instNatCast 📖 | CompOp | 499 mathmath: TangentBundle.continuousLinearMapAt_model_space, Cardinal.natCast_lt_toENat_iff, Topology.RelCWComplex.skeletonLT_union_iUnion_closedCell_eq_skeletonLT_succ, Module.length_compositionSeries, Nat.Prime.emultiplicity_choose_prime_pow_add_emultiplicity, Order.LTSeries.length_le_krullDim, contDiffOn_nat_succ_iff_contDiffOn_one_iteratedDerivWithin, Ideal.height_le_spanFinrank, MvPowerSeries.weightedOrder_monomial, ContDiffOn.rpow_const_of_le, Cardinal.toENat_eq_natCast_iff, Order.krullDim_lt_coe_iff, Cardinal.ofENat_lt_ofNat, Topology.CWComplex.exists_mem_openCell_of_mem_skeleton, coe_one, SimpleGraph.le_chromaticNumber_iff_colorable, contMDiffWithinAt_vectorSpace_iff_contDiffWithinAt, Module.End.isNilpotent_restrict_genEigenspace_nat, ContDiffMapSupportedIn.iteratedFDerivLM_apply, SimpleGraph.le_chromaticNumber_iff_coloring, AddCircle.card_torsion_le_of_isSMulRegular, CategoryTheory.injectiveDimension_le_iff, Cardinal.ofENat_le_ofNat, Set.ncard_le_encard, ContDiffMapSupportedIn.structureMapCLM_apply, Ring.krullDimLE_iff, contMDiff_addInvariantVectorField, untopD_coe_enat, natCast_le_of_coe_top_le_withTop, Order.length_le_coheight, Ideal.exists_finset_card_eq_height_of_isNoetherianRing, exists_spanRank_le_and_le_height_of_le_height, SimpleGraph.Walk.edist_le, Set.encard_pair, canLift, Mathlib.Tactic.ENatToNat.coe_sub, iInf_toNat, contMDiff_mulInvariantVectorField, Module.supportDim_add_length_eq_supportDim_of_isRegular, Order.height_nat, Module.End.genEigenspace_directed, lt_emultiplicity_of_lt_multiplicity, contDiff_nat_succ_iff_contDiff_one_iteratedDeriv, Real.contDiffAt_rpow_const_of_le, ceil_add_natCast, Topology.RelCWComplex.coe_skeletonLT, Module.End.maxGenEigenspace_eq, Topology.RelCWComplex.mem_skeleton_iff, AddMonoid.minOrder_le_addOrderOf, Nat.count_le_setENCard, SimpleGraph.two_le_chromaticNumber_of_adj, contMDiff_infty, Topology.RelCWComplex.cellFrontier_subset_skeletonLT, SimpleGraph.card_le_chromaticNumber_iff_forall_surjective, Subgroup.IsComplement.encard_left, contDiffOn_nat_iff_continuousOn_differentiableOn_deriv, SimpleGraph.exists_egirth_eq_length, Topology.CWComplex.iUnion_openCell_eq_skeletonLT, emultiplicity_lt_iff_not_dvd, Order.le_krullDim_iff, SimpleGraph.three_le_egirth, Dynamics.IsDynNetIn.card_le_netMaxcard, Cardinal.ofENat_eq_ofNat, SimpleGraph.chromaticNumber_cycleGraph_of_even, Stream'.Seq.length'_of_terminates, Module.End.maxGenEigenspace_eq_genEigenspace_finrank, Nat.Prime.emultiplicity_factorial, floor_add_natCast, forall_natCast_le_iff_le, contDiffWithinAt_nat, ZMod.minOrder_of_prime, add_one_natCast_le_withTop_of_lt, contDiffOn_infty, Nat.cast_analyticOrderNatAt, tangentBundle_model_space_coe_chartAt, SimpleGraph.chromaticNumber_top, contDiff_iff_forall_nat_le, SimpleGraph.Colorable.chromaticNumber_eq_sInf, epow_natCast, contMDiffAt_mulInvariantVectorField, Ideal.exists_ltSeries_length_eq_height, MvPowerSeries.weightedOrder_monomial_of_ne_zero, ZMod.minOrder, Topology.RelCWComplex.mem_skeletonLT_iff, FiniteMultiplicity.emultiplicity_eq_multiplicity, Topology.RelCWComplex.iUnion_openCell_eq_skeleton, Stream'.Seq.length'_le_iff, mdifferentiableAt_addInvariantVectorField, Cardinal.toENatAux_eq_nat, ContinuousLinearMap.isClosed_genEigenspace, MvPowerSeries.nat_le_order, Nat.Prime.emultiplicity_factorial_mul, ne_top_iff_exists, Order.coheight_eq_coe_add_one_iff, Topology.CWComplex.mem_skeletonLT_iff, Subgroup.IsComplement.encard_right, measurable_iff, Monoid.minOrder_le_natCard, lt_lift_iff, Mathlib.Tactic.ENatToNat.coe_mul, AddMonoid.le_minOrder, Cardinal.toENat_lt_natCast_iff, Polynomial.le_trailingDegree_monomial, Cardinal.toENatAux_nat, contDiff_all_iff_nat, MvPowerSeries.nat_le_weightedOrder, Module.End.genEigenspace_top_eq_maxUnifEigenspaceIndex, Cardinal.nat_eq_ofENat, emultiplicity_pow_prime_pow_sub_pow_prime_pow, Order.krullDim_le_of_krullDim_preimage_le, Module.End.map_genEigenrange_le, MeasureTheory.stoppedValue_eq, Set.coe_fintypeCard, Polynomial.trailingDegree_C_mul_X_pow, iInf_coe_lt_top, mdifferentiable_mulInvariantVectorField, ODE.contDiffOn_nat_picard_Icc, FiniteMultiplicity.emultiplicity_eq_iff_multiplicity_eq, analyticOrderAt_centeredMonomial, le_emultiplicity_of_le_multiplicity, CategoryTheory.injectiveDimension_ge_iff, contDiffOn_nat_iff_continuousOn_differentiableOn, SimpleGraph.chromaticNumber_eq_iInf, Stream'.Seq.drop_length', Topology.RelCWComplex.cellFrontier_subset_skeleton, Cardinal.natCast_lt_toENat, eq_top_iff_forall_gt, LinearMap.finrank_genEigenspace_le, Ideal.height_le_card_of_mem_minimalPrimes_span, SimpleGraph.chromaticNumber_le_card, Module.End.iSup_genEigenspace_eq, SimpleGraph.chromaticNumber_eq_two_iff, Set.encard_eq_three, contMDiff_vectorSpace_iff_contDiff, Nat.Prime.emultiplicity_choose', coe_sSup, coe_toNat_le_self, Module.End.eigenspace_le_genEigenspace, AddSubgroup.IsComplement.encard_right, AddSubgroup.IsComplement.encard_left, PowerSeries.order_monomial, IsDiscreteValuationRing.addVal_def', Order.krullDim_eq_iSup_length, TangentBundle.coordChange_model_space, Dynamics.IsDynCoverOf.coverMincard_le_card, CategoryTheory.projectiveDimension_lt_iff, Irreducible.addVal_pow, Order.coheight_eq_coe_iff_maximal_le_coheight, SimpleGraph.chromaticNumber_le_iff_colorable, SimpleGraph.chromaticNumber_eq_iff_colorable_not_colorable, Topology.RelCWComplex.openCell_subset_skeletonLT, toNat_eq_iff, Topology.RelCWComplex.closedCell_subset_skeletonLT, Set.Nat.encard_range, coe_toNat, Cardinal.toENat_lt_natCast, WithBot.add_le_add_natCast_left_iff, emultiplicity_pow_self, MvPowerSeries.ne_zero_iff_weightedOrder_finite, SimpleGraph.chromaticNumber_eq_card_iff, natCast_le_analyticOrderAt, contDiff_nat_iff_iteratedDeriv, Order.coheight_eq_iSup_head_eq, coe_mul, Nat.Prime.emultiplicity_choose, Int.two_pow_two_pow_add_two_pow_two_pow, coe_iSup, contDiffPointwiseHolderAt_iff, Submodule.spanFinrank_span_le_encard, ringKrullDim_le_ringKrullDim_quotient_add_card, natCast_lt_succ, iInf_eq_top_of_isEmpty, Nat.emultiplicity_two_factorial_lt, le_emultiplicity_of_pow_dvd, trivializationAt_model_space_apply, hasFTaylorSeriesUpToOn_top_iff, iInf_coe_eq_top, Ideal.height_le_iff, SimpleGraph.chromaticNumber_le_two_iff_isBipartite, SimpleGraph.CompleteBipartiteGraph.chromaticNumber, SimpleGraph.two_le_chromaticNumber_iff_ne_bot, ceil_natCast_add, hasFTaylorSeriesUpTo_succ_nat_iff_right, Topology.RelCWComplex.skeleton_union_iUnion_closedCell_eq_skeleton_succ, MeasureTheory.stoppedProcess_eq, hasFTaylorSeriesUpToOn_succ_nat_iff_right, InnerProductSpace.HarmonicOnNhd.contDiffOn, Order.height_eq_coe_add_one_iff, floor_sub_natCast, floor_coe, ringKrullDim_le_spanFinrank_maximalIdeal, Polynomial.trailingDegree_le_of_ne_zero, ringKrullDim_le_ringKrullDim_quotient_add_spanFinrank, PowerSeries.coe_toNat_order, FiniteMultiplicity.emultiplicity_le_of_multiplicity_le, AnalyticAt.analyticOrderAt_eq_natCast, SimpleGraph.le_chromaticNumber_iff_forall_surjective, Module.End.genEigenspace_eq_genEigenspace_maxUnifEigenspaceIndex_of_le, Order.height_le_coe_iff, Topology.RelCWComplex.iUnion_skeletonLT_eq_complex, instIsContMDiffRiemannianBundleOfNatWithTopENat_2, Order.height_eq_coe_iff, Polynomial.le_trailingDegree_C_mul_X_pow, Cardinal.ofNat_lt_ofENat, SimpleGraph.Colorable.chromaticNumber_le, ceil_sub_natCast, coe_iInf, tangentBundle_model_space_coe_chartAt_symm, tangentBundleModelSpaceHomeomorph_coe, lift_le_iff, ContDiffWithinAt.eventually_hasFTaylorSeriesUpToOn, PowerSeries.le_order_pow_of_constantCoeff_eq_zero, toNatHom_apply, Order.length_le_height, MvPowerSeries.order_le, tangentBundleCore_coordChange_model_space, contDiffOn_all_iff_nat, coe_toNat_eq_self, instIsManifoldMinSmoothnessOfNatWithTopENat, Nat.Prime.emultiplicity_choose_prime_pow, Order.coheight_le_of_krullDim_preimage_le, ringKrullDim_add_length_eq_ringKrullDim_of_isRegular, WithBot.natCast_add_cancel, AddCircle.card_torsion_le_of_isSMulRegular_int, iSup_natCast, Topology.RelCWComplex.iUnion_cellFrontier_subset_skeleton, Cardinal.natCast_le_toENat, MeasureTheory.stoppedValue_sub_eq_sum', coe_inj, HasFTaylorSeriesUpToOn.shift_of_succ, MvPowerSeries.exists_coeff_ne_zero_and_order, pow_dvd_iff_le_emultiplicity, SimpleGraph.cliqueNum_le_chromaticNumber, Polynomial.natTrailingDegree_le_trailingDegree, contDiffOn_iff_forall_nat_le, Set.encard_eq_coe_toFinset_card, SimpleGraph.ediam_le_two_mul_radius, Topology.RelCWComplex.iUnion_cellFrontier_subset_skeletonLT, Cardinal.ofENat_eq_nat, SimpleGraph.edist_eq_sInf, contDiffAt_succ_iff_hasFDerivAt, top_sub_coe, lift_lt_iff, Cardinal.toENat_le_natCast, Order.height_le_of_krullDim_preimage_le, Ideal.height_le_iff_covBy, contDiffWithinAt_infty, SimpleGraph.chromaticNumber_cycleGraph_of_odd, tangentBundle_model_space_chartAt, IsRegularLocalRing.spanFinrank_maximalIdeal, coe_sub, contMDiffAt_iff_nat, AddMonoid.le_minOrder_iff_forall_addSubgroup, ContDiffAt.rpow_const_of_le, Real.contDiffAt_rpow_const, ringKrullDim_add_natCard_le_ringKrullDim_mvPolynomial, ContDiff.rpow_const_of_le, Module.End.genEigenspace_eq_iSup_genEigenspace_nat, SimpleGraph.Connected.exists_walk_length_eq_edist, Cardinal.ofNat_le_ofENat, coe_lift, addLECancellable_coe, Submodule.spanRank_toENat_eq_iInf_finset_card, SimpleGraph.ediam_le_two_mul_eccent, Set.encard_le_coe_iff_finite_ncard_le, coe_sInf, Mathlib.Tactic.ENatToNat.coe_zero, isRegularLocalRing_iff, Order.coheight_le_iff', Order.coheight_eq_index_of_length_eq_head_coheight, mem_nhds_natCast_iff, ringKrullDim_le_ringKrullDim_add_card, recTopCoe_coe, CategoryTheory.projectiveDimension_le_iff, MvPowerSeries.weightedOrder_eq_nat, SimpleGraph.edist_eq_two_iff, Topology.RelCWComplex.iUnion_openCell_eq_skeletonLT, Module.End.genEigenspace_le_genEigenspace_maxUnifEigenspaceIndex, contMDiffAt_vectorSpace_iff_contDiffAt, le_coe_iff, Monoid.le_minOrder_iff_forall_subgroup, Mathlib.Tactic.ENatToNat.coe_ofNat, analyticOrderAt_deriv_of_pos, nhds_natCast, SimpleGraph.IsTree.chromaticNumber_le_two, CategoryTheory.projectiveDimension_ge_iff, WithBot.add_one_le_iff, Module.End.genEigenspace_zero_nat, mdifferentiable_addInvariantVectorField, FiniteMultiplicity.emultiplicity_lt_of_multiplicity_lt, SimpleGraph.le_chromaticNumber_of_pairwise_adj, contDiffAt_infty, Module.End.genEigenspace_top, VectorField.contMDiffWithinAt_mpullbackWithin_extChartAt_symm, TangentBundle.symmL_model_space, Cardinal.ofENat_nat, CategoryTheory.injectiveDimension_lt_iff, Topology.RelCWComplex.openCell_subset_skeleton, MvPowerSeries.exists_coeff_ne_zero_and_weightedOrder, Module.End.genEigenrange_nat, Polynomial.ringKrullDim_le, card_eq_coe_fintype_card, coe_lt_coe, PowerSeries.order_le, iSup_coe_eq_top, contDiff_nat_iff_continuous_differentiable, coe_le_coe, Order.coe_lt_coheight_iff, MvPowerSeries.weightedOrder_le, contDiffWithinAt_iff_forall_nat_le, WithBot.add_le_add_natCast_right_iff, Order.coheight_le_coe_iff, SimpleGraph.completeMultipartiteGraph.chromaticNumber, Topology.CWComplex.iUnion_openCell_eq_skeleton, tangentBundleModelSpaceHomeomorph_coe_symm, UniqueFactorizationMonoid.emultiplicity_eq_count_normalizedFactors, Set.Finite.exists_encard_eq_coe, Dynamics.netMaxcard_finite_iff, Set.encard_eq_four, Set.Finite.encard_eq_coe, Cardinal.ofENat_lt_nat, MeasureTheory.stoppedProcess_eq', Module.End.generalized_eigenvec_disjoint_range_ker, MeasureTheory.contDiff_charFun, Nat.Prime.emultiplicity_pow, Module.End.isNilpotent_restrict_sub_algebraMap, ringKrullDim_nat, Set.encard_coe_eq_coe_finsetCard, Nat.Prime.emultiplicity_factorial_le_div_pred, UniqueFactorizationMonoid.le_emultiplicity_iff_replicate_le_normalizedFactors, Cardinal.toENat_le_natCast_iff, cauchy_davenport_minOrder_add, ContDiffWithinAt.rpow_const_of_le, SimpleGraph.chromaticNumber_eq_biInf, ContDiff.iterate_deriv', Order.coheight_coe_enat, hasFTaylorSeriesUpToOn_succ_iff_left, padicValNat_eq_emultiplicity_of_ne_one, Real.contDiff_rpow_const_of_le, ContDiffPointwiseHolderAt.contDiffAt, Cardinal.toENatAux_le_nat, map_coe, Cardinal.toENat_le_nat, Cardinal.toENat_eq_natCast, hasFTaylorSeriesUpTo_top_iff, SimpleGraph.egirth_le_length, Set.encard_le_coe_iff, mdifferentiableAt_mulInvariantVectorField, isEmbedding_natCast, Polynomial.trailingDegree_eq_iff_natTrailingDegree_eq, MvPowerSeries.ne_zero_iff_order_finite, Module.End.genEigenspace_eq_genEigenspace_finrank_of_le, Set.encard_eq_two, contMDiffWithinAt_infty, floor_natCast_add, MvPowerSeries.order_monomial, toENNReal_coe, SimpleGraph.IsClique.card_le_chromaticNumber, lift_coe, WithBot.add_natCast_cancel, Module.End.genEigenspace_nat, height_le_ringKrullDim_quotient_add_spanFinrank, succ_coe, IsManifold.instOfNatWithTopENat_2, Order.coheight_eq_coe_iff, SimpleGraph.exists_walk_of_edist_ne_top, Module.End.genEigenspace_le_maximal, toNat_coe, Module.End.mem_genEigenspace_nat, emultiplicity_eq_coe, Set.Finite.encard_eq_coe_toFinset_card, Module.length_eq_finrank, Topology.RelCWComplex.iUnion_skeleton_eq_complex, IsDiscreteValuationRing.addVal_def, Int.two_pow_two_pow_sub_pow_two_pow, WithBot.lt_add_one_iff, Order.height_le_iff, emultiplicity_pow, Order.krullDim_eq_length_of_finiteDimensionalOrder, Dynamics.coverMincard_finite_iff, Cardinal.toENat_eq_nat, contDiff_infty, contMDiffAt_addInvariantVectorField, contMDiff_tangentBundleModelSpaceHomeomorph, Order.KrullDimLE.krullDim_le, emultiplicity_eq_iff_multiplicity_eq_of_ne_one, Set.exists_isChain_of_le_chainHeight, ringKrullDim_le_ringKrullDim_add_spanFinrank, emultiplicity_eq_of_dvd_of_not_dvd, Cardinal.nat_le_ofENat, SimpleGraph.Reachable.coe_dist_eq_edist, exists_nat_gt, toNat_eq_iff_eq_coe, contMDiffAt_infty, Topology.RelCWComplex.skeletonLT_I, Order.height_le_iff', IsRegularLocalRing.iff_finrank_cotangentSpace, contMDiff_tangentBundleModelSpaceHomeomorph_symm, analyticOrderAt_iterated_deriv, exist_minSmoothness_le_ne_infty, MvPowerSeries.order_eq_nat, Ideal.height_le_height_add_spanFinrank_of_le, Order.index_le_height, Order.coheight_eq, forall_ne_top, SimpleGraph.le_egirth, Nat.Prime.emultiplicity_pow_self, ceil_coe, SimpleGraph.chromaticNumber_eq_iff_forall_surjective, Module.End.hasGenEigenvector_iff, tendsto_nhds_top_iff_natCast_lt, SimpleGraph.edist_le, le_lift_iff, MvPolynomial.ringKrullDim_of_isNoetherianRing, Polynomial.trailingDegree_eq_natTrailingDegree, Monoid.le_minOrder, Submodule.FG.exists_span_set_encard_eq_spanFinrank, SimpleGraph.Reachable.exists_walk_length_eq_edist, Order.rev_index_le_coheight, Mathlib.Tactic.ENatToNat.coe_add, Cardinal.natCast_eq_toENat_iff, cauchy_davenport_minOrder_mul, eq_top_iff_forall_ge, Cardinal.ofENat_le_nat, coe_zero, Module.length_of_free_of_finite, SimpleGraph.chromaticNumber_pathGraph, SimpleGraph.two_lt_edist_iff, Module.End.genEigenspace_le_genEigenspace_finrank, Module.End.mem_genEigenspace, ContDiffPointwiseHolderAt.zero_exponent_iff, VectorField.eventually_contMDiffWithinAt_mpullbackWithin_extChartAt_symm, le_emultiplicity_iff_replicate_subperm_primeFactorsList, IsManifold.instLEInftyCastWithTopENat, Ideal.height_le_card_of_mem_minimalPrimes_span_finset, Cardinal.toENat_nat, PowerSeries.nat_le_order, Set.Finite.cast_ncard_eq, emultiplicity_pow_self_of_prime, contMDiffOn_vectorSpace_iff_contDiffOn, Polynomial.le_trailingDegree_X_pow, PowerSeries.order_X_pow, Order.height_eq_iSup_last_eq, Nat.emultiplicity_eq_card_pow_dvd, Order.length_le_height_last, SimpleGraph.Walk.three_le_chromaticNumber_of_odd_loop, inTangentCoordinates_model_space, Order.coe_lt_height_iff, Polynomial.trailingDegree_monomial, coe_add, MvPowerSeries.order_monomial_of_ne_zero, Mathlib.Tactic.ENatToNat.coe_one, List.Nodup.length_le_enatCard, contMDiffWithinAt_iff_nat, Cardinal.ofNat_eq_ofENat, Order.length_le_coheight_head, Topology.RelCWComplex.closedCell_subset_skeleton, natCast_lt_of_coe_top_le_withTop, Monoid.minOrder_le_orderOf, Cardinal.natCast_le_toENat_iff, hasFTaylorSeriesUpToOn_top_iff_add, Stream'.Seq.lt_length'_iff, padicValNat.maxPowDiv_eq_emultiplicity, multiplicity_le_emultiplicity, AddMonoid.minOrder_le_natCard, inCoordinates_tangent_bundle_core_model_space, Order.height_eq_coe_iff_minimal_le_height, Module.End.pos_finrank_genEigenspace_of_hasEigenvalue, lt_coe_add_one_iff, SimpleGraph.exists_of_le_vertexCoverNum, ContDiffMapSupportedIn.structureMapLM_apply, Order.krullDim_le_of_krullDim_preimage_le', contMDiff_snd_tangentBundle_modelSpace, SimpleGraph.chromaticNumber_eq_card_iff_forall_surjective, InnerProductSpace.HarmonicContOnCl.contDiffAt, MvPowerSeries.le_order_pow_of_constantCoeff_eq_zero, Polynomial.trailingDegree_X_pow, Polynomial.IsDistinguishedAt.coe_natDegree_eq_order_map, Order.coheight_le_iff, natCast_le_analyticOrderAt_iff_iteratedDeriv_eq_zero, iSup_coe_lt_top, range_natCast, contMDiffOn_infty, isOpenEmbedding_natCast, PowerSeries.order_monomial_of_ne_zero, contDiff_succ_iff_hasFDerivAt, padicValNat_eq_emultiplicity, Order.krullDimLE_iff, card_eq_coe_natCard, exists_ne_top, Order.height_eq_index_of_length_eq_height_last, Polynomial.trailingDegree_eq_iff_natTrailingDegree_eq_of_pos, Ideal.IsDedekindDomain.emultiplicity_map_eq_ramificationIdx_mul, coe_lt_top, SimpleGraph.IsAcyclic.chromaticNumber_le_two, Cardinal.nat_lt_ofENat, Cardinal.natCast_eq_toENat, PowerSeries.order_eq_nat, Set.chainHeight_eq_top_iff
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