Ordinal 📖 | CompOp | 992 mathmath: Cardinal.lt_ord_succ_card, Ordinal.iSup_eq_iSup, Ordinal.isSuccLimit_lift, PSet.rank_le_iff, Ordinal.opow_mul, Ordinal.iSup_eq_bsup, Ordinal.succ_nmul, Cardinal.aleph_le_beth, univLE_iff_exists_embedding, Ordinal.lt_omega0_opow_succ, Ordinal.toNimber_eq_zero, Ordinal.isNormal_iff_strictMono_limit, Cardinal.mk_iUnion_Ordinal_le_of_le, Ordinal.principal_add_omega, Ordinal.lift_card_iSup_le_sum_card, SetTheory.PGame.default_nim_one_rightMoves_eq, Ordinal.zero_nadd, Acc.rank_eq, ONote.repr_one, Ordinal.toPGame_lf_iff, Ordinal.IsNormal.refl, Ordinal.sup_eq_lsub_iff_lt_sup, ZFSet.IsOrdinal.rank_le_iff_subset, Ordinal.opow_one, SetTheory.Game.birthday_add_le, OrdinalApprox.lfpApprox_mono_mid, ZFSet.subset_vonNeumann, Ordinal.sub_zero, Ordinal.lift_type_lt, Ordinal.sInf_compl_lt_lift_ord_succ, Ordinal.typein_le_typein, Ordinal.pred_succ, Ordinal.lift_one, Ordinal.mem_range_typein_iff, Ordinal.IsAcc.isSuccLimit, Ordinal.gamma_le_gamma, Ordinal.add_succ, Ordinal.max_zero_left, Cardinal.isStrongLimit_preBeth, Ordinal.card_le_ofNat, Ordinal.Iio_one_default_eq, Ordinal.lsub_pos, Ordinal.nmul_le_iff₃, Ordinal.sup_eq_lsub_iff_succ, Cardinal.aleph_succ, Ordinal.one_nmul, Ordinal.isInitialIso_apply, Cardinal.preBeth_eq_zero, Ordinal.blsub_congr, Cardinal.aleph_pos, Ordinal.liftInitialSeg_coe, Ordinal.add_right_cancel, Ordinal.iSup_typein_succ, ONote.NFBelow_zero, Ordinal.existsAddOfLE, Ordinal.mul_le_nmul, 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.nadd_one_nmul, OrdinalApprox.gfp_mem_range_gfpApprox, Ordinal.le_invVeblen₂_iff, Ordinal.antisymm, Ordinal.toNatOrdinal_eq_one, Ordinal.type_lt_iff, Ordinal.succ_one, Ordinal.sub_eq_zero_iff_le, Ordinal.mod_self, 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, Ordinal.instAddRightMono, Profinite.NobelingProof.coe_πs, Ordinal.lift_lt, SetTheory.Game.birthday_sub_le, ZFSet.lt_rank_iff, Ordinal.mod_le, Cardinal.lift_eq_aleph_one, SetTheory.PGame.grundyValue_eq_iff_equiv_nim, Ordinal.not_lt_zero, Ordinal.gamma_zero_eq_nfp, Ordinal.card_le_aleph, Ordinal.isAcc_iff, Ordinal.invVeblen₂_zero, SetTheory.PGame.birthday_one, Ordinal.omega_zero, Ordinal.toNimber_symm_eq, Ordinal.bsup_id_succ, Ordinal.liftPrincipalSeg_top', Ordinal.sup_succ_le_lsub, Ordinal.iSup_le_lsub, Ordinal.card_iSup_Iio_le_sum_card, Ordinal.isOpen_singleton_iff, Ordinal.card_one, SetTheory.Game.birthday_natCast, NatOrdinal.toOrdinal_min, Ordinal.enum_symm_apply_coe, Ordinal.toGame_lt_iff, Ordinal.IsNormal.lt_iff, Ordinal.CNF_foldr, SetTheory.PGame.grundyValue_nim_add_nim, Nimber.succ_def, 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.enum_lt_enum, Ordinal.isSuccLimit_omega0, Ordinal.isInitialIso_symm_apply_coe, Ordinal.isInitial_preOmega, Ordinal.add_log_le_log_mul, Ordinal.card_zero, SetTheory.PGame.isEmpty_nim_zero_leftMoves, Cardinal.isNormal_preAleph, Ordinal.invVeblen₁_zero, Cardinal.bddAbove_ord_image_iff, Ordinal.epsilon_eq_deriv, SetTheory.PGame.birthday_moveLeft_lt, Ordinal.epsilon_zero_lt_gamma, Ordinal.log_zero_right, Ordinal.div_le, Ordinal.one_toPGame_leftMoves_default_eq, Ordinal.toGame_one, Cardinal.preAleph_nat, PSet.rank_mono, Ordinal.log_zero_left, Ordinal.toNimber_min, Ordinal.nmul_add_one, Ordinal.toPGame_zero, Ordinal.le_add_left, 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.principal_mul_omega0, Ordinal.div_opow_log_pos, Ordinal.one_add_ofNat, Ordinal.nadd_le_nadd_iff_right, Ordinal.isOpen_iff, Ordinal.CNF.zero_left, Ordinal.log_one_left, Ordinal.card_sInf_range_compl_le_lift, Nimber.toOrdinal_max, Ordinal.nat_nadd, not_surjective_of_ordinal_of_small, Cardinal.ord_eq_zero, Cardinal.preAleph_le_aleph, Ordinal.CNF.sorted, Ordinal.type_le_iff, Ordinal.limitRecOn_zero, Ordinal.isClosedBelow_iff, Ordinal.opow_mul_add_pos, Ordinal.log_le_self, Ordinal.Principal.sSup, Ordinal.coe_toZFSet, Ordinal.principal_opow_omega0, Ordinal.typein_top, NONote.repr_add, Nimber.toOrdinal_min, Ordinal.invVeblen₂_le_iff, Ordinal.enum_le_enum', SetTheory.PGame.nim_one_equiv, Ordinal.div_self, Ordinal.deriv_succ, Ordinal.bfamilyOfFamily'_typein, Ordinal.invVeblen₁_le, Cardinal.aleph_one_le_continuum, WellFoundedGT.rank_strictAnti, NatOrdinal.succ_def, Ordinal.CNF.coeff_zero_apply, Ordinal.nmul_nadd_one, Ordinal.nadd_le_nadd_iff_left, Ordinal.succ_zero, Ordinal.card_le_preAleph, Cardinal.aleph_mul_aleph0, Ordinal.mem_closure_iff_bsup, Ordinal.card_omega0_opow, Ordinal.natCast_mul_omega0, ONote.split_dvd, SetTheory.PGame.toRightMovesNim_one_symm, Profinite.NobelingProof.GoodProducts.smaller_factorization, Cardinal.preBeth_one, Ordinal.lt_nfpFamily_iff, Ordinal.zero_opow', Ordinal.omega0_pos, Ordinal.isClosed_iff_bsup, Ordinal.zero_sub, Ordinal.card_sInf_range_compl_le, Ordinal.isEmpty_zero_toPGame_leftMoves, Ordinal.not_bddAbove_principal, Ordinal.natCast_sub, Ordinal.CNF_ne_zero, Cardinal.univ_id, Cardinal.card_le_iff, Ordinal.isNormal_veblen, not_small_ordinal, Ordinal.sSup_eq_bsup, SetTheory.PGame.short_birthday, Ordinal.liftPrincipalSeg_coe, NatOrdinal.bot_eq_zero, Besicovitch.TauPackage.monotone_iUnionUpTo, Ordinal.bsup_succ_eq_blsub, Ordinal.opow_log_le_self, Cardinal.aleph_add_aleph, Ordinal.le_nadd_self, Ordinal.one_add_omega0, Ordinal.instZeroLEOneClass, Ordinal.iSup_add_nat, Ordinal.lsub_const, Ordinal.lt_one_iff_zero, Ordinal.nmul_succ, Ordinal.toNatOrdinal_min, Ordinal.isSuccLimit_add_iff, Cardinal.preAleph_omega0, Ordinal.lt_gamma0, Ordinal.foldr_le_nfpFamily, Profinite.NobelingProof.GoodProducts.P0, Ordinal.bot_eq_zero, 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, SetTheory.Game.birthday_zero, Ordinal.mem_range_omega_iff, Ordinal.nat_le_card, Ordinal.mem_toZFSet_iff, Ordinal.zero_CNF, SetTheory.PGame.lt_birthday_iff, ZFSet.rank_mono, Ordinal.mem_range_lift_of_card_le, Acc.rank_lt_of_rel, Ordinal.mul_mod, Cardinal.lt_omega_iff_card_lt, SetTheory.Game.birthday_one, Ordinal.principal_mul_ord, ONote.lt_def, ONote.oadd_mul_nfBelow, Ordinal.veblen_zero_lt_veblen_zero, Ordinal.natCast_opow, Ordinal.opow_one_add, ZFSet.isOrdinal_iff_mem_range_toZFSet, Cardinal.le_preAleph_ord, Cardinal.aleph1_le_lift, Ordinal.typein_lt_type, PSet.rank_insert, Ordinal.toZFSet_strictMono, Ordinal.card_le_one, Ordinal.lt_sub, Ordinal.lift_succ, Ordinal.smul_eq_mul, Ordinal.veblen_of_ne_zero, Ordinal.iSup_eq_lsub_or_succ_iSup_eq_lsub, Ordinal.sup_succ_eq_lsub, Ordinal.CNFRec_zero, Ordinal.veblen_opow_eq_opow_iff, Ordinal.type_le_iff', Ordinal.toPGame_one, Ordinal.sSup_ord, Cardinal.le_aleph_ord, ONote.NFBelow.lt, Ordinal.IsInitial.card_lt_card, OrdinalApprox.gfpApprox_add_one, NatOrdinal.toOrdinal_max, Ordinal.typein_lt_typein, Ordinal.eq_nat_or_omega0_le, Ordinal.enumOrd_zero, Ordinal.iterate_veblen_lt_gamma0, SetTheory.PGame.birthday_star, cardinalInterFilter_aleph_one_iff, Ordinal.nat_lt_card, IsWellFounded.rank_lt_of_rel, Ordinal.IsClosedBelow.iInter, ZFSet.rank_powerset, Ordinal.lt_nmul_iff₃, Ordinal.iSup_mul_nat, Ordinal.lt_epsilon_zero, Ordinal.isInitial_one, Ordinal.le_zero, Ordinal.iterate_omega0_opow_lt_epsilon0, Ordinal.card_eq_zero, Ordinal.lt_nmul_iff, Ordinal.instPosMulStrictMono, Ordinal.derivFamily_succ, Ordinal.le_self_nadd, 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, Ordinal.sub_self, SetTheory.Game.birthday_ordinalToGame, Profinite.NobelingProof.contained_eq_proj, Ordinal.lsub_eq_blsub', ONote.repr_add, SetTheory.Game.le_birthday, Ordinal.iterate_le_nfp, IsWellFounded.rank_eq_typein, PSet.rank_sUnion_le, Cardinal.beth_one, Ordinal.isSuccPrelimit_zero, Ordinal.CNF_sorted, Ordinal.le_nfp, ONote.repr_scale, Ordinal.omega0_le, Ordinal.bsup_eq_blsub_iff_succ, ONote.repr_zero, SetTheory.PGame.moveRight_nim, Ordinal.toNatOrdinal_one, Ordinal.sup_le_lsub, Ordinal.iSup_add_natCast, Ordinal.bsup_one, Cardinal.beth_le_beth, Ordinal.IsNormal.le_iff, Ordinal.nfp_mul_zero, Ordinal.mod_lt, PrincipalSeg.ordinal_type_lt, Ordinal.IsNormal.map_iSup, Ordinal.card_iSup_Iio_le_card_mul_iSup, Ordinal.zero_or_succ_or_isSuccLimit, Cardinal.preBeth_zero, Ordinal.nfp_le_iff, Cardinal.ord_aleph, SetTheory.PGame.nim_one_moveLeft, Ordinal.small_Iic, Nimber.add_nat, Ordinal.wellFoundedLT, Ordinal.card_lt_nat, Ordinal.bsup_zero, ZFSet.mem_vonNeumann', Ordinal.derivFamily_strictMono, Ordinal.nfp_zero, Ordinal.pred_surjective, ZFSet.vonNeumann_mem_vonNeumann_iff, 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, Cardinal.ord_eq_Inf, Cardinal.beth_zero, Ordinal.preOmega_ofNat, SetTheory.PGame.default_nim_one_leftMoves_eq, SetTheory.Game.birthday_eq_zero, Ordinal.invVeblen₂_gamma, Ordinal.preOmega_le_omega, Ordinal.veblen_zero, Ordinal.cof_succ, ZFSet.vonNeumann_strictMono, Ordinal.type_subrel, Ordinal.one_opow, Cardinal.isRegular_aleph_succ, Cardinal.ord_le_ord, Cardinal.beth_mono, Ordinal.gamma_pos, Ordinal.lt_lift_iff, OrdinalApprox.lfpApprox_monotone, Ordinal.principal_mul_omega, Cardinal.aleph1_lt_lift, Ordinal.isNormal_deriv, Ordinal.card_add, Ordinal.le_enum_succ, OrdinalApprox.gfpApprox_antitone, Ordinal.add_eq_zero_iff, Ordinal.type_eq_one_iff_unique, Ordinal.mem_toPSet_iff, Cardinal.isNormal_aleph, Ordinal.mul_eq_right_iff_opow_omega0_dvd, Ordinal.mul_succ, Ordinal.cmp_veblen, ONote.omega0_le_oadd, Cardinal.omega0_le_ord, Ordinal.one_toPGame_moveLeft, Ordinal.enum_typein, Ordinal.instAddLeftReflectLT, Ordinal.limitRecOn_succ, SetTheory.PGame.birthday_zero, Ordinal.sub_le, Ordinal.instAddLeftStrictMono, Ordinal.dvd_iff_mod_eq_zero, Cardinal.card_typein_lt, Profinite.NobelingProof.GoodProducts.linearIndependent_iff_smaller, Cardinal.card_typein_toType_lt, 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.instOrderTopology, Ordinal.type_pEmpty, Ordinal.max_eq_zero, Ordinal.bddAbove_range, Ordinal.cof_lsub_def_nonempty, Ordinal.bsup_eq_sup, Ordinal.one_add_natCast, NatOrdinal.toOrdinal_natCast, Ordinal.nmul_zero, Ordinal.lsub_eq_lsub, SetTheory.PGame.equiv_nim_grundyValue, Ordinal.epsilon_succ_eq_nfp, Cardinal.preBeth_lt_preBeth, Ordinal.lt_div, ONote.le_def, Cardinal.ord_lt_omega0, Ordinal.iSup_mul_natCast, Ordinal.mem_closure_iff_iSup, Ordinal.not_principal_iff, ZFSet.iUnion_vonNeumann, Ordinal.IsNormal.monotone, Cardinal.aleph_max, ZFSet.vonNeumann_injective, Ordinal.toNimber_one, Cardinal.ord_preAleph, Ordinal.lift_natCast, Ordinal.omega0_lt_omega1, Ordinal.bfamilyOfFamily_typein, Ordinal.pred_lt_iff_not_isSuccPrelimit, Ordinal.mk_toPGame, Ordinal.isNormal_iff_lt_succ_and_blsub_eq, Cardinal.isStrongLimit_beth, ZFSet.vonNeumann_zero, Ordinal.preOmega_zero, CategoryTheory.ObjectProperty.isoClosure_strictLimitsClosureIter_eq_limitsClosure, Ordinal.cof_eq_sInf_lsub, Ordinal.aleph0_le_card, 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.typein_injective, Ordinal.isNormal_veblen_zero, Ordinal.ord_cof_le, Cardinal.preBeth_le_preBeth, Ordinal.toZFSetIso_apply, Nimber.toOrdinal_eq_one, Ordinal.nadd_le_iff, Ordinal.mem_range_veblen_iff_le_invVeblen₁, Ordinal.add_eq_right_iff_mul_omega0_le, Ordinal.CNF.rec_zero, Ordinal.omega0_le_omega, Ordinal.mem_closure_tfae, Ordinal.bsup_eq_blsub_or_succ_bsup_eq_blsub, ONote.split_add_lt, OrdinalApprox.lfpApprox_mono_left, Ordinal.isInitial_zero, Ordinal.not_isSuccLimit_zero, Ordinal.toGame_zero, Ordinal.natCast_opow_omega0, Ordinal.isSuccLimit_iff, Ordinal.veblen_eq_veblen_iff, Ordinal.add_le_nadd, Ordinal.deriv_zero, Ordinal.pred_eq_iff_isSuccPrelimit, Ordinal.mod_opow_log_lt_self, Ordinal.mk_Iio_ordinal, Ordinal.bddAbove_of_small, Profinite.NobelingProof.πs_apply_apply, Ordinal.card_le_nat, Ordinal.iSup'_eq_bsup, Ordinal.typein_apply, Ordinal.pred_zero, Ordinal.one_nadd, Ordinal.ToType.mk_symm_apply_coe, Ordinal.mul_add_mod_self, Ordinal.type_fintype, Cardinal.range_aleph, Ordinal.bddAbove_iff_small, Cardinal.aleph0_le_preAleph, Cardinal.preAleph_succ, Ordinal.isNormal_derivFamily, Ordinal.strictMono_gamma, Ordinal.veblen_invVeblen₁_invVeblen₂, Ordinal.enum_succ_eq_top, SetTheory.PGame.nim_zero_equiv, Nimber.toOrdinal_one, Ordinal.toPGame_natCast, Ordinal.leftDistribClass, Ordinal.iterate_veblen_lt_gamma_zero, Ordinal.typein_surjOn, SetTheory.PGame.birthday_half, SetTheory.PGame.birthday_def, Ordinal.lt_omega0_opow, Cardinal.aleph_one_le_lift, Ordinal.zero_nmul, OrdinalApprox.exists_gfpApprox_eq_gfpApprox, PSet.rank_powerset, Ordinal.isInitial_omega, Ordinal.epsilon0_lt_gamma, ONote.repr_opow, Ordinal.omega0_lt_epsilon, Cardinal.preBeth_succ, IsWellFounded.rank_eq, SetTheory.PGame.birthday_eq_zero, Cardinal.not_injective_limitation_set, Ordinal.veblen_le_veblen_iff, Ordinal.bsup_congr, Ordinal.principal_one_iff, Cardinal.ord_nat, Ordinal.eq_zero_or_pos, Ordinal.small_Icc, Ordinal.zero_div, Ordinal.veblen_le_veblen_iff_right, Ordinal.ofNat_lt_card, Ordinal.isNormal_gamma, Ordinal.CNF.foldr, Cardinal.lift_le_aleph1, Cardinal.gc_ord_card, ZFSet.rank_range, Ordinal.toGame_nmul, not_injective_of_ordinal_of_small, Ordinal.lift_zero, Ordinal.bsup_eq_blsub_iff_lt_bsup, Ordinal.le_preOmega_self, Ordinal.isSuccPrelimit_lift, Ordinal.iSup_ord, WellFoundedLT.rank_strictMono, ZFSet.rank_insert, Ordinal.toGame_lf_iff, Ordinal.CNF.coeff_one_left, Ordinal.enum_le_enum, Cardinal.preAleph_zero, Ordinal.lsub_le_iff, Ordinal.sup_eq_sup, Ordinal.lt_wf, Ordinal.card_succ, Cardinal.ord_one, Ordinal.sub_le_self, Ordinal.mem_range_veblen, Ordinal.aleph0_le_cof, Ordinal.le_iSup, Ordinal.card_omega, Profinite.NobelingProof.isClosed_proj, Ordinal.iSup_eq_zero_iff, Ordinal.card_typein, Ordinal.lift_typein_top, Cardinal.IsRegular.ord_pos, Ordinal.typein_ordinal, Ordinal.epsilon0_eq_nfp, Ordinal.epsilon_zero_eq_nfp, Cardinal.lift_aleph, Ordinal.type_pUnit, Ordinal.toNatOrdinal_zero, Ordinal.div_pos, PSet.rank_singleton, Ordinal.CNF.coeff_zero_right, Ordinal.IsClosedBelow.sInter, Ordinal.ofNat_le_card, Ordinal.principal_add_one, Ordinal.veblen_mem_range_opow, NatOrdinal.toOrdinal_eq_zero, Ordinal.omega0_le_preOmega_iff, Ordinal.IsFundamentalSequence.ord_cof, Ordinal.invVeblen₂_le, OrdinalApprox.gfpApprox_mono_mid, Ordinal.mulLeftMono, Ordinal.deriv_zero_left, Ordinal.mem_range_gamma, Ordinal.sup_eq_bsup', Ordinal.instNoMaxOrder, Ordinal.CNF.one_left, Ordinal.bsup_succ_le_blsub, 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, Cardinal.preAleph_le_preAleph, Ordinal.card_eq_nat, Ordinal.small_Ioc, Ordinal.omega_strictMono, Ordinal.card_eq_one, Ordinal.principal_mul_two, Ordinal.gamma0_eq_nfp, Ordinal.toPGame_lt_iff, Ordinal.opow_natCast, Ordinal.lt_pred_iff_succ_lt, Ordinal.principal_mul_iff_mul_left_eq, ONote.fundamentalSequenceProp_inl_some, SetTheory.Game.birthday_ofNat, Ordinal.sup_eq_lsub, Ordinal.lift_card_sInf_compl_le, Ordinal.nfp_zero_left, Ordinal.iSup_eq_lsub_iff_lt_iSup, Ordinal.lsub_typein, Ordinal.lt_gamma_zero, Cardinal.aleph0_lt_aleph_one, Ordinal.IsNormal.strictMono, Ordinal.nadd_nat, Ordinal.lt_bsup_of_ne_bsup, RelEmbedding.ordinal_type_le, Ordinal.opow_zero, Ordinal.opow_lt_veblen_opow_iff, Ordinal.principal_add_omega0, Ordinal.mod_zero, Ordinal.toNatOrdinal_eq_zero, Ordinal.CNFRec_pos, SetTheory.Game.small_setOf_birthday_lt, Ordinal.mul_div_cancel, Ordinal.bsup_le_iff, Ordinal.lt_veblen_iff_invVeblen₁_le, Ordinal.isInitial_natCast, SetTheory.PGame.toLeftMovesNim_symm_lt, Ordinal.toGame_inj, Ordinal.natCast_mod_omega0, Ordinal.isEmpty_toType_zero, Cardinal.preAleph_lt_preAleph, Ordinal.univ_id, Ordinal.gamma_lt_gamma, Ordinal.lt_iSup_iff, Cardinal.aleph_mul_aleph, Ordinal.card_mul, Ordinal.nmul_one, Cardinal.beth_strictMono, Ordinal.nfp_id, Ordinal.bsup'_eq_iSup, SetTheory.Game.neg_birthday_le, Cardinal.isRegular_aleph_one, ZFSet.mem_vonNeumann_succ, Ordinal.mul_sub, Ordinal.instAddLeftReflectLE, Ordinal.nonempty_compl_range, ZFSet.rank_le_iff, Ordinal.le_lift_iff, Ordinal.iSup_Iio_eq_bsup, Ordinal.IsFundamentalSequence.succ, Profinite.NobelingProof.contained_proj, Cardinal.lift_le_aleph_one, SetTheory.PGame.moveLeft_toLeftMovesNim, Ordinal.nfpFamily_le_iff, MeasurableSpace.generateMeasurableRec_mono, ONote.repr_le_repr, Ordinal.one_le_iff_ne_zero, ZFSet.rank_iUnion, Cardinal.ord_injective, Ordinal.nadd_succ, Ordinal.veblen_lt_veblen_iff, Ordinal.instIsEmptyIioZero, Ordinal.lt_nfp_iff, CategoryTheory.ObjectProperty.strictLimitsClosureStep_strictLimitsClosureIter_eq_self, ONote.fundamentalSequenceProp_inr, Ordinal.toZFSet_injective, Ordinal.veblenWith_zero, OrdinalApprox.gfpApprox_mono_left, Ordinal.invVeblen₁_lt_iff, Ordinal.type_empty, ONote.repr_lt_repr, Ordinal.toPGame_moveLeft, Ordinal.principal_mul_omega0_opow_opow, Ordinal.preOmega_strictMono, Ordinal.type_unit, SetTheory.PGame.birthday_moveRight_lt, ZFSet.mem_vonNeumann, Ordinal.bsup_eq_iSup, Ordinal.principal_opow_omega, PSet.lt_rank_iff, Ordinal.derivFamily_zero, SetTheory.Game.birthday_star, Ordinal.card_preOmega, Ordinal.lsub_le_succ_iSup, 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.invVeblen₂_lt_iff, Ordinal.toNatOrdinal_natCast, NatOrdinal.toOrdinal_symm_eq, Cardinal.aleph1_eq_lift, ZFSet.rank_sUnion_le, NatOrdinal.toOrdinal_one, Cardinal.card_surjective, Ordinal.lt_lsub, Ordinal.mod_mod, Ordinal.toNimber_zero, Ordinal.card_nat, Ordinal.type_sum_lex, Ordinal.bsup_eq_blsub, Ordinal.mem_iff_iSup_of_isClosed, NatOrdinal.toOrdinal_toNatOrdinal, Ordinal.nadd_zero, Ordinal.sInf_compl_lt_ord_succ, Cardinal.beth_eq_preBeth, Cardinal.ord_strictMono, Cardinal.preAleph_le_preBeth, MeasurableSpace.generateMeasurableRec_omega_one, ONote.repr_ofNat, Cardinal.ord_lt_ord, Ordinal.blsub_const, 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.ToType.mk_apply, SetTheory.PGame.birthday_natCast, Ordinal.blsub_one, Ordinal.small_Iio, Ordinal.toPGame_moveLeft_hEq, Cardinal.omega0_lt_ord, SetTheory.PGame.nim_one_moveRight, Ordinal.typein_one_toType, Ordinal.succ_pos, Ordinal.add_sub_add_cancel, Ordinal.lsub_notMem_range, Ordinal.toNimber_toOrdinal, NONote.repr_opow, Ordinal.bsup_eq_zero_iff, Ordinal.toNimber_max, Ordinal.canonicallyOrderedAdd, Ordinal.bsup_le_blsub, Ordinal.toZFSet_monotone, Ordinal.mem_range_preOmega_iff, Ordinal.omega_max, Ordinal.toNimber_eq_one, Profinite.NobelingProof.Products.prop_of_isGood_of_contained, not_surjective_of_ordinal, Cardinal.aleph_eq_preAleph, Ordinal.omega_pos, Ordinal.invVeblen₂_lt, Ordinal.to_leftMoves_one_toPGame_symm, Ordinal.lt_omega0, Ordinal.blsub_eq_lsub, Ordinal.le_add_right, Ordinal.nadd_lt_nadd_iff_right, 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, Cardinal.isNormal_beth, Ordinal.typein_le_typein', Ordinal.succ_pred_eq_iff_not_isSuccPrelimit, Ordinal.toGame_injective, Ordinal.isNormal_add_right, Ordinal.toZFSet_zero, CountableInterFilter.toCardinalInterFilter, Cardinal.aleph_one_eq_lift, Ordinal.enum_inj, Ordinal.principal_add_omega0_opow, Ordinal.sup_eq_lsub_or_sup_succ_eq_lsub, Nimber.toOrdinal_symm_eq, Profinite.NobelingProof.injective_πs, Cardinal.aleph_toENat, Cardinal.preBeth_mono, Cardinal.countable_iff_lt_aleph_one, SetTheory.Game.birthday_quot_le_pGameBirthday, Ordinal.veblen_succ, Ordinal.instAddLeftMono, Ordinal.opow_succ, Ordinal.cof_eq_zero, Ordinal.veblen_zero_apply, Ordinal.deriv_zero_right, Ordinal.add_one_eq_succ, Ordinal.card_lt_aleph0, Ordinal.IsAcc.pos, Ordinal.blsub_eq_lsub', Ordinal.blsub_eq_zero_iff, Profinite.NobelingProof.GoodProducts.range_equiv_smaller_toFun_bijective, ZFSet.rank_pair, Ordinal.add_le_add_iff_right, SetTheory.PGame.nim_grundyValue, MeasurableSpace.generateMeasurableRec_omega1, Cardinal.isNormal_preBeth, ZFSet.IsOrdinal.rank_lt_iff_mem, Ordinal.toZFSet_succ, Ordinal.toPGame_injective, Ordinal.nfp_add_zero, Ordinal.preOmega_le_preOmega, Ordinal.epsilon_pos, Ordinal.lift_omega, Cardinal.isNormal_ord, Ordinal.preOmega_omega0, Ordinal.card_lt_ofNat, Ordinal.one_CNF, Ordinal.iSup_le_iff, Cardinal.aleph0_mul_aleph, Ordinal.preOmega_lt_preOmega, Ordinal.left_le_veblen, Cardinal.lift_lt_aleph1, Cardinal.ord_card_le, Ordinal.iSup_eq_lsub, Ordinal.not_bddAbove_compl_of_small, Ordinal.max_zero_right, Cardinal.mk_biUnion_le_of_le, Ordinal.veblen_lt_veblen_iff_right, Ordinal.nmul_le_iff, Besicovitch.TauPackage.lastStep_nonempty, NONote.repr_sub, ONote.scale_opowAux, Ordinal.lt_bsup, Ordinal.iSup_eq_lsub_iff, Ordinal.veblen_injective, Ordinal.blsub_zero, Ordinal.toPGame_le_iff, Nimber.toOrdinal_zero, NatOrdinal.toOrdinal_zero, 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.CNF_zero, Cardinal.isSuccLimit_omega, Ordinal.iSup_iterate_eq_nfp, Cardinal.ord_le_omega0, Ordinal.self_le_succ_pred, Cardinal.aleph_one_lt_lift, Ordinal.typein_inj, Ordinal.bsup_eq_bsup, Ordinal.veblenWith_of_ne_zero, SetTheory.PGame.moveRight_nim_heq, Ordinal.sub_ne_zero_iff_lt, Ordinal.type_eq_zero_iff_isEmpty, Nimber.toOrdinal_toNimber, Ordinal.le_one_iff, Ordinal.natCast_lt_epsilon, InitialSeg.ordinal_type_le, Ordinal.principal_swap_iff, Ordinal.lsub_eq_zero_iff, Ordinal.lift_mul, Ordinal.instAddRightReflectLT, Cardinal.mk_iUnion_Ordinal_lift_le_of_le, Ordinal.zero_opow, Ordinal.lt_veblen_invVeblen₁, Ordinal.toNatOrdinal_toOrdinal, SetTheory.PGame.moveLeft_nim_heq, 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.toLeftMovesToPGame_symm_lt, Ordinal.toZFSetIso_symm_apply, Cardinal.ord_le_type, Cardinal.preBeth_nat, Ordinal.lsub_unique, NatOrdinal.toOrdinal_eq_one, SetTheory.PGame.moveLeft_nim, Ordinal.lt_nadd_iff, Cardinal.mem_range_aleph_iff, Ordinal.lsub_le_sup_succ, Cardinal.ord_mono, Cardinal.aleph_lt_aleph, Ordinal.instIsLeftCancelAdd, Ordinal.principal_mul_one, Cardinal.mk_biUnion_le_of_le_lift, ZFSet.vonNeumann_succ, Ordinal.nmul_eq_mul, Ordinal.succ_iSup_le_lsub_iff, Ordinal.toZFSet_mem_toZFSet_iff, Ordinal.le_div, Ordinal.invVeblen₁_eq_iff, Ordinal.small_Ico, Ordinal.lsub_sum, NONote.repr_mul, Ordinal.IsInitial.mem_range_preOmega, Cardinal.lt_ord, Ordinal.nhds_eq_pure, Ordinal.succ_nadd, Ordinal.natCast_add_omega0, ZFSet.rank_union, Ordinal.IsNormal.trans, Cardinal.aleph_toNat, Ordinal.veblen_zero_inj, Ordinal.range_preOmega, Ordinal.one_lt_omega0, Ordinal.sub_sub, Ordinal.preOmega_max, Ordinal.one_le_card, Ordinal.nadd_one, SetTheory.PGame.nim_add_nim_equiv, Ordinal.veblen_zero_strictMono, Ordinal.le_add_sub, Ordinal.toGame_nadd, SetTheory.PGame.moveRight_toRightMovesNim, Ordinal.right_le_veblen, Cardinal.succ_aleph0, Ordinal.card_iSup_le_sum_card, Ordinal.CNF.zero_right, Ordinal.toNatOrdinal_max, ZFSet.le_succ_rank_sUnion, Ordinal.IsFundamentalSequence.zero, Nimber.toOrdinal_eq_zero, Ordinal.natCast_lt_gamma, Ordinal.toGame_natCast, Ordinal.type_fin, Ordinal.toPGameEmbedding_apply, PSet.rank_pair, Ordinal.le_omega_self, Ordinal.mod_def, ONote.repr_sub, Cardinal.aleph_zero, Ordinal.lift_le, Ordinal.isNormal_iff_strictMono_and_continuous, Ordinal.isSuccLimit_iff_omega0_dvd, Ordinal.gamma_succ_eq_nfp, SetTheory.PGame.isEmpty_nim_zero_rightMoves, Ordinal.uncountable, Ordinal.principal_zero, Ordinal.lt_lsub_iff, SetTheory.PGame.toRightMovesNim_symm_lt, ONote.NFBelow.repr_lt, Ordinal.le_nfpFamily, Ordinal.add_one_nmul, Ordinal.zero_mod, Ordinal.principal_mul_iff_le_two_or_omega0_opow_opow, Ordinal.lt_epsilon0, Ordinal.toGame_le_iff, Ordinal.veblen_pos, Ordinal.div_one, Ordinal.omega0_opow_epsilon, Ordinal.instCharZero, Ordinal.div_zero, Cardinal.lift_preAleph, Ordinal.omega_eq_preOmega, Cardinal.lift_lt_aleph_one, Ordinal.toNatOrdinal_symm_eq, Ordinal.monotone_gamma, Ordinal.mul_div_le, ONote.nfBelow_ofNat, Ordinal.natCast_div, Ordinal.instNeZeroOne, Ordinal.top_typein, SetTheory.PGame.toLeftMovesNim_one_symm, Ordinal.sInf_empty, Ordinal.sup_typein_succ, Ordinal.liftPrincipalSeg_top, Ordinal.enum_type, Ordinal.nadd_lt_nadd_iff_left, Ordinal.nadd_eq_add, Ordinal.opow_eq_zero, Ordinal.one_toType_eq, Ordinal.isNormal_omega, MeasurableSpace.generateMeasurable_eq_rec, Ordinal.toPGame_moveLeft', Profinite.NobelingProof.succ_mono, Ordinal.card_eq_ofNat, Ordinal.log_one_right, Ordinal.veblen_left_monotone
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