card π | CompOp | 1193 mathmath: Fintype.all_card_le_rel_image_card_iff_exists_injective, expect_ite_mem, card_choose_two_lt_card_subsetSum_of_nonneg, Equiv.Perm.SameCycle.exists_pow_eq_of_mem_support, Fin.card_Ioi, Sym2.card_toFinset_of_not_isDiag, card_sdiff_lt_card_sdiff_iff, rothNumberNat_spec, Shatters.card_le_vcDim, addEnergy_eq_sum_sq', CompositionAsSet.card_boundaries_eq_succ_length, finrank_span_finset_eq_card, card_le_card_of_forall_subsingleton', finrank_span_set_eq_card, Equiv.Perm.SameCycle.exists_pow_eq, natCast_le_rank_iff_finset, Finpartition.IsEquipartition.filter_ne_average_add_one_eq_average, quadraticChar_card_sqrts, card_pi, SlashInvariantForm.coe_prodEqualWeights, card_compls, card_univ, SimpleGraph.deleteFar_iff, card_inv, SimpleGraph.EdgeDisjointTriangles.card_edgeFinset_le, EquitableOn.le_add_one, prod_eq_pow_card, Fintype.card_ofFinset, card_mul_cast_addConst, card_strictMono, Nat.roughNumbersUpTo_card_le, Finsupp.card_Ioc, card_le_card_biUnion, SimpleGraph.isBipartiteWith_degree_le', CompositionAsSet.card_boundaries_pos, product_self_eq_disjiUnion_perm_aux, Infinite.exists_subset_card_eq, Equiv.Perm.cycleType_eq', IncidenceAlgebra.zeta_mul_kappa, SimpleGraph.DeleteFar.le_card_sub_card, linearIndependent_le_span_finset, Equiv.Perm.card_support_swap_mul, Tuple.lt_card_lt_iff_apply_lt_of_monotone, IsLowerSet.le_card_inter_finset, SimpleGraph.two_mul_card_edgeFinset, card_erase_lt_of_mem, SimpleGraph.edgeDensity_def, Finsupp.card_Ico, mem_upShadow_iff_exists_mem_card_add, Rel.card_interedges_le_mul, SimpleGraph.sum_degrees_eq_twice_card_edges, card_Ico_mul_right, Pi.card_Ici, Equiv.Perm.card_support_le_one, SzemerediRegularity.a_add_one_le_four_pow_parts_card, Equiv.Perm.card_of_cycleType_mul_eq, card_eq_of_bijective, ruzsa_triangle_inequality_invMul_mul_mul, Polynomial.card_support_le_one_of_eraseLead_eq_zero, grade_eq, Equiv.Perm.cycleType_eq, ENNReal.finset_card_const_le_le_of_tsum_le, AddMonoidHom.card_fiber_eq_of_mem_range, mulConst_mul_card, card_compl_add_card, card_mul_divConst, Fin.card_Ici, card_insertNthEquiv_filter_piFinset, Finpartition.IsEquipartition.average_le_card_part, card_imageβ, card_mul_dens, card_erase_add_one, Nat.nth_eq_zero, List.card_fixedLengthDigits, SzemerediRegularity.card_chunk, card_mul_subConst, card_memberSubfamily_add_card_nonMemberSubfamily, SimpleGraph.card_edgeFinset_sup_edge, sum_div_card_sq_le_sum_sq_div_card, ruzsa_triangle_inequality_add_sub_add, Ideal.exists_finset_card_eq_height_of_isNoetherianRing, mem_shadow_iterate_iff_exists_sdiff, ruzsa_triangle_inequality_sub_add_sub, sum_card_fiberwise_eq_card_filter, Height.logHeightβ_sum_le, Equiv.Perm.OnCycleFactors.mem_range_toPermHom_iff', Finpartition.IsEquipartition.card_biUnion_offDiag_le', SimpleGraph.dart_edge_fiber_card, Int.card_Ioo, Multiset.card_Ico, card_Iic_prod, sum_Ico_le_sum, card_dvd_card_add_right, schnirelmannDensity_le_iff_forall, Cardinal.card_le_of_finset, Nat.count_eq_card_filter_range, le_schnirelmannDensity_iff, SimpleGraph.extremalNumber_le_iff_of_nonneg, ModularForm.prod_slash, lubell_yamamoto_meshalkin_inequality_sum_card_div_choose, Pi.card_Iic, Nat.smoothNumbersUpTo_card_add_roughNumbersUpTo_card, local_lubell_yamamoto_meshalkin_inequality_mul, card_eq_iff_eq_univ, mulEnergy_univ_left, card_insertNone, diag_card, mulEnergy_univ_right, SimpleGraph.isMaximumClique_iff, card_le_card_add_self', le_card_of_inj_on_range, card_Ico_add_right, card_eq_one, MeasureTheory.Measure.haar.index_elim, Set.Intersecting.is_max_iff_card_eq, card_eq_sum_ones, card_le_card_add_left_of_injective, SimpleGraph.IsClique.card_le_of_coloring, AddGroup.rank_le, Real.rpow_sum_le_const_mul_sum_rpow_of_nonneg, Finpartition.IsEquipartition.card_large_parts_eq_mod, isPrimePow_iff_card_primeFactors_eq_one, Dynamics.IsDynCoverOf.iterate_le_pow, card_mul_le_card_shadow_mul, Fintype.card_Iic, PairReduction.card_pairSetSeq_le_logSizeRadius_mul, card_Ioo_finset, card_add_card_compl, one_lt_card_iff_nontrivial, sum_card_bipartiteAbove_eq_sum_card_bipartiteBelow, Nat.card_eq_finsetCard, divConst_mul_card, Finpartition.IsEquipartition.card_parts_eq_average, Set.Infinite.exists_subset_card_eq, ModularForm.prod_slash_sum_weights, even_sum_iff_even_card_odd, MvPolynomial.schwartz_zippel_totalDegree, Polynomial.card_support_eraseLead_add_one, SimpleGraph.card_set_walk_length_eq, inclusion_exclusion_card_inf_compl, card_toLeft_le, SimpleGraph.card_interedges_add_card_interedges_compl, SimpleGraph.card_edgeFinset_le_card_choose_two, Fintype.card_filter_piFinset_eq, Lagrange.natDegree_nodal, card_one, Dynamics.IsDynNetIn.card_le_netMaxcard, IncidenceAlgebra.zeta_mul_zeta, PMF.uniformOfFinset_apply_of_mem, card_vadd_le, mulConst_le_card, card_pow_le, card_snocEquiv_filter_piFinset, Fintype.card_piFinset_const, Rel.card_interedges_finpartition, card_dvd_card_smul_right, AddGroup.fg_iff', SimpleGraph.card_edgeFinset_map, card_imageβ_singleton_left, SimpleGraph.farFromTriangleFree_iff, SimpleGraph.odd_card_odd_degree_vertices_ne, Dynamics.netMaxcard_infinite_iff, prod_mul_pow_card, Equiv.Perm.card_support_eq_zero, card_filter_eq_iff, prod_sub, expect_ite_zero, card_imageβ_le, IsLowerSet.card_inter_le_finset, card_equiv, SzemerediRegularity.m_le_card_of_mem_chunk_parts, exists_of_schnirelmannDensity_eq_zero, BoxIntegral.Prepartition.card_filter_mem_Icc_le, Polynomial.natDegree_finset_prod_X_sub_C_eq_card, card_inter, card_mul_addConst, addDysonETransform.card, card_le_one_iff_subsingleton_coe, PNat.card_Icc, PiLp.dist_eq_card, Fin.card_filter_univ_succ, ruzsa_triangle_inequality_mul_div_mul, card_div_choose_le_card_shadow_div_choose, Fintype.sum_piFinset_apply, Nat.totient_eq_card_coprime, card_product, CompositionAsSet.length_lt_card_boundaries, Colex.mem_initSeg, SimpleGraph.IsSRGWith.card_neighborFinset_union_eq, Finpartition.isEquipartition_iff_card_parts_eq_average, Lagrange.eq_interpolate_iff, Fin.card_uIcc, Tuple.lt_card_gt_iff_apply_gt_of_antitone, card_erase_eq_ite, Colex.IsInitSeg.exists_initSeg, FormalMultilinearSeries.nnnorm_changeOrigin_le, Tree.treesOfNumNodesEq_card_eq_catalan, card_compl, local_lubell_yamamoto_meshalkin_inequality_div, card_add_le, card_sdiff, Multiset.toFinset_card_le, card_dfinsupp, equitableOn_iff_le_le_add_one, natCast_card_filter, card_le_card, Nat.card_multiples, Finpartition.IsEquipartition.card_part_eq_average_iff, ruzsa_triangle_inequality_mul_mul_invMul, divConst_le_card, prod_powersetCard, card_sdiff_of_subset, FormalMultilinearSeries.nnnorm_changeOriginSeries_le_tsum, Equiv.Perm.Disjoint.card_support_mul, SimpleGraph.isBipartiteWith_sum_degrees_eq_card_edges, FormalMultilinearSeries.changeOriginIndexEquiv_symm_apply_fst, Nat.factorization_eq_card_pow_dvd_of_lt, UV.card_shadow_compression_le, ArithmeticFunction.sigma_zero_apply, cast_subConst_mul_card, PairReduction.pow_logSizeRadius_le_card_le_logSizeRadius, addEnergy_univ_left, card_eraseNone_le, Cardinal.mk_le_iff_forall_finset_subset_card_le, card_le_card_of_surjOn, SimpleGraph.card_edgeFinset_of_isExtremal_free, Dynamics.IsDynCoverOf.preimage, Finpartition.IsEquipartition.card_interedges_sparsePairs_le, Polynomial.isUnitTrinomial_iff, card_map, lubell_yamamoto_meshalkin_inequality_sum_inv_choose, Nat.Partition.card_restricted_eq_card_countRestricted, mulRothNumber_spec, card_sups_iff, AddSubgroup.rank_closure_finset_le_card, SimpleGraph.isClique_map_finset_iff, SimpleGraph.IsNClique.card_eq, addEnergy_eq_sum_sq, SimpleGraph.IsMaximumIndepSet.maximum, SimpleGraph.isBipartiteWith_sum_degrees_eq_card_edges', card_le_card_add_self, LinearMap.IsSymmetric.card_filter_eigenvalues_eq, cast_card_union, card_union, pluennecke_ruzsa_inequality_nsmul_add, card_nbij', offDiag_card, SimpleGraph.LocallyLinear.card_edgeFinset, Finpartition.card_parts_le_card, FormalMultilinearSeries.changeOriginIndexEquiv_symm_apply_snd_snd_coe, mulEnergy_eq_sum_sq', card_le_card_sub_right, AlternatingGroup.card_of_cycleType_singleton, Ideal.card_primesOverFinset_le_finrank, ThreeAPFree.addRothNumber_eq, Equiv.Perm.two_le_card_support_of_ne_one, card_range, filter_product_card, Equiv.Perm.fixed_point_card_lt_of_ne_one, IsLowerSet.le_card_inter_finset', card_le_one_iff_subset_singleton, card_piDiag, eq_iff_card_ge_of_superset, Polynomial.card_roots_toFinset_le_card_roots_derivative_diff_roots_succ, PairReduction.card_le_logSizeRadius_le_pow_logSizeRadius, ModularForm.coe_prodEqualWeights, NumberField.InfinitePlace.card_filter_mk_eq, SkewPolynomial.card_support_eq_zero, Fin.card_Ico, Nat.divisors_card_eq_one_iff, Int.card_Ioc, all_card_le_biUnion_card_iff_existsInjective', card_vadd_finset, SimpleGraph.card_edgeFinset_le_extremalNumber, card_singleton_inter, card_sym2, Nat.Partition.hasProd_powerSeriesMk_card_countRestricted, card_inv_le, SimpleGraph.farFromTriangleFree.le_card_sub_card, card_Iio_finset, Equiv.Perm.card_of_cycleType_eq_zero_iff, Group.rank_le, Nat.card_antidiagonal, Cubic.card_roots_of_disc_ne_zero, Dynamics.IsDynCoverOf.nonempty_inter, NNReal.rpow_sum_le_const_mul_sum_rpow, finrank_span_le_card, Caratheodory.minCardFinsetOfMemConvexHull_card_le_card, card_sigmaLift, SimpleGraph.isExtremal_free_iff, Cubic.card_roots_of_discr_ne_zero, Finpartition.card_nonuniformWitnesses_le, card_lt_iff_ne_univ, Composition.card_boundaries_eq_succ_length, SimpleGraph.IsTuranMaximal.card_parts_le, card_add_card_subsetSum_lt_card_subsetSum_insert_max, one_lt_card_iff, Equiv.Perm.Basis.card_ofPermHom_support, NumberField.InfinitePlace.card_eq_card_isUnramifiedIn, Rel.card_interedges_finpartition_right, SimpleGraph.card_edgeFinset_turanGraph_add, Fintype.card_Ici, IsAddCyclic.card_nsmul_eq_zero_le, SimpleGraph.maximumIndepSet_card_eq_indepNum, card_sub_add_le_card_sub_add_card_add, Multiset.card_Ioc, Sym2.card_image_diag, Tuple.lt_card_ge_iff_apply_ge_of_antitone, Finpartition.IsEquipartition.sum_nonUniforms_lt', Nat.Ioc_filter_dvd_card_eq_div, SimpleGraph.le_card_edgeFinset_killCopies_add_copyCount, card_eraseNone_of_not_mem, Ideal.index_pow_le, card_le_card_of_injOn, FiniteField.card_image_polynomial_eval, Equiv.Perm.IsCycleOn.exists_pow_eq, Int.card_box, AhlswedeZhang.IsAntichain.le_infSum, Pi.card_Ioc, add_nonneg_card_nsmul, sum_range_le_sum, Nat.lt_card_toFinset_of_nth_ne_zero, Matrix.det_sum_le, Fintype.card_Icc, mulDysonETransform.card, powersetCard_card_add, card_mul_mulConst, Fintype.card_Ioo, Pi.card_Icc, Fintype.subtype_card, card_eraseNone_of_mem, Nat.Prime.emultiplicity_choose', Nat.exists_lt_card_finite_nth_eq, card_diffs_le, IsAntichain.sperner, Lagrange.degree_interpolate_erase_lt, le_card_mul_mul_mulEnergy, SimpleGraph.card_interedges_le_mul, powerset_card_biUnion, Module.le_rank_iff_exists_finset, ruzsa_triangle_inequality_add_add_negAdd, Equiv.Perm.IsThreeCycle.card_support, exists_card_eq, card_preimage, Int.card_Ico_of_le, card_mul_cast_subConst, inclusion_exclusion_sum_inf_compl, sum_conjClasses_card_eq_card, Equiv.Perm.OnCycleFactors.mem_range_toPermHom'_iff, Dynamics.IsDynCoverOf.coverMincard_le_card, ValueDistribution.proximity_sum_top_le, Nat.totient_div_of_dvd, card_mul_inv_eq_convolution_inv, cauchy_davenport_of_isAddTorsionFree, Fintype.card_piFinset, expect_eq_single_of_mem, card_smul_expect, card_le_three, Polynomial.card_support_eq, card_sdiff_add_card_inter, Finpartition.IsEquipartition.card_part_le_average_add_one, Lagrange.degree_interpolate_lt, Nonempty.card_pos, card_Icc_finset, exists_finset_linearIndependent_of_le_finrank, padicValNat_choose', SetTheory.PGame.Domineering.moveLeft_smaller, ruzsa_triangle_inequality_mul_div_div, card_Ioo_eq_card_Icc_sub_two, card_Iio_eq_card_Iic_sub_one, card_le_card_add_left, card_disjiUnion, MonovaryOn.sum_mul_sum_le_card_mul_sum, card_filter_eq_zero_iff, card_le_five, ProbabilityTheory.mgf_sum_of_identDistribβ, card_imageβ_singleton_right, card_mul_expect, dens_eq_card_div_card, SimpleGraph.even_card_odd_degree_vertices, Cardinal.mk_coe_finset, sum_card_slice, sum_comp, Finpartition.IsEquipartition.card_small_parts_eq_mod, DFinsupp.card_Iic, prod_comp, Pi.card_uIcc, card_Ico_one_mul, card_le_card_add_right, AddGroup.rank_spec, noncommSum_eq_card_nsmul, SimpleGraph.Iso.card_edgeFinset_eq, Real.rpow_sum_le_const_mul_sum_rpow, Finsupp.card_Icc, Polynomial.IsUnitTrinomial.card_support_eq_three, card_le_card_sdiff_add_card, ruzsa_triangle_inequality_invMul_invMul_invMul, Group.rank_spec, card_eq_of_equiv_fintype, Polynomial.card_support_binomial, IsApproximateSubgroup.card_mul_self_le, card_nsmul_le_sum, card_biUnion, Fin.card_filter_val_lt, ThreeGPFree.le_mulRothNumber, card_succ_choose_two_lt_card_subsetSum_of_pos, Multiset.card_uIcc, ruzsaSzemerediNumber_spec, card_dvd_card_imageβ_left, Multiset.card_le_card_toFinset_add_one_iff, SetTheory.PGame.Domineering.moveRight_smaller, YoungDiagram.rowLen_eq_card, SimpleGraph.isNIndepSet_iff, Finsupp.card_uIcc, FormalMultilinearSeries.nnnorm_changeOriginSeries_apply_le_tsum, IsUpperSet.le_card_inter_finset, Besicovitch.card_le_multiplicity_of_Ξ΄, Cardinal.exists_finset_eq_card, Fintype.exists_lt_card_fiber_of_mul_lt_card, Finsupp.card_Ioo, Nat.Prime.emultiplicity_choose, SzemerediRegularity.card_le_m_add_one_of_mem_chunk_parts, Nat.Ioc_filter_modEq_card, Pi.card_Iio, Nonempty.card_nsmul_mono, card_union_eq_card_add_card, card_nthRoots_subgroup_units, Int.Ioc_filter_modEq_card, SimpleGraph.extremalNumber_top, addRothNumber_spec, Nat.card_Ioo, Subgroup.index_le_of_leftCoset_cover_const, card_filter, Nat.Partition.powerSeriesMk_card_restricted_eq_tprod, ringKrullDim_le_ringKrullDim_quotient_add_card, powersetCard_eq_filter, Equiv.Perm.card_of_cycleType, SimpleGraph.card_edgeFinset_deleteIncidenceSet_le_extremalNumber, Fintype.exists_card_fiber_le_of_card_le_nsmul, sorted_zero_eq_min', card_erase_of_mem, Int.card_Ico, Fintype.card_of_finset', Int.card_Ioc_of_le, card_erase_le, Nat.card_Iic, card_le_four, Equiv.Perm.IsCycle.cycleType, Equiv.Perm.mem_cycleType_iff, MultilinearMap.map_add_sub_map_add_sub_linearDeriv, PolynomialLaw.exists_range_Ο_eq_of_fg, NumberField.InfinitePlace.card_isUnramified, Fin.lt_card_filter_univ_iff_apply_of_imp, IsApproximateAddSubgroup.card_nsmul_le, card_zero, card_le_one, sum_const_nat, le_addEnergy, card_bij, SetTheory.PGame.Domineering.card_of_mem_left, mem_upShadow_iterate_iff_exists_card, card_le_card_mul_rightβ, DFinsupp.card_Ioo, Finpartition.exists_enumeration, Rel.mul_edgeDensity_le_edgeDensity, ruzsa_triangle_inequality_div_mul_mul, Polynomial.card_support_eq', centroidWeights_apply, SimpleGraph.card_edgeFinset_top_eq_card_choose_two, SimpleGraph.dart_card_eq_twice_card_edges, pluennecke_ruzsa_inequality_pow_div_pow_mul, Polynomial.card_support_mul_le, Lagrange.degree_nodal, Equiv.Perm.one_lt_card_support_of_ne_one, addConst_le_card, List.card_toFinset, dens_mul_card, EquitableOn.le, Set.powersetCard.card_eq, card_eq_two, Fin.card_Icc, Sym2.card_toFinset_of_isDiag, ruzsa_triangle_inequality_negAdd_negAdd_negAdd, AntivaryOn.card_smul_sum_le_sum_smul_sum, card_nsmul_quotient_add_nsmul_inter_addSubgroup_le, AddSubgroup.exists_index_le_card_of_leftCoset_cover, card_union_add_card_inter, Set.Finite.card_toFinset, MonovaryOn.sum_smul_sum_le_card_smul_sum, card_insert_le, card_le_card_mul_left_of_injective, card_inter_vadd, Nat.Ico_filter_modEq_card, NumberField.InfinitePlace.card_isUnramified_compl, Subgroup.exists_index_le_card_of_leftCoset_cover, Equiv.Perm.IsCycleOn.pow_card_apply, card_le_card_mul_self', card_div_mul_le_card_div_mul_card_mul, Height.mulHeightβ_sum_le, Nat.Partition.powerSeriesMk_card_restricted_eq_powerSeriesMk_card_countRestricted, card_Ico_zero_add, three_lt_card_iff, Set.toFinset_card, Subgroup.rank_closure_finset_le_card, prod_const, SimpleGraph.not_isUniform_iff, Besicovitch.exists_goodΞ΄, card_le_card_diffs, card_Ico_finset, card_image_of_injective, Equiv.Perm.IsCycle.orderOf, card_sigma, lp.norm_eq_card_dsupport, Equiv.Perm.card_support_prod_list_of_pairwise_disjoint, SetTheory.PGame.Domineering.moveLeft_card, cast_mulConst_mul_card, vadd_finset_card_le, Fintype.all_card_le_filter_rel_iff_exists_injective, card_le_card_mul_self, card_union_le, three_lt_card, card_insert_of_notMem, rank_span_finset_le, Nat.subtype_card, PNat.card_Ico, Nat.card_Icc, Fintype.card_subtype, expect_dite_eq', Finpartition.card_atomise_le, card_le_card_biUnion_add_one, SimpleGraph.extremalNumber_of_fintypeCard_eq, card_eq_sum_card_image, card_consEquiv_filter_piFinset, card_attachFin, SimpleGraph.DeleteFar.le_card_edgeFinset, Equiv.Perm.card_compl_support_modEq, covBy_iff_card_sdiff_eq_one, AlternatingGroup.card_of_cycleType, Polynomial.card_support_eq_three, Finsupp.card_support_le_one', Int.Ico_filter_dvd_card, Nat.multiplicity_choose_aux, inclusion_exclusion_card_biUnion, Polynomial.card_supp_le_succ_natDegree, card_finset_fin_le, Fintype.card_filter_piFinset_eq_of_mem, Down.card_compression, Equiv.Perm.card_support_extend_domain, card_le_two, MeasureTheory.integral_biUnion_eq_sum_powerset, card_infs_le, szemeredi_regularity, mem_powersetCard, PMF.toOuterMeasure_uniformOfFinset_apply, PairReduction.card_finset_logSizeBallSeq_le, card_eq_four, Finpartition.coe_energy, Dynamics.IsDynCoverOf.coverEntropyEntourage_le_log_card_div, card_smul_inter, FormalMultilinearSeries.changeOriginIndexEquiv_apply_fst, Fin.card_Iio, card_sq_le_card_mul_mulEnergy, MvPolynomial.schwartz_zippel_sup_sum, Fintype.card_filter_piFinset_const_eq_of_mem, SimpleGraph.maximumClique_card_eq_cliqueNum, Equiv.Perm.le_card_support_of_mem_cycleType, le_card_diffs_mul_card_diffs, card_le_card_of_injective, Set.ncard_eq_toFinset_card', le_card_falling_div_choose, card_filter_add_card_filter_not, Finpartition.card_mod_card_parts_le, UniqueMul.iff_card_le_one, Nat.Partition.hasProd_powerSeriesMk_card_restricted, MeasureTheory.Measure.haar.addIndex_defined, Int.card_uIcc, Int.card_Icc_of_le, FormalMultilinearSeries.changeOriginIndexEquiv_symm_apply_snd_fst, IsPrimitiveRoot.card_primitiveRoots, SimpleGraph.degree_le_between_add, card_Ioc_eq_card_Icc_sub_one, Fin.card_Ioo, Nat.card_Ico, card_truncatedInf_union_add_card_truncatedInf_sups, IsPrimitiveRoot.card_nthRootsFinset, Fintype.exists_lt_card_fiber_of_nsmul_lt_card, SimpleGraph.card_edgeFinset_replaceVertex_of_not_adj, finrank_span_finset_le_card, SimpleGraph.exists_isFiveWheelLike_of_maximal_cliqueFree_not_isCompleteMultipartite, Nat.smoothNumbersUpTo_card_le, Fintype.existsUnique_iff_card_one, Nat.factorization_choose', pow_card_le_prod, card_filter_le_iff, card_le_one_iff, RootPairing.IsG2.card_base_support_eq_two, SimpleGraph.IsFiveWheelLike.card_right, card_mul_iff, pluennecke_ruzsa_inequality_pow_div, Fintype.exists_le_card_fiber_of_mul_le_card, ZMod.gauss_lemma, card_le_card_div_self, card_toLeft_add_card_toRight, AffineBasis.coord_apply_centroid, ValueDistribution.characteristic_sum_top_le, Set.encard_eq_coe_toFinset_card, ruzsa_triangle_inequality_add_sub_sub, card_perms_of_finset, Nat.roughNumbersUpTo_card_le', schnirelmannDensity_le_div, odd_sum_iff_odd_card_odd, card_Ioo_eq_card_Ioc_sub_one, sq_sum_le_card_mul_sum_sq, card_inter_add_card_sdiff, length_toList, MultilinearMap.map_add_eq_map_add_linearDeriv_add, le_card_iff_exists_subset_card, card_eq_sum_card_fiberwise, card_image_le, MeasureTheory.Measure.count_apply_finset', DFinsupp.card_uIcc, Equiv.Perm.card_support_swap, addConvolution_le_card_left, sum_card_slice_div_choose_le_one, SimpleGraph.Subgraph.IsSpanning.card_verts, SimpleGraph.le_card_edgeFinset_killCopies, Fin.card_filter_univ_succ', addConst_mul_card, List.toFinset_card_le, ThreeAPFree.le_addRothNumber, IsAddCyclic.card_addOrderOf_eq_totient, SimpleGraph.card_edgeFinset_replaceVertex_of_adj, Subgroup.exists_finset_card_le_mul, SimpleGraph.IsFiveWheelLike.card_inter, Nat.exists_lt_card_nth_eq, Set.powersetCard.mem_iff, ruzsa_triangle_inequality_mulInv_mul_mul, ruzsa_triangle_inequality_mul_mul_mul, Equiv.Perm.zpow_eq_zpow_on_iff, Nat.card_divisors, SimpleGraph.card_neighborFinset_eq_degree, le_mulEnergy, Nat.nth_injOn, Lagrange.degree_basis, sum_le_card_nsmul, Tuple.lt_card_le_iff_apply_le_of_monotone, Finsupp.card_pi, exists_finset_linearIndependent_of_le_rank, card_attach, Nat.Coprime.card_divisors_mul, Colex.isInitSeg_iff_exists_initSeg, le_card_add_mul_addEnergy, sum_add_card_nsmul, SimpleGraph.LocallyLinear.le_ruzsaSzemerediNumber, Pi.card_Ico, Nonempty.card_pow_mono, Submodule.spanRank_toENat_eq_iInf_finset_card, card_sq_le_card_mul_addEnergy, card_Ico_eq_card_Icc_sub_one, pluennecke_ruzsa_inequality_nsmul_sub_nsmul_sub, Nat.count_le_card, card_inter_add_card_union, Ideal.sum_pow_mem_span_pow, SimpleGraph.triangle_counting', sum_powerset_neg_one_pow_card_of_nonempty, Finpartition.card_bind, Behrend.card_sphere_le_rothNumberNat, MeasureTheory.Measure.haar.addIndex_elim, pred_card_le_card_erase, card_sub_card_eq, Tuple.graph.card, sum_pow_mul_eq_add_pow, card_Ioi_eq_card_Ici_sub_one, card_insert_eq_ite, cast_subConst, card_lt_univ_of_notMem, card_sdiff_eq_card_sdiff_iff, Polynomial.card_support_eraseLead, Polynomial.card_support_eq_zero, SimpleGraph.Walk.IsEulerian.card_filter_odd_degree, padicValNat_choose, ringKrullDim_le_ringKrullDim_add_card, IsCyclic.card_orderOf_eq_totient, nnratCast_dens, card_mul_le, equitableOn_iff, Multiset.card_toFinset, MulETransform.card, card_eq_succ_iff_cons, Lagrange.degree_interpolate_le, subConst_le_card, DFinsupp.card_pi, card_nsmul_add_sum, card_bijective, SimpleGraph.IsSRGWith.card_neighborFinset_union_of_not_adj, Equiv.Perm.IsCycleOn.pow_apply_eq_pow_apply, Nat.Partition.powerSeriesMk_card_countRestricted_eq_tprod, Cardinal.mk_eq_nat_iff_finset, CompositionAsSet.lt_length', FormalMultilinearSeries.changeOriginSeries_summable_auxβ, le_card_quotient_mul_sq_inter_subgroup, prod_neg, PNat.card_uIcc, card_le_univ, le_card_quotient_add_sq_inter_addSubgroup, Finpartition.IsEquipartition.sum_nonUniforms_lt, ruzsa_triangle_inequality_mulInv_mulInv_mulInv, SimpleGraph.le_card_nonuniformWitness, card_biUnion_le_of_intersecting, prod_powerset, card_lt_card, SimpleGraph.sum_degrees_support_eq_twice_card_edges, card_pair_eq_one_or_two, SzemerediRegularity.card_eq_of_mem_parts_chunk, Nat.primesBelow_card_eq_primeCounting', mem_falling, card_le_of_interleaved, exists_finite_card_le_of_finite_of_linearIndependent_of_span, Finpartition.card_filter_atomise_le_two_pow, card_add_singleton, MeasureTheory.Measure.count_apply_finset, Complex.card_primitiveRoots, sum_powerset, card_neg, IsCyclic.card_pow_eq_one_le, BoxIntegral.TaggedPrepartition.IsHenstock.card_filter_tag_eq_le, Multiset.toFinset_card_eq_one_iff, SimpleGraph.isBipartiteWith_degree_le, Polynomial.card_support_eq_two, Nat.Partition.card_odds_eq_card_distincts, PairReduction.card_finset_logSizeBallSeq_card_eq_zero, card_support_eq_three_iff, cast_mulConst, card_empty, all_card_le_biUnion_card_iff_exists_injective, mulEnergy_eq_sum_sq, Nat.Ico_filter_coprime_le, subConst_mul_card, Polynomial.card_support_eq_one, smul_finset_card_le, mulETransformLeft.card, List.toFinset_card_of_nodup, Dynamics.IsDynNetIn.card_le_card_of_isDynCoverOf, DirectSum.IsInternal.card_filter_subordinateOrthonormalBasisIndex_eq, card_mul_cast_mulConst, Fin.sum_pow_mul_eq_add_pow, exists_of_linearIndepOn_of_finite_span, Fin.card_Iic, Int.card_Icc, Rel.abs_edgeDensity_sub_edgeDensity_le_one_sub_mul, Equiv.Perm.pow_mod_card_support_cycleOf_self_apply, card_le_six, Cardinal.exists_finset_le_card, card_cons, convolution_le_card_left, PNat.card_Ioo, Fintype.exists_card_fiber_lt_of_card_lt_mul, Submodule.exists_finset_span_eq_linearIndepOn, CompositionAsSet.lt_length, card_fin, mem_shadow_iterate_iff_exists_card, SimpleGraph.IsSRGWith.card_neighborFinset_union_of_adj, Polynomial.card_support_C_mul_X_pow_le_one, le_card_infs_mul_card_sups, card_add_iff, SimpleGraph.dart_fst_fiber_card_eq_degree, card_eq_zero, FormalMultilinearSeries.changeOriginSeries_summable_auxβ, mem_shadow_iff_exists_sdiff, SimpleGraph.extremalNumber_le_iff, card_dvd_card_imageβ_right, Nat.filter_coprime_Ico_eq_totient, Finsupp.card_support_eq_one', ThreeGPFree.mulRothNumber_eq, mem_powersetCard_univ, SimpleGraph.card_edgeFinset_deleteIncidenceSet, card_bij', card_compl_lt_iff_nonempty, sum_smul_sum_eq_sum_perm, card_Ioc_finset, UniqueAdd.iff_card_le_one, PiLp.edist_eq_card, card_pow_mono, inclusion_exclusion_sum_biUnion, card_insert_of_mem, Dynamics.netMaxcard_finite_iff, SimpleGraph.lt_extremalNumber_iff, MonoidHom.card_fiber_eq_of_mem_range, Set.sized_singleton, pow_sum_le_card_mul_sum_pow, card_Ioo_eq_card_Ico_sub_one, DFinsupp.card_Ico, sum_mul_sum_eq_sum_perm, Equiv.Perm.OnCycleFactors.mem_range_toPermHom_iff, cauchy_davenport_mul_of_linearOrder_isCancelMul, Nat.card_multiples', Multiset.toFinset_card_of_nodup, Nat.card_divisors_le_self, Finpartition.card_bot, exists_disjoint_union_of_even_card_iff, mem_upShadow_iff_exists_sdiff, SimpleGraph.right_nonuniformWitnesses_card, card_inter_smul, natCast_card_mul_nnratCast_dens, card_eq_succ, addRothNumber_le, Nat.nth_strictMonoOn, card_dvd_card_mul_left, Int.Ico_filter_modEq_card, Group.fg_iff', card_image_iff, le_card_sdiff, card_div_le, Polynomial.eraseLead_support_card_lt, LinearIndependent.finset_card_le_finrank, Set.encard_coe_eq_coe_finsetCard, cast_addConst_mul_card, cauchy_davenport_minOrder_add, Equiv.Perm.card_support_conj, Finpartition.card_mono, ProbabilityTheory.mgf_sum_of_identDistrib, legendreSym.card_sqrts, card_Iic_finset, card_disjSups_le, ZMod.gauss_lemma_aux, SimpleGraph.isMaximumIndepSet_iff, card_singleton_add, YoungDiagram.colLen_eq_card, Multiset.toFinset_card_eq_card_iff_nodup, Nat.card_eq_card_toFinset, card_le_card_pow, SimpleGraph.IsNIndepSet.card_eq, card_le_card_biUnion_add_card_fiber, PairReduction.exists_radius_le, card_le_card_mul_right_of_injective, Finsupp.card_Iic, card_sups_le, card_le_card_shatterer, card_le_card_mul_right, le_mulEnergy_self, SimpleGraph.TripartiteFromTriangles.card_triangles, prod_indicator_const, smul_prod, IsApproximateSubgroup.card_pow_le, Equiv.Perm.IsCycleOn.zpow_apply_eq, card_le_card_imageβ_right, Sym2.card_image_offDiag, card_le_card_mul_leftβ, cast_card_erase_of_mem, card_le_one_of_subsingleton, card_disjSum, card_pow_quotient_mul_pow_inter_subgroup_le, Besicovitch.card_le_of_separated, Fintype.card_uIcc, Sigma.card_Ioo, Polynomial.natSepDegree_eq_of_isAlgClosed, Equiv.Perm.IsCycleOn.zpow_apply_eq_zpow_apply, powersetCard_nonempty, Finsupp.card_Iio, Nat.card_Ioc, card_biUnion_le, Prod.card_box_succ, Behrend.card_box, Sigma.card_Ico, erdos_ko_rado, SimpleGraph.IsTuranMaximal.card_parts, Sym2.card_toFinset, ruzsa_triangle_inequality_mul_mulInv_mul, Sigma.card_Ioc, card_infs_iff, Nat.factorization_eq_card_pow_dvd, CompositionAsSet.mem_boundaries_iff_exists_blocks_sum_take_eq, SimpleGraph.left_nonuniformWitnesses_card, ruzsa_triangle_inequality_div_mul_div, SimpleGraph.FarFromTriangleFree.le_card_cliqueFinset, SzemerediRegularity.pow_mul_m_le_card_part, Finpartition.IsEquipartition.exists_partsEquiv, PolynomialLaw.range_Ο, Equiv.Perm.IsCycle.two_le_card_support, card_le_card_of_forall_subsingleton, sum_eq_card_nsmul, SimpleGraph.IsClique.card_le_chromaticNumber, card_le_card_sub_self, Equiv.Perm.two_le_card_support_cycleOf_iff, Fintype.card_Ioc, cast_divConst_mul_card, MeasureTheory.Measure.count_apply_finite', card_le_card_sub_left, card_le_diff_of_interleaved, Option.card_toFinset, card_toRight_le, vsub_card_le, mulRothNumber_le, cast_card_sdiff, Besicovitch.card_le_multiplicity, SimpleGraph.completeBipartiteGraph_isContained_iff, Holor.cprankMax_sum, card_pos, Multiset.card_Iic, Equiv.Perm.two_dvd_card_support, card_mk, one_le_card, card_image_of_injOn, SimpleGraph.lt_extremalNumber_iff_of_nonneg, Cubic.card_roots_le, schnirelmannDensity_lt_iff, Fintype.card_Ioi, SetTheory.PGame.Domineering.card_of_mem_right, Rel.card_interedges_finpartition_left, SimpleGraph.isNClique_iff, SimpleGraph.card_incidenceFinset_eq_degree, card_smul_inter_smul, AddETransform.card, two_lt_card, card_imageβ_iff, Fintype.card_Iio, mem_upShadow_iff_exists_mem_card_add_one, cauchy_davenport_of_isMulTorsionFree, Cardinal.mk_set_eq_nat_iff_finset, prod_indicator_const_apply, expect_dite_eq, card_le_card_nsmul, SzemerediRegularity.coe_m_add_one_pos, ruzsa_triangle_inequality_sub_sub_sub, card_shatterer_le_sum_vcDim, cast_divConst, SzemerediRegularity.card_auxβ, PMF.uniformOfFinset_apply, Polynomial.card_le_degree_of_subset_roots, SimpleGraph.Subgraph.finset_card_neighborSet_eq_degree, powerset_card_disjiUnion, Set.Finite.encard_eq_coe_toFinset_card, card_smul_le, PNat.card_Ioc, SimpleGraph.IsIndepSet.card_le_indepNum, Nat.count_lt_card, card_sdiff_add_card_eq_card, Equiv.Perm.IsCycle.sign, MeasureTheory.Measure.haar.index_defined, SimpleGraph.degree_le_between_add_compl, pluennecke_ruzsa_inequality_pow_div_pow_div, centroidWeights_eq_const, card_powersetCard, Dynamics.coverMincard_finite_iff, Matrix.det_sum_smul_le, SetTheory.PGame.Domineering.moveRight_card, SimpleGraph.degree_le_card_edgeFinset, Equiv.Perm.card_support_eq_two, card_subtype, Polynomial.Gal.card_complex_roots_eq_card_real_add_card_not_gal_inv, Set.ncard_eq_toFinset_card, Fintype.card_filter_piFinset_const, mulETransformRight.card, AffineIndependent.card_lt_card_of_affineSpan_lt_affineSpan, mem_slice, Fin.card_Ioc, card_le_card_mul_selfβ, Equiv.Perm.parts_partition, Equiv.Perm.cycleType_def, ruzsa_triangle_inequality_add_addNeg_add, SimpleGraph.card_interedges_div_card, filter_card_add_filter_neg_card_eq_card, AffineIndependent.card_le_card_of_subset_affineSpan, Equiv.Perm.length_toList, Finpartition.sum_card_parts, card_sub_le, Multiset.card_Icc, card_le_card_div_right, Finpartition.card_extend, SimpleGraph.card_edgeFinset_turanGraph, card_pair, addETransformLeft.card, card_mul_singleton, exists_eq_insert_iff, two_lt_card_iff, card_def, SimpleGraph.edgeSet_univ_card, Nat.card_Iio, SimpleGraph.card_edgeFinset_induce_support, MvPolynomial.schwartz_zippel_sum_degreeOf, SimpleGraph.card_edgeFinset_completeEquipartiteGraph, Fintype.card_finset_len, SimpleGraph.Walk.IsTrail.length_le_card_edgeFinset, card_Ici_prod, card_Icc_prod, PairReduction.card_pairSet_le, Numbering.card_prefixed, sum_powerset_neg_one_pow_card, pluennecke_ruzsa_inequality_pow_mul, Module.finrank_eq_card_finset_basis, FormalMultilinearSeries.changeOriginIndexEquiv_apply_snd, card_filter_le, card_disjUnion, length_sort, card_le_card_div_left, card_le_card_imageβ_left, Equiv.Perm.CycleType.count_def, SimpleGraph.IsClique.card_le_of_colorable, card_vadd_inter, Fintype.card_Ico, card_sdiff_le_card_sdiff_iff, SimpleGraph.IsFiveWheelLike.card_left, pluennecke_ruzsa_inequality_nsmul_sub, sum_powerset_apply_card, SimpleGraph.card_toFinset_mem_edgeFinset, ruzsa_triangle_inequality_addNeg_addNeg_addNeg, card_val, Polynomial.card_support_le_one_iff_monomial, Fintype.card_of_subtype, Sym2.two_mul_card_image_offDiag, Nat.factorization_choose, card_le_card_mul_left, Polynomial.card_support_eq_one_of_eraseLead_eq_zero, MeasureTheory.Measure.count_apply_finite, Submodule.mem_span_set_iff_exists_finsupp_le_finrank, card_nsmul_le, ruzsa_triangle_inequality_div_div_div, Fintype.exists_le_card_fiber_of_nsmul_le_card, Fintype.sum_pow_mul_eq_add_pow, Set.BijOn.finsetCard_eq, AntivaryOn.card_mul_sum_le_sum_mul_sum, Finsupp.card_support_le_one, mem_shadow_iterate_iff_exists_mem_card_add, SimpleGraph.cycleGraph_degree_two_le, Multiset.card_toEnumFinset, sum_powersetCard, SimpleGraph.IsTuranMaximal.degree_eq_card_sub_part_card, le_rank_iff_exists_linearIndependent_finset, Equiv.Perm.sum_cycleType, sum_le_sum_range, SimpleGraph.copyCount_eq_card_image_copyToSubgraph, MeasureTheory.measureReal_biUnion_eq_sum_powerset, Fintype.exists_card_fiber_le_of_card_le_mul, MvPolynomial.esymm_eq_sum_subtype, Equiv.Perm.cycle_zpow_mem_support_iff, card_eq_three, noncommProd_eq_pow_card, card_nbij, SimpleGraph.CliqueFree.card_edgeFinset_le, Nat.card_pair_lcm_eq, SzemerediRegularity.card_biUnion_star_le_m_add_one_card_star_mul, SimpleGraph.card_edgeSet, IsApproximateAddSubgroup.card_add_self_le, card_eraseNone_eq_card_erase, cauchy_davenport_minOrder_mul, sum_card_addOrderOf_eq_card_nsmul_eq_zero, IsNonarchimedean.finset_powerset_image_add, card_union_of_disjoint, pluennecke_ruzsa_inequality_nsmul_sub_nsmul_add, addEnergy_eq_card_filter, CompositionAsSet.boundary_length, mem_shadow_iff_exists_mem_card_add_one, card_diffs_iff, SimpleGraph.card_neighborSet_union_compl_neighborSet, indicator_biUnion_eq_sum_powerset, Equiv.Perm.card_of_cycleType_singleton, Submodule.index_smul_le, mulEnergy_eq_card_filter, PairReduction.card_finset_logSizeBallSeq_add_one_lt, Colex.isInitSeg_initSeg, card_uIcc_prod, Polynomial.natSepDegree_eq_of_splits, Finpartition.IsEquipartition.exists_partPreservingEquiv, Ideal.height_le_card_of_mem_minimalPrimes_span_finset, Sigma.card_Icc, Numbering.dens_prefixed, powersetCard_eq_empty, IsUpperSet.card_inter_le_finset, pow_sum_div_card_le_sum_pow, card_le_card_add_right_of_injective, Lagrange.natDegree_basis, Real.posLog_sum, expect_eq_sum_div_card, ValueDistribution.characteristic_sum_top_eventuallyLE, sum_boole, SimpleGraph.isNClique_bot_iff, AddSubgroup.index_le_of_leftCoset_cover_const, Group.card_center_add_sum_card_noncenter_eq_card, Nat.emultiplicity_eq_card_pow_dvd, Fintype.exists_card_fiber_lt_of_card_lt_nsmul, Rel.edgeDensity_sub_edgeDensity_le_one_sub_mul, SimpleGraph.Subgraph.IsMatching.even_card, Fintype.card_coe, FormalMultilinearSeries.changeOriginSeriesTerm_changeOriginIndexEquiv_symm, expect_ite_eq, card_nsmul_mono, DFinsupp.card_Iio, SimpleGraph.card_edgeFinset_eq_extremalNumber_top_iff_nonempty_iso_turanGraph, Polynomial.coeff_prod_of_natDegree_le, SimpleGraph.card_edgeFinset_induce_of_support_subset, one_lt_card, Multiset.card_Ioo, product_self_eq_disjiUnion_perm, DFinsupp.card_Icc, add_one_le_card_pow, Fin.card_filter_univ_eq_vector_get_eq_count, sum_card_orderOf_eq_card_pow_eq_one, UV.card_compression, ZMod.eisenstein_lemma_aux, card_add_neg_eq_addConvolution_neg, cast_card, nnratCast_dens_mul_natCast_card, Finsupp.card_support_eq_zero, one_half_le_sum_primes_ge_one_div, pow_card_mul_prod, card_univ_diff, mem_upShadow_iterate_iff_exists_sdiff, Polynomial.card_roots_toFinset_le_derivative, Equiv.Perm.IsCycleOn.pow_apply_eq, univ_filter_card_eq, addEnergy_univ_right, Behrend.exists_large_sphere_aux, card_singleton_mul, LinearMap.le_rank_iff_exists_linearIndependent_finset, sum_le_sum_Ioc, ZMod.cauchy_davenport, SimpleGraph.IsClique.card_le_cliqueNum, Int.card_Ioo_of_lt, addConvolution_le_card_right, card_smul_finset, ZMod.div_eq_filter_card, convolution_le_card_right, card_vadd_inter_vadd, card_dvd_card_add_left, card_neg_le, SimpleGraph.card_cliqueFinset_le, AlternatingGroup.card_of_cycleType_mul_eq, card_mul_cast_divConst, SimpleGraph.edgeFinset_card, cauchy_davenport_add_of_linearOrder_isCancelAdd, Polynomial.normalizedFactors_cyclotomic_card, le_addEnergy_self, expect_ite_eq', eq_iff_card_le_of_subset, Finpartition.not_isEquipartition, cast_addConst, DivisorChain.card_subset_divisors_le_length_of_chain, SimpleGraph.triangle_counting, Pi.card_Ioo, Set.Intersecting.exists_card_eq, Pi.card_Ioi, schnirelmannDensity_mul_le_card_filter, PMF.toMeasure_uniformOfFinset_apply, CompositionAsSet.boundary_zero, ruzsa_triangle_inequality_add_add_add, Set.ncard_coe_finset, PairReduction.logSizeRadius_le_card_smallBall, card_mono, DFinsupp.card_Ioc, prod_le_pow_card, Set.Intersecting.card_le, Real.posLog_norm_sum_le, CovBy.card_finset, card_finsupp, Nat.card_uIcc, card_eq_of_equiv, Int.Ioc_filter_dvd_card, ruzsa_triangle_inequality_negAdd_add_add, ruzsa_triangle_inequality_addNeg_add_add, Equiv.Perm.IsCycle.isConj_iff, card_truncatedSup_union_add_card_truncatedSup_infs, card_eq_of_equiv_fin, card_sdiff_add_card, Polynomial.card_support_trinomial, Finsupp.card_support_eq_one, Set.Sized.card_le, card_dvd_card_vadd_right, max_abv_sum_one_le, sum_const, PiLp.norm_eq_card, cast_card_inter, ENNReal.rpow_sum_le_const_mul_sum_rpow, SimpleGraph.mul_card_edgeFinset_turanGraph_le, SimpleGraph.IsMaximumClique.maximum, Behrend.exists_large_sphere, Rel.card_interedges_add_card_interedges_compl, SimpleGraph.IsTree.card_edgeFinset, powersetCard_self, card_powerset, Nat.filter_Ico_card_eq_of_periodic, card_dvd_card_mul_right, Rel.card_interedges_comm, Nat.image_nth_Iio_card, ruzsa_triangle_inequality_sub_add_add, Finpartition.IsEquipartition.card_interedges_sparsePairs_le', card_singleton, Submodule.spanFinrank_eq_iInf, Nat.card_finMulAntidiag_of_squarefree, Nat.card_eq_card_finite_toFinset, SimpleGraph.isBipartiteWith_sum_degrees_eq_twice_card_edges, addETransformRight.card, SimpleGraph.card_edgeFinset_induce_compl_singleton, mem_upShadow_iterate_iff_exists_mem_card_add
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