% 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_657__5374448_1 ) ; }
% This file was generated by Isabelle (most likely Sledgehammer)
% 2020-12-16 14:31:54.365

% Could-be-implicit typings (6)
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 (34)
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_Ooffset__poly_001t__Nat__Onat, type,
    fundam170929432ly_nat : poly_nat > nat > poly_nat).
thf(sy_c_Fundamental__Theorem__Algebra__Mirabelle__sywschxjbb_Ooffset__poly_001t__Real__Oreal, type,
    fundam1552870388y_real : poly_real > real > poly_real).
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__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__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__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__Real__Oreal, type,
    ord_less_eq_real : real > real > $o).
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__Real__Oreal, type,
    pcompose_real : poly_real > poly_real > poly_real).
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__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_c_Real__Vector__Spaces_Onorm__class_Onorm_001t__Real__Oreal, type,
    real_V646646907m_real : real > 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 (248)
thf(fact_0_constant__def, axiom,
    ((fundam1158420650omplex = (^[F : complex > complex]: (![X : complex]: (![Y : complex]: ((F @ X) = (F @ Y)))))))). % constant_def
thf(fact_1_nc, axiom,
    ((~ ((fundam1158420650omplex @ (poly_complex2 @ p)))))). % nc
thf(fact_2_that, axiom,
    ((fundam1158420650omplex @ (poly_complex2 @ q)))). % that
thf(fact_3_less_Oprems, axiom,
    ((~ ((fundam1158420650omplex @ (poly_complex2 @ pa)))))). % less.prems
thf(fact_4_q_I1_J, axiom,
    (((fundam1709708056omplex @ q) = (fundam1709708056omplex @ pa)))). % q(1)
thf(fact_5_poly__eq__poly__eq__iff, axiom,
    ((![P : poly_complex, Q : poly_complex]: (((poly_complex2 @ P) = (poly_complex2 @ Q)) = (P = Q))))). % poly_eq_poly_eq_iff
thf(fact_6_poly__eq__poly__eq__iff, axiom,
    ((![P : poly_real, Q : poly_real]: (((poly_real2 @ P) = (poly_real2 @ Q)) = (P = Q))))). % poly_eq_poly_eq_iff
thf(fact_7_q_I2_J, axiom,
    ((![X2 : complex]: ((poly_complex2 @ q @ X2) = (poly_complex2 @ pa @ (plus_plus_complex @ c @ X2)))))). % q(2)
thf(fact_8_False, axiom,
    ((~ (((poly_complex2 @ pa @ c) = zero_zero_complex))))). % False
thf(fact_9_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_10_poly__offset__poly, axiom,
    ((![P : poly_complex, H : complex, X3 : complex]: ((poly_complex2 @ (fundam1201687030omplex @ P @ H) @ X3) = (poly_complex2 @ P @ (plus_plus_complex @ H @ X3)))))). % poly_offset_poly
thf(fact_11_poly__offset__poly, axiom,
    ((![P : poly_real, H : real, X3 : real]: ((poly_real2 @ (fundam1552870388y_real @ P @ H) @ X3) = (poly_real2 @ P @ (plus_plus_real @ H @ X3)))))). % poly_offset_poly
thf(fact_12_poly__offset__poly, axiom,
    ((![P : poly_nat, H : nat, X3 : nat]: ((poly_nat2 @ (fundam170929432ly_nat @ P @ H) @ X3) = (poly_nat2 @ P @ (plus_plus_nat @ H @ X3)))))). % poly_offset_poly
thf(fact_13_poly__offset, axiom,
    ((![P : poly_real, A : real]: (?[Q2 : poly_real]: (((fundam1947011094e_real @ Q2) = (fundam1947011094e_real @ P)) & (![X2 : real]: ((poly_real2 @ Q2 @ X2) = (poly_real2 @ P @ (plus_plus_real @ A @ X2))))))))). % poly_offset
thf(fact_14_poly__offset, axiom,
    ((![P : poly_complex, A : complex]: (?[Q2 : poly_complex]: (((fundam1709708056omplex @ Q2) = (fundam1709708056omplex @ P)) & (![X2 : complex]: ((poly_complex2 @ Q2 @ X2) = (poly_complex2 @ P @ (plus_plus_complex @ A @ X2))))))))). % poly_offset
thf(fact_15_poly__pcompose, axiom,
    ((![P : poly_complex, Q : poly_complex, X3 : complex]: ((poly_complex2 @ (pcompose_complex @ P @ Q) @ X3) = (poly_complex2 @ P @ (poly_complex2 @ Q @ X3)))))). % poly_pcompose
thf(fact_16_poly__pcompose, axiom,
    ((![P : poly_real, Q : poly_real, X3 : real]: ((poly_real2 @ (pcompose_real @ P @ Q) @ X3) = (poly_real2 @ P @ (poly_real2 @ Q @ X3)))))). % poly_pcompose
thf(fact_17_poly__pcompose, axiom,
    ((![P : poly_nat, Q : poly_nat, X3 : nat]: ((poly_nat2 @ (pcompose_nat @ P @ Q) @ X3) = (poly_nat2 @ P @ (poly_nat2 @ Q @ X3)))))). % poly_pcompose
thf(fact_18_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_19_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_20__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_21_c, axiom,
    ((![W : complex]: (ord_less_eq_real @ (real_V638595069omplex @ (poly_complex2 @ pa @ c)) @ (real_V638595069omplex @ (poly_complex2 @ pa @ W)))))). % c
thf(fact_22__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,
    ((?[Q2 : poly_complex]: (((fundam1709708056omplex @ Q2) = (fundam1709708056omplex @ pa)) & (![X2 : complex]: ((poly_complex2 @ Q2 @ X2) = (poly_complex2 @ pa @ (plus_plus_complex @ c @ X2)))))))). % \<open>\<exists>q. psize q = psize p \<and> (\<forall>x. poly q x = poly p (c + x))\<close>
thf(fact_23__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,
    ((~ ((![Q2 : poly_complex]: (((fundam1709708056omplex @ Q2) = (fundam1709708056omplex @ pa)) => (~ ((![X2 : complex]: ((poly_complex2 @ Q2 @ X2) = (poly_complex2 @ pa @ (plus_plus_complex @ c @ X2)))))))))))). % \<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_24_poly__0, axiom,
    ((![X3 : complex]: ((poly_complex2 @ zero_z1746442943omplex @ X3) = zero_zero_complex)))). % poly_0
thf(fact_25_poly__0, axiom,
    ((![X3 : real]: ((poly_real2 @ zero_zero_poly_real @ X3) = zero_zero_real)))). % poly_0
thf(fact_26_poly__0, axiom,
    ((![X3 : nat]: ((poly_nat2 @ zero_zero_poly_nat @ X3) = zero_zero_nat)))). % poly_0
thf(fact_27_poly__add, axiom,
    ((![P : poly_complex, Q : poly_complex, X3 : complex]: ((poly_complex2 @ (plus_p1547158847omplex @ P @ Q) @ X3) = (plus_plus_complex @ (poly_complex2 @ P @ X3) @ (poly_complex2 @ Q @ X3)))))). % poly_add
thf(fact_28_poly__add, axiom,
    ((![P : poly_real, Q : poly_real, X3 : real]: ((poly_real2 @ (plus_plus_poly_real @ P @ Q) @ X3) = (plus_plus_real @ (poly_real2 @ P @ X3) @ (poly_real2 @ Q @ X3)))))). % poly_add
thf(fact_29_poly__add, axiom,
    ((![P : poly_nat, Q : poly_nat, X3 : nat]: ((poly_nat2 @ (plus_plus_poly_nat @ P @ Q) @ X3) = (plus_plus_nat @ (poly_nat2 @ P @ X3) @ (poly_nat2 @ Q @ X3)))))). % poly_add
thf(fact_30_poly__all__0__iff__0, axiom,
    ((![P : poly_complex]: ((![X : complex]: ((poly_complex2 @ P @ X) = zero_zero_complex)) = (P = zero_z1746442943omplex))))). % poly_all_0_iff_0
thf(fact_31_poly__all__0__iff__0, axiom,
    ((![P : poly_real]: ((![X : real]: ((poly_real2 @ P @ X) = zero_zero_real)) = (P = zero_zero_poly_real))))). % poly_all_0_iff_0
thf(fact_32_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_33_norm__le__zero__iff, axiom,
    ((![X3 : real]: ((ord_less_eq_real @ (real_V646646907m_real @ X3) @ zero_zero_real) = (X3 = zero_zero_real))))). % norm_le_zero_iff
thf(fact_34_norm__le__zero__iff, axiom,
    ((![X3 : complex]: ((ord_less_eq_real @ (real_V638595069omplex @ X3) @ zero_zero_real) = (X3 = zero_zero_complex))))). % norm_le_zero_iff
thf(fact_35_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_36_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_37_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_38_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_39_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_40_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_41_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_42_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_43_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_44_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_45_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_46_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_47_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_48_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_49_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_50_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_51_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_52_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_53_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_54_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_55_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_56_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_57_le__zero__eq, axiom,
    ((![N : nat]: ((ord_less_eq_nat @ N @ zero_zero_nat) = (N = zero_zero_nat))))). % le_zero_eq
thf(fact_58_not__gr__zero, axiom,
    ((![N : nat]: ((~ ((ord_less_nat @ zero_zero_nat @ N))) = (N = zero_zero_nat))))). % not_gr_zero
thf(fact_59_zero__eq__add__iff__both__eq__0, axiom,
    ((![X3 : nat, Y2 : nat]: ((zero_zero_nat = (plus_plus_nat @ X3 @ Y2)) = (((X3 = zero_zero_nat)) & ((Y2 = zero_zero_nat))))))). % zero_eq_add_iff_both_eq_0
thf(fact_60_add__eq__0__iff__both__eq__0, axiom,
    ((![X3 : nat, Y2 : nat]: (((plus_plus_nat @ X3 @ Y2) = zero_zero_nat) = (((X3 = zero_zero_nat)) & ((Y2 = zero_zero_nat))))))). % add_eq_0_iff_both_eq_0
thf(fact_61_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_62_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_63_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_64_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_65_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_66_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_67_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_68_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_69_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_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_double__zero__sym, axiom,
    ((![A : real]: ((zero_zero_real = (plus_plus_real @ A @ A)) = (A = zero_zero_real))))). % double_zero_sym
thf(fact_74_double__zero, axiom,
    ((![A : real]: (((plus_plus_real @ A @ A) = zero_zero_real) = (A = zero_zero_real))))). % double_zero
thf(fact_75_add_Oright__neutral, axiom,
    ((![A : complex]: ((plus_plus_complex @ A @ zero_zero_complex) = A)))). % add.right_neutral
thf(fact_76_add_Oright__neutral, axiom,
    ((![A : real]: ((plus_plus_real @ A @ zero_zero_real) = A)))). % add.right_neutral
thf(fact_77_add_Oright__neutral, axiom,
    ((![A : nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A)))). % add.right_neutral
thf(fact_78_add_Oleft__neutral, axiom,
    ((![A : complex]: ((plus_plus_complex @ zero_zero_complex @ A) = A)))). % add.left_neutral
thf(fact_79_add_Oleft__neutral, axiom,
    ((![A : real]: ((plus_plus_real @ zero_zero_real @ A) = A)))). % add.left_neutral
thf(fact_80_add_Oleft__neutral, axiom,
    ((![A : nat]: ((plus_plus_nat @ zero_zero_nat @ A) = A)))). % add.left_neutral
thf(fact_81_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_82_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_83_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_84_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_85_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_86_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_87_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_88_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_89_psize__eq__0__iff, axiom,
    ((![P : poly_complex]: (((fundam1709708056omplex @ P) = zero_zero_nat) = (P = zero_z1746442943omplex))))). % psize_eq_0_iff
thf(fact_90_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_91_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_92_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_93_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_94_zero__less__norm__iff, axiom,
    ((![X3 : real]: ((ord_less_real @ zero_zero_real @ (real_V646646907m_real @ X3)) = (~ ((X3 = zero_zero_real))))))). % zero_less_norm_iff
thf(fact_95_zero__less__norm__iff, axiom,
    ((![X3 : complex]: ((ord_less_real @ zero_zero_real @ (real_V638595069omplex @ X3)) = (~ ((X3 = zero_zero_complex))))))). % zero_less_norm_iff
thf(fact_96_norm__eq__zero, axiom,
    ((![X3 : real]: (((real_V646646907m_real @ X3) = zero_zero_real) = (X3 = zero_zero_real))))). % norm_eq_zero
thf(fact_97_norm__eq__zero, axiom,
    ((![X3 : complex]: (((real_V638595069omplex @ X3) = zero_zero_real) = (X3 = zero_zero_complex))))). % norm_eq_zero
thf(fact_98_norm__zero, axiom,
    (((real_V646646907m_real @ zero_zero_real) = zero_zero_real))). % norm_zero
thf(fact_99_norm__zero, axiom,
    (((real_V638595069omplex @ zero_zero_complex) = zero_zero_real))). % norm_zero
thf(fact_100_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_101_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_102_norm__not__less__zero, axiom,
    ((![X3 : complex]: (~ ((ord_less_real @ (real_V638595069omplex @ X3) @ zero_zero_real)))))). % norm_not_less_zero
thf(fact_103_norm__triangle__lt, axiom,
    ((![X3 : real, Y2 : real, E : real]: ((ord_less_real @ (plus_plus_real @ (real_V646646907m_real @ X3) @ (real_V646646907m_real @ Y2)) @ E) => (ord_less_real @ (real_V646646907m_real @ (plus_plus_real @ X3 @ Y2)) @ E))))). % norm_triangle_lt
thf(fact_104_norm__triangle__lt, axiom,
    ((![X3 : complex, Y2 : complex, E : real]: ((ord_less_real @ (plus_plus_real @ (real_V638595069omplex @ X3) @ (real_V638595069omplex @ Y2)) @ E) => (ord_less_real @ (real_V638595069omplex @ (plus_plus_complex @ X3 @ Y2)) @ E))))). % norm_triangle_lt
thf(fact_105_norm__add__less, axiom,
    ((![X3 : real, R : real, Y2 : real, S : real]: ((ord_less_real @ (real_V646646907m_real @ X3) @ R) => ((ord_less_real @ (real_V646646907m_real @ Y2) @ S) => (ord_less_real @ (real_V646646907m_real @ (plus_plus_real @ X3 @ Y2)) @ (plus_plus_real @ R @ S))))))). % norm_add_less
thf(fact_106_norm__add__less, axiom,
    ((![X3 : complex, R : real, Y2 : complex, S : real]: ((ord_less_real @ (real_V638595069omplex @ X3) @ R) => ((ord_less_real @ (real_V638595069omplex @ Y2) @ S) => (ord_less_real @ (real_V638595069omplex @ (plus_plus_complex @ X3 @ Y2)) @ (plus_plus_real @ R @ S))))))). % norm_add_less
thf(fact_107_norm__ge__zero, axiom,
    ((![X3 : complex]: (ord_less_eq_real @ zero_zero_real @ (real_V638595069omplex @ X3))))). % norm_ge_zero
thf(fact_108_poly__bound__exists, axiom,
    ((![R : real, P : poly_real]: (?[M : real]: ((ord_less_real @ zero_zero_real @ M) & (![Z3 : real]: ((ord_less_eq_real @ (real_V646646907m_real @ Z3) @ R) => (ord_less_eq_real @ (real_V646646907m_real @ (poly_real2 @ P @ Z3)) @ M)))))))). % poly_bound_exists
thf(fact_109_poly__bound__exists, axiom,
    ((![R : real, P : poly_complex]: (?[M : real]: ((ord_less_real @ zero_zero_real @ M) & (![Z3 : complex]: ((ord_less_eq_real @ (real_V638595069omplex @ Z3) @ R) => (ord_less_eq_real @ (real_V638595069omplex @ (poly_complex2 @ P @ Z3)) @ M)))))))). % poly_bound_exists
thf(fact_110_offset__poly__eq__0__iff, axiom,
    ((![P : poly_nat, H : nat]: (((fundam170929432ly_nat @ P @ H) = zero_zero_poly_nat) = (P = zero_zero_poly_nat))))). % offset_poly_eq_0_iff
thf(fact_111_offset__poly__eq__0__iff, axiom,
    ((![P : poly_real, H : real]: (((fundam1552870388y_real @ P @ H) = zero_zero_poly_real) = (P = zero_zero_poly_real))))). % offset_poly_eq_0_iff
thf(fact_112_offset__poly__eq__0__iff, axiom,
    ((![P : poly_complex, H : complex]: (((fundam1201687030omplex @ P @ H) = zero_z1746442943omplex) = (P = zero_z1746442943omplex))))). % offset_poly_eq_0_iff
thf(fact_113_offset__poly__0, axiom,
    ((![H : nat]: ((fundam170929432ly_nat @ zero_zero_poly_nat @ H) = zero_zero_poly_nat)))). % offset_poly_0
thf(fact_114_offset__poly__0, axiom,
    ((![H : real]: ((fundam1552870388y_real @ zero_zero_poly_real @ H) = zero_zero_poly_real)))). % offset_poly_0
thf(fact_115_offset__poly__0, axiom,
    ((![H : complex]: ((fundam1201687030omplex @ zero_z1746442943omplex @ H) = zero_z1746442943omplex)))). % offset_poly_0
thf(fact_116_zero__reorient, axiom,
    ((![X3 : complex]: ((zero_zero_complex = X3) = (X3 = zero_zero_complex))))). % zero_reorient
thf(fact_117_zero__reorient, axiom,
    ((![X3 : real]: ((zero_zero_real = X3) = (X3 = zero_zero_real))))). % zero_reorient
thf(fact_118_zero__reorient, axiom,
    ((![X3 : nat]: ((zero_zero_nat = X3) = (X3 = zero_zero_nat))))). % zero_reorient
thf(fact_119_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_120_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_121_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_122_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_123_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_124_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_125_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_126_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_127_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_128_add_Ocommute, axiom,
    ((plus_plus_complex = (^[A2 : complex]: (^[B2 : complex]: (plus_plus_complex @ B2 @ A2)))))). % add.commute
thf(fact_129_add_Ocommute, axiom,
    ((plus_plus_real = (^[A2 : real]: (^[B2 : real]: (plus_plus_real @ B2 @ A2)))))). % add.commute
thf(fact_130_add_Ocommute, axiom,
    ((plus_plus_nat = (^[A2 : nat]: (^[B2 : nat]: (plus_plus_nat @ B2 @ A2)))))). % add.commute
thf(fact_131_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_132_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_133_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_134_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_135_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_136_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_137_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_138_group__cancel_Oadd2, axiom,
    ((![B3 : complex, K : complex, B : complex, A : complex]: ((B3 = (plus_plus_complex @ K @ B)) => ((plus_plus_complex @ A @ B3) = (plus_plus_complex @ K @ (plus_plus_complex @ A @ B))))))). % group_cancel.add2
thf(fact_139_group__cancel_Oadd2, axiom,
    ((![B3 : real, K : real, B : real, A : real]: ((B3 = (plus_plus_real @ K @ B)) => ((plus_plus_real @ A @ B3) = (plus_plus_real @ K @ (plus_plus_real @ A @ B))))))). % group_cancel.add2
thf(fact_140_group__cancel_Oadd2, axiom,
    ((![B3 : nat, K : nat, B : nat, A : nat]: ((B3 = (plus_plus_nat @ K @ B)) => ((plus_plus_nat @ A @ B3) = (plus_plus_nat @ K @ (plus_plus_nat @ A @ B))))))). % group_cancel.add2
thf(fact_141_group__cancel_Oadd1, axiom,
    ((![A3 : complex, K : complex, A : complex, B : complex]: ((A3 = (plus_plus_complex @ K @ A)) => ((plus_plus_complex @ A3 @ B) = (plus_plus_complex @ K @ (plus_plus_complex @ A @ B))))))). % group_cancel.add1
thf(fact_142_group__cancel_Oadd1, axiom,
    ((![A3 : real, K : real, A : real, B : real]: ((A3 = (plus_plus_real @ K @ A)) => ((plus_plus_real @ A3 @ B) = (plus_plus_real @ K @ (plus_plus_real @ A @ B))))))). % group_cancel.add1
thf(fact_143_group__cancel_Oadd1, axiom,
    ((![A3 : nat, K : nat, A : nat, B : nat]: ((A3 = (plus_plus_nat @ K @ A)) => ((plus_plus_nat @ A3 @ B) = (plus_plus_nat @ K @ (plus_plus_nat @ A @ B))))))). % group_cancel.add1
thf(fact_144_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_145_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_146_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_147_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_148_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_149_zero__le, axiom,
    ((![X3 : nat]: (ord_less_eq_nat @ zero_zero_nat @ X3)))). % zero_le
thf(fact_150_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_151_gr__implies__not__zero, axiom,
    ((![M2 : nat, N : nat]: ((ord_less_nat @ M2 @ N) => (~ ((N = zero_zero_nat))))))). % gr_implies_not_zero
thf(fact_152_not__less__zero, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ zero_zero_nat)))))). % not_less_zero
thf(fact_153_gr__zeroI, axiom,
    ((![N : nat]: ((~ ((N = zero_zero_nat))) => (ord_less_nat @ zero_zero_nat @ N))))). % gr_zeroI
thf(fact_154_add_Ogroup__left__neutral, axiom,
    ((![A : complex]: ((plus_plus_complex @ zero_zero_complex @ A) = A)))). % add.group_left_neutral
thf(fact_155_add_Ogroup__left__neutral, axiom,
    ((![A : real]: ((plus_plus_real @ zero_zero_real @ A) = A)))). % add.group_left_neutral
thf(fact_156_add_Ocomm__neutral, axiom,
    ((![A : complex]: ((plus_plus_complex @ A @ zero_zero_complex) = A)))). % add.comm_neutral
thf(fact_157_add_Ocomm__neutral, axiom,
    ((![A : real]: ((plus_plus_real @ A @ zero_zero_real) = A)))). % add.comm_neutral
thf(fact_158_add_Ocomm__neutral, axiom,
    ((![A : nat]: ((plus_plus_nat @ A @ zero_zero_nat) = A)))). % add.comm_neutral
thf(fact_159_comm__monoid__add__class_Oadd__0, axiom,
    ((![A : complex]: ((plus_plus_complex @ zero_zero_complex @ A) = A)))). % comm_monoid_add_class.add_0
thf(fact_160_comm__monoid__add__class_Oadd__0, axiom,
    ((![A : real]: ((plus_plus_real @ zero_zero_real @ A) = A)))). % comm_monoid_add_class.add_0
thf(fact_161_comm__monoid__add__class_Oadd__0, axiom,
    ((![A : nat]: ((plus_plus_nat @ zero_zero_nat @ A) = A)))). % comm_monoid_add_class.add_0
thf(fact_162_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_163_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_164_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_165_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_166_le__iff__add, axiom,
    ((ord_less_eq_nat = (^[A2 : nat]: (^[B2 : nat]: (?[C3 : nat]: (B2 = (plus_plus_nat @ A2 @ C3)))))))). % le_iff_add
thf(fact_167_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_168_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_169_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_170_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_171_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_172_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_173_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_174_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_175_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_176_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_177_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_178_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_179_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_180_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_181_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_182_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_183_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_184_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_185_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_186_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_187_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_188_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_189_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_190_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_191_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_192_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_193_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_194_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_195_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_196_add__nonpos__eq__0__iff, axiom,
    ((![X3 : real, Y2 : real]: ((ord_less_eq_real @ X3 @ zero_zero_real) => ((ord_less_eq_real @ Y2 @ zero_zero_real) => (((plus_plus_real @ X3 @ Y2) = zero_zero_real) = (((X3 = zero_zero_real)) & ((Y2 = zero_zero_real))))))))). % add_nonpos_eq_0_iff
thf(fact_197_add__nonpos__eq__0__iff, axiom,
    ((![X3 : nat, Y2 : nat]: ((ord_less_eq_nat @ X3 @ zero_zero_nat) => ((ord_less_eq_nat @ Y2 @ zero_zero_nat) => (((plus_plus_nat @ X3 @ Y2) = zero_zero_nat) = (((X3 = zero_zero_nat)) & ((Y2 = zero_zero_nat))))))))). % add_nonpos_eq_0_iff
thf(fact_198_add__nonneg__eq__0__iff, axiom,
    ((![X3 : real, Y2 : real]: ((ord_less_eq_real @ zero_zero_real @ X3) => ((ord_less_eq_real @ zero_zero_real @ Y2) => (((plus_plus_real @ X3 @ Y2) = zero_zero_real) = (((X3 = zero_zero_real)) & ((Y2 = zero_zero_real))))))))). % add_nonneg_eq_0_iff
thf(fact_199_add__nonneg__eq__0__iff, axiom,
    ((![X3 : nat, Y2 : nat]: ((ord_less_eq_nat @ zero_zero_nat @ X3) => ((ord_less_eq_nat @ zero_zero_nat @ Y2) => (((plus_plus_nat @ X3 @ Y2) = zero_zero_nat) = (((X3 = zero_zero_nat)) & ((Y2 = zero_zero_nat))))))))). % add_nonneg_eq_0_iff
thf(fact_200_add__nonpos__nonpos, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ A @ zero_zero_real) => ((ord_less_eq_real @ B @ zero_zero_real) => (ord_less_eq_real @ (plus_plus_real @ A @ B) @ zero_zero_real)))))). % add_nonpos_nonpos
thf(fact_201_add__nonpos__nonpos, axiom,
    ((![A : nat, B : nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) => ((ord_less_eq_nat @ B @ zero_zero_nat) => (ord_less_eq_nat @ (plus_plus_nat @ A @ B) @ zero_zero_nat)))))). % add_nonpos_nonpos
thf(fact_202_add__nonneg__nonneg, axiom,
    ((![A : real, B : real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ zero_zero_real @ B) => (ord_less_eq_real @ zero_zero_real @ (plus_plus_real @ A @ B))))))). % add_nonneg_nonneg
thf(fact_203_add__nonneg__nonneg, axiom,
    ((![A : nat, B : nat]: ((ord_less_eq_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ zero_zero_nat @ B) => (ord_less_eq_nat @ zero_zero_nat @ (plus_plus_nat @ A @ B))))))). % add_nonneg_nonneg
thf(fact_204_add__increasing2, axiom,
    ((![C2 : real, B : real, A : real]: ((ord_less_eq_real @ zero_zero_real @ C2) => ((ord_less_eq_real @ B @ A) => (ord_less_eq_real @ B @ (plus_plus_real @ A @ C2))))))). % add_increasing2
thf(fact_205_add__increasing2, axiom,
    ((![C2 : nat, B : nat, A : nat]: ((ord_less_eq_nat @ zero_zero_nat @ C2) => ((ord_less_eq_nat @ B @ A) => (ord_less_eq_nat @ B @ (plus_plus_nat @ A @ C2))))))). % add_increasing2
thf(fact_206_add__decreasing2, axiom,
    ((![C2 : real, A : real, B : real]: ((ord_less_eq_real @ C2 @ zero_zero_real) => ((ord_less_eq_real @ A @ B) => (ord_less_eq_real @ (plus_plus_real @ A @ C2) @ B)))))). % add_decreasing2
thf(fact_207_add__decreasing2, axiom,
    ((![C2 : nat, A : nat, B : nat]: ((ord_less_eq_nat @ C2 @ zero_zero_nat) => ((ord_less_eq_nat @ A @ B) => (ord_less_eq_nat @ (plus_plus_nat @ A @ C2) @ B)))))). % add_decreasing2
thf(fact_208_add__increasing, axiom,
    ((![A : real, B : real, C2 : real]: ((ord_less_eq_real @ zero_zero_real @ A) => ((ord_less_eq_real @ B @ C2) => (ord_less_eq_real @ B @ (plus_plus_real @ A @ C2))))))). % add_increasing
thf(fact_209_add__increasing, axiom,
    ((![A : nat, B : nat, C2 : nat]: ((ord_less_eq_nat @ zero_zero_nat @ A) => ((ord_less_eq_nat @ B @ C2) => (ord_less_eq_nat @ B @ (plus_plus_nat @ A @ C2))))))). % add_increasing
thf(fact_210_add__decreasing, axiom,
    ((![A : real, C2 : real, B : real]: ((ord_less_eq_real @ A @ zero_zero_real) => ((ord_less_eq_real @ C2 @ B) => (ord_less_eq_real @ (plus_plus_real @ A @ C2) @ B)))))). % add_decreasing
thf(fact_211_add__decreasing, axiom,
    ((![A : nat, C2 : nat, B : nat]: ((ord_less_eq_nat @ A @ zero_zero_nat) => ((ord_less_eq_nat @ C2 @ B) => (ord_less_eq_nat @ (plus_plus_nat @ A @ C2) @ B)))))). % add_decreasing
thf(fact_212_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_213_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_214_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_215_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_216_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_217_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_218_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_219_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_220_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_221_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_222_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_223_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_224_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_225_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_226_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_227_norm__triangle__mono, axiom,
    ((![A : real, R : real, B : real, S : real]: ((ord_less_eq_real @ (real_V646646907m_real @ A) @ R) => ((ord_less_eq_real @ (real_V646646907m_real @ B) @ S) => (ord_less_eq_real @ (real_V646646907m_real @ (plus_plus_real @ A @ B)) @ (plus_plus_real @ R @ S))))))). % norm_triangle_mono
thf(fact_228_norm__triangle__mono, axiom,
    ((![A : complex, R : real, B : complex, S : real]: ((ord_less_eq_real @ (real_V638595069omplex @ A) @ R) => ((ord_less_eq_real @ (real_V638595069omplex @ B) @ S) => (ord_less_eq_real @ (real_V638595069omplex @ (plus_plus_complex @ A @ B)) @ (plus_plus_real @ R @ S))))))). % norm_triangle_mono
thf(fact_229_norm__triangle__ineq, axiom,
    ((![X3 : real, Y2 : real]: (ord_less_eq_real @ (real_V646646907m_real @ (plus_plus_real @ X3 @ Y2)) @ (plus_plus_real @ (real_V646646907m_real @ X3) @ (real_V646646907m_real @ Y2)))))). % norm_triangle_ineq
thf(fact_230_norm__triangle__ineq, axiom,
    ((![X3 : complex, Y2 : complex]: (ord_less_eq_real @ (real_V638595069omplex @ (plus_plus_complex @ X3 @ Y2)) @ (plus_plus_real @ (real_V638595069omplex @ X3) @ (real_V638595069omplex @ Y2)))))). % norm_triangle_ineq
thf(fact_231_norm__triangle__le, axiom,
    ((![X3 : real, Y2 : real, E : real]: ((ord_less_eq_real @ (plus_plus_real @ (real_V646646907m_real @ X3) @ (real_V646646907m_real @ Y2)) @ E) => (ord_less_eq_real @ (real_V646646907m_real @ (plus_plus_real @ X3 @ Y2)) @ E))))). % norm_triangle_le
thf(fact_232_norm__triangle__le, axiom,
    ((![X3 : complex, Y2 : complex, E : real]: ((ord_less_eq_real @ (plus_plus_real @ (real_V638595069omplex @ X3) @ (real_V638595069omplex @ Y2)) @ E) => (ord_less_eq_real @ (real_V638595069omplex @ (plus_plus_complex @ X3 @ Y2)) @ E))))). % norm_triangle_le
thf(fact_233_norm__add__leD, axiom,
    ((![A : real, B : real, C2 : real]: ((ord_less_eq_real @ (real_V646646907m_real @ (plus_plus_real @ A @ B)) @ C2) => (ord_less_eq_real @ (real_V646646907m_real @ B) @ (plus_plus_real @ (real_V646646907m_real @ A) @ C2)))))). % norm_add_leD
thf(fact_234_norm__add__leD, axiom,
    ((![A : complex, B : complex, C2 : real]: ((ord_less_eq_real @ (real_V638595069omplex @ (plus_plus_complex @ A @ B)) @ C2) => (ord_less_eq_real @ (real_V638595069omplex @ B) @ (plus_plus_real @ (real_V638595069omplex @ A) @ C2)))))). % norm_add_leD
thf(fact_235_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_236_less__nat__zero__code, axiom,
    ((![N : nat]: (~ ((ord_less_nat @ N @ zero_zero_nat)))))). % less_nat_zero_code
thf(fact_237_neq0__conv, axiom,
    ((![N : nat]: ((~ ((N = zero_zero_nat))) = (ord_less_nat @ zero_zero_nat @ N))))). % neq0_conv
thf(fact_238_add__gr__0, axiom,
    ((![M2 : nat, N : nat]: ((ord_less_nat @ zero_zero_nat @ (plus_plus_nat @ M2 @ N)) = (((ord_less_nat @ zero_zero_nat @ M2)) | ((ord_less_nat @ zero_zero_nat @ N))))))). % add_gr_0
thf(fact_239_nat__add__left__cancel__less, axiom,
    ((![K : nat, M2 : nat, N : nat]: ((ord_less_nat @ (plus_plus_nat @ K @ M2) @ (plus_plus_nat @ K @ N)) = (ord_less_nat @ M2 @ N))))). % nat_add_left_cancel_less
thf(fact_240_le0, axiom,
    ((![N : nat]: (ord_less_eq_nat @ zero_zero_nat @ N)))). % le0
thf(fact_241_bot__nat__0_Oextremum, axiom,
    ((![A : nat]: (ord_less_eq_nat @ zero_zero_nat @ A)))). % bot_nat_0.extremum
thf(fact_242_nat__add__left__cancel__le, axiom,
    ((![K : nat, M2 : nat, N : nat]: ((ord_less_eq_nat @ (plus_plus_nat @ K @ M2) @ (plus_plus_nat @ K @ N)) = (ord_less_eq_nat @ M2 @ N))))). % nat_add_left_cancel_le
thf(fact_243_add__is__0, axiom,
    ((![M2 : nat, N : nat]: (((plus_plus_nat @ M2 @ N) = zero_zero_nat) = (((M2 = zero_zero_nat)) & ((N = zero_zero_nat))))))). % add_is_0
thf(fact_244_Nat_Oadd__0__right, axiom,
    ((![M2 : nat]: ((plus_plus_nat @ M2 @ zero_zero_nat) = M2)))). % Nat.add_0_right
thf(fact_245_less__eq__nat_Osimps_I1_J, axiom,
    ((![N : nat]: (ord_less_eq_nat @ zero_zero_nat @ N)))). % less_eq_nat.simps(1)
thf(fact_246_add__leE, axiom,
    ((![M2 : nat, K : nat, N : nat]: ((ord_less_eq_nat @ (plus_plus_nat @ M2 @ K) @ N) => (~ (((ord_less_eq_nat @ M2 @ N) => (~ ((ord_less_eq_nat @ K @ N)))))))))). % add_leE
thf(fact_247_le__0__eq, axiom,
    ((![N : nat]: ((ord_less_eq_nat @ N @ zero_zero_nat) = (N = zero_zero_nat))))). % le_0_eq

% Conjectures (1)
thf(conj_0, conjecture,
    ($false)).
