Ordinal 📖 | CompOp | 1356 mathmath: Ordinal.isPrincipal_add_iff_add_self_lt, Cardinal.lt_ord_succ_card, Ordinal.iSup_eq_iSup, Ordinal.isSuccLimit_lift, PSet.rank_le_iff, Ordinal.opow_mul, Ordinal.iSup_eq_bsup, Mathlib.Meta.NormNum.isNat_ordinalMod, Cardinal.aleph_le_beth, List.SortedGT.lt_ord_of_lt, univLE_iff_exists_embedding, Ordinal.opow_le_opow_right, Ordinal.veblenWith_le_veblenWith_iff_right, Ordinal.lt_omega0_opow_succ, Ordinal.isNormal_iff_strictMono_limit, Cardinal.mk_iUnion_Ordinal_le_of_le, Ordinal.principal_add_omega, Ordinal.boundedLimitRec_succ, Ordinal.lift_card_iSup_le_sum_card, Acc.rank_eq, ONote.repr_one, Ordinal.iSup_pow_natCast, Ordinal.IsNormal.refl, Ordinal.IsNormal.veblenWith, Ordinal.cof_iSup_add_one_le, Ordinal.add_absorp, Ordinal.card_add_one, Ordinal.sup_eq_lsub_iff_lt_sup, Ordinal.CNF.coeff_injective, ZFSet.IsOrdinal.rank_le_iff_subset, Ordinal.opow_one, Ordinal.cof_iSup_le_lift, OrdinalApprox.lfpApprox_mono_mid, Profinite.NobelingProof.GoodProducts.sum_to_range, ZFSet.subset_vonNeumann, Ordinal.isPrincipal_swap_iff, Ordinal.sub_zero, Cardinal.nfpFamily_lt_ord_of_isRegular, Ordinal.lift_type_lt, Ordinal.sInf_compl_lt_lift_ord_succ, Ordinal.typein_le_typein, Ordinal.pred_succ, Ordinal.isNormal_mul_right, Ordinal.lift_one, Ordinal.mem_range_typein_iff, Ordinal.IsAcc.isSuccLimit, Ordinal.gamma_le_gamma, Ordinal.isPrincipal_iff_of_monotone, Ordinal.add_succ, Ordinal.exists_lt_mul, Ordinal.isPrincipal_add_iff_zero_or_omega0_opow, Ordinal.max_zero_left, Cardinal.isStrongLimit_preBeth, Profinite.NobelingProof.injective_πs', Ordinal.card_le_ofNat, Ordinal.dvd_add_iff, Ordinal.Iio_one_default_eq, Ordinal.lsub_pos, Cardinal.blsub_lt_ord_lift_of_isRegular, Ordinal.sup_eq_lsub_iff_succ, Cardinal.aleph_succ, Ordinal.mem_range_lift_of_le, Ordinal.instIsLeftCancelMulZero, Ordinal.isInitialIso_apply, Cardinal.preBeth_eq_zero, Ordinal.not_bddAbove_fp_family, Ordinal.blsub_congr, Ordinal.principal_mul_of_le_two, Cardinal.aleph_pos, Ordinal.liftInitialSeg_coe, Ordinal.cof_iSup_Iio, Ordinal.add_right_cancel, Ordinal.iSup_typein_succ, ONote.NFBelow_zero, Ordinal.existsAddOfLE, Ordinal.invVeblen₂_eq_iff, Ordinal.blsub_le_iff, ONote.nf_repr_split', Cardinal.isSuccLimit_ord, Ordinal.noZeroDivisors, Ordinal.cof_zero, Ordinal.omega_lt_omega, Ordinal.omega0_lt_omega_one, Ordinal.log_of_left_le_one, OrdinalApprox.gfp_mem_range_gfpApprox, Ordinal.le_invVeblen₂_iff, Ordinal.antisymm, Ordinal.cof_Iio, Ordinal.type_lt_iff, Ordinal.IsNormal.apply_le_nfp, Ordinal.veblenWith_zero_lt_veblenWith_zero, Ordinal.succ_one, Ordinal.sub_eq_zero_iff_le, Ordinal.mod_self, Ordinal.cof_add_one, Ordinal.deriv_add_eq_mul_omega0_add, Cardinal.ord.orderEmbedding_coe, Ordinal.CNF.coeff_zero_left, Ordinal.omega0_lt_preOmega_iff, ZFSet.rank_empty, Ordinal.mulRightMono, Profinite.NobelingProof.GoodProducts.linearIndependent_iff_union_smaller, Ordinal.instAddRightMono, Profinite.NobelingProof.coe_πs, Ordinal.isPrincipal_add_ord, Ordinal.lift_lt, ZFSet.lt_rank_iff, Ordinal.CNF.eval_single_add', Ordinal.apply_le_nfp, Ordinal.mod_le, Cardinal.lift_eq_aleph_one, Ordinal.add_le_iff_of_isSuccLimit, Ordinal.principal_add_of_le_one, Ordinal.not_lt_zero, Ordinal.gamma_zero_eq_nfp, Ordinal.card_le_aleph, Ordinal.isAcc_iff, Ordinal.opow_omega0, Ordinal.invVeblen₂_zero, Ordinal.omega_zero, Ordinal.bsup_id_succ, Ordinal.fp_iff_derivFamily, Ordinal.type_lt_mem_range_succ, Ordinal.liftPrincipalSeg_top', Ordinal.div_two_opow_log, Ordinal.sup_succ_le_lsub, Ordinal.CNF.coeff_opow_mul_add, Ordinal.iSup_le_lsub, Ordinal.card_iSup_Iio_le_sum_card, Ordinal.isOpen_singleton_iff, Profinite.NobelingProof.Products.limitOrdinal, Ordinal.card_one, Ordinal.enum_symm_apply_coe, Ordinal.IsNormal.lt_iff, Ordinal.deriv_strictMono, Ordinal.blsub_eq_blsub, Ordinal.enum_zero_le, PSet.le_succ_rank_sUnion, Ordinal.principal_opow_ord, Ordinal.principal_add_ord, Ordinal.lt_mul_div_add, Ordinal.omega_le_omega, Ordinal.IsNormal.nfp_le_apply, Ordinal.enum_lt_enum, Ordinal.isSuccLimit_omega0, Ordinal.mul_div_gc, Ordinal.isInitialIso_symm_apply_coe, Ordinal.isInitial_preOmega, CategoryTheory.IsGrothendieckAbelian.generatingMonomorphisms.exists_ordinal, Ordinal.nfp_le_fp, Ordinal.add_log_le_log_mul, Profinite.NobelingProof.Products.eval_πs, Ordinal.card_zero, Ordinal.isPrincipal_add_one, Ordinal.card_typein_min_le_mk, Cardinal.aleph0_lt_iff_aleph_one_le, Cardinal.isNormal_preAleph, Ordinal.invVeblen₁_zero, Cardinal.bddAbove_ord_image_iff, Ordinal.epsilon_eq_deriv, Ordinal.epsilon_zero_lt_gamma, Ordinal.enumOrd_range, Ordinal.lt_log_of_lt_opow, Ordinal.CNF.coeff_eq_zero_of_lt, Ordinal.log_zero_right, Ordinal.iSup_lt_of_lt_cof, Ordinal.div_le, Ordinal.isPrincipal_mul_omega0_opow_opow, Ordinal.sSup_add_one_lt_of_lt_cof, Cardinal.preAleph_nat, Ordinal.lt_mul_iff_div_lt, PSet.rank_mono, Ordinal.log_zero_left, Profinite.NobelingProof.GoodProducts.linearIndependent_comp_of_eval, Mathlib.Meta.NormNum.isNat_ordinalLT_true, Ordinal.IsNormal.isSuccLimit, Ordinal.le_add_left, Ordinal.log_eq_zero, Ordinal.pred_le_self, Ordinal.cof_eq_one_iff_is_succ, ZFSet.vonNeumann_subset_vonNeumann_iff, Ordinal.div_lt, Ordinal.range_omega, Ordinal.not_bddAbove_isInitial, not_injective_of_ordinal, Ordinal.opow_add, Ordinal.lt_mul_succ_div, ONote.repr_mul, Ordinal.div_add_mod, Ordinal.veblen_gamma_zero, Ordinal.mul_add_div, Ordinal.isSuccLimit_add_iff_of_isSuccLimit, Ordinal.cof_preOmega, Ordinal.principal_mul_omega0, Ordinal.nfp_mul_opow_omega0_add, Ordinal.div_opow_log_pos, Ordinal.isPrincipal_zero, Ordinal.one_add_ofNat, Profinite.NobelingProof.Products.eval_πs', Profinite.NobelingProof.GoodProducts.span_sum, Profinite.NobelingProof.GoodProducts.range_equiv_factorization, Ordinal.isOpen_iff, Ordinal.CNF.zero_left, Ordinal.log_one_left, Ordinal.card_sInf_range_compl_le_lift, Ordinal.isSuccLimit_opow_left, Ordinal.left_eq_zero_of_add_eq_zero, ZFSet.vonNeumann_add_one, Ordinal.iSup_le, Cardinal.ord_pos, Ordinal.le_iff_derivFamily, Cardinal.ord_eq_zero, Cardinal.preAleph_le_aleph, Ordinal.left_lt_opow, Ordinal.CNF.sorted, Ordinal.type_le_iff, Ordinal.limitRecOn_zero, Ordinal.isClosedBelow_iff, Ordinal.IsInitial.principal_mul, Mathlib.Meta.NormNum.isNat_ordinalNPow, Ordinal.opow_mul_add_pos, Ordinal.log_le_self, Ordinal.Principal.sSup, Ordinal.lift_cof_iSup_add_one, Ordinal.coe_toZFSet, Ordinal.gamma0_le_of_veblen_le, Ordinal.principal_opow_omega0, Ordinal.typein_top, NONote.repr_add, Ordinal.isSuccLimit_opow, Ordinal.invVeblen₂_le_iff, ONote.NF.out, Ordinal.enum_le_enum', Ordinal.apply_lt_nfpFamily_iff, Ordinal.div_self, Ordinal.deriv_succ, Ordinal.IsFundamentalSeq.le_ord_cof, Ordinal.bfamilyOfFamily'_typein, Ordinal.invVeblen₁_le, Ordinal.mul_lt_of_lt_div, Cardinal.aleph_one_le_continuum, WellFoundedGT.rank_strictAnti, Ordinal.mul_lt_omega0_opow, Ordinal.CNF.coeff_zero_apply, Cardinal.bsup_lt_ord_of_isRegular, MeasurableSpace.generateMeasurableRec_of_omega_one_le, Profinite.NobelingProof.succ_exact, Ordinal.veblenWith_right_strictMono, Ordinal.succ_zero, Ordinal.div_mul_cancel, Ordinal.card_le_preAleph, Cardinal.aleph_mul_aleph0, Ordinal.mem_closure_iff_bsup, Ordinal.card_omega0_opow, Ordinal.natCast_mul_omega0, Ordinal.iSup_pow, ONote.split_dvd, Ordinal.bddAbove_range_add_one_iff, Profinite.NobelingProof.GoodProducts.smaller_factorization, Ordinal.deriv_limit, Cardinal.preBeth_one, Ordinal.epsilon_zero_le_of_omega0_opow_le, Ordinal.lt_nfpFamily_iff, Ordinal.zero_opow', Ordinal.omega0_pos, Ordinal.cof_one, Ordinal.isClosed_iff_bsup, Ordinal.zero_sub, Ordinal.card_sInf_range_compl_le, Ordinal.not_bddAbove_principal, Ordinal.veblenWith_zero_strictMono, Ordinal.eq_zero_or_opow_omega0_le_of_mul_eq_right, Ordinal.iSup_add_one_lt_of_lt_cof, Ordinal.CNF.coeff_of_not_mem_CNF, Ordinal.natCast_sub, ONote.NF.of_dvd_omega0, Ordinal.nfp_le_of_isPrincipal, Cardinal.univ_id, Profinite.NobelingProof.πs'_apply_apply, Cardinal.card_le_iff, Ordinal.isNormal_veblen, Ordinal.dvd_of_mod_eq_zero, Ordinal.enumOrd_le_enumOrd, not_small_ordinal, Ordinal.sSup_eq_bsup, Ordinal.liftPrincipalSeg_coe, Besicovitch.TauPackage.monotone_iUnionUpTo, Ordinal.bsup_le, Ordinal.IsFundamentalSeq.zero, Ordinal.bsup_succ_eq_blsub, Ordinal.opow_log_le_self, Ordinal.isPrincipal_mul_omega0, Cardinal.aleph_add_aleph, Ordinal.one_add_omega0, Ordinal.instZeroLEOneClass, Ordinal.iSup_add_nat, Ordinal.lsub_const, Ordinal.lt_one_iff_zero, ZFSet.exists_mem_vonNeumann, Ordinal.isSuccLimit_add_iff, Cardinal.preAleph_omega0, Ordinal.lt_gamma0, Ordinal.foldr_le_nfpFamily, Profinite.NobelingProof.GoodProducts.P0, Ordinal.bot_eq_zero, Ordinal.CNF.snd_lt, Ordinal.principal_add_iff_add_left_eq_self, PSet.rank_lt_of_mem, Ordinal.iSup_sum, Ordinal.type_eq_zero_of_empty, Ordinal.nontrivial, Ordinal.pred_le_iff_le_succ, Cardinal.beth_succ, Ordinal.mem_range_omega_iff, Ordinal.nat_le_card, Ordinal.IsNormal.limit_lt, Ordinal.mem_toZFSet_iff, Ordinal.CNF.of_lt, Ordinal.right_le_opow, ZFSet.rank_mono, Ordinal.mem_range_lift_of_card_le, Acc.rank_lt_of_rel, Ordinal.ord_mk_lt_type, Ordinal.mul_mod, Cardinal.lt_omega_iff_card_lt, Cardinal.lsub_lt_ord_of_isRegular, Ordinal.principal_mul_ord, ONote.lt_def, Ordinal.one_add_of_omega0_le, ONote.oadd_mul_nfBelow, Ordinal.log_opow_mul, Ordinal.veblen_zero_lt_veblen_zero, Ordinal.natCast_opow, Ordinal.opow_one_add, Ordinal.opow_dvd_opow, ZFSet.isOrdinal_iff_mem_range_toZFSet, Ordinal.lift_cof_iSup, Cardinal.le_preAleph_ord, Cardinal.aleph1_le_lift, Ordinal.typein_lt_type, Ordinal.apply_lt_nfp, PSet.rank_insert, Ordinal.blsub_lt_ord_lift, Ordinal.toZFSet_strictMono, Ordinal.IsAcc.inter_Ioo_nonempty, Ordinal.card_le_one, Ordinal.lt_sub, Ordinal.opow_mul_add_lt_opow, Ordinal.lift_succ, Ordinal.smul_eq_mul, Ordinal.veblen_of_ne_zero, Ordinal.iSup_eq_lsub_or_succ_iSup_eq_lsub, Ordinal.opow_le_opow_iff_right, Ordinal.sup_succ_eq_lsub, Ordinal.veblen_opow_eq_opow_iff, Ordinal.CNF.coeff_of_mem_CNF, Ordinal.type_le_iff', Cardinal.lsub_lt_ord_lift_of_isRegular, Ordinal.div_opow_log_lt, Ordinal.isPrincipal_add_of_isPrincipal_mul, Ordinal.sSup_ord, Ordinal.IsClosedBelow.forall_lt, Cardinal.le_aleph_ord, ONote.NFBelow.lt, Ordinal.not_isPrincipal_iff, Ordinal.IsInitial.card_lt_card, OrdinalApprox.gfpApprox_add_one, Ordinal.typein_lt_typein, Ordinal.eq_nat_or_omega0_le, Ordinal.one_lt_pow, Ordinal.enumOrd_zero, Ordinal.iterate_veblen_lt_gamma0, cardinalInterFilter_aleph_one_iff, Ordinal.nat_lt_card, Ordinal.nfpFamily_lt_ord_lift, IsWellFounded.rank_lt_of_rel, Ordinal.CNF.eval_single, Ordinal.IsClosedBelow.iInter, ZFSet.rank_powerset, Ordinal.iSup_mul_nat, Ordinal.isPrincipal_one_iff, Ordinal.lt_epsilon_zero, Ordinal.enum_lt_fin, Ordinal.veblenWith_zero_inj, Ordinal.le_sub_of_le, Ordinal.isNormal_veblenWith, Ordinal.isInitial_one, Ordinal.lt_mul_add_one_iff, Ordinal.boundedLimitRec_zero, Ordinal.le_zero, Ordinal.CNF.sortedGT, Ordinal.iterate_omega0_opow_lt_epsilon0, Ordinal.card_eq_zero, Ordinal.nfpFamily_le_fp, Ordinal.instPosMulStrictMono, Ordinal.derivFamily_succ, Ordinal.IsNormal.id_le, Ordinal.isNormal_iff_lt_succ_and_bsup_eq, Cardinal.aleph_le_aleph, Cardinal.ord_eq_one, Ordinal.IsNormal.le_apply, Ordinal.mod_one, Ordinal.cof_add, Ordinal.natCast_mod, Ordinal.lt_add_iff, Cardinal.cof_omega_one, Ordinal.div_le_left, Ordinal.lt_opow_succ_log_self, Ordinal.sub_self, Ordinal.log_opow, Ordinal.not_bddAbove_setOf_isPrincipal, Profinite.NobelingProof.contained_eq_proj, Ordinal.IsFundamentalSeq.strictMono, Ordinal.lsub_eq_blsub', Ordinal.nfp_mul_eq_opow_omega0, Ordinal.invVeblen₁_of_lt_opow, ONote.repr_add, Ordinal.type_lt_mem_range_succ_iff, Ordinal.iterate_le_nfp, IsWellFounded.rank_eq_typein, PSet.rank_sUnion_le, Cardinal.beth_one, Profinite.NobelingProof.GoodProducts.injective_sum_to, Ordinal.isSuccPrelimit_zero, Ordinal.IsNormal.apply_lt_nfp, Ordinal.le_nfp, ONote.repr_scale, Ordinal.omega0_le, Ordinal.bsup_eq_blsub_iff_succ, Ordinal.IsFundamentalSeq.add_one, Ordinal.IsNormal.limit_le, ONote.repr_zero, Ordinal.derivFamily_add_one, Ordinal.lt_add_iff_of_isSuccLimit, Ordinal.sup_le_lsub, Cardinal.cof_preOmega_add_one, Ordinal.iSup_add_natCast, Ordinal.bsup_one, Ordinal.enumOrd_mem, Cardinal.beth_le_beth, Ordinal.IsNormal.le_iff, Ordinal.nfp_mul_zero, Ordinal.mod_lt, PrincipalSeg.ordinal_type_lt, Ordinal.IsNormal.map_iSup, Ordinal.not_bddAbove_fp, Ordinal.card_iSup_Iio_le_card_mul_iSup, Ordinal.zero_or_succ_or_isSuccLimit, Cardinal.preBeth_zero, Ordinal.nfp_le_iff, Profinite.NobelingProof.GoodProducts.good_lt_maxProducts, Cardinal.ord_aleph, Ordinal.nfp_lt_ord, Ordinal.small_Iic, Profinite.NobelingProof.GoodProducts.union_succ, Ordinal.isSuccPrelimit_mul_right, Ordinal.isPrincipal_opow_omega0, Cardinal.aleph1_le_mk_iff, Ordinal.IsInitial.principal_opow, Ordinal.nfp_le_apply, Ordinal.wellFoundedLT, Ordinal.veblenWith_lt_veblenWith_iff, Ordinal.card_lt_nat, Ordinal.bsup_zero, ZFSet.mem_vonNeumann', Ordinal.derivFamily_strictMono, Ordinal.nfp_zero, Ordinal.pred_surjective, Ordinal.blsub_le_of_brange_subset, Ordinal.log_mono_right, ZFSet.vonNeumann_mem_vonNeumann_iff, Profinite.NobelingProof.Products.eval_πs_image', Ordinal.one_lt_card, Ordinal.mem_closed_iff_bsup, Ordinal.sup_eq_bsup, Ordinal.lt_blsub_iff, Ordinal.add_sub_cancel, Cardinal.ord_le, Ordinal.isNormal_preOmega, Ordinal.Principal.iSup, Cardinal.ord_zero, Ordinal.div_eq_zero_of_lt, Ordinal.isPrincipal_add_iff_add_lt_ne_self, Cardinal.ord_eq_Inf, Ordinal.sub_lt_of_le, Cardinal.beth_zero, Ordinal.nfpFamily_lt_ord, Ordinal.preOmega_ofNat, Ordinal.invVeblen₂_gamma, Ordinal.preOmega_le_omega, Ordinal.cof_iSup, Ordinal.veblen_zero, Ordinal.cof_succ, Ordinal.lsub_lt_ord, ZFSet.vonNeumann_strictMono, Ordinal.type_subrel, Ordinal.isNormal_opow, Ordinal.one_opow, Cardinal.isRegular_aleph_succ, Cardinal.ord_le_ord, Cardinal.beth_mono, Ordinal.gamma_pos, Ordinal.isPrincipal_add_opow_of_isPrincipal_add, Ordinal.not_principal_iff_of_monotone, Ordinal.lt_lift_iff, Ordinal.isSuccLimit_of_isPrincipal_add, OrdinalApprox.lfpApprox_monotone, Ordinal.principal_mul_omega, Cardinal.aleph1_lt_lift, Ordinal.isNormal_deriv, Cardinal.lt_aleph_one_iff, Ordinal.card_add, Ordinal.le_enum_succ, Ordinal.opow_limit, Ordinal.left_le_veblenWith, OrdinalApprox.gfpApprox_antitone, Ordinal.add_eq_zero_iff, Ordinal.CNF.eval_lt, Cardinal.preAleph_limit, Ordinal.type_eq_one_iff_unique, Ordinal.mem_toPSet_iff, Cardinal.isNormal_aleph, Ordinal.mul_eq_right_iff_opow_omega0_dvd, Ordinal.mul_succ, Mathlib.Meta.NormNum.isNat_ordinalMul, Ordinal.cmp_veblen, Ordinal.veblenWith_add_one, ONote.omega0_le_oadd, Cardinal.omega0_le_ord, Order.cof_Iio, Ordinal.enum_typein, Ordinal.instAddLeftReflectLT, Ordinal.opow_mul_add_lt_opow_mul, Ordinal.limitRecOn_succ, Ordinal.sub_le, Ordinal.instAddLeftStrictMono, Ordinal.dvd_iff_mod_eq_zero, Ordinal.cof_iSup_Iio_add_one, Ordinal.enum_lt_nat, Cardinal.card_typein_lt, Profinite.NobelingProof.GoodProducts.linearIndependent_iff_smaller, Cardinal.ord_eq_iInf, Ordinal.isNormal_enumOrd, Cardinal.card_typein_toType_lt, Ordinal.blsub_lt_ord, Ordinal.blsub_type, Cardinal.lift_eq_aleph1, Ordinal.principal_add_iff_zero_or_omega0_opow, Ordinal.zero_opow_le, Cardinal.ord_ofNat, OrdinalApprox.lfpApprox_add_one, Ordinal.principal_add_iff_add_lt_ne_self, Ordinal.principal_add_mul_of_principal_add, Ordinal.instOrderTopology, Ordinal.type_pEmpty, Ordinal.lt_blsub, Ordinal.IsNormal.le_set', Ordinal.max_eq_zero, Ordinal.bddAbove_range, Ordinal.cof_lsub_def_nonempty, Ordinal.bsup_eq_sup, Ordinal.principal_add_of_principal_mul, Ordinal.natCast_add_of_omega0_le, Ordinal.one_add_natCast, Ordinal.lsub_eq_lsub, Ordinal.isPrincipal_opow_ord, Ordinal.lift_iSup_add_one_lt_of_lt_cof, Ordinal.CNF.eval_add, Ordinal.CNF.support_coeff, Ordinal.isPrincipal_add_omega0, Ordinal.accPt_subtype, Mathlib.Meta.NormNum.isNat_ordinalLT_false, Ordinal.epsilon_succ_eq_nfp, Ordinal.CNF.of_le_one, Cardinal.preBeth_lt_preBeth, Ordinal.veblen_add_one, Ordinal.card_opow_le_of_omega0_le_right, Ordinal.lt_div, ONote.le_def, Cardinal.preBeth_add_one, Ordinal.IsPrincipal.iSup, ONote.repr_opow_aux₁, Ordinal.veblenWith_lt_veblenWith_iff_right, Cardinal.ord_lt_omega0, Ordinal.iSup_mul_natCast, Ordinal.mem_closure_iff_iSup, Ordinal.lt_bsup_of_limit, Ordinal.sSup_le_sSup_add_one, Ordinal.not_principal_iff, ZFSet.iUnion_vonNeumann, Ordinal.iSup_lt_ord_lift, Ordinal.IsNormal.monotone, Cardinal.aleph_max, Ordinal.isSuccLimit_of_principal_add, ZFSet.vonNeumann_injective, Ordinal.IsInitial.isPrincipal_mul, Cardinal.blsub_lt_ord_of_isRegular, Cardinal.ord_preAleph, Ordinal.CNF.coeff_of_notMem_CNF, Ordinal.lift_natCast, Ordinal.omega0_lt_omega1, Ordinal.bfamilyOfFamily_typein, Ordinal.pred_lt_iff_not_isSuccPrelimit, Ordinal.log_opow_mul_add, Profinite.NobelingProof.GoodProducts.linearIndependent_iff_sum, Ordinal.typein_enum, Ordinal.isNormal_iff_lt_succ_and_blsub_eq, Cardinal.isStrongLimit_beth, Ordinal.card_opow_omega0, ZFSet.vonNeumann_zero, Ordinal.blsub_le, Ordinal.preOmega_zero, CategoryTheory.ObjectProperty.isoClosure_strictLimitsClosureIter_eq_limitsClosure, Ordinal.gamma_zero_le_of_veblen_le, Ordinal.cof_eq_sInf_lsub, Ordinal.aleph0_le_card, Ordinal.typein_surj, Ordinal.natCast_pow, Ordinal.natCast_mul, Ordinal.mul_mod_mul, Ordinal.isInitial_succ, Ordinal.natCast_succ, PSet.rank_empty, Ordinal.type_prod_lex, Ordinal.coe_preOmega, Ordinal.veblen_zero_le_veblen_zero, Cardinal.preAleph_max, Ordinal.lift_add, Ordinal.opow_dvd_opow_iff, Ordinal.typein_injective, Ordinal.isNormal_veblen_zero, Ordinal.ord_cof_le, Cardinal.preBeth_le_preBeth, Profinite.NobelingProof.C0_projOrd, Ordinal.toZFSetIso_apply, Ordinal.le_mul_right, Ordinal.bsup_le_of_brange_subset, Ordinal.mem_range_veblen_iff_le_invVeblen₁, Ordinal.add_eq_right_iff_mul_omega0_le, Mathlib.Meta.NormNum.isNat_ordinalDiv, Ordinal.CNF.rec_zero, Ordinal.omega0_le_omega, Ordinal.bsup_lt_ord_lift, Ordinal.mem_closure_tfae, Cardinal.iSup_lt_ord_lift_of_isRegular, Ordinal.mul_add_div_mul, Ordinal.bsup_eq_blsub_or_succ_bsup_eq_blsub, Ordinal.nsmul_eq_mul, ONote.split_add_lt, OrdinalApprox.lfpApprox_mono_left, Ordinal.isInitial_zero, Ordinal.not_isSuccLimit_zero, Ordinal.bsup_id_add_one, Ordinal.natCast_opow_omega0, Ordinal.isSuccLimit_iff, Ordinal.veblen_eq_veblen_iff, Ordinal.deriv_zero, Ordinal.pred_eq_iff_isSuccPrelimit, Ordinal.exists_lt_add_of_not_isPrincipal_add, Profinite.NobelingProof.C1_projOrd, Ordinal.mod_opow_log_lt_self, Ordinal.mk_Iio_ordinal, Ordinal.bddAbove_of_small, Profinite.NobelingProof.πs_apply_apply, Cardinal.preAleph_add_one, Ordinal.card_le_nat, Ordinal.iSup'_eq_bsup, Ordinal.typein_apply, Ordinal.lsub_le_of_range_subset, Cardinal.bsup_lt_ord_lift_of_isRegular, Ordinal.pred_zero, Ordinal.nfp_add_eq_mul_omega0, Ordinal.ToType.mk_symm_apply_coe, Ordinal.mul_add_mod_self, Ordinal.deriv_eq_enumOrd, Ordinal.type_fintype, Cardinal.preAleph_le_of_isSuccPrelimit, Cardinal.range_aleph, Ordinal.mul_eq_opow_log_succ, Ordinal.deriv_id_of_nfp_id, Ordinal.bddAbove_iff_small, Cardinal.beth_limit, Cardinal.aleph0_le_preAleph, Ordinal.IsFundamentalSeq.id, Ordinal.lt_iSup_add_one, Cardinal.preAleph_succ, Ordinal.IsFundamentalSequence.monotone, Ordinal.isNormal_derivFamily, Profinite.NobelingProof.GoodProducts.square_commutes, Ordinal.strictMono_gamma, Cardinal.derivFamily_lt_ord, Ordinal.veblen_invVeblen₁_invVeblen₂, Ordinal.IsPrincipal.iterate_lt, Ordinal.enum_succ_eq_top, Ordinal.isPrincipal_add_omega, Ordinal.leftDistribClass, Ordinal.iterate_veblen_lt_gamma_zero, Ordinal.typein_surjOn, Ordinal.iSup_sequence_lt_omega_one, Ordinal.lt_omega0_opow, Ordinal.enumOrd_le_of_forall_lt, Cardinal.aleph_one_le_lift, Ordinal.cof_lift_iSup_add_one_le, Cardinal.beth_add_one, Ordinal.IsNormal.eq_iff_zero_and_succ, OrdinalApprox.exists_gfpApprox_eq_gfpApprox, PSet.rank_powerset, Ordinal.blsub_pos, Ordinal.isInitial_omega, Ordinal.epsilon0_lt_gamma, ONote.repr_opow, Ordinal.omega0_lt_epsilon, Cardinal.preBeth_succ, Mathlib.Meta.NormNum.isNat_ordinalLE_true, IsWellFounded.rank_eq, Ordinal.iSup_typein_limit, Ordinal.log_eq_iff, Cardinal.not_injective_limitation_set, Ordinal.veblen_le_veblen_iff, Ordinal.bsup_succ_of_mono, Ordinal.IsInitial.isPrincipal_add, Ordinal.bsup_congr, Ordinal.principal_one_iff, Ordinal.enumOrd_le_of_subset, Cardinal.ord_nat, Ordinal.eq_zero_or_pos, Ordinal.small_Icc, Ordinal.isSuccPrelimit_type_lt_iff, Ordinal.zero_div, Ordinal.veblen_le_veblen_iff_right, Ordinal.ofNat_lt_card, Ordinal.isNormal_gamma, Ordinal.isSuccLimit_mul, Ordinal.CNF.foldr, Ordinal.natCast_lt_omega0, Cardinal.lift_le_aleph1, Ordinal.derivFamily_limit, Cardinal.gc_ord_card, ZFSet.rank_range, Profinite.NobelingProof.contained_C1, Cardinal.derivFamily_lt_ord_lift, Ordinal.enumOrd_succ_le, Ordinal.lift_zero, Ordinal.bsup_eq_blsub_iff_lt_bsup, Ordinal.type_lt_ordinal, Ordinal.le_preOmega_self, Ordinal.not_lt_enum_ord_mk_min_compl, Ordinal.isSuccPrelimit_lift, Cardinal.succ_preAleph, Ordinal.iSup_ord, WellFoundedLT.rank_strictMono, ZFSet.rank_insert, Ordinal.CNF.coeff_one_left, Ordinal.enum_le_enum, Cardinal.preAleph_zero, Ordinal.lsub_le_iff, Ordinal.sup_eq_sup, Ordinal.lt_opow_iff_log_lt', Ordinal.lt_wf, Mathlib.Meta.NormNum.isNat_ordinalSub, Ordinal.sSup_lt_of_lt_cof, Ordinal.log_mod_opow_log_lt_log_self, Ordinal.card_succ, Cardinal.IsRegular.cof_omega_eq, Cardinal.ord_one, Ordinal.sub_le_self, Profinite.NobelingProof.Products.lt_ord_of_lt, Ordinal.isPrincipal_mul_of_le_two, Ordinal.mem_range_veblen, Ordinal.aleph0_le_cof, Ordinal.le_iSup, Ordinal.card_omega, Profinite.NobelingProof.isClosed_proj, Ordinal.iSup_eq_zero_iff, Ordinal.isPrincipal_add_iff_add_left_eq_self, Ordinal.card_typein, Ordinal.lift_typein_top, Cardinal.IsRegular.ord_pos, Ordinal.typein_ordinal, Ordinal.veblen_lt_veblen_veblen_iff, Ordinal.epsilon0_eq_nfp, Ordinal.epsilon_zero_eq_nfp, Ordinal.apply_le_nfpFamily, Ordinal.le_bsup, Cardinal.lift_aleph, Ordinal.type_pUnit, Ordinal.div_pos, PSet.rank_singleton, Ordinal.exists_lt_add_of_not_principal_add, Ordinal.CNF.coeff_zero_right, Ordinal.IsClosedBelow.sInter, Ordinal.ofNat_le_card, Ordinal.principal_add_one, Ordinal.veblen_mem_range_opow, Ordinal.omega0_le_preOmega_iff, Ordinal.IsFundamentalSequence.ord_cof, Ordinal.invVeblen₂_le, OrdinalApprox.gfpApprox_mono_mid, Ordinal.isSuccPrelimit_iff_omega0_dvd, Ordinal.mulLeftMono, Ordinal.card_opow_eq_of_omega0_le_right, Ordinal.deriv_zero_left, Ordinal.le_sub_of_add_le, Ordinal.mem_range_gamma, Ordinal.sup_eq_bsup', Ordinal.instNoMaxOrder, Profinite.NobelingProof.swapTrue_mem_C1, Ordinal.CNF.one_left, Ordinal.bsup_succ_le_blsub, Ordinal.nfpFamily_monotone, Ordinal.lift_preOmega, Ordinal.succ_iSup_eq_lsub_iff, Ordinal.omega0_lt_gamma, Cardinal.aleph0_le_aleph, Ordinal.zero_lt_card, Ordinal.CNF.rec_pos, Ordinal.lift_type_le, Ordinal.IsInitial.card_le_card, Ordinal.le_enumOrd_self, Cardinal.preAleph_le_preAleph, Ordinal.card_eq_nat, Ordinal.small_Ioc, Ordinal.omega_strictMono, Ordinal.card_eq_one, Ordinal.principal_mul_two, Ordinal.lt_opow_of_log_lt, Ordinal.gamma0_eq_nfp, Ordinal.deriv_mul_eq_opow_omega0_mul, Ordinal.isPrincipal_mul_omega, Ordinal.opow_natCast, Ordinal.lt_pred_iff_succ_lt, Ordinal.div_le_of_le_mul, Ordinal.principal_mul_iff_mul_left_eq, ONote.fundamentalSequenceProp_inl_some, Ordinal.veblenWith_one, Ordinal.sup_eq_lsub, Ordinal.veblenWith_le_veblenWith_iff, Ordinal.lift_card_sInf_compl_le, Ordinal.blsub_succ_of_mono, Ordinal.nfp_zero_left, Ordinal.opow_le_opow, Ordinal.iSup_eq_lsub_iff_lt_iSup, Ordinal.cmp_veblenWith, Ordinal.lsub_typein, ONote.NF.of_dvd_omega0_opow, Ordinal.lt_gamma_zero, Cardinal.aleph0_lt_aleph_one, Ordinal.IsNormal.strictMono, Ordinal.veblenWith_lt_veblenWith_veblenWith_iff, Ordinal.lt_bsup_of_ne_bsup, RelEmbedding.ordinal_type_le, Ordinal.CNF.snd_pos, Ordinal.opow_zero, Ordinal.opow_lt_veblen_opow_iff, Ordinal.principal_add_omega0, Ordinal.mod_zero, Ordinal.forall_lt_mul, Ordinal.IsNormal.map_iSup_of_bddAbove, Ordinal.mul_div_cancel, Ordinal.nfp_monotone, Cardinal.preBeth_limit, Ordinal.bsup_le_iff, Ordinal.enum_zero_eq_bot, Ordinal.veblenWith_succ, Ordinal.two_opow_log_add, Ordinal.lt_veblen_iff_invVeblen₁_le, Ordinal.isInitial_natCast, Cardinal.nfpFamily_lt_ord_lift_of_isRegular, Ordinal.isSuccLimit_add, Ordinal.natCast_mod_omega0, Ordinal.isEmpty_toType_zero, Cardinal.preAleph_lt_preAleph, Ordinal.univ_id, Ordinal.sub_eq_of_add_eq, Ordinal.gamma_lt_gamma, Ordinal.add_mul_of_isSuccLimit, Ordinal.lt_iSup_iff, Cardinal.aleph_mul_aleph, Ordinal.card_mul, Ordinal.IsNormal.map_sSup_of_bddAbove, Ordinal.CNF.lt_snd, Cardinal.beth_strictMono, Ordinal.nfp_id, Ordinal.le_log_of_opow_le, Ordinal.iSup_add_one_le_iff, Ordinal.card_opow_le_of_omega0_le_left, Ordinal.bsup'_eq_iSup, Ordinal.mul_le_right_iff_opow_omega0_dvd, Cardinal.isRegular_aleph_one, Ordinal.IsNormal.apply_omega0, ZFSet.mem_vonNeumann_succ, Ordinal.mul_sub, Ordinal.instAddLeftReflectLE, Ordinal.nonempty_compl_range, Ordinal.iSup_add_one, ZFSet.rank_le_iff, Ordinal.le_lift_iff, Mathlib.Meta.NormNum.isNat_ordinalOPow, Ordinal.iSup_Iio_eq_bsup, Ordinal.IsFundamentalSequence.succ, Ordinal.iSup_Iio_add_one, Profinite.NobelingProof.contained_proj, Ordinal.IsNormal.fp_iff_deriv, Ordinal.enumOrd_surjective, Cardinal.lift_le_aleph_one, Ordinal.add_omega0, Ordinal.nfpFamily_le_iff, MeasurableSpace.generateMeasurableRec_mono, Ordinal.iSup_eq_of_range_eq, ONote.repr_le_repr, Ordinal.card_opow_eq_of_omega0_le_left, Ordinal.one_le_iff_ne_zero, ZFSet.rank_iUnion, Ordinal.veblenWith_injective, Ordinal.IsNormal.map_sSup, Cardinal.ord_injective, Ordinal.veblen_lt_veblen_iff, Ordinal.instIsEmptyIioZero, Ordinal.lt_nfp_iff, Ordinal.opow_add_one, CategoryTheory.ObjectProperty.strictLimitsClosureStep_strictLimitsClosureIter_eq_self, ONote.fundamentalSequenceProp_inr, Ordinal.mem_brange, Ordinal.enumOrd_lt_enumOrd, Ordinal.toZFSet_injective, Ordinal.veblenWith_zero, OrdinalApprox.gfpApprox_mono_left, Ordinal.invVeblen₁_lt_iff, Ordinal.type_empty, ONote.repr_lt_repr, Ordinal.iSup_sequence_lt_omega1, Ordinal.principal_mul_omega0_opow_opow, Ordinal.preOmega_strictMono, Ordinal.type_unit, Ordinal.veblenWith_zero_le_veblenWith_zero, ZFSet.mem_vonNeumann, Ordinal.bsup_eq_iSup, Ordinal.principal_opow_omega, Ordinal.enumOrd_isNormal_iff_isClosed, PSet.lt_rank_iff, Ordinal.derivFamily_zero, Ordinal.card_preOmega, Ordinal.lt_opow_of_isSuccLimit, Ordinal.omega0_opow_mul_nat_lt, Ordinal.epsilon0_le_of_omega0_opow_le, Ordinal.lsub_le_succ_iSup, Ordinal.one_lt_of_isSuccLimit, Ordinal.typein_lt_self, OrdinalApprox.exists_lfpApprox_eq_lfpApprox, Ordinal.lt_veblen, Ordinal.toZFSet_subset_toZFSet_iff, Ordinal.type_eq_one_of_unique, Ordinal.nat_lt_omega0, Ordinal.isNormal_veblenWith', Ordinal.CNF.ne_zero, Ordinal.add_sub_cancel_of_le, Ordinal.IsAcc.forall_lt, Ordinal.invVeblen₂_lt_iff, Profinite.NobelingProof.GoodProducts.sum_equiv_comp_eval_eq_elim, Ordinal.IsInitial.le_ord_iff_card_le, Ordinal.CNF.eval_zero_right, Ordinal.pred_add_one, Ordinal.IsFundamentalSequence.lt, Ordinal.isSuccLimit_of_isPrincipal_mul, Cardinal.aleph1_eq_lift, ZFSet.rank_sUnion_le, Ordinal.nfp_le, Ordinal.lt_mul_iff_of_isSuccLimit, Ordinal.relIso_enum', Cardinal.card_surjective, Ordinal.mem_range_deriv, Ordinal.lt_lsub, Ordinal.mod_mod, Ordinal.card_nat, Ordinal.type_sum_lex, Ordinal.bsup_eq_blsub, Ordinal.mem_iff_iSup_of_isClosed, Ordinal.IsInitial.principal_add, Ordinal.mem_range_veblenWith, Ordinal.sInf_compl_lt_ord_succ, Cardinal.beth_eq_preBeth, Ordinal.add_omega0_opow, Ordinal.principal_add_of_principal_mul_opow, Cardinal.ord_strictMono, Ordinal.add_mul_succ, Cardinal.preAleph_le_of_strictMono, Cardinal.preAleph_le_preBeth, MeasurableSpace.generateMeasurableRec_omega_one, Ordinal.CNF.opow_mul_add, ONote.repr_ofNat, Cardinal.ord_lt_ord, Ordinal.blsub_const, Ordinal.mul_add_mod_mul, Ordinal.bsup_lt_ord, Ordinal.bsup_not_succ_of_ne_bsup, Ordinal.isPrincipal_mul_iff_le_two_or_omega0_opow_opow, ZFSet.rank_lt_of_mem, Ordinal.isClosed_iff_iSup, Ordinal.enumOrd_univ, Ordinal.small_Ioo, Cardinal.preAleph_pos, Ordinal.bsup_eq_sup', Cardinal.beth_lt_beth, Ordinal.isSuccLimit_mul_right, Ordinal.ToType.mk_apply, IsWellFounded.mem_range_rank_of_le, Ordinal.lift_iSup_lt_of_lt_cof, Ordinal.CNF.eval_single_add, Ordinal.opow_mul_lt_opow, Ordinal.blsub_one, Ordinal.small_Iio, Ordinal.typein_lt_nat, Profinite.NobelingProof.Products.isGood_mono, Ordinal.cof_pos, Ordinal.isSuccPrelimit_mul_left, Profinite.NobelingProof.CC_comp_zero, Cardinal.omega0_lt_ord, Ordinal.typein_one_toType, Ordinal.id_le_enumOrd, Ordinal.succ_pos, Ordinal.add_sub_add_cancel, Ordinal.lsub_notMem_range, Ordinal.apply_lt_nfpFamily, Ordinal.IsInitial.isPrincipal_opow, NONote.repr_opow, Ordinal.IsFundamentalSeq.comp, Ordinal.opow_lt_opow_iff_right, Ordinal.bsup_eq_zero_iff, ONote.repr_opow_aux₂, Ordinal.isEmpty_toType_iff, Ordinal.canonicallyOrderedAdd, Ordinal.bsup_le_blsub, Ordinal.cof_eq_one_iff, Ordinal.toZFSet_monotone, Ordinal.mem_range_preOmega_iff, Ordinal.sup_typein_limit, Profinite.NobelingProof.CC_exact, Ordinal.omega_max, Ordinal.CNF.fst_le_log, Ordinal.mul_le_iff_le_div, Profinite.NobelingProof.Products.prop_of_isGood_of_contained, not_surjective_of_ordinal, Cardinal.aleph_eq_preAleph, Ordinal.omega_pos, Ordinal.invVeblen₂_lt, Ordinal.lt_omega0, Ordinal.blsub_eq_lsub, Ordinal.enumOrd_injective, Ordinal.le_add_right, Ordinal.preOmega_le_of_forall_lt, Cardinal.isRegular_preAleph_add_one, Ordinal.isPrincipal_mul_one, Ordinal.lt_invVeblen₂_iff, Ordinal.add_le_iff, Cardinal.preBeth_strictMono, Ordinal.veblen_right_strictMono, Ordinal.toType_empty_iff_eq_zero, OrdinalApprox.lfp_mem_range_lfpApprox, Ordinal.isPrincipal_add_mul_of_isPrincipal_add, Ordinal.CNF.coeff_of_le_one, Cardinal.isNormal_beth, Ordinal.mul_omega0_opow_opow, Ordinal.typein_le_typein', Ordinal.succ_pred_eq_iff_not_isSuccPrelimit, Ordinal.isNormal_add_right, Ordinal.veblen_eq_opow_iff, Ordinal.toZFSet_zero, Cardinal.aleph1_le_mk, CountableInterFilter.toCardinalInterFilter, Ordinal.mod_mod_of_dvd, Cardinal.aleph_one_eq_lift, Ordinal.one_lt_opow, Ordinal.enum_inj, Ordinal.principal_add_omega0_opow, Ordinal.sup_eq_lsub_or_sup_succ_eq_lsub, Profinite.NobelingProof.injective_πs, Cardinal.aleph_toENat, Ordinal.mod_eq_zero_of_dvd, Ordinal.bddAbove_range_comp, Cardinal.preBeth_mono, Cardinal.countable_iff_lt_aleph_one, Ordinal.veblen_succ, Ordinal.nfp_mul_one, Ordinal.type_Iio_lt, Ordinal.instAddLeftMono, Ordinal.opow_succ, Ordinal.cof_eq_zero, Ordinal.veblen_zero_apply, Ordinal.deriv_zero_right, Ordinal.add_one_eq_succ, MeasurableSpace.generateMeasurableRec_of_omega1_le, Ordinal.card_lt_aleph0, Ordinal.nfpFamily_le_apply, Ordinal.IsAcc.pos, Ordinal.blsub_eq_lsub', Ordinal.IsNormal.le_iff_deriv, Ordinal.lsub_le, Profinite.NobelingProof.coe_πs', Ordinal.isPrincipal_mul_two, Ordinal.omega0_le_of_isSuccLimit, Ordinal.blsub_eq_zero_iff, Ordinal.opow_le_iff_le_log, Ordinal.nfpFamily_le, Profinite.NobelingProof.GoodProducts.range_equiv_smaller_toFun_bijective, ZFSet.rank_pair, ZFSet.vonNeumann_of_isSuccPrelimit, Ordinal.add_le_add_iff_right, Ordinal.le_mul_left, Ordinal.IsPrincipal.sSup, MeasurableSpace.generateMeasurableRec_omega1, Cardinal.isNormal_preBeth, ZFSet.IsOrdinal.rank_lt_iff_mem, Cardinal.aleph_limit, Ordinal.toZFSet_succ, Ordinal.nfp_add_zero, Cardinal.aleph_one_le_iff, Ordinal.typein_lt_fin, Ordinal.preOmega_le_preOmega, Ordinal.deriv_eq_id_of_nfp_eq_id, Ordinal.mul_two, Ordinal.veblenWith_eq_veblenWith_iff, Ordinal.epsilon_pos, Ordinal.opow_lt_opow_left_of_succ, Cardinal.nfp_lt_ord_of_isRegular, Ordinal.isPrincipal_add_of_le_one, Ordinal.sub_lt_of_lt_add, Ordinal.mem_range_derivFamily, Ordinal.lift_omega, Cardinal.isNormal_ord, Ordinal.preOmega_omega0, Cardinal.deriv_lt_ord, Ordinal.card_lt_ofNat, Ordinal.iSup_le_iSup_add_one, Ordinal.iSup_le_iff, Cardinal.aleph0_mul_aleph, Ordinal.preOmega_lt_preOmega, Ordinal.left_le_veblen, Cardinal.lift_lt_aleph1, Cardinal.iSup_lt_ord_of_isRegular, Cardinal.ord_card_le, Ordinal.iSup_eq_lsub, Ordinal.not_bddAbove_compl_of_small, Ordinal.log_pos, Ordinal.max_zero_right, Cardinal.mk_biUnion_le_of_le, Ordinal.veblen_lt_veblen_iff_right, Ordinal.Principal.iterate_lt, Besicovitch.TauPackage.lastStep_nonempty, NONote.repr_sub, Ordinal.iSup_add_one_le, ONote.scale_opowAux, Ordinal.opow_right_inj, Ordinal.lt_bsup, Ordinal.iSup_eq_lsub_iff, Ordinal.veblen_injective, Ordinal.blsub_zero, Ordinal.range_enumOrd, Ordinal.cof_iSup_add_one, Ordinal.lsub_empty, Ordinal.iSup_natCast, Ordinal.mul_div_mul_cancel, ZFSet.rank_singleton, Ordinal.add_le_right_iff_mul_omega0_le, Ordinal.iterate_omega0_opow_lt_epsilon_zero, Ordinal.lsub_eq_blsub, Ordinal.lift_ofNat, Ordinal.isPrincipal_add_omega0_opow, Ordinal.isPrincipal_mul_iff_mul_left_eq, Cardinal.isSuccLimit_omega, Ordinal.isSuccLimit_mul_left, Mathlib.Meta.NormNum.isNat_ordinalLE_false, Ordinal.iSup_iterate_eq_nfp, Cardinal.ord_le_omega0, Ordinal.cof_omega, Ordinal.self_le_succ_pred, Cardinal.aleph_one_lt_lift, Ordinal.typein_inj, Ordinal.bsup_eq_bsup, Ordinal.lt_iSup_add_one_iff, Ordinal.veblenWith_of_ne_zero, Ordinal.isSuccPrelimit_type_lt, Ordinal.isPrincipal_add_of_isPrincipal_mul_opow, Ordinal.principal_add_opow_of_principal_add, Ordinal.sub_ne_zero_iff_lt, Ordinal.type_eq_zero_iff_isEmpty, Ordinal.le_one_iff, Ordinal.lift_add_one, Ordinal.natCast_lt_epsilon, InitialSeg.ordinal_type_le, Ordinal.principal_swap_iff, Ordinal.apply_omega0_of_isNormal, Ordinal.lsub_eq_zero_iff, Ordinal.lift_mul, Ordinal.instAddRightReflectLT, Ordinal.familyOfBFamily'_enum, Ordinal.bddAbove_image, Cardinal.mk_iUnion_Ordinal_lift_le_of_le, Ordinal.zero_opow, Ordinal.lt_veblen_invVeblen₁, Ordinal.mod_eq_of_lt, Ordinal.invVeblen₁_epsilon, Ordinal.preOmega_natCast, Ordinal.blsub_le_bsup_succ, Cardinal.preBeth_pos, Ordinal.IsNormal.le_iff_eq, ONote.nf_repr_split, Ordinal.card_opow_le, Ordinal.enum_zero_le', Ordinal.isSuccLimit_of_principal_mul, Ordinal.toZFSetIso_symm_apply, Cardinal.ord_le_type, Cardinal.preBeth_nat, Ordinal.isSuccLimit_of_mem_frontier, Ordinal.lsub_unique, Ordinal.lt_omega0_omega0_opow, Ordinal.familyOfBFamily_enum, Ordinal.opow_pos, Ordinal.IsFundamentalSeq.iSup_add_one_eq, Ordinal.opow_le_of_le_log, Cardinal.mem_range_aleph_iff, Ordinal.lsub_le_sup_succ, Cardinal.ord_mono, Cardinal.aleph_lt_aleph, List.Sorted.lt_ord_of_lt, Ordinal.instIsLeftCancelAdd, Ordinal.mul_omega0, Ordinal.principal_mul_one, Cardinal.mk_biUnion_le_of_le_lift, Ordinal.IsFundamentalSeq.isCofinal_range, Ordinal.fp_iff_deriv, ZFSet.vonNeumann_succ, Ordinal.isPrincipal_opow_omega, Ordinal.succ_iSup_le_lsub_iff, Ordinal.toZFSet_mem_toZFSet_iff, Ordinal.IsFundamentalSeq.comp_isNormal, Ordinal.le_div, Ordinal.nfp_le_of_principal, Ordinal.IsNormal.le_set, Ordinal.invVeblen₁_eq_iff, Ordinal.veblenWith_pos, Ordinal.natCast_lt_of_isSuccLimit, Ordinal.IsNormal.apply_of_isSuccLimit, Ordinal.IsFundamentalSequence.strict_mono, Ordinal.principal_iff_of_monotone, Ordinal.small_Ico, Ordinal.lsub_sum, Ordinal.iSup_lt_ord, NONote.repr_mul, Profinite.NobelingProof.Products.eval_πs_image, Ordinal.IsInitial.mem_range_preOmega, Cardinal.lt_ord, Ordinal.nhds_eq_pure, Ordinal.natCast_add_omega0, Ordinal.cof_iSup_le, ZFSet.rank_union, Ordinal.IsNormal.trans, Ordinal.deriv_add_one, Ordinal.lsub_lt_ord_lift, Cardinal.aleph_toNat, Ordinal.veblen_zero_inj, Ordinal.range_preOmega, Ordinal.opow_le_iff_le_log', Ordinal.opow_le_opow_left, Ordinal.one_lt_omega0, Ordinal.sub_sub, Ordinal.preOmega_max, Ordinal.one_le_card, Ordinal.right_eq_zero_of_add_eq_zero, Ordinal.veblen_zero_strictMono, Ordinal.le_add_sub, Ordinal.right_le_veblen, Ordinal.isNormal_veblenWith_zero, Cardinal.succ_aleph0, Ordinal.card_iSup_le_sum_card, Ordinal.opow_le_of_isSuccLimit, Ordinal.CNF.zero_right, Ordinal.iterate_lt_nfp, Cardinal.le_ord_iff_card_le_of_lt_aleph0, ZFSet.le_succ_rank_sUnion, Ordinal.IsFundamentalSequence.zero, Ordinal.relIso_enum, Ordinal.le_iff_deriv, Ordinal.natCast_lt_gamma, Ordinal.type_fin, Profinite.NobelingProof.GoodProducts.union, PSet.rank_pair, Ordinal.le_omega_self, Ordinal.mod_def, ONote.repr_sub, Cardinal.aleph_zero, Ordinal.lift_le, Ordinal.bddAbove_add_one_image_iff, Ordinal.isSuccLimit_iff_omega0_dvd, Ordinal.gamma_succ_eq_nfp, Ordinal.uncountable, Ordinal.enumOrd_strictMono, Ordinal.left_le_opow, Ordinal.principal_zero, Ordinal.lt_lsub_iff, Ordinal.veblenWith_left_monotone, Ordinal.eq_enumOrd, ONote.NFBelow.repr_lt, Ordinal.le_of_dvd, Ordinal.isPrincipal_mul_ord, Cardinal.cof_omega_add_one, Ordinal.le_nfpFamily, Ordinal.zero_mod, Ordinal.principal_mul_iff_le_two_or_omega0_opow_opow, Ordinal.IsFundamentalSeq.iSup_eq, Ordinal.lt_epsilon0, Cardinal.aleph_add_one, Ordinal.veblen_pos, Ordinal.div_one, Ordinal.omega0_opow_epsilon, Ordinal.IsNormal.veblenWith_zero, Ordinal.instCharZero, Ordinal.div_zero, Cardinal.lift_preAleph, Ordinal.omega_eq_preOmega, Cardinal.lift_lt_aleph_one, Ordinal.toZFSet_add_one, Ordinal.monotone_gamma, Cardinal.isRegular_aleph_add_one, Ordinal.mul_div_le, ONote.nfBelow_ofNat, Ordinal.natCast_div, Ordinal.instNeZeroOne, Ordinal.veblenWith_mem_range, Ordinal.top_typein, Ordinal.lt_opow_iff_log_lt, Ordinal.isSuccLimit_sub, Profinite.NobelingProof.Products.head_lt_ord_of_isGood, Ordinal.sInf_empty, Ordinal.derivFamily_eq_enumOrd, Ordinal.sup_typein_succ, Ordinal.mul_le_iff_of_isSuccLimit, Ordinal.liftPrincipalSeg_top, Ordinal.enum_type, Ordinal.mul_omega0_dvd, Ordinal.right_le_veblenWith, Ordinal.opow_eq_zero, Ordinal.one_toType_eq, Ordinal.isNormal_omega, Cardinal.isRegular_preAleph_succ, Ordinal.not_isPrincipal_iff_of_monotone, Ordinal.one_lt_cof_iff, MeasurableSpace.generateMeasurable_eq_rec, Profinite.NobelingProof.succ_mono, Ordinal.apply_lt_veblenWith_apply_iff, Cardinal.succ_aleph, Ordinal.card_eq_ofNat, Ordinal.log_one_right, Ordinal.succ_lt_iSup_of_ne_iSup, Ordinal.lt_mul_iff, Ordinal.ord_mk_le_type, Ordinal.veblen_left_monotone
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