((coeff_poly_complex @ (map_po366287630omplex @ F @ P3) @ N) = (F @ (coeff_complex @ P3 @ N))))))). % coeff_map_poly
thf(fact_140_coeff__map__poly, axiom,
    ((![F : complex > nat, P3 : poly_complex, N : nat]: (((F @ zero_zero_complex) = zero_zero_nat) => ((coeff_nat @ (map_poly_complex_nat @ F @ P3) @ N) = (F @ (coeff_complex @ P3 @ N))))))). % coeff_map_poly
thf(fact_141_coeff__map__poly, axiom,
    ((![F : complex > complex, P3 : poly_complex, N : nat]: (((F @ zero_zero_complex) = zero_zero_complex) => ((coeff_complex @ (map_po1637612550omplex @ F @ P3) @ N) = (F @ (coeff_complex @ P3 @ N))))))). % coeff_map_poly
thf(fact_142_map__poly__pCons, axiom,
    ((![F : poly_complex > poly_complex, C : poly_complex, P3 : poly_poly_complex]: (((F @ zero_z1746442943omplex) = zero_z1746442943omplex) => ((map_po1985147926omplex @ F @ (pCons_poly_complex @ C @ P3)) = (pCons_poly_complex @ (F @ C) @ (map_po1985147926omplex @ F @ P3))))))). % map_poly_pCons
thf(fact_143_map__poly__pCons, axiom,
    ((![F : poly_complex > nat, C : poly_complex, P3 : poly_poly_complex]: (((F @ zero_z1746442943omplex) = zero_zero_nat) => ((map_po1895962672ex_nat @ F @ (pCons_poly_complex @ C @ P3)) = (pCons_nat @ (F @ C) @ (map_po1895962672ex_nat @ F @ P3))))))). % map_poly_pCons
thf(fact_144_map__poly__pCons, axiom,
    ((![F : poly_complex > complex, C : poly_complex, P3 : poly_poly_complex]: (((F @ zero_z1746442943omplex) = zero_zero_complex) => ((map_po944112910omplex @ F @ (pCons_poly_complex @ C @ P3)) = (pCons_complex @ (F @ C) @ (map_po944112910omplex @ F @ P3))))))). % map_poly_pCons
thf(fact_145_map__poly__pCons, axiom,
    ((![F : nat > poly_complex, C : nat, P3 : poly_nat]: (((F @ zero_zero_nat) = zero_z1746442943omplex) => ((map_po2099259440omplex @ F @ (pCons_nat @ C @ P3)) = (pCons_poly_complex @ (F @ C) @ (map_po2099259440omplex @ F @ P3))))))). % map_poly_pCons
thf(fact_146_map__poly__pCons, axiom,
    ((![F : nat > nat, C : nat, P3 : poly_nat]: (((F @ zero_zero_nat) = zero_zero_nat) => ((map_poly_nat_nat @ F @ (pCons_nat @ C @ P3)) = (pCons_nat @ (F @ C) @ (map_poly_nat_nat @ F @ P3))))))). % map_poly_pCons
thf(fact_147_map__poly__pCons, axiom,
    ((![F : nat > complex, C : nat, P3 : poly_nat]: (((F @ zero_zero_nat) = zero_zero_complex) => ((map_poly_nat_complex @ F @ (pCons_nat @ C @ P3)) = (pCons_complex @ (F @ C) @ (map_poly_nat_complex @ F @ P3))))))). % map_poly_pCons
thf(fact_148_map__poly__pCons, axiom,
    ((![F : complex > poly_complex, C : complex, P3 : poly_complex]: (((F @ zero_zero_complex) = zero_z1746442943omplex) => ((map_po366287630omplex @ F @ (pCons_complex @ C @ P3)) = (pCons_poly_complex @ (F @ C) @ (map_po366287630omplex @ F @ P3))))))). % map_poly_pCons
thf(fact_149_map__poly__pCons, axiom,
    ((![F : complex > nat, C : complex, P3 : poly_complex]: (((F @ zero_zero_complex) = zero_zero_nat) => ((map_poly_complex_nat @ F @ (pCons_complex @ C @ P3)) = (pCons_nat @ (F @ C) @ (map_poly_complex_nat @ F @ P3))))))). % map_poly_pCons
thf(fact_150_map__poly__pCons, axiom,
    ((![F : complex > complex, C : complex, P3 : poly_complex]: (((F @ zero_zero_complex) = zero_zero_complex) => ((map_po1637612550omplex @ F @ (pCons_complex @ C @ P3)) = (pCons_complex @ (F @ C) @ (map_po1637612550omplex @ F @ P3))))))). % map_poly_pCons
thf(fact_151_poly__0__coeff__0, axiom,
    ((![P3 : poly_poly_complex]: ((poly_poly_complex2 @ P3 @ zero_z1746442943omplex) = (coeff_poly_complex @ P3 @ zero_zero_nat))))). % poly_0_coeff_0
thf(fact_152_poly__0__coeff__0, axiom,
    ((![P3 : poly_nat]: ((poly_nat2 @ P3 @ zero_zero_nat) = (coeff_nat @ P3 @ zero_zero_nat))))). % poly_0_coeff_0
thf(fact_153_poly__0__coeff__0, axiom,
    ((![P3 : poly_complex]: ((poly_complex2 @ P3 @ zero_zero_complex) = (coeff_complex @ P3 @ zero_zero_nat))))). % poly_0_coeff_0
thf(fact_154_fundamental__theorem__of__algebra, axiom,
    ((![P3 : poly_complex]: ((~ ((fundam1158420650omplex @ (poly_complex2 @ P3)))) => (?[Z : complex]: ((poly_complex2 @ P3 @ Z) = zero_zero_complex)))))). % fundamental_theorem_of_algebra
thf(fact_155_order__root, axiom,
    ((![P3 : poly_poly_complex, A : poly_complex]: (((poly_poly_complex2 @ P3 @ A) = zero_z1746442943omplex) = (((P3 = zero_z1040703943omplex)) | ((~ (((order_poly_complex @ A @ P3) = zero_zero_nat))))))))). % order_root
thf(fact_156_order__root, axiom,
    ((![P3 : poly_complex, A : complex]: (((poly_complex2 @ P3 @ A) = zero_zero_complex) = (((P3 = zero_z1746442943omplex)) | ((~ (((order_complex @ A @ P3) = zero_zero_nat))))))))). % order_root
thf(fact_157_pcompose__eq__0, axiom,
    ((![P3 : poly_complex, Q : poly_complex]: (((pcompose_complex @ P3 @ Q) = zero_z1746442943omplex) => ((ord_less_nat @ zero_zero_nat @ (degree_complex @ Q)) => (P3 = zero_z1746442943omplex)))))). % pcompose_eq_0
thf(fact_158_not__gr__zero, axiom,
    ((![N : nat]: ((~ ((ord_less_nat @ zero_zero_nat @ N))) = (N = zero_zero_nat))))). % not_gr_zero
thf(fact_159_neq0__conv, axiom,
    ((![N : nat]: ((~ ((N = zero_zero_nat))) = (ord_less_nat @ zero_zero_nat @ N))))). % neq0_conv
thf(fact_160_less__nat__zero__code, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ zero_zero_nat)))))). % less_nat_zero_code
thf(fact_161_bot__nat__0_Onot__eq__extremum, axiom,
    ((![A : nat]: ((~ ((A = zero_zero_nat))) = (ord_less_nat @ zero_zero_nat @ A))))). % bot_nat_0.not_eq_extremum
thf(fact_162_Suc__less__eq, axiom,
    ((![M : nat, N : nat]: ((ord_less_nat @ (suc @ M) @ (suc @ N)) = (ord_less_nat @ M @ N))))). % Suc_less_eq
thf(fact_163_Suc__mono, axiom,
    ((![M : nat, N : nat]: ((ord_less_nat @ M @ N) => (ord_less_nat @ (suc @ M) @ (suc @ N)))))). % Suc_mono
thf(fact_164_lessI, axiom,
    ((![N : nat]: (ord_less_nat @ N @ (suc @ N))))). % lessI
thf(fact_165_less__Suc0, axiom,
    ((![N : nat]: ((ord_less_nat @ N @ (suc @ zero_zero_nat)) = (N = zero_zero_nat))))). % less_Suc0
thf(fact_166_zero__less__Suc, axiom,
    ((![N : nat]: (ord_less_nat @ zero_zero_nat @ (suc @ N))))). % zero_less_Suc
thf(fact_167_less__one, axiom,
    ((![N : nat]: ((ord_less_nat @ N @ one_one_nat) = (N = zero_zero_nat))))). % less_one
thf(fact_168_gr0I, axiom,
    ((![N : nat]: ((~ ((N = zero_zero_nat))) => (ord_less_nat @ zero_zero_nat @ N))))). % gr0I
thf(fact_169_not__gr0, axiom,
    ((![N : nat]: ((~ ((ord_less_nat @ zero_zero_nat @ N))) = (N = zero_zero_nat))))). % not_gr0
thf(fact_170_not__less0, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ zero_zero_nat)))))). % not_less0
thf(fact_171_less__zeroE, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ zero_zero_nat)))))). % less_zeroE
thf(fact_172_gr__implies__not0, axiom,
    ((![M : nat, N : nat]: ((ord_less_nat @ M @ N) => (~ ((N = zero_zero_nat))))))). % gr_implies_not0
thf(fact_173_infinite__descent0, axiom,
    ((![P2 : nat > $o, N : nat]: ((P2 @ zero_zero_nat) => ((![N2 : nat]: ((ord_less_nat @ zero_zero_nat @ N2) => ((~ ((P2 @ N2))) => (?[M3 : nat]: ((ord_less_nat @ M3 @ N2) & (~ ((P2 @ M3)))))))) => (P2 @ N)))))). % infinite_descent0
thf(fact_174_bot__nat__0_Oextremum__strict, axiom,
    ((![A : nat]: (~ ((ord_less_nat @ A @ zero_zero_nat)))))). % bot_nat_0.extremum_strict
thf(fact_175_gr__zeroI, axiom,
    ((![N : nat]: ((~ ((N = zero_zero_nat))) => (ord_less_nat @ zero_zero_nat @ N))))). % gr_zeroI
thf(fact_176_not__less__zero, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ zero_zero_nat)))))). % not_less_zero
thf(fact_177_gr__implies__not__zero, axiom,
    ((![M : nat, N : nat]: ((ord_less_nat @ M @ N) => (~ ((N = zero_zero_nat))))))). % gr_implies_not_zero
thf(fact_178_zero__less__iff__neq__zero, axiom,
    ((![N : nat]: ((ord_less_nat @ zero_zero_nat @ N) = (~ ((N = zero_zero_nat))))))). % zero_less_iff_neq_zero
thf(fact_179_zero__less__one, axiom,
    ((ord_less_nat @ zero_zero_nat @ one_one_nat))). % zero_less_one
thf(fact_180_not__one__less__zero, axiom,
    ((~ ((ord_less_nat @ one_one_nat @ zero_zero_nat))))). % not_one_less_zero
thf(fact_181_less__Suc__eq__0__disj, axiom,
    ((![M : nat, N : nat]: ((ord_less_nat @ M @ (suc @ N)) = (((M = zero_zero_nat)) | ((?[J : nat]: (((M = (suc @ J))) & ((ord_less_nat @ J @ N)))))))))). % less_Suc_eq_0_disj
thf(fact_182_gr0__implies__Suc, axiom,
    ((![N : nat]: ((ord_less_nat @ zero_zero_nat @ N) => (?[M2 : nat]: (N = (suc @ M2))))))). % gr0_implies_Suc
thf(fact_183_All__less__Suc2, axiom,
    ((![N : nat, P2 : nat > $o]: ((![I : nat]: (((ord_less_nat @ I @ (suc @ N))) => ((P2 @ I)))) = (((P2 @ zero_zero_nat)) & ((![I : nat]: (((ord_less_nat @ I @ N)) => ((P2 @ (suc @ I))))))))))). % All_less_Suc2
thf(fact_184_gr0__conv__Suc, axiom,
    ((![N : nat]: ((ord_less_nat @ zero_zero_nat @ N) = (?[M4 : nat]: (N = (suc @ M4))))))). % gr0_conv_Suc
thf(fact_185_Ex__less__Suc2, axiom,
    ((![N : nat, P2 : nat > $o]: ((?[I : nat]: (((ord_less_nat @ I @ (suc @ N))) & ((P2 @ I)))) = (((P2 @ zero_zero_nat)) | ((?[I : nat]: (((ord_less_nat @ I @ N)) & ((P2 @ (suc @ I))))))))))). % Ex_less_Suc2
thf(fact_186_constant__def, axiom,
    ((fundam1158420650omplex = (^[F2 : complex > complex]: (![X4 : complex]: (![Y4 : complex]: ((F2 @ X4) = (F2 @ Y4)))))))). % constant_def
thf(fact_187_not__less__less__Suc__eq, axiom,
    ((![N : nat, M : nat]: ((~ ((ord_less_nat @ N @ M))) => ((ord_less_nat @ N @ (suc @ M)) = (N = M)))))). % not_less_less_Suc_eq
thf(fact_188_strict__inc__induct, axiom,
    ((![I2 : nat, J2 : nat, P2 : nat > $o]: ((ord_less_nat @ I2 @ J2) => ((![I3 : nat]: ((J2 = (suc @ I3)) => (P2 @ I3))) => ((![I3 : nat]: ((ord_less_nat @ I3 @ J2) => ((P2 @ (suc @ I3)) => (P2 @ I3)))) => (P2 @ I2))))))). % strict_inc_induct
thf(fact_189_less__Suc__induct, axiom,
    ((![I2 : nat, J2 : nat, P2 : nat > nat > $o]: ((ord_less_nat @ I2 @ J2) => ((![I3 : nat]: (P2 @ I3 @ (suc @ I3))) => ((![I3 : nat, J3 : nat, K2 : nat]: ((ord_less_nat @ I3 @ J3) => ((ord_less_nat @ J3 @ K2) => ((P2 @ I3 @ J3) => ((P2 @ J3 @ K2) => (P2 @ I3 @ K2)))))) => (P2 @ I2 @ J2))))))). % less_Suc_induct
thf(fact_190_less__trans__Suc, axiom,
    ((![I2 : nat, J2 : nat, K : nat]: ((ord_less_nat @ I2 @ J2) => ((ord_less_nat @ J2 @ K) => (ord_less_nat @ (suc @ I2) @ K)))))). % less_trans_Suc
thf(fact_191_Suc__less__SucD, axiom,
    ((![M : nat, N : nat]: ((ord_less_nat @ (suc @ M) @ (suc @ N)) => (ord_less_nat @ M @ N))))). % Suc_less_SucD
thf(fact_192_less__antisym, axiom,
    ((![N : nat, M : nat]: ((~ ((ord_less_nat @ N @ M))) => ((ord_less_nat @ N @ (suc @ M)) => (M = N)))))). % less_antisym
thf(fact_193_Suc__less__eq2, axiom,
    ((![N : nat, M : nat]: ((ord_less_nat @ (suc @ N) @ M) = (?[M5 : nat]: (((M = (suc @ M5))) & ((ord_less_nat @ N @ M5)))))))). % Suc_less_eq2
thf(fact_194_All__less__Suc, axiom,
    ((![N : nat, P2 : nat > $o]: ((![I : nat]: (((ord_less_nat @ I @ (suc @ N))) => ((P2 @ I)))) = (((P2 @ N)) & ((![I : nat]: (((ord_less_nat @ I @ N)) => ((P2 @ I)))))))))). % All_less_Suc

% Helper facts (3)
thf(help_If_3_1_If_001t__Nat__Onat_T, axiom,
    ((![P2 : $o]: ((P2 = $true) | (P2 = $false))))).
thf(help_If_2_1_If_001t__Nat__Onat_T, axiom,
    ((![X3 : nat, Y3 : nat]: ((if_nat @ $false @ X3 @ Y3) = Y3)))).
thf(help_If_1_1_If_001t__Nat__Onat_T, axiom,
    ((![X3 : nat, Y3 : nat]: ((if_nat @ $true @ X3 @ Y3) = X3)))).

% Conjectures (4)
thf(conj_0, hypothesis,
    ($true)).
thf(conj_1, hypothesis,
    ($true)).
thf(conj_2, hypothesis,
    ((![N3 : nat]: ((~ ((p = zero_z1746442943omplex))) => (((degree_complex @ p) = (suc @ N3)) => thesis))))).
thf(conj_3, conjecture,
    (thesis)).
