% 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_676__5374590_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:32:05.201

% Could-be-implicit typings (9)
thf(ty_n_t__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
    poly_poly_complex : $tType).
thf(ty_n_t__Polynomial__Opoly_It__Polynomial__Opoly_It__Real__Oreal_J_J, type,
    poly_poly_real : $tType).
thf(ty_n_t__Polynomial__Opoly_It__Polynomial__Opoly_It__Nat__Onat_J_J, type,
    poly_poly_nat : $tType).
thf(ty_n_t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    poly_complex : $tType).
thf(ty_n_t__Polynomial__Opoly_It__Real__Oreal_J, type,
    poly_real : $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__Real__Oreal, type,
    real : $tType).
thf(ty_n_t__Nat__Onat, type,
    nat : $tType).

% Explicit typings (36)
thf(sy_c_Fundamental__Theorem__Algebra__Mirabelle__sywschxjbb_Oconstant_001t__Complex__Ocomplex_001t__Complex__Ocomplex, type,
    fundam1158420650omplex : (complex > complex) > $o).
thf(sy_c_Fundamental__Theorem__Algebra__Mirabelle__sywschxjbb_Opsize_001t__Complex__Ocomplex, type,
    fundam1709708056omplex : poly_complex > nat).
thf(sy_c_Fundamental__Theorem__Algebra__Mirabelle__sywschxjbb_Opsize_001t__Nat__Onat, type,
    fundam1567013434ze_nat : poly_nat > nat).
thf(sy_c_Fundamental__Theorem__Algebra__Mirabelle__sywschxjbb_Opsize_001t__Real__Oreal, type,
    fundam1947011094e_real : poly_real > nat).
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__Real__Oreal_J, type,
    plus_plus_poly_real : poly_real > poly_real > poly_real).
thf(sy_c_Groups_Oplus__class_Oplus_001t__Real__Oreal, type,
    plus_plus_real : real > real > real).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Complex__Ocomplex, type,
    zero_zero_complex : complex).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Nat__Onat, type,
    zero_zero_nat : nat).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    zero_z1746442943omplex : poly_complex).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Nat__Onat_J, type,
    zero_zero_poly_nat : poly_nat).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Complex__Ocomplex_J_J, type,
    zero_z1040703943omplex : poly_poly_complex).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Nat__Onat_J_J, type,
    zero_z1059985641ly_nat : poly_poly_nat).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Polynomial__Opoly_It__Real__Oreal_J_J, type,
    zero_z1423781445y_real : poly_poly_real).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Polynomial__Opoly_It__Real__Oreal_J, type,
    zero_zero_poly_real : poly_real).
thf(sy_c_Groups_Ozero__class_Ozero_001t__Real__Oreal, type,
    zero_zero_real : real).
thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat, type,
    ord_less_nat : nat > nat > $o).
thf(sy_c_Orderings_Oord__class_Oless_001t__Polynomial__Opoly_It__Real__Oreal_J, type,
    ord_less_poly_real : poly_real > poly_real > $o).
thf(sy_c_Orderings_Oord__class_Oless_001t__Real__Oreal, type,
    ord_less_real : real > real > $o).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat, type,
    ord_less_eq_nat : nat > nat > $o).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Polynomial__Opoly_It__Real__Oreal_J, type,
    ord_le1180086932y_real : poly_real > poly_real > $o).
thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Real__Oreal, type,
    ord_less_eq_real : real > real > $o).
thf(sy_c_Polynomial_Opoly_001t__Complex__Ocomplex, type,
    poly_complex2 : poly_complex > complex > complex).
thf(sy_c_Polynomial_Opoly_001t__Nat__Onat, type,
    poly_nat2 : poly_nat > nat > nat).
thf(sy_c_Polynomial_Opoly_001t__Polynomial__Opoly_It__Complex__Ocomplex_J, type,
    poly_poly_complex2 : poly_poly_complex > poly_complex > poly_complex).
thf(sy_c_Polynomial_Opoly_001t__Polynomial__Opoly_It__Nat__Onat_J, type,
    poly_poly_nat2 : poly_poly_nat > poly_nat > poly_nat).
thf(sy_c_Polynomial_Opoly_001t__Polynomial__Opoly_It__Real__Oreal_J, type,
    poly_poly_real2 : poly_poly_real > poly_real > poly_real).
thf(sy_c_Polynomial_Opoly_001t__Real__Oreal, type,
    poly_real2 : poly_real > real > real).
thf(sy_c_Real__Vector__Spaces_Onorm__class_Onorm_001t__Complex__Ocomplex, type,
    real_V638595069omplex : complex > real).
thf(sy_v_c____, type,
    c : complex).
thf(sy_v_p, type,
    p : poly_complex).
thf(sy_v_pa____, type,
    pa : poly_complex).
thf(sy_v_q____, type,
    q : poly_complex).

% Relevant facts (245)
thf(fact_0_nc, axiom,
    ((~ ((fundam1158420650omplex @ (poly_complex2 @ p)))))). % nc
thf(fact_1_less_Oprems, axiom,
    ((~ ((fundam1158420650omplex @ (poly_complex2 @ pa)))))). % less.prems
thf(fact_2_q_I2_J, axiom,
    ((![X : complex]: ((poly_complex2 @ q @ X) = (poly_complex2 @ pa @ (plus_plus_complex @ c @ X)))))). % q(2)
thf(fact_3_False, axiom,
    ((~ (((poly_complex2 @ pa @ c) = zero_zero_complex))))). % False
thf(fact_4_q_I1_J, axiom,
    (((fundam1709708056omplex @ q) = (fundam1709708056omplex @ pa)))). % q(1)
thf(fact_5__092_060open_062constant_A_Ipoly_Aq_J_A_092_060Longrightarrow_062_AFalse_092_060close_062, axiom,
    ((~ ((fundam1158420650omplex @ (poly_complex2 @ q)))))). % \<open>constant (poly q) \<Longrightarrow> False\<close>
thf(fact_6_qnc, axiom,
    ((~ ((fundam1158420650omplex @ (poly_complex2 @ q)))))). % qnc
thf(fact_7_poly__0, axiom,
    ((![X2 : poly_nat]: ((poly_poly_nat2 @ zero_z1059985641ly_nat @ X2) = zero_zero_poly_nat)))). % poly_0
thf(fact_8_poly__0, axiom,
    ((![X2 : poly_real]: ((poly_poly_real2 @ zero_z1423781445y_real @ X2) = zero_zero_poly_real)))). % poly_0
thf(fact_9_poly__0, axiom,
    ((![X2 : poly_complex]: ((poly_poly_complex2 @ zero_z1040703943omplex @ X2) = zero_z1746442943omplex)))). % poly_0
thf(fact_10_poly__0, axiom,
    ((![X2 : complex]: ((poly_complex2 @ zero_z1746442943omplex @ X2) = zero_zero_complex)))). % poly_0
thf(fact_11_poly__0, axiom,
    ((![X2 : real]: ((poly_real2 @ zero_zero_poly_real @ X2) = zero_zero_real)))). % poly_0
thf(fact_12_poly__0, axiom,
    ((![X2 : nat]: ((poly_nat2 @ zero_zero_poly_nat @ X2) = zero_zero_nat)))). % poly_0
thf(fact_13__092_060open_062_092_060exists_062q_O_Apsize_Aq_A_061_Apsize_Ap_A_092_060and_062_A_I_092_060forall_062x_O_Apoly_Aq_Ax_A_061_Apoly_Ap_A_Ic_A_L_Ax_J_J_092_060close_062, axiom,
    ((?[Q : poly_complex]: (((fundam1709708056omplex @ Q) = (fundam1709708056omplex @ pa)) & (![X : complex]: ((poly_complex2 @ Q @ X) = (poly_complex2 @ pa @ (plus_plus_complex @ c @ X)))))))). % \<open>\<exists>q. psize q = psize p \<and> (\<forall>x. poly q x = poly p (c + x))\<close>
thf(fact_14__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062q_O_A_092_060lbrakk_062psize_Aq_A_061_Apsize_Ap_059_A_092_060forall_062x_O_Apoly_Aq_Ax_A_061_Apoly_Ap_A_Ic_A_L_Ax_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom,
    ((~ ((![Q : poly_complex]: (((fundam1709708056omplex @ Q) = (fundam1709708056omplex @ pa)) => (~ ((![X : complex]: ((poly_complex2 @ Q @ X) = (poly_complex2 @ pa @ (plus_plus_complex @ c @ X)))))))))))). % \<open>\<And>thesis. (\<And>q. \<lbrakk>psize q = psize p; \<forall>x. poly q x = poly p (c + x)\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_15_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_16_poly__all__0__iff__0, axiom,
    ((![P : poly_real]: ((![X3 : real]: ((poly_real2 @ P @ X3) = zero_zero_real)) = (P = zero_zero_poly_real))))). % poly_all_0_iff_0
thf(fact_17_poly__all__0__iff__0, axiom,
    ((![P : poly_poly_real]: ((![X3 : poly_real]: ((poly_poly_real2 @ P @ X3) = zero_zero_poly_real)) = (P = zero_z1423781445y_real))))). % poly_all_0_iff_0
thf(fact_18_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_19_c, axiom,
    ((![W : complex]: (ord_less_eq_real @ (real_V638595069omplex @ (poly_complex2 @ pa @ c)) @ (real_V638595069omplex @ (poly_complex2 @ pa @ W)))))). % c
thf(fact_20_poly__eq__poly__eq__iff, axiom,
    ((![P : poly_complex, Q2 : poly_complex]: (((poly_complex2 @ P) = (poly_complex2 @ Q2)) = (P = Q2))))). % poly_eq_poly_eq_iff
thf(fact_21_poly__eq__poly__eq__iff, axiom,
    ((![P : poly_real, Q2 : poly_real]: (((poly_real2 @ P) = (poly_real2 @ Q2)) = (P = Q2))))). % poly_eq_poly_eq_iff
thf(fact_22_zero__reorient, axiom,
    ((![X2 : complex]: ((zero_zero_complex = X2) = (X2 = zero_zero_complex))))). % zero_reorient
thf(fact_23_zero__reorient, axiom,
    ((![X2 : real]: ((zero_zero_real = X2) = (X2 = zero_zero_real))))). % zero_reorient
thf(fact_24_zero__reorient, axiom,
    ((![X2 : nat]: ((zero_zero_nat = X2) = (X2 = zero_zero_nat))))). % zero_reorient
thf(fact_25_zero__reorient, axiom,
    ((![X2 : poly_nat]: ((zero_zero_poly_nat = X2) = (X2 = zero_zero_poly_nat))))). % zero_reorient
thf(fact_26_zero__reorient, axiom,
    ((![X2 : poly_real]: ((zero_zero_poly_real = X2) = (X2 = zero_zero_poly_real))))). % zero_reorient
thf(fact_27_zero__reorient, axiom,
    ((![X2 : poly_complex]: ((zero_z1746442943omplex = X2) = (X2 = zero_z1746442943omplex))))). % zero_reorient
thf(fact_28_less_Ohyps, axiom,
    ((![P : poly_complex]: ((ord_less_nat @ (fundam1709708056omplex @ P) @ (fundam1709708056omplex @ pa)) => ((~ ((fundam1158420650omplex @ (poly_complex2 @ P)))) => (?[Z : complex]: ((poly_complex2 @ P @ Z) = zero_zero_complex))))))). % less.hyps
thf(fact_29__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062c_O_A_092_060forall_062w_O_Acmod_A_Ipoly_Ap_Ac_J_A_092_060le_062_Acmod_A_Ipoly_Ap_Aw_J_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom,
    ((~ ((![C : complex]: (~ ((![W : complex]: (ord_less_eq_real @ (real_V638595069omplex @ (poly_complex2 @ pa @ C)) @ (real_V638595069omplex @ (poly_complex2 @ pa @ W))))))))))). % \<open>\<And>thesis. (\<And>c. \<forall>w. cmod (poly p c) \<le> cmod (poly p w) \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
thf(fact_30_add_Oleft__neutral, axiom,
    ((![A : complex]: ((plus_plus_complex @ zero_zero_complex @ A) = A)))). % add.left_neutral
thf(fact_31_add_Oleft__neutral, axiom,
    ((![A : real]: ((plus_plus_real @ zero_zero_real @ A) = A)))). % add.left_neutral
thf(fact_32_add_Oleft__neutral, axiom,
    ((![A : nat]: ((plus_plus_nat @ zero_zero_nat @ A) = A)))). % add.left_neutral
thf(fact_33_add_Oleft__neutral, axiom,
    ((![A : poly_nat]: ((plus_plus_poly_nat @ zero_zero_poly_nat @ A) = A)))). % add.left_neutral
thf(fact_34_add_Oleft__neutral, axiom,
    ((![A : poly_real]: ((plus_plus_poly_real @ zero_zero_poly_real @ A) = A)))). % add.left_neutral
thf(fact_35_add_Oleft__neutral, axiom,
    ((![A : poly_complex]: ((plus_p1547158847omplex @ zero_z1746442943omplex @ A) = A)))). % add.left_neutral
thf(fact_36_add_Oright__neutral, axiom,
    ((![A : complex]: ((plus_plus_complex @ A @ zero_zero_complex) = A)))). % add.right_neutral
thf(fact_37_add_Oright__neutral, axiom,
    ((![A : real]: ((plus_plus_real @ A @ zero_zero_real) = A)))). % add.right_neutral
thf(fact_38_add_Oright__neutral, axiom,
    ((![A : nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A)))). % add.right_neutral
thf(fact_39_add_Oright__neutral, axiom,
    ((![A : poly_nat]: ((plus_plus_poly_nat @ A @ zero_zero_poly_nat) = A)))). % add.right_neutral
thf(fact_40_add_Oright__neutral, axiom,
    ((![A : poly_real]: ((plus_plus_poly_real @ A @ zero_zero_poly_real) = A)))). % add.right_neutral
thf(fact_41_add_Oright__neutral, axiom,
    ((![A : poly_complex]: ((plus_p1547158847omplex @ A @ zero_z1746442943omplex) = A)))). % add.right_neutral
thf(fact_42_add__left__cancel, axiom,
    ((![A : complex, B : complex, C2 : complex]: (((plus_plus_complex @ A @ B) = (plus_plus_complex @ A @ C2)) = (B = C2))))). % add_left_cancel
thf(fact_43_add__left__cancel, axiom,
    ((![A : real, B : real, C2 : real]: (((plus_plus_real @ A @ B) = (plus_plus_real @ A @ C2)) = (B = C2))))). % add_left_cancel
thf(fact_44_add__left__cancel, axiom,
    ((![A : nat, B : nat, C2 : nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ A @ C2)) = (B = C2))))). % add_left_cancel
thf(fact_45_add__right__cancel, axiom,
    ((![B : complex, A : complex, C2 : complex]: (((plus_plus_complex @ B @ A) = (plus_plus_complex @ C2 @ A)) = (B = C2))))). % add_right_cancel
thf(fact_46_add__right__cancel, axiom,
    ((![B : real, A : real, C2 : real]: (((plus_plus_real @ B @ A) = (plus_plus_real @ C2 @ A)) = (B = C2))))). % add_right_cancel
thf(fact_47_add__right__cancel, axiom,
    ((![B : nat, A : nat, C2 : nat]: (((plus_plus_nat @ B @ A) = (plus_plus_nat @ C2 @ A)) = (B = C2))))). % add_right_cancel
thf(fact_48_le__zero__eq, axiom,
    ((![N : nat]: ((ord_less_eq_nat @ N @ zero_zero_nat) = (N = zero_zero_nat))))). % le_zero_eq
thf(fact_49_not__gr__zero, axiom,
    ((![N : nat]: ((~ ((ord_less_nat @ zero_zero_nat @ N))) = (N = zero_zero_nat))))). % not_gr_zero
thf(fact_50_zero__eq__add__iff__both__eq__0, axiom,
    ((![X2 : nat, Y : nat]: ((zero_zero_nat = (plus_plus_nat @ X2 @ Y)) = (((X2 = zero_zero_nat)) & ((Y = zero_zero_nat))))))). % zero_eq_add_iff_both_eq_0
thf(fact_51_add__eq__0__iff__both__eq__0, axiom,
    ((![X2 : nat, Y : nat]: (((plus_plus_nat @ X2 @ Y) = zero_zero_nat) = (((X2 = zero_zero_nat)) & ((Y = zero_zero_nat))))))). % add_eq_0_iff_both_eq_0
thf(fact_52_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_53_add__cancel__right__right, axiom,
    ((![A : real, B : real]: ((A = (plus_plus_real @ A @ B)) = (B = zero_zero_real))))). % add_cancel_right_right
thf(fact_54_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_55_add__cancel__right__right, axiom,
    ((![A : poly_nat, B : poly_nat]: ((A = (plus_plus_poly_nat @ A @ B)) = (B = zero_zero_poly_nat))))). % add_cancel_right_right
thf(fact_56_add__cancel__right__right, axiom,
    ((![A : poly_real, B : poly_real]: ((A = (plus_plus_poly_real @ A @ B)) = (B = zero_zero_poly_real))))). % add_cancel_right_right
thf(fact_57_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_58_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_59_add__cancel__right__left, axiom,
    ((![A : real, B : real]: ((A = (plus_plus_real @ B @ A)) = (B = zero_zero_real))))). % add_cancel_right_left
thf(fact_60_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_61_add__cancel__right__left, axiom,
    ((![A : poly_nat, B : poly_nat]: ((A = (plus_plus_poly_nat @ B @ A)) = (B = zero_zero_poly_nat))))). % add_cancel_right_left
thf(fact_62_add__cancel__right__left, axiom,
    ((![A : poly_real, B : poly_real]: ((A = (plus_plus_poly_real @ B @ A)) = (B = zero_zero_poly_real))))). % add_cancel_right_left
thf(fact_63_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_64_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_65_add__cancel__left__right, axiom,
    ((![A : real, B : real]: (((plus_plus_real @ A @ B) = A) = (B = zero_zero_real))))). % add_cancel_left_right
thf(fact_66_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_67_add__cancel__left__right, axiom,
    ((![A : poly_nat, B : poly_nat]: (((plus_plus_poly_nat @ A @ B) = A) = (B = zero_zero_poly_nat))))). % add_cancel_left_right
thf(fact_68_add__cancel__left__right, axiom,
    ((![A : poly_real, B : poly_real]: (((plus_plus_poly_real @ A @ B) = A) = (B = zero_zero_poly_real))))). % add_cancel_left_right
thf(fact_69_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_70_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_71_add__cancel__left__left, axiom,
    ((![B : real, A : real]: (((plus_plus_real @ B @ A) = A) = (B = zero_zero_real))))). % add_cancel_left_left
thf(fact_72_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_73_add__cancel__left__left, axiom,
    ((![B : poly_nat, A : poly_nat]: (((plus_plus_poly_nat @ B @ A) = A) = (B = zero_zero_poly_nat))))). % add_cancel_left_left
thf(fact_74_add__cancel__left__left, axiom,
    ((![B : poly_real, A : poly_real]: (((plus_plus_poly_real @ B @ A) = A) = (B = zero_zero_poly_real))))). % add_cancel_left_left
thf(fact_75_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_76_double__zero__sym, axiom,
    ((![A : real]: ((zero_zero_real = (plus_plus_real @ A @ A)) = (A = zero_zero_real))))). % double_zero_sym
thf(fact_77_double__zero__sym, axiom,
    ((![A : poly_real]: ((zero_zero_poly_real = (plus_plus_poly_real @ A @ A)) = (A = zero_zero_poly_real))))). % double_zero_sym
thf(fact_78_double__zero, axiom,
    ((![A : real]: (((plus_plus_real @ A @ A) = zero_zero_real) = (A = zero_zero_real))))). % double_zero
thf(fact_79_double__zero, axiom,
    ((![A : poly_real]: (((plus_plus_poly_real @ A @ A) = zero_zero_poly_real) = (A = zero_zero_poly_real))))). % double_zero
thf(fact_80_add__le__cancel__left, axiom,
    ((![C2 : real, A : real, B : real]: ((ord_less_eq_real @ (plus_plus_real @ C2 @ A) @ (plus_plus_real @ C2 @ B)) = (ord_less_eq_real @ A @ B))))). % add_le_cancel_left
thf(fact_81_add__le__cancel__left, axiom,
    ((![C2 : nat, A : nat, B : nat]: ((ord_less_eq_nat @ (plus_plus_nat @ C2 @ A) @ (plus_plus_nat @ C2 @ B)) = (ord_less_eq_nat @ A @ B))))). % add_le_cancel_left
thf(fact_82_add__le__cancel__right, axiom,
    ((![A : real, C2 : real, B : real]: ((ord_less_eq_real @ (plus_plus_real @ A @ C2) @ (plus_plus_real @ B @ C2)) = (ord_less_eq_real @ A @ B))))). % add_le_cancel_right
thf(fact_83_add__le__cancel__right, axiom,
    ((![A : nat, C2 : nat, B : nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ C2) @ (plus_plus_nat @ B @ C2)) = (ord_less_eq_nat @ A @ B))))). % add_le_cancel_right
thf(fact_84_add__less__cancel__left, axiom,
    ((![C2 : nat, A : nat, B : nat]: ((ord_less_nat @ (plus_plus_nat @ C2 @ A) @ (plus_plus_nat @ C2 @ B)) = (ord_less_nat @ A @ B))))). % add_less_cancel_left
thf(fact_85_add__less__cancel__left, axiom,
    ((![C2 : real, A : real, B : real]: ((ord_less_real @ (plus_plus_real @ C2 @ A) @ (plus_plus_real @ C2 @ B)) = (ord_less_real @ A @ B))))). % add_less_cancel_left
thf(fact_86_add__less__cancel__right, axiom,
    ((![A : nat, C2 : nat, B : nat]: ((ord_less_nat @ (plus_plus_nat @ A @ C2) @ (plus_plus_nat @ B @ C2)) = (ord_less_nat @ A @ B))))). % add_less_cancel_right
thf(fact_87_add__less__cancel__right, axiom,
    ((![A : real, C2 : real, B : real]: ((ord_less_real @ (plus_plus_real @ A @ C2) @ (plus_plus_real @ B @ C2)) = (ord_less_real @ A @ B))))). % add_less_cancel_right
thf(fact_88_poly__add, axiom,
    ((![P : poly_complex, Q2 : poly_complex, X2 : complex]: ((poly_complex2 @ (plus_p1547158847omplex @ P @ Q2) @ X2) = (plus_plus_complex @ (poly_complex2 @ P @ X2) @ (poly_complex2 @ Q2 @ X2)))))). % poly_add
thf(fact_89_poly__add, axiom,
    ((![P : poly_real, Q2 : poly_real, X2 : real]: ((poly_real2 @ (plus_plus_poly_real @ P @ Q2) @ X2) = (plus_plus_real @ (poly_real2 @ P @ X2) @ (poly_real2 @ Q2 @ X2)))))). % poly_add
thf(fact_90_poly__add, axiom,
    ((![P : poly_nat, Q2 : poly_nat, X2 : nat]: ((poly_nat2 @ (plus_plus_poly_nat @ P @ Q2) @ X2) = (plus_plus_nat @ (poly_nat2 @ P @ X2) @ (poly_nat2 @ Q2 @ X2)))))). % poly_add
thf(fact_91_psize__eq__0__iff, axiom,
    ((![P : poly_nat]: (((fundam1567013434ze_nat @ P) = zero_zero_nat) = (P = zero_zero_poly_nat))))). % psize_eq_0_iff
thf(fact_92_psize__eq__0__iff, axiom,
    ((![P : poly_real]: (((fundam1947011094e_real @ P) = zero_zero_nat) = (P = zero_zero_poly_real))))). % psize_eq_0_iff
thf(fact_93_psize__eq__0__iff, axiom,
    ((![P : poly_complex]: (((fundam1709708056omplex @ P) = zero_zero_nat) = (P = zero_z1746442943omplex))))). % psize_eq_0_iff
thf(fact_94_zero__le__double__add__iff__zero__le__single__add, axiom,
    ((![A : poly_real]: ((ord_le1180086932y_real @ zero_zero_poly_real @ (plus_plus_poly_real @ A @ A)) = (ord_le1180086932y_real @ zero_zero_poly_real @ A))))). % zero_le_double_add_iff_zero_le_single_add
thf(fact_95_zero__le__double__add__iff__zero__le__single__add, axiom,
    ((![A : real]: ((ord_less_eq_real @ zero_zero_real @ (plus_plus_real @ A @ A)) = (ord_less_eq_real @ zero_zero_real @ A))))). % zero_le_double_add_iff_zero_le_single_add
thf(fact_96_double__add__le__zero__iff__single__add__le__zero, axiom,
    ((![A : poly_real]: ((ord_le1180086932y_real @ (plus_plus_poly_real @ A @ A) @ zero_zero_poly_real) = (ord_le1180086932y_real @ A @ zero_zero_poly_real))))). % double_add_le_zero_iff_single_add_le_zero
thf(fact_97_double__add__le__zero__iff__single__add__le__zero, axiom,
    ((![A : real]: ((ord_less_eq_real @ (plus_plus_real @ A @ A) @ zero_zero_real) = (ord_less_eq_real @ A @ zero_zero_real))))). % double_add_le_zero_iff_single_add_le_zero
thf(fact_98_le__add__same__cancel2, axiom,
    ((![A : poly_real, B : poly_real]: ((ord_le1180086932y_real @ A @ (plus_plus_poly_real @ B @ A)) = (ord_le1180086932y_real @ zero_zero_poly_real @ B))))). % le_add_same_cancel2
thf(fact_99_le__add__same__cancel2, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ A @ (plus_plus_real @ B @ A)) = (ord_less_eq_real @ zero_zero_real @ B))))). % le_add_same_cancel2
thf(fact_100_le__add__same__cancel2, axiom,
    ((![A : nat, B : nat]: ((ord_less_eq_nat @ A @ (plus_plus_nat @ B @ A)) = (ord_less_eq_nat @ zero_zero_nat @ B))))). % le_add_same_cancel2
thf(fact_101_le__add__same__cancel1, axiom,
    ((![A : poly_real, B : poly_real]: ((ord_le1180086932y_real @ A @ (plus_plus_poly_real @ A @ B)) = (ord_le1180086932y_real @ zero_zero_poly_real @ B))))). % le_add_same_cancel1
thf(fact_102_le__add__same__cancel1, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ A @ (plus_plus_real @ A @ B)) = (ord_less_eq_real @ zero_zero_real @ B))))). % le_add_same_cancel1
thf(fact_103_le__add__same__cancel1, axiom,
    ((![A : nat, B : nat]: ((ord_less_eq_nat @ A @ (plus_plus_nat @ A @ B)) = (ord_less_eq_nat @ zero_zero_nat @ B))))). % le_add_same_cancel1
thf(fact_104_add__le__same__cancel2, axiom,
    ((![A : poly_real, B : poly_real]: ((ord_le1180086932y_real @ (plus_plus_poly_real @ A @ B) @ B) = (ord_le1180086932y_real @ A @ zero_zero_poly_real))))). % add_le_same_cancel2
thf(fact_105_add__le__same__cancel2, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ (plus_plus_real @ A @ B) @ B) = (ord_less_eq_real @ A @ zero_zero_real))))). % add_le_same_cancel2
thf(fact_106_add__le__same__cancel2, axiom,
    ((![A : nat, B : nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ B) = (ord_less_eq_nat @ A @ zero_zero_nat))))). % add_le_same_cancel2
thf(fact_107_add__le__same__cancel1, axiom,
    ((![B : poly_real, A : poly_real]: ((ord_le1180086932y_real @ (plus_plus_poly_real @ B @ A) @ B) = (ord_le1180086932y_real @ A @ zero_zero_poly_real))))). % add_le_same_cancel1
thf(fact_108_add__le__same__cancel1, axiom,
    ((![B : real, A : real]: ((ord_less_eq_real @ (plus_plus_real @ B @ A) @ B) = (ord_less_eq_real @ A @ zero_zero_real))))). % add_le_same_cancel1
thf(fact_109_add__le__same__cancel1, axiom,
    ((![B : nat, A : nat]: ((ord_less_eq_nat @ (plus_plus_nat @ B @ A) @ B) = (ord_less_eq_nat @ A @ zero_zero_nat))))). % add_le_same_cancel1
thf(fact_110_zero__less__double__add__iff__zero__less__single__add, axiom,
    ((![A : poly_real]: ((ord_less_poly_real @ zero_zero_poly_real @ (plus_plus_poly_real @ A @ A)) = (ord_less_poly_real @ zero_zero_poly_real @ A))))). % zero_less_double_add_iff_zero_less_single_add
thf(fact_111_zero__less__double__add__iff__zero__less__single__add, axiom,
    ((![A : real]: ((ord_less_real @ zero_zero_real @ (plus_plus_real @ A @ A)) = (ord_less_real @ zero_zero_real @ A))))). % zero_less_double_add_iff_zero_less_single_add
thf(fact_112_double__add__less__zero__iff__single__add__less__zero, axiom,
    ((![A : poly_real]: ((ord_less_poly_real @ (plus_plus_poly_real @ A @ A) @ zero_zero_poly_real) = (ord_less_poly_real @ A @ zero_zero_poly_real))))). % double_add_less_zero_iff_single_add_less_zero
thf(fact_113_double__add__less__zero__iff__single__add__less__zero, axiom,
    ((![A : real]: ((ord_less_real @ (plus_plus_real @ A @ A) @ zero_zero_real) = (ord_less_real @ A @ zero_zero_real))))). % double_add_less_zero_iff_single_add_less_zero
thf(fact_114_less__add__same__cancel2, axiom,
    ((![A : poly_real, B : poly_real]: ((ord_less_poly_real @ A @ (plus_plus_poly_real @ B @ A)) = (ord_less_poly_real @ zero_zero_poly_real @ B))))). % less_add_same_cancel2
thf(fact_115_less__add__same__cancel2, axiom,
    ((![A : nat, B : nat]: ((ord_less_nat @ A @ (plus_plus_nat @ B @ A)) = (ord_less_nat @ zero_zero_nat @ B))))). % less_add_same_cancel2
thf(fact_116_less__add__same__cancel2, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ (plus_plus_real @ B @ A)) = (ord_less_real @ zero_zero_real @ B))))). % less_add_same_cancel2
thf(fact_117_less__add__same__cancel1, axiom,
    ((![A : poly_real, B : poly_real]: ((ord_less_poly_real @ A @ (plus_plus_poly_real @ A @ B)) = (ord_less_poly_real @ zero_zero_poly_real @ B))))). % less_add_same_cancel1
thf(fact_118_less__add__same__cancel1, axiom,
    ((![A : nat, B : nat]: ((ord_less_nat @ A @ (plus_plus_nat @ A @ B)) = (ord_less_nat @ zero_zero_nat @ B))))). % less_add_same_cancel1
thf(fact_119_less__add__same__cancel1, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ (plus_plus_real @ A @ B)) = (ord_less_real @ zero_zero_real @ B))))). % less_add_same_cancel1
thf(fact_120_add__less__same__cancel2, axiom,
    ((![A : poly_real, B : poly_real]: ((ord_less_poly_real @ (plus_plus_poly_real @ A @ B) @ B) = (ord_less_poly_real @ A @ zero_zero_poly_real))))). % add_less_same_cancel2
thf(fact_121_add__less__same__cancel2, axiom,
    ((![A : nat, B : nat]: ((ord_less_nat @ (plus_plus_nat @ A @ B) @ B) = (ord_less_nat @ A @ zero_zero_nat))))). % add_less_same_cancel2
thf(fact_122_add__less__same__cancel2, axiom,
    ((![A : real, B : real]: ((ord_less_real @ (plus_plus_real @ A @ B) @ B) = (ord_less_real @ A @ zero_zero_real))))). % add_less_same_cancel2
thf(fact_123_add__less__same__cancel1, axiom,
    ((![B : poly_real, A : poly_real]: ((ord_less_poly_real @ (plus_plus_poly_real @ B @ A) @ B) = (ord_less_poly_real @ A @ zero_zero_poly_real))))). % add_less_same_cancel1
thf(fact_124_add__less__same__cancel1, axiom,
    ((![B : nat, A : nat]: ((ord_less_nat @ (plus_plus_nat @ B @ A) @ B) = (ord_less_nat @ A @ zero_zero_nat))))). % add_less_same_cancel1
thf(fact_125_add__less__same__cancel1, axiom,
    ((![B : real, A : real]: ((ord_less_real @ (plus_plus_real @ B @ A) @ B) = (ord_less_real @ A @ zero_zero_real))))). % add_less_same_cancel1
thf(fact_126_ab__semigroup__add__class_Oadd__ac_I1_J, axiom,
    ((![A : complex, B : complex, C2 : complex]: ((plus_plus_complex @ (plus_plus_complex @ A @ B) @ C2) = (plus_plus_complex @ A @ (plus_plus_complex @ B @ C2)))))). % ab_semigroup_add_class.add_ac(1)
thf(fact_127_ab__semigroup__add__class_Oadd__ac_I1_J, axiom,
    ((![A : real, B : real, C2 : real]: ((plus_plus_real @ (plus_plus_real @ A @ B) @ C2) = (plus_plus_real @ A @ (plus_plus_real @ B @ C2)))))). % ab_semigroup_add_class.add_ac(1)
thf(fact_128_ab__semigroup__add__class_Oadd__ac_I1_J, axiom,
    ((![A : nat, B : nat, C2 : nat]: ((plus_plus_nat @ (plus_plus_nat @ A @ B) @ C2) = (plus_plus_nat @ A @ (plus_plus_nat @ B @ C2)))))). % ab_semigroup_add_class.add_ac(1)
thf(fact_129_add__mono__thms__linordered__field_I5_J, axiom,
    ((![I : nat, J : nat, K : nat, L : nat]: (((ord_less_nat @ I @ J) & (ord_less_nat @ K @ L)) => (ord_less_nat @ (plus_plus_nat @ I @ K) @ (plus_plus_nat @ J @ L)))))). % add_mono_thms_linordered_field(5)
thf(fact_130_add__mono__thms__linordered__field_I5_J, axiom,
    ((![I : real, J : real, K : real, L : real]: (((ord_less_real @ I @ J) & (ord_less_real @ K @ L)) => (ord_less_real @ (plus_plus_real @ I @ K) @ (plus_plus_real @ J @ L)))))). % add_mono_thms_linordered_field(5)
thf(fact_131_add__mono__thms__linordered__field_I4_J, axiom,
    ((![I : real, J : real, K : real, L : real]: (((ord_less_eq_real @ I @ J) & (ord_less_real @ K @ L)) => (ord_less_real @ (plus_plus_real @ I @ K) @ (plus_plus_real @ J @ L)))))). % add_mono_thms_linordered_field(4)
thf(fact_132_add__mono__thms__linordered__field_I4_J, axiom,
    ((![I : nat, J : nat, K : nat, L : nat]: (((ord_less_eq_nat @ I @ J) & (ord_less_nat @ K @ L)) => (ord_less_nat @ (plus_plus_nat @ I @ K) @ (plus_plus_nat @ J @ L)))))). % add_mono_thms_linordered_field(4)
thf(fact_133_add__mono__thms__linordered__field_I3_J, axiom,
    ((![I : real, J : real, K : real, L : real]: (((ord_less_real @ I @ J) & (ord_less_eq_real @ K @ L)) => (ord_less_real @ (plus_plus_real @ I @ K) @ (plus_plus_real @ J @ L)))))). % add_mono_thms_linordered_field(3)
thf(fact_134_add__mono__thms__linordered__field_I3_J, axiom,
    ((![I : nat, J : nat, K : nat, L : nat]: (((ord_less_nat @ I @ J) & (ord_less_eq_nat @ K @ L)) => (ord_less_nat @ (plus_plus_nat @ I @ K) @ (plus_plus_nat @ J @ L)))))). % add_mono_thms_linordered_field(3)
thf(fact_135_add__mono__thms__linordered__field_I2_J, axiom,
    ((![I : nat, J : nat, K : nat, L : nat]: (((I = J) & (ord_less_nat @ K @ L)) => (ord_less_nat @ (plus_plus_nat @ I @ K) @ (plus_plus_nat @ J @ L)))))). % add_mono_thms_linordered_field(2)
thf(fact_136_add__mono__thms__linordered__field_I2_J, axiom,
    ((![I : real, J : real, K : real, L : real]: (((I = J) & (ord_less_real @ K @ L)) => (ord_less_real @ (plus_plus_real @ I @ K) @ (plus_plus_real @ J @ L)))))). % add_mono_thms_linordered_field(2)
thf(fact_137_add__mono__thms__linordered__field_I1_J, axiom,
    ((![I : nat, J : nat, K : nat, L : nat]: (((ord_less_nat @ I @ J) & (K = L)) => (ord_less_nat @ (plus_plus_nat @ I @ K) @ (plus_plus_nat @ J @ L)))))). % add_mono_thms_linordered_field(1)
thf(fact_138_add__mono__thms__linordered__field_I1_J, axiom,
    ((![I : real, J : real, K : real, L : real]: (((ord_less_real @ I @ J) & (K = L)) => (ord_less_real @ (plus_plus_real @ I @ K) @ (plus_plus_real @ J @ L)))))). % add_mono_thms_linordered_field(1)
thf(fact_139_add__mono__thms__linordered__semiring_I4_J, axiom,
    ((![I : real, J : real, K : real, L : real]: (((I = J) & (K = L)) => ((plus_plus_real @ I @ K) = (plus_plus_real @ J @ L)))))). % add_mono_thms_linordered_semiring(4)
thf(fact_140_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_141_add__mono__thms__linordered__semiring_I3_J, axiom,
    ((![I : real, J : real, K : real, L : real]: (((ord_less_eq_real @ I @ J) & (K = L)) => (ord_less_eq_real @ (plus_plus_real @ I @ K) @ (plus_plus_real @ J @ L)))))). % add_mono_thms_linordered_semiring(3)
thf(fact_142_add__mono__thms__linordered__semiring_I3_J, axiom,
    ((![I : nat, J : nat, K : nat, L : nat]: (((ord_less_eq_nat @ I @ J) & (K = L)) => (ord_less_eq_nat @ (plus_plus_nat @ I @ K) @ (plus_plus_nat @ J @ L)))))). % add_mono_thms_linordered_semiring(3)
thf(fact_143_add__mono__thms__linordered__semiring_I2_J, axiom,
    ((![I : real, J : real, K : real, L : real]: (((I = J) & (ord_less_eq_real @ K @ L)) => (ord_less_eq_real @ (plus_plus_real @ I @ K) @ (plus_plus_real @ J @ L)))))). % add_mono_thms_linordered_semiring(2)
thf(fact_144_add__mono__thms__linordered__semiring_I2_J, axiom,
    ((![I : nat, J : nat, K : nat, L : nat]: (((I = J) & (ord_less_eq_nat @ K @ L)) => (ord_less_eq_nat @ (plus_plus_nat @ I @ K) @ (plus_plus_nat @ J @ L)))))). % add_mono_thms_linordered_semiring(2)
thf(fact_145_add__mono__thms__linordered__semiring_I1_J, axiom,
    ((![I : real, J : real, K : real, L : real]: (((ord_less_eq_real @ I @ J) & (ord_less_eq_real @ K @ L)) => (ord_less_eq_real @ (plus_plus_real @ I @ K) @ (plus_plus_real @ J @ L)))))). % add_mono_thms_linordered_semiring(1)
thf(fact_146_add__mono__thms__linordered__semiring_I1_J, axiom,
    ((![I : nat, J : nat, K : nat, L : nat]: (((ord_less_eq_nat @ I @ J) & (ord_less_eq_nat @ K @ L)) => (ord_less_eq_nat @ (plus_plus_nat @ I @ K) @ (plus_plus_nat @ J @ L)))))). % add_mono_thms_linordered_semiring(1)
thf(fact_147_group__cancel_Oadd1, axiom,
    ((![A2 : complex, K : complex, A : complex, B : complex]: ((A2 = (plus_plus_complex @ K @ A)) => ((plus_plus_complex @ A2 @ B) = (plus_plus_complex @ K @ (plus_plus_complex @ A @ B))))))). % group_cancel.add1
thf(fact_148_group__cancel_Oadd1, axiom,
    ((![A2 : real, K : real, A : real, B : real]: ((A2 = (plus_plus_real @ K @ A)) => ((plus_plus_real @ A2 @ B) = (plus_plus_real @ K @ (plus_plus_real @ A @ B))))))). % group_cancel.add1
thf(fact_149_group__cancel_Oadd1, axiom,
    ((![A2 : nat, K : nat, A : nat, B : nat]: ((A2 = (plus_plus_nat @ K @ A)) => ((plus_plus_nat @ A2 @ B) = (plus_plus_nat @ K @ (plus_plus_nat @ A @ B))))))). % group_cancel.add1
thf(fact_150_group__cancel_Oadd2, axiom,
    ((![B2 : complex, K : complex, B : complex, A : complex]: ((B2 = (plus_plus_complex @ K @ B)) => ((plus_plus_complex @ A @ B2) = (plus_plus_complex @ K @ (plus_plus_complex @ A @ B))))))). % group_cancel.add2
thf(fact_151_group__cancel_Oadd2, axiom,
    ((![B2 : real, K : real, B : real, A : real]: ((B2 = (plus_plus_real @ K @ B)) => ((plus_plus_real @ A @ B2) = (plus_plus_real @ K @ (plus_plus_real @ A @ B))))))). % group_cancel.add2
thf(fact_152_group__cancel_Oadd2, axiom,
    ((![B2 : nat, K : nat, B : nat, A : nat]: ((B2 = (plus_plus_nat @ K @ B)) => ((plus_plus_nat @ A @ B2) = (plus_plus_nat @ K @ (plus_plus_nat @ A @ B))))))). % group_cancel.add2
thf(fact_153_add_Oassoc, axiom,
    ((![A : complex, B : complex, C2 : complex]: ((plus_plus_complex @ (plus_plus_complex @ A @ B) @ C2) = (plus_plus_complex @ A @ (plus_plus_complex @ B @ C2)))))). % add.assoc
thf(fact_154_add_Oassoc, axiom,
    ((![A : real, B : real, C2 : real]: ((plus_plus_real @ (plus_plus_real @ A @ B) @ C2) = (plus_plus_real @ A @ (plus_plus_real @ B @ C2)))))). % add.assoc
thf(fact_155_add_Oassoc, axiom,
    ((![A : nat, B : nat, C2 : nat]: ((plus_plus_nat @ (plus_plus_nat @ A @ B) @ C2) = (plus_plus_nat @ A @ (plus_plus_nat @ B @ C2)))))). % add.assoc
thf(fact_156_add_Oleft__cancel, axiom,
    ((![A : complex, B : complex, C2 : complex]: (((plus_plus_complex @ A @ B) = (plus_plus_complex @ A @ C2)) = (B = C2))))). % add.left_cancel
thf(fact_157_add_Oleft__cancel, axiom,
    ((![A : real, B : real, C2 : real]: (((plus_plus_real @ A @ B) = (plus_plus_real @ A @ C2)) = (B = C2))))). % add.left_cancel
thf(fact_158_add_Oright__cancel, axiom,
    ((![B : complex, A : complex, C2 : complex]: (((plus_plus_complex @ B @ A) = (plus_plus_complex @ C2 @ A)) = (B = C2))))). % add.right_cancel
thf(fact_159_add_Oright__cancel, axiom,
    ((![B : real, A : real, C2 : real]: (((plus_plus_real @ B @ A) = (plus_plus_real @ C2 @ A)) = (B = C2))))). % add.right_cancel
thf(fact_160_add_Ocommute, axiom,
    ((plus_plus_complex = (^[A3 : complex]: (^[B3 : complex]: (plus_plus_complex @ B3 @ A3)))))). % add.commute
thf(fact_161_add_Ocommute, axiom,
    ((plus_plus_real = (^[A3 : real]: (^[B3 : real]: (plus_plus_real @ B3 @ A3)))))). % add.commute
thf(fact_162_add_Ocommute, axiom,
    ((plus_plus_nat = (^[A3 : nat]: (^[B3 : nat]: (plus_plus_nat @ B3 @ A3)))))). % add.commute
thf(fact_163_add_Oleft__commute, axiom,
    ((![B : complex, A : complex, C2 : complex]: ((plus_plus_complex @ B @ (plus_plus_complex @ A @ C2)) = (plus_plus_complex @ A @ (plus_plus_complex @ B @ C2)))))). % add.left_commute
thf(fact_164_add_Oleft__commute, axiom,
    ((![B : real, A : real, C2 : real]: ((plus_plus_real @ B @ (plus_plus_real @ A @ C2)) = (plus_plus_real @ A @ (plus_plus_real @ B @ C2)))))). % add.left_commute
thf(fact_165_add_Oleft__commute, axiom,
    ((![B : nat, A : nat, C2 : nat]: ((plus_plus_nat @ B @ (plus_plus_nat @ A @ C2)) = (plus_plus_nat @ A @ (plus_plus_nat @ B @ C2)))))). % add.left_commute
thf(fact_166_add__mono, axiom,
    ((![A : real, B : real, C2 : real, D : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_eq_real @ C2 @ D) => (ord_less_eq_real @ (plus_plus_real @ A @ C2) @ (plus_plus_real @ B @ D))))))). % add_mono
thf(fact_167_add__mono, axiom,
    ((![A : nat, B : nat, C2 : nat, D : nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_eq_nat @ C2 @ D) => (ord_less_eq_nat @ (plus_plus_nat @ A @ C2) @ (plus_plus_nat @ B @ D))))))). % add_mono
thf(fact_168_add__left__imp__eq, axiom,
    ((![A : complex, B : complex, C2 : complex]: (((plus_plus_complex @ A @ B) = (plus_plus_complex @ A @ C2)) => (B = C2))))). % add_left_imp_eq
thf(fact_169_add__left__imp__eq, axiom,
    ((![A : real, B : real, C2 : real]: (((plus_plus_real @ A @ B) = (plus_plus_real @ A @ C2)) => (B = C2))))). % add_left_imp_eq
thf(fact_170_add__left__imp__eq, axiom,
    ((![A : nat, B : nat, C2 : nat]: (((plus_plus_nat @ A @ B) = (plus_plus_nat @ A @ C2)) => (B = C2))))). % add_left_imp_eq
thf(fact_171_add__right__imp__eq, axiom,
    ((![B : complex, A : complex, C2 : complex]: (((plus_plus_complex @ B @ A) = (plus_plus_complex @ C2 @ A)) => (B = C2))))). % add_right_imp_eq
thf(fact_172_add__right__imp__eq, axiom,
    ((![B : real, A : real, C2 : real]: (((plus_plus_real @ B @ A) = (plus_plus_real @ C2 @ A)) => (B = C2))))). % add_right_imp_eq
thf(fact_173_add__right__imp__eq, axiom,
    ((![B : nat, A : nat, C2 : nat]: (((plus_plus_nat @ B @ A) = (plus_plus_nat @ C2 @ A)) => (B = C2))))). % add_right_imp_eq
thf(fact_174_add__left__mono, axiom,
    ((![A : real, B : real, C2 : real]: ((ord_less_eq_real @ A @ B) => (ord_less_eq_real @ (plus_plus_real @ C2 @ A) @ (plus_plus_real @ C2 @ B)))))). % add_left_mono
thf(fact_175_add__left__mono, axiom,
    ((![A : nat, B : nat, C2 : nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (plus_plus_nat @ C2 @ A) @ (plus_plus_nat @ C2 @ B)))))). % add_left_mono
thf(fact_176_add__neg__nonpos, axiom,
    ((![A : poly_real, B : poly_real]: ((ord_less_poly_real @ A @ zero_zero_poly_real) => ((ord_le1180086932y_real @ B @ zero_zero_poly_real) => (ord_less_poly_real @ (plus_plus_poly_real @ A @ B) @ zero_zero_poly_real)))))). % add_neg_nonpos
thf(fact_177_add__neg__nonpos, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ zero_zero_real) => ((ord_less_eq_real @ B @ zero_zero_real) => (ord_less_real @ (plus_plus_real @ A @ B) @ zero_zero_real)))))). % add_neg_nonpos
thf(fact_178_add__neg__nonpos, axiom,
    ((![A : nat, B : nat]: ((ord_less_nat @ A @ zero_zero_nat) => ((ord_less_eq_nat @ B @ zero_zero_nat) => (ord_less_nat @ (plus_plus_nat @ A @ B) @ zero_zero_nat)))))). % add_neg_nonpos
thf(fact_179_add__nonneg__pos, axiom,
    ((![A : poly_real, B : poly_real]: ((ord_le1180086932y_real @ zero_zero_poly_real @ A) => ((ord_less_poly_real @ zero_zero_poly_real @ B) => (ord_less_poly_real @ zero_zero_poly_real @ (plus_plus_poly_real @ A @ B))))))). % add_nonneg_pos
thf(fact_180_add__nonneg__pos, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_real @ zero_zero_real @ B) => (ord_less_real @ zero_zero_real @ (plus_plus_real @ A @ B))))))). % add_nonneg_pos
thf(fact_181_add__nonneg__pos, axiom,
    ((![A : nat, B : nat]: ((ord_less_eq_nat @ zero_zero_nat @ A) => ((ord_less_nat @ zero_zero_nat @ B) => (ord_less_nat @ zero_zero_nat @ (plus_plus_nat @ A @ B))))))). % add_nonneg_pos
thf(fact_182_add__nonpos__neg, axiom,
    ((![A : poly_real, B : poly_real]: ((ord_le1180086932y_real @ A @ zero_zero_poly_real) => ((ord_less_poly_real @ B @ zero_zero_poly_real) => (ord_less_poly_real @ (plus_plus_poly_real @ A @ B) @ zero_zero_poly_real)))))). % add_nonpos_neg
thf(fact_183_add__nonpos__neg, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ A @ zero_zero_real) => ((ord_less_real @ B @ zero_zero_real) => (ord_less_real @ (plus_plus_real @ A @ B) @ zero_zero_real)))))). % add_nonpos_neg
thf(fact_184_add__nonpos__neg, axiom,
    ((![A : nat, B : nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) => ((ord_less_nat @ B @ zero_zero_nat) => (ord_less_nat @ (plus_plus_nat @ A @ B) @ zero_zero_nat)))))). % add_nonpos_neg
thf(fact_185_add__pos__nonneg, axiom,
    ((![A : poly_real, B : poly_real]: ((ord_less_poly_real @ zero_zero_poly_real @ A) => ((ord_le1180086932y_real @ zero_zero_poly_real @ B) => (ord_less_poly_real @ zero_zero_poly_real @ (plus_plus_poly_real @ A @ B))))))). % add_pos_nonneg
thf(fact_186_add__pos__nonneg, axiom,
    ((![A : real, B : real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_eq_real @ zero_zero_real @ B) => (ord_less_real @ zero_zero_real @ (plus_plus_real @ A @ B))))))). % add_pos_nonneg
thf(fact_187_add__pos__nonneg, axiom,
    ((![A : nat, B : nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ zero_zero_nat @ B) => (ord_less_nat @ zero_zero_nat @ (plus_plus_nat @ A @ B))))))). % add_pos_nonneg
thf(fact_188_less__eqE, axiom,
    ((![A : nat, B : nat]: ((ord_less_eq_nat @ A @ B) => (~ ((![C : nat]: (~ ((B = (plus_plus_nat @ A @ C))))))))))). % less_eqE
thf(fact_189_add__right__mono, axiom,
    ((![A : real, B : real, C2 : real]: ((ord_less_eq_real @ A @ B) => (ord_less_eq_real @ (plus_plus_real @ A @ C2) @ (plus_plus_real @ B @ C2)))))). % add_right_mono
thf(fact_190_add__right__mono, axiom,
    ((![A : nat, B : nat, C2 : nat]: ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (plus_plus_nat @ A @ C2) @ (plus_plus_nat @ B @ C2)))))). % add_right_mono
thf(fact_191_le__iff__add, axiom,
    ((ord_less_eq_nat = (^[A3 : nat]: (^[B3 : nat]: (?[C3 : nat]: (B3 = (plus_plus_nat @ A3 @ C3)))))))). % le_iff_add
thf(fact_192_add__strict__mono, axiom,
    ((![A : nat, B : nat, C2 : nat, D : nat]: ((ord_less_nat @ A @ B) => ((ord_less_nat @ C2 @ D) => (ord_less_nat @ (plus_plus_nat @ A @ C2) @ (plus_plus_nat @ B @ D))))))). % add_strict_mono
thf(fact_193_add__strict__mono, axiom,
    ((![A : real, B : real, C2 : real, D : real]: ((ord_less_real @ A @ B) => ((ord_less_real @ C2 @ D) => (ord_less_real @ (plus_plus_real @ A @ C2) @ (plus_plus_real @ B @ D))))))). % add_strict_mono
thf(fact_194_add__le__less__mono, axiom,
    ((![A : real, B : real, C2 : real, D : real]: ((ord_less_eq_real @ A @ B) => ((ord_less_real @ C2 @ D) => (ord_less_real @ (plus_plus_real @ A @ C2) @ (plus_plus_real @ B @ D))))))). % add_le_less_mono
thf(fact_195_add__le__less__mono, axiom,
    ((![A : nat, B : nat, C2 : nat, D : nat]: ((ord_less_eq_nat @ A @ B) => ((ord_less_nat @ C2 @ D) => (ord_less_nat @ (plus_plus_nat @ A @ C2) @ (plus_plus_nat @ B @ D))))))). % add_le_less_mono
thf(fact_196_add__less__le__mono, axiom,
    ((![A : real, B : real, C2 : real, D : real]: ((ord_less_real @ A @ B) => ((ord_less_eq_real @ C2 @ D) => (ord_less_real @ (plus_plus_real @ A @ C2) @ (plus_plus_real @ B @ D))))))). % add_less_le_mono
thf(fact_197_add__less__le__mono, axiom,
    ((![A : nat, B : nat, C2 : nat, D : nat]: ((ord_less_nat @ A @ B) => ((ord_less_eq_nat @ C2 @ D) => (ord_less_nat @ (plus_plus_nat @ A @ C2) @ (plus_plus_nat @ B @ D))))))). % add_less_le_mono
thf(fact_198_add__le__imp__le__left, axiom,
    ((![C2 : real, A : real, B : real]: ((ord_less_eq_real @ (plus_plus_real @ C2 @ A) @ (plus_plus_real @ C2 @ B)) => (ord_less_eq_real @ A @ B))))). % add_le_imp_le_left
thf(fact_199_add__le__imp__le__left, axiom,
    ((![C2 : nat, A : nat, B : nat]: ((ord_less_eq_nat @ (plus_plus_nat @ C2 @ A) @ (plus_plus_nat @ C2 @ B)) => (ord_less_eq_nat @ A @ B))))). % add_le_imp_le_left
thf(fact_200_add__le__imp__le__right, axiom,
    ((![A : real, C2 : real, B : real]: ((ord_less_eq_real @ (plus_plus_real @ A @ C2) @ (plus_plus_real @ B @ C2)) => (ord_less_eq_real @ A @ B))))). % add_le_imp_le_right
thf(fact_201_add__le__imp__le__right, axiom,
    ((![A : nat, C2 : nat, B : nat]: ((ord_less_eq_nat @ (plus_plus_nat @ A @ C2) @ (plus_plus_nat @ B @ C2)) => (ord_less_eq_nat @ A @ B))))). % add_le_imp_le_right
thf(fact_202_add__strict__left__mono, axiom,
    ((![A : nat, B : nat, C2 : nat]: ((ord_less_nat @ A @ B) => (ord_less_nat @ (plus_plus_nat @ C2 @ A) @ (plus_plus_nat @ C2 @ B)))))). % add_strict_left_mono
thf(fact_203_add__strict__left__mono, axiom,
    ((![A : real, B : real, C2 : real]: ((ord_less_real @ A @ B) => (ord_less_real @ (plus_plus_real @ C2 @ A) @ (plus_plus_real @ C2 @ B)))))). % add_strict_left_mono
thf(fact_204_add__strict__increasing, axiom,
    ((![A : poly_real, B : poly_real, C2 : poly_real]: ((ord_less_poly_real @ zero_zero_poly_real @ A) => ((ord_le1180086932y_real @ B @ C2) => (ord_less_poly_real @ B @ (plus_plus_poly_real @ A @ C2))))))). % add_strict_increasing
thf(fact_205_add__strict__increasing, axiom,
    ((![A : real, B : real, C2 : real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_eq_real @ B @ C2) => (ord_less_real @ B @ (plus_plus_real @ A @ C2))))))). % add_strict_increasing
thf(fact_206_add__strict__increasing, axiom,
    ((![A : nat, B : nat, C2 : nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ B @ C2) => (ord_less_nat @ B @ (plus_plus_nat @ A @ C2))))))). % add_strict_increasing
thf(fact_207_add__strict__right__mono, axiom,
    ((![A : nat, B : nat, C2 : nat]: ((ord_less_nat @ A @ B) => (ord_less_nat @ (plus_plus_nat @ A @ C2) @ (plus_plus_nat @ B @ C2)))))). % add_strict_right_mono
thf(fact_208_add__strict__right__mono, axiom,
    ((![A : real, B : real, C2 : real]: ((ord_less_real @ A @ B) => (ord_less_real @ (plus_plus_real @ A @ C2) @ (plus_plus_real @ B @ C2)))))). % add_strict_right_mono
thf(fact_209_add__strict__increasing2, axiom,
    ((![A : poly_real, B : poly_real, C2 : poly_real]: ((ord_le1180086932y_real @ zero_zero_poly_real @ A) => ((ord_less_poly_real @ B @ C2) => (ord_less_poly_real @ B @ (plus_plus_poly_real @ A @ C2))))))). % add_strict_increasing2
thf(fact_210_add__strict__increasing2, axiom,
    ((![A : real, B : real, C2 : real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_real @ B @ C2) => (ord_less_real @ B @ (plus_plus_real @ A @ C2))))))). % add_strict_increasing2
thf(fact_211_add__strict__increasing2, axiom,
    ((![A : nat, B : nat, C2 : nat]: ((ord_less_eq_nat @ zero_zero_nat @ A) => ((ord_less_nat @ B @ C2) => (ord_less_nat @ B @ (plus_plus_nat @ A @ C2))))))). % add_strict_increasing2
thf(fact_212_add__less__imp__less__left, axiom,
    ((![C2 : nat, A : nat, B : nat]: ((ord_less_nat @ (plus_plus_nat @ C2 @ A) @ (plus_plus_nat @ C2 @ B)) => (ord_less_nat @ A @ B))))). % add_less_imp_less_left
thf(fact_213_add__less__imp__less__left, axiom,
    ((![C2 : real, A : real, B : real]: ((ord_less_real @ (plus_plus_real @ C2 @ A) @ (plus_plus_real @ C2 @ B)) => (ord_less_real @ A @ B))))). % add_less_imp_less_left
thf(fact_214_add__less__imp__less__right, axiom,
    ((![A : nat, C2 : nat, B : nat]: ((ord_less_nat @ (plus_plus_nat @ A @ C2) @ (plus_plus_nat @ B @ C2)) => (ord_less_nat @ A @ B))))). % add_less_imp_less_right
thf(fact_215_add__less__imp__less__right, axiom,
    ((![A : real, C2 : real, B : real]: ((ord_less_real @ (plus_plus_real @ A @ C2) @ (plus_plus_real @ B @ C2)) => (ord_less_real @ A @ B))))). % add_less_imp_less_right
thf(fact_216_complex__mod__triangle__sub, axiom,
    ((![W2 : complex, Z2 : complex]: (ord_less_eq_real @ (real_V638595069omplex @ W2) @ (plus_plus_real @ (real_V638595069omplex @ (plus_plus_complex @ W2 @ Z2)) @ (real_V638595069omplex @ Z2)))))). % complex_mod_triangle_sub
thf(fact_217_pos__add__strict, axiom,
    ((![A : poly_real, B : poly_real, C2 : poly_real]: ((ord_less_poly_real @ zero_zero_poly_real @ A) => ((ord_less_poly_real @ B @ C2) => (ord_less_poly_real @ B @ (plus_plus_poly_real @ A @ C2))))))). % pos_add_strict
thf(fact_218_pos__add__strict, axiom,
    ((![A : nat, B : nat, C2 : nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_nat @ B @ C2) => (ord_less_nat @ B @ (plus_plus_nat @ A @ C2))))))). % pos_add_strict
thf(fact_219_pos__add__strict, axiom,
    ((![A : real, B : real, C2 : real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ B @ C2) => (ord_less_real @ B @ (plus_plus_real @ A @ C2))))))). % pos_add_strict
thf(fact_220_canonically__ordered__monoid__add__class_OlessE, axiom,
    ((![A : nat, B : nat]: ((ord_less_nat @ A @ B) => (~ ((![C : nat]: ((B = (plus_plus_nat @ A @ C)) => (C = zero_zero_nat))))))))). % canonically_ordered_monoid_add_class.lessE
thf(fact_221_add__pos__pos, axiom,
    ((![A : poly_real, B : poly_real]: ((ord_less_poly_real @ zero_zero_poly_real @ A) => ((ord_less_poly_real @ zero_zero_poly_real @ B) => (ord_less_poly_real @ zero_zero_poly_real @ (plus_plus_poly_real @ A @ B))))))). % add_pos_pos
thf(fact_222_add__pos__pos, axiom,
    ((![A : nat, B : nat]: ((ord_less_nat @ zero_zero_nat @ A) => ((ord_less_nat @ zero_zero_nat @ B) => (ord_less_nat @ zero_zero_nat @ (plus_plus_nat @ A @ B))))))). % add_pos_pos
thf(fact_223_add__pos__pos, axiom,
    ((![A : real, B : real]: ((ord_less_real @ zero_zero_real @ A) => ((ord_less_real @ zero_zero_real @ B) => (ord_less_real @ zero_zero_real @ (plus_plus_real @ A @ B))))))). % add_pos_pos
thf(fact_224_add__neg__neg, axiom,
    ((![A : poly_real, B : poly_real]: ((ord_less_poly_real @ A @ zero_zero_poly_real) => ((ord_less_poly_real @ B @ zero_zero_poly_real) => (ord_less_poly_real @ (plus_plus_poly_real @ A @ B) @ zero_zero_poly_real)))))). % add_neg_neg
thf(fact_225_add__neg__neg, axiom,
    ((![A : nat, B : nat]: ((ord_less_nat @ A @ zero_zero_nat) => ((ord_less_nat @ B @ zero_zero_nat) => (ord_less_nat @ (plus_plus_nat @ A @ B) @ zero_zero_nat)))))). % add_neg_neg
thf(fact_226_add__neg__neg, axiom,
    ((![A : real, B : real]: ((ord_less_real @ A @ zero_zero_real) => ((ord_less_real @ B @ zero_zero_real) => (ord_less_real @ (plus_plus_real @ A @ B) @ zero_zero_real)))))). % add_neg_neg
thf(fact_227_add__nonpos__eq__0__iff, axiom,
    ((![X2 : nat, Y : nat]: ((ord_less_eq_nat @ X2 @ zero_zero_nat) => ((ord_less_eq_nat @ Y @ zero_zero_nat) => (((plus_plus_nat @ X2 @ Y) = zero_zero_nat) = (((X2 = zero_zero_nat)) & ((Y = zero_zero_nat))))))))). % add_nonpos_eq_0_iff
thf(fact_228_poly__minimum__modulus__disc, axiom,
    ((![R : real, P : poly_complex]: (?[Z : complex]: (![W : complex]: ((ord_less_eq_real @ (real_V638595069omplex @ W) @ R) => (ord_less_eq_real @ (real_V638595069omplex @ (poly_complex2 @ P @ Z)) @ (real_V638595069omplex @ (poly_complex2 @ P @ W))))))))). % poly_minimum_modulus_disc
thf(fact_229_poly__minimum__modulus, axiom,
    ((![P : poly_complex]: (?[Z : complex]: (![W : complex]: (ord_less_eq_real @ (real_V638595069omplex @ (poly_complex2 @ P @ Z)) @ (real_V638595069omplex @ (poly_complex2 @ P @ W)))))))). % poly_minimum_modulus
thf(fact_230_poly__IVT__neg, axiom,
    ((![A : real, B : real, P : poly_real]: ((ord_less_real @ A @ B) => ((ord_less_real @ zero_zero_real @ (poly_real2 @ P @ A)) => ((ord_less_real @ (poly_real2 @ P @ B) @ zero_zero_real) => (?[X4 : real]: ((ord_less_real @ A @ X4) & ((ord_less_real @ X4 @ B) & ((poly_real2 @ P @ X4) = zero_zero_real)))))))))). % poly_IVT_neg
thf(fact_231_poly__IVT__pos, axiom,
    ((![A : real, B : real, P : poly_real]: ((ord_less_real @ A @ B) => ((ord_less_real @ (poly_real2 @ P @ A) @ zero_zero_real) => ((ord_less_real @ zero_zero_real @ (poly_real2 @ P @ B)) => (?[X4 : real]: ((ord_less_real @ A @ X4) & ((ord_less_real @ X4 @ B) & ((poly_real2 @ P @ X4) = zero_zero_real)))))))))). % poly_IVT_pos
thf(fact_232_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_233_less__nat__zero__code, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ zero_zero_nat)))))). % less_nat_zero_code
thf(fact_234_bot__nat__0_Oextremum, axiom,
    ((![A : nat]: (ord_less_eq_nat @ zero_zero_nat @ A)))). % bot_nat_0.extremum
thf(fact_235_Nat_Oadd__0__right, axiom,
    ((![M : nat]: ((plus_plus_nat @ M @ zero_zero_nat) = M)))). % Nat.add_0_right
thf(fact_236_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_237_le0, axiom,
    ((![N : nat]: (ord_less_eq_nat @ zero_zero_nat @ N)))). % le0
thf(fact_238_nat__add__left__cancel__less, axiom,
    ((![K : nat, M : nat, N : nat]: ((ord_less_nat @ (plus_plus_nat @ K @ M) @ (plus_plus_nat @ K @ N)) = (ord_less_nat @ M @ N))))). % nat_add_left_cancel_less
thf(fact_239_add__gr__0, axiom,
    ((![M : nat, N : nat]: ((ord_less_nat @ zero_zero_nat @ (plus_plus_nat @ M @ N)) = (((ord_less_nat @ zero_zero_nat @ M)) | ((ord_less_nat @ zero_zero_nat @ N))))))). % add_gr_0
thf(fact_240_neq0__conv, axiom,
    ((![N : nat]: ((~ ((N = zero_zero_nat))) = (ord_less_nat @ zero_zero_nat @ N))))). % neq0_conv
thf(fact_241_real__sup__exists, axiom,
    ((![P2 : real > $o]: ((?[X_1 : real]: (P2 @ X_1)) => ((?[Z3 : real]: (![X4 : real]: ((P2 @ X4) => (ord_less_real @ X4 @ Z3)))) => (?[S : real]: (![Y2 : real]: ((?[X3 : real]: (((P2 @ X3)) & ((ord_less_real @ Y2 @ X3)))) = (ord_less_real @ Y2 @ S))))))))). % real_sup_exists
thf(fact_242_bot__nat__0_Oextremum__uniqueI, axiom,
    ((![A : nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) => (A = zero_zero_nat))))). % bot_nat_0.extremum_uniqueI
thf(fact_243_bot__nat__0_Oextremum__unique, axiom,
    ((![A : nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) = (A = zero_zero_nat))))). % bot_nat_0.extremum_unique
thf(fact_244_add__eq__self__zero, axiom,
    ((![M : nat, N : nat]: (((plus_plus_nat @ M @ N) = M) => (N = zero_zero_nat))))). % add_eq_self_zero

% Conjectures (1)
thf(conj_0, conjecture,
    (((poly_complex2 @ pa @ c) = (poly_complex2 @ q @ zero_zero_complex)))).
