Finset

📁 Source: Mathlib/Tactic/Positivity/Finset.lean

Statistics

Metric	Count
Definitions Finset, evalFinsetCard, evalFinsetDens, evalFinsetSum, evalFintypeCard	5
Theorems	0
Total	5

Mathlib.Meta.Positivity

Definitions

Name	Category	Theorems
evalFinsetCard 📖	CompOp	—
evalFinsetDens 📖	CompOp	—
evalFinsetSum 📖	CompOp	—
evalFintypeCard 📖	CompOp	—

(root)

Definitions

Name	Category	Theorems
Finset 📖	CompData	5228 math math: Finset.val_strictMono, Finpartition.mem_part_ofSetSetoid_iff_rel, Polynomial.supp_subset_range, Finset.insert_Ico_succ_left_eq_Ico, Finset.toLeft_monotone, List.mem_toFinset, Polynomial.support_monomial, LieAlgebra.IsKilling.rootSystem_toLinearMap_apply, Fintype.univ_empty, Finset.iSup_biUnion, Finset.bot_eq_empty, MeasureTheory.SimpleFunc.coe_range, Fintype.all_card_le_rel_image_card_iff_exists_injective, Function.update_eq_updateFinset, SimpleGraph.TripartiteFromTriangles.Graph.in₀₂_iff', Finset.expect_ite_mem, Affine.Simplex.isTangentAt_insphere_iff_eq_touchpoint, Finset.coe_eq_singleton, SimpleGraph.edgeFinset_mono, Equiv.Perm.support_closure_subset_union, Finset.map_traverse, Finsupp.range_subset_insert_frange, WittVector.remainder_vars, LowerSemicontinuousOn.inter_biInter_preimage_Iic_eq_empty_iff_exists_finset, UV.compress_injOn, Finset.sup_one, RootPairing.Base.exists_mem_support_pos_pairingIn_ne_zero, SimpleGraph.cliqueSet_bot, Finset.disjSups_subset_iff, Finset.notMem_singleton, AffineIndependent.indicator_extend_eq_of_affineCombination_comp_embedding_eq, Finset.pairwiseDisjoint_singleton_iff_injOn, Finset.min'_union, DFinsupp.support_zipWith, Finset.sup_add_sup, Finset.isScalarTower, Finset.Colex.mem_initSeg_self, Finset.lt_wf, Finset.Colex.toColex_le_singleton, Finset.Nonempty.zero_mem_sub, Finsupp.support_finset_sum, Finset.empty_inter, Finset.insert_compl_self, Finset.insert_val, roth_3ap_theorem, MvPolynomial.vars_X, MvPolynomial.support_sum, Finset.coe_sort_coe, Finset.Nonempty.subset_one_iff, Set.Finite.toFinset_vsub, RootPairing.GeckConstruction.h_def, Finset.mulEnergy_self_eq_zero_iff, Finset.insert_Ico_left_eq_Ico_pred, Finset.set_biInter_finset_image, Finset.mul_inter_subset, Finsupp.rangeSingleton_support, Finpartition.empty_parts, Fintype.piFinset_vadd_finset, MvPolynomial.support_mul, Finset.filter_notMem_eq_sdiff, Nat.mem_properDivisors_prime_pow, YoungDiagram.cells_bot, Finset.add_empty, Finset.smulAntidiagonal_mono_right, Finset.card_sdiff_lt_card_sdiff_iff, rothNumberNat_spec, Finset.notMem_Ioi_self, ProbabilityTheory.Kernel.iIndepSet_iff_meas_biInter, Finset.right_notMem_Ioo, Set.Finite.toFinset_prod, MeasureTheory.SimpleFunc.range_indicator, Set.powersetCard.exist_mem_powersetCard_of_inf, Finset.vadd_nonempty_iff, Finset.map_op_one, Finset.addEnergy_eq_sum_sq', Finsupp.sum_indicator_index_eq_sum_attach, Summable.sum_add_tsum_subtype_compl, Finset.pimage_eq_image_filter, Finset.coe_one, Submodule.exists_finset_of_mem_iSup, SimpleGraph.cliqueFinset_eq_empty_iff, Finset.geomSum_lt_geomSum_iff_toColex_lt_toColex, Finsupp.mem_support_iff, Finset.univ_infs_univ, Finset.max_union, Filter.mem_pi', Finset.infs_nonempty, Finset.zero_mem_sub_iff, DFinsupp.support_mono, Int.mem_divisorsAntidiag, natCast_le_rank_iff_finset, Fintype.mem_piFinset, Nat.smoothNumbersUpTo_subset_image, Finset.sup_singleton_eq_self, Finpartition.IsEquipartition.filter_ne_average_add_one_eq_average, Finset.piecewise_insert, Equiv.Perm.mem_toList_iff, Finset.exists_card_fiber_lt_of_card_lt_nsmul, Finset.mul_empty, MeasureTheory.SimpleFunc.sum_measure_preimage_singleton, Set.toFinset_union, Finset.smul_finset_subset_smul_finset_iff, Finset.disjoint_map, Ideal.pow_multiset_sum_mem_span_pow, Nat.bijOn_digitsAppend', Finset.pairwise_subtype_iff_pairwise_finset, Finset.mem_pow, mem_zpowers_iff_mem_range_orderOf, Fintype.coe_image_univ, Finset.mem_univ, Finset.Ico_subset_Ico_right, RootPairing.GeckConstruction.isSl2Triple, Filter.frequently_exists_finset, MvPolynomial.exists_finset_rename, Metric.AreSeparated.finset_iUnion_right_iff, Finsupp.mem_supported_support, Finset.pair_comm, OrderEmbedding.birkhoffFinset_inf, Finset.smul_finset_sdiff, Finset.sum_mono_set, isOpen_pi_iff, Finset.card_inv, Finset.exists_mem_eq_inf, Finset.mul_subset_iff_right, finite_cover_nhds, Finset.sum_ite_mem, Finset.set_biUnion_biUnion, Finset.addETransformRight.fst_add_snd_subset, Finset.inter_erase, Finset.inter_union_distrib_right, SimpleGraph.EdgeDisjointTriangles.card_edgeFinset_le, Finpartition.isPartition_parts, Finset.zero_mem_subsetSum, Affine.Simplex.sSameSide_excenter_singleton_point, Finset.powerset_eq_singleton_empty, Finset.empty_vsub, Nat.properDivisors_zero, YoungDiagram.cells_subset_iff, Finset.empty_mul, Finset.isUnit_coe, Finset.inter_sdiff_assoc, Finset.compl_ssubset_compl, exteriorPower.basis_apply, Finset.preimage_add_left_singleton, Equiv.finsetCongr_refl, Set.Sized.empty_mem_iff, Finset.image₂_inter_singleton, Finset.map_zero, Finset.mk_mem_sym2_iff, Finset.card_mul_cast_addConst, Finset.card_strictMono, Finset.inv_smul_mem_iff, WithBot.sum_eq_bot_iff, MeasureTheory.GridLines.T_lmarginal_antitone, Finset.union_union_distrib_right, Finset.sup_product_right, SimpleGraph.cliqueFinset_mono, Finset.sum_union_inter, Finset.singletonAddMonoidHom_apply, Equiv.Perm.mem_cycleFactorsFinset_conj, Nat.roughNumbersUpTo_card_le, Finset.Ico_eq_empty, Nat.finMulAntidiag_zero_right, Finset.closure_biUnion, List.support_formPerm_le, CategoryTheory.Limits.ProductsFromFiniteCofiltered.liftToFinsetLimitCone_isLimit_lift, RootPairing.Base.span_coroot_support, Finset.coe_infs, Finset.product_biUnion, SSet.horn₃₁.desc.multicofork_π_two, Finsupp.card_Ioc, Summable.sum_add_tsum_compl, RootPairing.Base.cartanMatrixIn_def, MonoidAlgebra.support_one_subset, MvPolynomial.mem_image_support_coeff_finSuccEquiv, Finset.sum_boole_mul, SimpleGraph.edgeFinset_subset_sym2_of_support_subset, Finset.mem_sumLift₂, Finset.toLeft_eq_univ, Finset.instAddLeftMono, Finset.disjiUnion_filter_eq, Finset.inter_inter_distrib_left, SetTheory.PGame.Domineering.mem_right, Finset.fold_const, Finset.image₂_curry, Finset.affineCombination_apply_eq_lineMap_sum, Function.Injective.map_atTop_finset_prod_eq, MeasureTheory.SimpleFunc.range_comp_subset_range, Nat.binomial_succ_succ, Submodule.iUnion_ssubset_of_forall_ne_top_of_card_lt, Finset.noncommSum_singleton, Finset.SupIndep.attach, Finset.le_fold_max, Finset.insert_Ico_add_one_left_eq_Ico, Finset.Ioi_disjUnion_Iio, Equiv.Perm.Basis.injective, Fintype.coe_finsetEquivSet, Finset.mem_singleton, MeasureTheory.sum_measureReal_singleton, RootPairing.Base.algebraMap_cartanMatrixIn_apply, Lagrange.basis_pair_right, Finset.singleton_pow, Finset.singleton_sub, Finset.max'_singleton, Finset.min_zero, Set.subsingleton_toFinset_iff, Equiv.Perm.support_prod_of_pairwise_disjoint, Equiv.Perm.Basis.toCentralizer_equivariant, Set.powersetCard.val_ofFinEmb, Finset.piAntidiag_zero, Finset.SupIndep.product, Submodule.isInternal_prime_power_torsion_of_pid, Finsupp.single_eq_indicator, Finset.isCentralVAdd, IsLinearSet.closure_finset, MvPolynomial.coeff_X_mul', Finset.image_vadd_comm, Finset.inf_id_set_eq_sInter, Finset.image_op_inv, Set.biUnion_finsetSigma, Finset.product_union, Finpartition.nonUniforms_mono, RootPairing.GeckConstruction.instHasTrivialRadical, YoungDiagram.mem_row_iff, Finset.prod_empty, Finsupp.support_extendDomain_subset, Polynomial.support_trinomial, Finset.dens_sdiff_comm, Finset.eq_univ_iff_forall, Finset.mem_range_iff_mem_finset_range_of_mod_eq, ProbabilityTheory.Kernel.iIndep.meas_biInter, Finset.univ_pi_univ, Finset.Ico_subset_Ico_union_Ico, RootPairing.Base.injective_pairingIn, Finset.le_inf_div, Finset.compl_inter, Fin.attachFin_Iic, Finset.coe_Ico, Finset.isAddUnit_iff, Finset.preimage_mul_left_one, Finset.Nonempty.zero_smul, Finset.image_neg, Nat.Ioc_succ_singleton, Nat.divisorsHom_apply, Finset.product_image_fst, Finset.zero_nonempty, RootPairing.GeckConstruction.instIsLieAbelianSubtypeMatrixSumMemFinsetSupportLieSubalgebraCartanSubalgebra, Finset.coe_eq_empty, Geometry.SimplicialComplex.mem_space_iff, Finset.subset_product_image_snd, ProbabilityTheory.Kernel.partialTraj_succ_of_le, SSet.horn.faceSingletonComplIso_inv_ι_assoc, Finset.attach_eq_univ, AddMonoidHom.noncommPiCoprod_apply, Finset.inter_subset_ite, IocProdIoc_preimage, GradedAlgebra.exists_finset_adjoin_eq_top_and_homogeneous_ne_zero, Finset.tendsto_Ico_neg_atTop_atTop, Finset.mem_image_const, Finset.empty_product, RootPairing.GeckConstruction.h_mem_cartanSubalgebra, Finset.inf'_sup_inf', Finset.weightedVSubOfPoint_insert, Finset.bind_def, Finset.add_sum_eq_sum_insertNone, InfPrime.finset_inf_le, Finset.prod_eq_prod_extend, Finset.vaddAntidiagonal_mono_left, Finpartition.equitabilise_aux, Finset.left_mem_Icc, Finsupp.card_Ico, MeasureTheory.IsSetSemiring.pairwiseDisjoint_insert_disjointOfDiff, Finset.Colex.toColex_univ, Rel.interedges_biUnion, Finset.isEmpty_coe_sort, Finset.image_uncurry_product, Affine.Simplex.sign_excenterWeights_singleton_pos, DFinsupp.mapRange_def, Finset.mem_upShadow_iff_exists_mem_card_add, Finset.union_mul, Finset.forall_mem_not_eq, SSet.stdSimplex.faceSingletonIso_zero_hom_comp_ι_eq_δ, PairReduction.point_notMem_finset_logSizeBallSeq_add_one, SummationFilter.neBot_or_eq_bot, Finset.le_sup'_iff, Finset.Nonempty.eq_singleton_default, Affine.Simplex.excenter_singleton_mem_affineSpan_range, Finset.neg_insert, Finset.product_pow, Finset.pairwiseDisjoint_range_singleton, Finset.Icc_subset_Iic_self, Polynomial.support_C_mul_X, Finset.infs_comm, Finset.sigma_image_fst_preimage_mk, AddSubmonoid.mem_closure_finset, Finset.exists_ne_zero_of_sum_ne_zero, Nat.swap_mem_divisorsAntidiagonal, Finset.compl_eq_univ_sdiff, Nat.mem_factoredNumbers', ProbabilityTheory.iIndepFun_iff, Finset.vadd_finset_eq_univ, exteriorPower.coe_basis, Finset.seqRight_def, Finset.vaddAssocClass'', Equiv.Perm.cycleFactorsFinset_eq_empty_iff, Finset.fold_min_lt, finrank_vectorSpan_image_finset_le, Finset.neg_op_vadd_finset_distrib, Finset.image_injective, ProbabilityTheory.iIndep.meas_biInter, Finset.op_smul_finset_mul_eq_mul_smul_finset, exteriorPower.ιMulti_family_linearIndependent_field, Finset.mem_singleton_self, Finset.neg_filter_univ, Finset.multipliable, Finset.sigma_nonempty, Finset.coe_biUnion, SzemerediRegularity.a_add_one_le_four_pow_parts_card, Finset.image_empty, Finset.image₂_inter_right, Set.subset_toFinset, Finset.not_nonempty_empty, Finset.ruzsa_triangle_inequality_invMul_mul_mul, Finset.slice_subset, Finset.ordConnected_range_coe, Finset.disjiUnion_singleton_eq_self, Nat.mem_finMulAntidiag, Finset.inv_smul_finset_distrib, YoungDiagram.mem_cells, linearIndepOn_finset_iff, Cycle.nil_toFinset, Finset.exists_of_one_lt_card_pi, Finset.grade_eq, Ideal.exists_minimal_isPrimary_decomposition_of_isPrimary_decomposition, Equiv.restrictPreimageFinset_symm_apply_coe, Equiv.Perm.cycleType_eq, Finset.sdiff_singleton_eq_erase, Finset.mk_mem_sigmaLift, Finset.inter_sub_union_subset_union, Finset.vadd_eq_empty, Finset.dens_inter_add_dens_sdiff, Equiv.Perm.support_eq_empty_iff, Set.Finite.coeSort_toFinset, Finset.left_notMem_Ioo, Finset.isAtom_iff, Finset.uIcc_eq_union, Set.powersetCard.isPretransitive, Finset.mulConst_mul_card, SimpleGraph.Dart.edge_fiber, MeasureTheory.Measure.ae_mem_finset_iff, Filter.mem_iInf_finite, Finset.gcd_empty, Polynomial.monic_restriction, Finset.card_compl_add_card, LieAlgebra.IsKilling.instIsReducedSubtypeWeightMemLieSubalgebraFinsetRootDualRootSystem, Finset.card_mul_divConst, SimpleGraph.isNClique_singleton, Finset.card_insertNthEquiv_filter_piFinset, cauchySeq_finset_iff_nat_tsum_vanishing, IsPrimitiveRoot.mem_nthRootsFinset, exteriorPower.basis_repr_ne, Finset.insert_eq, Finsupp.if_mem_support, RootPairing.Base.cartanMatrix_map_abs, MeasureTheory.exists_nonempty_inter_of_measureReal_univ_lt_sum_measureReal, Set.powersetCard.ofFinEmb_surjective, ProbabilityTheory.iIndepFun_iff_measure_inter_preimage_eq_mul, RootPairing.Base.root_mem_span_int, UniqueFactorizationMonoid.primeFactors_zero, Nat.one_mem_properDivisors_iff_one_lt, CategoryTheory.preservesFiniteColimits_liftToFinset, Finset.product_singleton, IsSemilinearSet.biUnion_finset, Equiv.Perm.Basis.toCentralizer_apply, LocallyFiniteOrder.finset_mem_Icc, Equiv.Perm.notMem_support, Finset.diag_union, Finset.inf_lt_iff, SimpleGraph.TripartiteFromTriangles.toTriangle_surjOn, LieAlgebra.IsKilling.rootSystem_coroot_apply, Rel.edgeDensity_empty_right, Fin.image_succ_univ, Finset.sdiff_nonempty, Finset.sup_add_le, SimpleGraph.edgeFinset_sdiff, MvPolynomial.support_monomial, Finset.empty_ssubset, Finset.coe_singleton, le_addRothNumber_product, Finset.card_mul_subConst, Finset.Iio_ssubset_Iio, MeasureTheory.ProbabilityMeasure.exists_lt_measure_biUnion_of_isOpen, Finset.filter_const, Finset.card_memberSubfamily_add_card_nonMemberSubfamily, Turing.PartrecToTM2.codeSupp_self, Finset.mem_sym_iff, Mathlib.Meta.NormNum.Finset.prod_empty, Finset.coe_empty, Finset.image_smul_product, Finset.sup_eq_union', Finpartition.parts_subset_extendOfLE, Affine.Simplex.mongePointVSubFaceCentroidWeightsWithCircumcenter_eq_sub, DFinsupp.disjoint_iff, SimpleGraph.TripartiteFromTriangles.rel_iff, Finset.singleton_zpow, RootPairing.GeckConstruction.trace_h_eq_zero, Finset.Ioc_union_Ioc_eq_Ioc, Finset.Nonempty.exists_mem, SimpleGraph.IsNClique.exists_not_adj_of_cliqueFree_succ, Finset.inter_eq_inter_iff_left, Finset.val_lt_iff, Affine.Triangle.sbtw_touchpoint_singleton, Finset.disjoint_coe, Finset.pairwiseDisjoint_coe, Finset.set_encard_biUnion_le, Finset.ruzsa_triangle_inequality_add_sub_add, Ideal.exists_finset_card_eq_height_of_isNoetherianRing, Finset.convolution_ne_zero, Equiv.Perm.disjoint_ofSubtype_noncommPiCoprod, Finset.mem_shadow_iterate_iff_exists_sdiff, Finset.Icc_succ_succ, Geometry.SimplicialComplex.vertices_eq, AlgebraicGeometry.Scheme.OpenCover.finiteSubcover_f, Nat.prod_mem_factoredNumbers, Finset.ruzsa_triangle_inequality_sub_add_sub, Set.finite_mem_finset, Finset.sum_card_fiberwise_eq_card_filter, Finset.insert_Icc_left_eq_Icc_sub_one, Finpartition.card_filter_equitabilise_big, Fin.mem_piFinset_iff_pivot_removeNth, Finset.sumLexLift_inr_inl, Finset.sort_empty, Finset.Nat.sigmaAntidiagonalTupleEquivTuple_symm_apply_snd_coe, ProbabilityTheory.iIndepFun.measure_inter_preimage_eq_mul, MvPolynomial.mem_support_iff, BoxIntegral.unitPartition.mem_prepartition_boxes_iff, Ideal.IsPrime.prod_le, Fin.attachFin_Ioo_eq_Ioi, Finset.inter_self, Finset.disjoint_union_right, Nat.filter_range_nth_subset_insert, Equiv.Perm.OnCycleFactors.mem_range_toPermHom_iff', Finpartition.IsEquipartition.card_biUnion_offDiag_le', Set.toFinset_compl, Finset.isScalarTower'', Equiv.Perm.support_cycleOf_le, MvPolynomial.mem_range_map_iff_coeffs_subset, Finsupp.support_single_add_single, Finset.continuous_restrict_apply, Finset.Ioo_subset_Ici_self, Finset.Nontrivial.mul_right, MvPolynomial.notMem_support_iff, Finset.subtype_mono, Multiset.card_Ico, Behrend.sphere_subset_preimage_metric_sphere, Finset.max'_one, Fintype.piFinset_vadd, Finset.range_union_range, Finset.filter_product_right, Finset.symmDiff_eq_union_iff, Multiset.canLiftFinset, Affine.Simplex.touchpoint_empty_injective, Finset.union_sdiff_self_eq_union, SimpleGraph.cliqueSet_mono, Finset.coe_filter, Finset.empty_diffs, Finset.coe_prod, Finsupp.support_zero, FirstOrder.Language.Theory.models_iff_finset_models, Finset.sup_insert, Set.sized.union, Finset.inf'_zero, Finset.image₂_left_identity, RootPairing.Base.cartanMatrixIn_nondegenerate, Finset.sdiff_nonempty_of_card_lt_card, Finset.preimage_inr, Finset.erase_injOn, Submodule.mem_span_image_iff_exists_fun, Finset.prod_add, Finset.image_smul_distrib, Finset.instCommutativeDisjSups, BoxIntegral.unitPartition.mem_admissibleIndex_iff, Set.Finite.ssubset_toFinset, Set.Infinite.exists_notMem_finset, Finset.Nonempty.sup_eq_top_iff, DFinsupp.mem_neLocus, Multiset.coeEquiv_apply_coe, Finset.addETransformLeft_neg, Finset.right_mem_Ioc, Finset.inf'_lt_iff, Finset.coeMonoidHom_apply, Finset.inter_subset_right, Finset.singleton_val, Finset.range_add_one', Finset.coe_attachFin, isIrreducible_iff_sUnion_isClosed, Finset.insert_Ioc_right_eq_Ioc_add_one, exteriorPower.ιMulti_family_span_fixedDegree_of_span, Polynomial.coeffs_monomial, IsSemilinearSet.closure_finset, SemigroupIdeal.fg_iff, Finset.one_mem_one, Finset.prod_ite_one, Set.toFinset_ssubset_toFinset, Rel.mk_mem_interedges_comm, Finset.attach_nonempty_iff, DFinsupp.prod_eq_zero_iff, Ideal.Factors.fact_ramificationIdx_neZero, Nat.factoredNumbers_insert, Finset.disjoint_filter_filter_neg, Affine.Simplex.sign_signedInfDist_lineMap_incenter_touchpoint, Finset.smul_finset_inter, Finset.Colex.toColex_lt_toColex_iff_max'_mem, Finset.insert_Ico_right_eq_Ico_add_one_of_not_isMax, Polynomial.eval₂_restriction, Finset.Ioi_insert, Fin.orderIsoTriple_zero, Topology.RelCWComplex.cellFrontier_subset_base_union_finite_closedCell, Finset.add_union, Finset.set_biUnion_coe, Finset.smul_finset_univ, Function.Embedding.exists_of_card_le_finset, Finset.image₂_eq_empty_iff, Finset.coe_Iic, Finset.nonMemberSubfamily_union, Finset.lt_sup'_iff, Finset.coe_vadd_finset, Finset.monotone_iff_forall_le_cons, Finset.coe_eq_pair, summable_mul_prod_iff_summable_mul_sigma_antidiagonal, Finset.mem_insert_self, Finset.subset_empty, BoxIntegral.Prepartition.top_boxes, Finset.card_insertNone, Finset.map_op_inv, Finset.coe_univ, Int.erdos_ginzburg_ziv, Finset.mem_finsuppAntidiag, Equidecomp.IsDecompOn.comp, setOf_liouvilleWith_subset_aux, Multiset.toFinset_cons, Set.powersetCard.mem_mulActionHom_compl, Set.toFinset_symmDiff, Finset.mem_sup, Finsupp.mem_supported, UpperHalfPlane.prod_eq_zero_iff, Finset.prod_union_eq_left, Nat.properDivisors_one, Finset.ite_subset_union, LieModule.genWeightSpaceChain_def', Sum.Lex.Ioo_inr_inl, MeasureTheory.inter_cylinder, MeasureTheory.Measure.ae_mem_finset_iff_map_eq_sum_dirac, Finset.mem_mk, Finset.sum_pair, Finset.not_injOn_of_card_image_lt, Finset.falling_zero_subset, Finset.dens_sdiff_add_dens_inter, dimH_coe_finset, Finset.image_const, Finset.disjSum_subset, SSet.horn₃₂.desc.multicofork_π_one, Option.toFinset_none, Finset.subset_smul_finset_iff, Nat.properDivisors_eq_empty, Finset.nullMeasurableSet_biUnion, RootPairing.Base.cartanMatrix_apply_eq_zero_iff, Equiv.Perm.Basis.mem_support_self', prod_eq_tprod_mulIndicator, Finset.slice_subset_falling, MeasureTheory.isProjectiveLimit_nat_iff, Finset.disjSum_empty, Finset.Nonempty.sub, SimpleGraph.isMaximumClique_iff, Finset.card_le_card_add_self', FreeAbelianGroup.support_zero, Finset.memberSubfamily_image_erase, Finset.mem_uIcc', Finset.tendsto_Ioc_neg_atTop_atTop, Finset.powerset_insert, SimpleGraph.regularityReduced_adj, hasSum_sum_support_of_ne_finset_zero, Finset.isLindelof_biUnion, Finset.card_eq_one, DiscreteQuotient.finsetClopens_inj, MeasureTheory.Measure.haar.index_elim, Finset.map_consEquiv_filter_piFinset, DFinsupp.mk_neg, Finset.vadd_finset_singleton, Finset.isGδ_compl, Finset.disjSups_singleton, Finset.mem_Ici, Finset.sized_compls, biUnion_range_succ_disjointed, SkewMonoidAlgebra.support_one, Finset.min_union, Equiv.Perm.OnCycleFactors.kerParam_range_card, Finset.union_compl, Filter.iInf_principal_finset, Matrix.adjp_apply, SummationFilter.eventually_mem_or_not_mem, List.toFinset_append, Finpartition.IsEquipartition.card_large_parts_eq_mod, Finpartition.indiscrete_isEquipartition, Finset.inf_le_iff, Finset.ssubset_singleton_iff, Finset.instLawfulMonad, Finset.set_biUnion_finset_image, Finset.Nat.antidiagonalTuple_one, Finset.mem_sum, Finset.ordConnected_range_val, Finset.inf_sub_left, OrthogonalFamily.norm_sq_diff_sum, Finpartition.disjoint, Polynomial.contentIdeal_def, Finset.add_mul_subset, Finset.sum_ite_eq', Finset.addConst_neg_right, Finsupp.comapDomain_smul_of_injective, HallMarriageTheorem.hall_hard_inductive, Finset.singleton_vsub_singleton, corners_theorem, Polynomial.lift_of_splits, Finset.card_add_card_compl, Finset.Colex.le_iff_max'_mem, CategoryTheory.Limits.CoproductsFromFiniteFiltered.finiteSubcoproductsCocone_pt, Set.Finite.toFinset_eq_empty, Finset.prodMk_sup'_sup', SimpleGraph.edgeDensity_empty_right, hasProd_prod_support_of_ne_finset_one, Finset.tendsto_Ioo_atBot_prod_atTop, Equiv.Perm.OnCycleFactors.kerParam_injective, Finset.dimH_zero, IsSemilinearSet.biInter_finset, IsStrictOrderedRing.int_mem_Icc_of_mul_mem_Ioo, Polynomial.restriction_one, Nat.card_eq_finsetCard, Multiset.toFinset_eq_empty, Finset.one_mem_div_iff, Equiv.Perm.mem_support_iff_of_commute, Finset.divConst_mul_card, Nat.exists_mem_span_nat_finset_of_ge, Finset.summable, Set.Infinite.exists_subset_card_eq, Finset.measurable_restrict, finprod_mem_finset_product, Finset.Nat.antidiagonalEquivFin_symm_apply_coe, Sym2.filter_image_mk_isDiag, Finset.Colex.toColex_sdiff_le_toColex_sdiff', Finset.coe_nonempty, SkewMonoidAlgebra.support_one_subset, Finset.sdiff_val, Finset.antitone_iff_forall_insert_le, Finset.Nat.sigmaAntidiagonalTupleEquivTuple_symm_apply_fst, DFinsupp.subtypeSupportEqEquiv_apply_coe, Finset.instIsTransSubset, UniqueMul.exists_iff_exists_existsUnique, Finsupp.support_mul, mem_image_univ_iff_mem_range, Finset.prod_singleton, Finset.compl_erase, RootPairing.Base.linearIndependent_pair_of_ne, MonoidAlgebra.mem_adjoin_support, Finset.inter_union_self, Finset.swap_mem_mulAntidiagonal, Finset.biUnion_subset_iff_forall_subset, Finset.inclusion_exclusion_card_inf_compl, Finset.image₂_subset_iff_right, Finset.sum_sdiff_eq_sum_sdiff_iff, Affine.Simplex.sign_touchpointWeights_empty, MvPolynomial.support_sdiff_support_subset_support_add, Finset.div_zero_subset, Finsupp.eq_single_iff, Finset.inr_mem_sumLexLift, Finset.imageMonoidHom_apply, DFinsupp.mem_support_toFun, Finset.preimage_mul_left_singleton, SummationFilter.support_eq_limsInf, Equiv.Perm.support_one, Finset.exists_disjoint_union_of_even_card, mem_generatePiSystem_iUnion_elim, Finset.add_singleton, Fintype.card_filter_piFinset_eq, Finset.coe_range, Ioc_subset_biUnion_Ioc, RootPairing.Base.linearIndepOn_coroot, Finset.vadd_empty, Finset.insert_def, Nat.filter_range_nth_eq_insert_of_finite, Finset.inter_filter, Finset.orderIsoOfFin_symm_apply, DirectSum.mk_smul, Finset.map_snocEquiv_filter_piFinset, Nat.Partition.toFinsuppAntidiag_mem_finsuppAntidiag, Finset.Ico_self, Finpartition.parts_bot, Finset.card_one, RootPairing.Base.cartanMatrix_nondegenerate, Finset.addConvolution_eq_zero, Profinite.NobelingProof.spanFunctorIsoIndexFunctor_hom_app_hom_hom_apply_coe, MeasureTheory.IsSetSemiring.empty_notMem_disjointOfDiff, Fintype.prod_extend_by_one, RootPairing.GeckConstruction.mem_ωConjLieSubmodule_iff, Finset.biUnion_nonempty, SimpleGraph.TripartiteFromTriangles.Graph.in₀₁_iff', Set.Finite.toFinset_add, Finset.mem_image, Nat.mem_properDivisors_iff_exists, Finpartition.mk_mem_nonUniforms, DirectSum.mk_injective, Finset.card_vadd_le, Finset.inf_id_eq_sInf, Finset.prod_indicator_biUnion_finset_sub_indicator, Finset.Ioc_subset_Iic_self, Finset.card_pow_le, Lagrange.basis_singleton, Finset.Icc_subset_uIcc', Function.updateFinset_congr, Finset.card_snocEquiv_filter_piFinset, SimpleGraph.TripartiteFromTriangles.cliqueFinset_eq_map, LinearMap.trace_eq_matrix_trace_of_finset, PrimeSpectrum.isCompact_isOpen_iff, IsNonarchimedean.finset_image_add, Finset.max_singleton, Finset.summable_compl_iff, Finset.empty_union, IsPrimitiveRoot.is_roots_of_minpoly, Set.toFinset_eq_empty, Finset.coe_powerset, Finset.vadd_finset_univ, Finset.inv_op_smul_finset_distrib, Finset.sups_inter_subset_right, Finset.singletonMonoidHom_apply, mulRothNumber_map_mul_left, Nat.eq_prod_primes_mul_sq_of_mem_smoothNumbers, Finset.disjoint_image, Finset.image_mul_left', Rel.card_interedges_finpartition, Affine.Simplex.excenter_singleton_injective, SimpleGraph.TripartiteFromTriangles.Graph.in₂₁_iff', SkewMonoidAlgebra.support_sum, Finset.image_div_product, Finset.Subset.rfl, Finset.eventuallyEq_iInter, AddGroup.fg_iff', CategoryTheory.Limits.CoproductsFromFiniteFiltered.liftToFinsetColimIso_aux_assoc, isLinearSet_iff, Finset.card_image₂_singleton_left, Finset.union_inter_distrib_left, Finset.disjoint_self_iff_empty, Finset.sup_div_right, Set.Finite.toFinset_insert', linearIndepOn_finset_iffₒₛ, Equiv.Perm.IsThreeCycle.support_eq_iff_mem_support, Finset.Colex.lt_iff_exists_forall_lt, Finset.nsmul_empty, Int.univ_addEquiv, MultilinearMap.map_piecewise_sub_map_piecewise, Dynamics.netMaxcard_infinite_iff, Finset.dens_union_add_dens_inter, Finset.Nonempty.add, Polynomial.natDegree_notMem_eraseLead_support, Equiv.Perm.SameCycle.mem_support_iff, Finset.inf_mul_left, Algebra.EssFiniteType.adjoin_mem_finset, IsOfFinAddOrder.mem_zmultiples_iff_mem_range_addOrderOf, MeasureTheory.Measure.isProjectiveLimit_infinitePi, Set.biUnion_finsetSigma_univ, Finset.prod_sub, Finset.neg_filter, Nat.divisors_subset_of_dvd, Finset.coe_bipartiteBelow, Finset.expect_ite_zero, Algebra.adjoin_attach_biUnion, Finset.vadd_addConvolution_eq_addConvolution_neg_add, coe_primesOverFinset, Equiv.Perm.IsCycle.commute_iff', Fin.orderIsoSingleton_apply, Ideal.subset_union_prime', ProbabilityTheory.IsGaussianProcess.hasGaussianLaw, Finset.mem_mulAntidiagonal, Finset.map_val_val_powersetCard, Finset.addDysonETransform.subset, Nat.primeFactors_subset_of_mem_smoothNumbers, TotallyBounded.exists_prodMk_finset_mem_hausdorffEntourage, SimpleGraph.FarFromTriangleFree.cliqueFinset_nonempty', Fin.insertNth_mem_piFinset_insertNth, Finsupp.notMem_support_iff, cauchySeq_finset_of_summable_norm, DFinsupp.subtypeDomain_def, Finsupp.mapDomain_support, Finset.filter_false, Finset.sup_singleton, indicator_biUnion_finset_eventuallyEq, iInf_eq_iInf_finset', tendstoUniformly_tsum_of_cofinite_eventually, MvPolynomial.support_eq_empty, MonomialOrder.degree_mem_support_iff, Finset.compl_union, Finset.card_inter, Finset.image_swap_product, Polynomial.support_C_mul_X', Finset.smul_finset_subset_smul_finset_iff₀, Multiset.support_sum_subset, Finset.sdiff_eq_filter, ENNReal.tsum_biUnion_le, Finset.Ioo_subset_Icc_self, Finset.FinsetCoe.canLift, Finset.mem_sort, Finset.card_mul_addConst, Finset.addDysonETransform.card, Prime.exists_mem_finset_dvd, Finset.neg_inter, SimpleGraph.componentComplFunctor_obj, Finsupp.fun_support_eq, ExpGrowth.expGrowthSup_sum, cauchySeq_finset_iff_nat_tprod_vanishing, ConcaveOn.exists_le_of_centerMass, DFinsupp.notMem_support_iff, Finset.zero_mem_smul_finset_iff, Submodule.fg_biSup, Finset.product_inter, TopologicalSpace.NoetherianSpace.exists_finset_irreducible, IsLocalization.coeffIntegerNormalization_mem_support, Affine.Simplex.touchpoint_singleton_mem_interior_faceOpposite, Finset.card_le_one_iff_subsingleton_coe, Set.powersetCard.coe_coe, Finset.Colex.toColex_strictMono, Set.powersetCard.faithfulSMul, LocallyFinite.exists_finset_nhds_support_subset, Finset.ssubset_iff_subset_ne, Turing.PartrecToTM2.contSupp_halt, Finset.product_image_snd, DependsOn.updateFinset, Finset.shadow_compls, MeasureTheory.SimpleFunc.mem_range, Geometry.SimplicialComplex.faces_bot, Finset.erase_injOn', MonoidAlgebra.support_gen_of_gen', Finset.union_comm, RootPairing.GeckConstruction.cartanSubalgebra_eq_lieSpan, Finset.sum_indicator_eq_sum_inter, MvPolynomial.mem_vars, not_mulDissociated, Finset.range_succ, Polynomial.mem_support_derivative, Finset.Ico_diff_Ico_left, Finset.frequently_exists, Finset.map_symm_subset, MeasureTheory.integrableOn_finset_iUnion, Finset.mulDysonETransform_snd, Set.toFinset_diff, Finset.singleton_diffs_singleton, Filter.iInf_sets_eq_finite', Equiv.Perm.support_pow_le, Geometry.SimplicialComplex.isRelLowerSet_faces, Finset.ruzsa_triangle_inequality_mul_div_mul, Finset.inf'_congr, Finset.support_sum_subset, Finset.subset_map_inl, Finset.filter_nonempty_iff, Finset.Ioo_eq_filter_ssubsets, SimpleGraph.IsFiveWheelLike.isNClique_right, Set.powersetCard.compl_symm, hasSumUniformly_iff_tendstoUniformly, DFinsupp.zipWith_def, Finset.sum_attach_eq_sum_dite, Function.Semiconj.finset_map, CategoryTheory.Limits.ProductsFromFiniteCofiltered.liftToFinsetObj_obj, Finset.union_product, Fin.orderIsoPair_zero, Finset.card_product, Finset.inter_sdiff_self, Polynomial.rootsExpandPowEquivRoots_apply, Finset.coe_coeMonoidHom, IntermediateField.finiteDimensional_iSup_of_finset, Finset.Colex.mem_initSeg, Finset.Subset.refl, RootPairing.Base.exists_root_eq_sum_nat_or_neg, Tuple.monotone_proj, Finset.monotone_iff_forall_le_insert, pairwise_coprime_iff_coprime_prod, SimpleGraph.IsSRGWith.card_neighborFinset_union_eq, Finpartition.isEquipartition_iff_card_parts_eq_average, Finset.add_eq_empty, SSet.horn₂₂.sq, Finset.mem_convexHull', Finset.attach_eq_empty_iff, Equiv.Perm.OnCycleFactors.nat_card_range_toPermHom, Finset.smul_mem_smul_finset_iff, Finset.expect_inv_index, Set.biInter_finsetSigma', Finset.image_subset_image_iff, Finset.Ioi_ssubset_Ioi, Finset.mem_zero, sigmaAntidiagonalEquivProd_symm_apply_snd, MeasureTheory.cylinder_eq_cylinder_union, Nat.mem_divisors, Finsupp.disjoint_iff, Finset.lt_eq_subset, Lagrange.nodal_empty, Equiv.Perm.isCycleOn_support_cycleOf, MvPolynomial.coeffs_one, Turing.TM2to1.trStmts₁_run, Finset.SupIndep.sup, Finset.prod_empty', Finpartition.mem_avoid, Finset.insert_eq_self, Finset.card_erase_eq_ite, BoxIntegral.Prepartition.injective_boxes, Equiv.Perm.support_swap_mul_eq, Finset.Ico_filter_le_left, Finset.not_nontrivial_singleton, Finset.insertNone_eraseNone, Finset.sup_set_eq_biUnion, ProbabilityTheory.Kernel.iIndepSet.meas_biInter, Finset.smul_mem_smul_finset_iff₀, Finset.inf_zero, FormalMultilinearSeries.nnnorm_changeOrigin_le, finsum_mem_coe_finset, FirstOrder.Ring.lift_genericPolyMap, Finset.sum_pos_iff, Finset.inter_vadd_subset, Finset.image_surjOn_powerset, ProbabilityTheory.iCondIndep_iff, MvPolynomial.coeffs_one_of_nontrivial, Finset.geomSum_le_geomSum_iff_toColex_le_toColex, Nat.Prime.properDivisors, Finset.insert_empty, ProbabilityTheory.iCondIndepFun_iff_condExp_inter_preimage_eq_mul, Finset.inf_prodMap, Finset.filter_and_not, SummationFilter.conditional_filter_eq_map_range, Finset.max'_mem, MeasureTheory.SimpleFunc.mem_range_of_measure_ne_zero, CategoryTheory.preservesFiniteLimits_liftToFinset, Equiv.Perm.zpow_apply_mem_support_of_mem_cycleFactorsFinset_iff, Finset.card_compl, Finset.image_vsub_product, Set.Finite.mem_toFinset, Set.Finset.coe_einfsep, Finset.sup_div_le, Finset.coe_sub, Sum.Ioc_inl_inr, Finsupp.span_le_supported_biUnion_support, Finset.union_assoc, SimpleGraph.coe_edgeFinset, Finset.card_add_le, SimpleGraph.infinite_iff_in_eventualRange, SimpleGraph.extend_finset_to_connected, Finset.attach_insert, Fintype.finsetEquivSet_apply, Finset.card_sdiff, Finset.infsep_pos_iff_nontrivial, Finset.nontrivial_coe, Finset.singleton_subset_set_iff, Finset.finsuppAntidiag_empty_of_ne_zero, Finset.mem_vadd, Equiv.Perm.support_swap_mul_swap, Finset.sum_insert_of_eq_zero_if_notMem, Finset.insert_inj_on, Finset.insert_subset_iff, Finset.ssubset_iff_exists_subset_erase, Finset.range_add, Finset.mem_uIcc_of_le, Finset.equitableOn_iff_le_le_add_one, Finset.erase_eq, Finset.compl_singleton, SimpleGraph.notMem_neighborFinset_self, Polynomial.support_trinomial', Equiv.Perm.cycleFactorsFinset_eq_finset, prod_indicator_apply, Finset.image_vadd_distrib, Finset.singleton_mul, Finset.ruzsa_triangle_inequality_mul_mul_invMul, Finset.coe_wcovBy_coe, Finset.prod_powersetCard, Finset.singleton_product_singleton, Finset.nullMeasurableSet_biInter, SimpleGraph.edgeFinset_deleteIncidenceSet_eq_sdiff, not_addDissociated, Nat.roughNumbersUpTo_eq_biUnion, Finset.iInf_insert, Function.Commute.finset_map, Finset.piCongrLeft_comp_restrict, Finset.piAntidiag_empty, Profinite.NobelingProof.fin_comap_jointlySurjective, FormalMultilinearSeries.nnnorm_changeOriginSeries_le_tsum, Polynomial.nthRootsFinset_toSet, Finset.union_eq_left, UpperSemicontinuousOn.inter_biInter_preimage_Ici_eq_empty_iff_exists_finset, Finset.lcm_singleton, Finset.Colex.toColex_le_toColex_iff_max'_mem, AhlswedeZhang.supSum_union_add_supSum_infs, Finset.powerset_sups_powerset_self, Finset.Ico_union_Ico', Finset.nsmul_eq_empty, SimpleGraph.coe_cliqueFinset, Finset.exists_minimal, Finset.hasSum_support, MeasureTheory.union_cylinder, Finset.smul_finset_symmDiff, exists_birkhoff_representation, Finset.filter_empty, Set.powersetCard.stabilizer_coe, SkewMonoidAlgebra.support_eq_empty, List.coe_toFinset, Finset.le_inf_add, Submodule.mem_span_finset, SimpleGraph.neighborFinset_completeEquipartiteGraph, Finset.smul_finset_univ₀, Finset.erase_wcovBy, Finset.set_biInter_coe, DirectSum.support_of, Finsupp.sum_ite_eq, PairReduction.point_mem_logSizeBallSeq_init, Equiv.finsetCongr_trans, Affine.Simplex.isTangentAt_insphere_touchpoint, cauchySeq_finset_of_norm_bounded_eventually, Finset.mem_vaddAntidiagonal, Finset.inter_sub_subset, Finset.Icc_subset_Ioc_iff, RootPairing.Base.exists_mem_span_pairingIn_ne_zero_and_pairwise_ne, Finset.Iic_union_Ioc_eq_Iic, Finset.preimage_add_left_zero, Equiv.Perm.coe_support_eq_set_support, Profinite.isIso_indexCone_lift, wittStructureRat_vars, Module.exists_nontrivial_relation_of_finrank_lt_card, Profinite.NobelingProof.GoodProducts.spanFin, Submodule.isInternal_prime_power_torsion_of_is_torsion_by_ideal, Finset.instCommutativeUnion, AddAction.stabilizer_finset_univ, Finsupp.mem_rangeSingleton_apply_iff, SSet.stdSimplex.face_eq_ofSimplex, Finset.div_nonempty, Finset.Icc_subset_Icc_left, FormalMultilinearSeries.changeOriginIndexEquiv_symm_apply_fst, PartitionOfUnity.exists_finset_nhds, Affine.Simplex.inner_mongePoint_vsub_face_centroid_vsub, Finset.partiallyWellOrderedOn, DFinsupp.support_mk_subset, SSet.horn₃₁.desc.multicofork_pt, Finset.mem_filter_univ, AbsolutelyContinuousOnInterval.tendsto_volume_totalLengthFilter_nhds_zero, Finset.inf_union, RootPairing.Base.coroot_mem_span_int, Finset.diffs_union_right, Set.biInter_finsetSigma, Finset.cast_subConst_mul_card, Finset.finite_toSet_toFinset, Finset.Ico_disjoint_Ico_consecutive, Finset.centerMass_id_mem_convexHull, Int.prodMk_mem_divisorsAntidiag, Equiv.Perm.IsCycle.cycleFactorsFinset_eq_singleton, Finset.Nonempty.pow, Finset.Nonempty.zsmul, Finset.Ici_mul_Ioi_subset', Set.Finite.toFinset_subset, SimpleGraph.neighborFinset_compl, Finset.card_eraseNone_le, SimpleGraph.interedges_empty_left, Finset.coe_coeAddMonoidHom, Polynomial.degree_restriction, MvPolynomial.coeffs_C, Finset.inv_singleton, absorbs_biUnion_finset, Finset.eventuallyLE_iInter, Equiv.Perm.cycleFactorsFinset_eq_singleton_self_iff, Finset.centerMass_id_mem_convexHull_of_nonpos, Finset.seq_def, Finset.iSup_coe, IsCompact.exists_finite_cover_smul, MeasureTheory.Measure.infinitePi_pi, Finset.max_pair, LinearMap.det_def, Finset.instIrreflSSubset, SimpleGraph.TripartiteFromTriangles.Graph.in₁₀_iff, Finset.insert_Icc_right_eq_Icc_succ, Finset.inr_mem_disjSum, Finpartition.IsEquipartition.card_interedges_sparsePairs_le, PartitionOfUnity.eventually_fintsupport_subset, Finset.inf_sup, Finset.coe_erase, OrderEmbedding.coe_birkhoffFinset, SimpleGraph.cliqueSet_map_of_equiv, Finset.isScalarTower', Finset.eraseNone_union, SimpleGraph.end_componentCompl_infinite, Finset.univ_of_card_le_three, Finset.vadd_subset_iff, Equiv.Perm.mem_support, Set.biUnion_empty_finset, AffineIndependent.indicator_eq_of_affineCombination_eq, Finset.iInf_coe, Finset.iSup_singleton, SupIrred.finset_sup_eq, Finset.Colex.IsInitSeg.total, IntermediateField.fg_adjoin_finset, MeasureTheory.closedCompactCylinders.isCompact, Finset.image_add_right, Affine.Triangle.excenter_eq_incenter_or_excenter_singleton_of_ne, Finset.insert_Ico_left_eq_Ico_sub_one_of_not_isMin, MvPolynomial.support_add, Fintype.piFinset_add, Finset.image_eq_empty, Finset.coe_infsep_of_offDiag_nonempty, Finset.erase_inter_comm, Finset.singleton_eq_univ, mulRothNumber_spec, Finset.prod_pair, Finset.nonMemberSubfamily_inter, Finset.card_sups_iff, AddSubgroup.rank_closure_finset_le_card, Finset.inter_comm, Finset.toFinset_coe, Finset.image₂_insert_left, SSet.horn.faceSingletonComplIso_inv_ι, SimpleGraph.isClique_map_finset_iff, SimpleGraph.isMaximalIndepSet_compl, biSup_finsetSigma', Module.Basis.reindexFinsetRange_apply, Set.iInter_eq_iInter_finset, Finset.eraseNone_none, Affine.Simplex.affineSpan_faceOpposite_eq_orthRadius_insphere, Finset.sups_infs_subset_left, Finset.addEnergy_eq_sum_sq, SimpleGraph.neighborFinset_disjoint_singleton, SimpleGraph.mem_incidenceFinset, Finset.coe_mem, Finset.mul_mem_smul_finset_iff, Finset.coe_sdiff, PMF.mem_support_ofFinset_iff, Ideal.IsPrime.inf_le', Finset.insert_Ico_left_eq_Ico_pred_of_not_isMin, IsLocalizedModule.finsetIntegerMultiple_image, Finset.mem_inv_smul_finset_iff, Finset.preimage_mul_right_one', Finset.inter_compl, MeasurableEquiv.coe_IicProdIoc_symm, Fintype.IsSimpleOrder.univ, isLUB_hasProd, Turing.PartrecToTM2.supports_union, CategoryTheory.Limits.CoproductsFromFiniteFiltered.liftToFinsetColimitCocone_isColimit_desc, Finset.isLUB_sup_id, Finset.univ_sups_univ, Finset.instReflSubset, Finset.top_eq_univ, Finset.card_le_card_add_self, Finset.zero_mem_neg_add_iff, Finset.antidiagonal_zero, Finset.insert_sdiff_insert, Finset.disjSum_strictMono_left, CategoryTheory.Limits.CoproductsFromFiniteFiltered.liftToFinsetObj_obj, Finset.Colex.singleton_le_toColex, Set.powersetCard.instInfinite, Finset.mem_subsetSum_iff, Finset.zero_product_zero, Finset.sum_piecewise, Finset.image₂_subset_iff, Finset.mem_sub, Finset.cast_card_union, ENNReal.tendsto_tsum_compl_atTop_zero, Finset.weightedVSub_empty, Finset.insert_Ico_sub_one_right_eq_Ico, Finset.smul_singleton, Finset.Icc_diff_Ioc_self, SimpleGraph.TripartiteFromTriangles.graph_triple, MeasureTheory.exists_nonempty_inter_of_measure_univ_lt_sum_measure, Fin.attachFin_Icc, Finset.card_union, Finset.pluennecke_ruzsa_inequality_nsmul_add, IsNoetherian.range_finsetBasis, Finset.Colex.toColex_image_lt_toColex_image, AddMonoid.exponent_eq_max'_addOrderOf, Finset.isWellFounded_ssubset, Set.powersetCard.nontrivial_iff, SimpleGraph.edgeFinset_replaceVertex_of_adj, Finset.Nat.antidiagonalTuple_zero_right, Finset.eq_singleton_iff_nonempty_unique_mem, Finset.mem_range_succ_iff, PairReduction.disjoint_smallBall_logSizeBallSeq, Finset.image₂_empty_right, Finset.singleton_sups_singleton, Polynomial.coeffs_empty_iff, Finset.prod_pi_mulSingle, Finset.min'_mem, Finset.exists_le_of_prod_le', SimpleGraph.LocallyLinear.card_edgeFinset, Finpartition.card_parts_le_card, Finset.mem_Iic, FormalMultilinearSeries.changeOriginIndexEquiv_symm_apply_snd_snd_coe, Finset.mulEnergy_eq_sum_sq', Finset.image_op_one, Finset.smul_finset_singleton, Set.powersetCard.isPretransitive_alternatingGroup, Finset.union_vadd_inter_subset_union, Set.union_finset_finite_of_range_finite, Finset.vadd_inter_subset, Finset.card_le_card_sub_right, Polynomial.rootsExpandEquivRoots_apply, Finset.Icc_subset_Ico_iff, Finset.seqLeft_def, Fintype.piFinset_neg, Finset.minimal_iff_forall_diff_singleton, Ideal.span_eq_top_iff_finite, Finset.subtype_eq_univ, Finset.image_pow_of_ne_zero, Finset.bddAbove, Rel.interedges_empty_left, ProbabilityTheory.iIndepFun.meas_biInter, Finset.sdiff_eq_self_iff_disjoint, DFinsupp.mem_singleton_apply_iff, Subgroup.leftCoset_cover_const_iff_surjOn, Affine.Simplex.ExcenterExists.excenter_eq_incenter_iff, Finset.covBy_iff_exists_cons, WithBot.Ico_bot_coe, Finset.smulCommClass_finset, Equiv.Perm.mem_support_cycleOf_iff, MeasureTheory.Measure.map_piSingleton, Finpartition.indiscrete_parts, Finset.pimage_union, Finset.filter_product_card, Finset.infs_sups_subset_right, Submodule.span_attach_biUnion, Finsupp.mapDomain_injOn, Affine.Triangle.touchpoint_singleton_sbtw, Finset.right_mem_uIcc, RootPairing.GeckConstruction.lie_h_e, Affine.Simplex.face_eq_mkOfPoint, Finset.card_le_one_iff_subset_singleton, Set.biInter_finsetSigma_univ, Finset.Ico_subset_Ico_left, IsPrimitiveRoot.injOn_pow, Fin.attachFin_Ico_eq_Ici, OrderIso.finsetSetFinite_symm_apply, Function.updateFinset_singleton, Finset.instAsymmSSubset, Nat.primeFactors_mono, Finpartition.extend_parts, TwoUniqueProds.uniqueMul_of_one_lt_card, ProbabilityTheory.iIndepSets_iff, Finset.wellFoundedOn_bUnion, FreeAbelianGroup.support_of, Polynomial.card_roots_toFinset_le_card_roots_derivative_diff_roots_succ, Finset.prod_pi_mulSingle', Finset.offDiag_singleton, MeasureTheory.SimpleFunc.preimage_eq_empty_iff, Finset.map_op_nsmul, Part.toFinset_some, isIrreducible_iff_sInter, Finset.product_eq_biUnion, FiniteDimensional.span_finset, Finset.sups_singleton, LocallyFiniteOrder.finset_mem_Ioo, Finset.sups_assoc, Finset.truncatedSup_empty, Finset.exists_card_fiber_le_of_card_le_mul, Finset.isGLB_inf, AddMonoidAlgebra.support_mul_single_subset, Finset.sized_slice, Finsupp.sum_ite_eq', Finset.univ_subset_iff, Finset.all_card_le_biUnion_card_iff_existsInjective', Finset.card_vadd_finset, SimpleGraph.IsFiveWheelLike.snd_notMem, Finset.coe_offDiag, Finset.image₂_def, Set.powersetCard.isPretransitive_of_isMultiplyPretransitive', Finset.image_nsmul_of_ne_zero, Nat.mem_divisorsAntidiagonal, Finset.card_singleton_inter, Nat.mem_factoredNumbers_iff_forall_le, Finset.coe_pair, Set.powersetCard.addAction_stabilizer_coe, Sum.Ioo_inl_inr, Finset.prod_neg_index, Set.toFinset_zero, LocallyFinite.exists_finset_support, Algebra.Presentation.coeffs_relation_subset_coeffs, Cycle.toFinset_eq_nil, SummationFilter.symmetricIoo_filter, Finset.card_inv_le, Finset.one_subset, Set.definable_finset_biInter, Finset.mem_insert_coe, SSet.stdSimplex.range_δ, PartitionOfUnity.coe_finsupport, cauchySeq_finset_iff_vanishing_norm, Finset.card_Iio_finset, Nat.divisors_mul, MeasureTheory.IsSetSemiring.mem_supClosure_iff, Finset.image₂_inter_union_subset, PMF.mem_support_ofMultiset_iff, Finpartition.bot_isUniform, Finsupp.rangeIcc_toFun, Finset.sup_mul_le, Set.powersetCard.addActionHom_of_embedding_surjective, SimpleGraph.isUniform_singleton, Multiset.toFinset_add, Finset.support_of_fiberwise_sum_subset_image, Finset.Ico_inter_Ico_consecutive, IsMin.finsetIio_eq, Finset.set_biUnion_singleton, Finset.Iic_add_Iic_subset, AddSubmonoid.mem_closure_iff_exists_finset_subset, Finset.inter_left_comm, SkewPolynomial.support_zero, RootPairing.EmbeddedG2.indexEquivAllRoots_symm_apply, Finset.smulCommClass_finset'', Finset.diag_union_offDiag, Finpartition.top_isEquipartition, Finset.diffs_eq_empty, Turing.PartrecToTM2.codeSupp_tail, Finset.biUnion_slice, addRothNumber_union_le, Finset.image_inter, Finset.vaddAssocClass, Equiv.Perm.Disjoint.disjoint_cycleFactorsFinset, Finset.filter_fst_eq_antidiagonal, Finset.singleton_diffs, Multiset.mem_sup_map_support_iff, PartitionOfUnity.exists_finset_nhds_support_subset, Finset.mem_finsupp_iff, hasProdLocallyUniformlyOn_iff_tendstoLocallyUniformlyOn, Finsupp.indicator_apply, Finset.coe_Icc, Finset.max'_pair, Finset.Ico_insert_right, Finset.pairwiseDisjoint_smul_iff, Finset.union_sub, Set.disjoint_toFinset, Affine.Simplex.excenter_empty, Polynomial.support_binomial', Finpartition.parts_top_subset, Ideal.iInf_sup_eq_top, Finset.sup'_singleton, Finset.smul_univ, Polynomial.exists_image_comap_of_monic, InfIrred.finset_inf_eq, SimpleGraph.disjoint_edgeFinset, IntermediateField.exists_finset_maximalFor_isTranscendenceBasis_separableClosure, Finset.card_preimage_eq_sum_card_image_eq, IsDedekindDomain.exists_forall_sub_mem_ideal, Finset.range_eq_empty_iff, DyckWord.equivTreesOfNumNodesEq_symm_apply_coe, Part.coe_toFinset, Finset.coe_bipartiteAbove, Finset.tendsto_Ioc_atBot_prod_atTop, Finset.filter_univ_mem, MvPolynomial.zero_notMem_coeffs, Finset.fold_singleton, MeasureTheory.Measure.pi_prod_map_IocProdIoc, Finpartition.card_nonuniformWitnesses_le, Finset.addEnergy_empty_left, Finset.vadd_finset_symmDiff, Finset.subset_addSpan, Finset.upShadow_empty, LinearRecurrence.sol_eq_of_eq_init, MonoidAlgebra.mem_span_support, Finset.inter_eq_inter_iff_right, Finset.coe_singletonAddMonoidHom, Finset.uIcc_injective_right, ProbabilityTheory.Kernel.iIndepSets.meas_biInter, Finset.sup_product_left, IsOfFinOrder.mem_powers_iff_mem_range_orderOf, Finset.Shatters.subset_iff, MvPolynomial.support_expand_subset, Cardinal.mk_compl_finset_of_infinite, SimpleGraph.IsTuranMaximal.card_parts_le, SummationFilter.HasSupport.eventually_le_support, DFinsupp.filter_def, Finset.card_add_card_subsetSum_lt_card_subsetSum_insert_max, Subalgebra.fg_adjoin_finset, Finset.one_lt_card_iff, Equiv.Perm.Basis.card_ofPermHom_support, NumberField.InfinitePlace.card_eq_card_isUnramifiedIn, Rel.card_interedges_finpartition_right, Finset.prod_ite_eq', Finset.eq_weightedVSubOfPoint_subset_iff_eq_weightedVSubOfPoint_subtype, Finset.tprod_subtype', Finset.mem_attach, Finpartition.part_eq_empty, LocallyFiniteOrderTop.finset_mem_Ici, Finset.powerset_infs_powerset_self, Fintype.prod_add, IsUltrametricDist.exists_norm_finset_prod_le, Finset.Subset.antisymm_iff, Finset.erase_eq_empty_iff, Finset.vadd_finset_inter, Finset.map_subtype_subset, Finset.card_sub_add_le_card_sub_add_card_add, Filter.mem_iInf_finite', Multiset.card_Ioc, Finset.instIsNonstrictStrictOrderSubsetSSubset, Finset.injOn_of_card_image_eq, Finset.Ico_eq_filter_ssubsets, AddMonoidAlgebra.support_single_mul_subset, Finset.map_one, Finset.not_nonempty_iff_eq_empty, Finset.val_eq_zero, Affine.Simplex.touchpointWeights_empty_pos, Finset.sum_inter_add_sum_diff, Finset.union_nonempty, Finpartition.IsEquipartition.sum_nonUniforms_lt', Finset.eq_empty_iff_forall_notMem, MonoidHom.noncommPiCoprod_apply, Finset.nonMemberSubfamily_image_insert, IsUltrametricDist.exists_norm_finset_prod_le_of_nonempty, UniqueProds.uniqueMul_of_nonempty, Polynomial.restriction_zero, MeasureTheory.isProjectiveMeasureFamily_pi, Tuple.graphEquiv₂_apply, Set.toFinset_vadd_set, Finset.vsub_subset_iff, Polynomial.support_C, Equiv.Perm.Basis.ofPermHom_apply, Finset.sum_erase_attach, Algebra.essFiniteType_cond_iff, Finset.Nat.antidiagonalTuple_zero_zero, Finset.preimage_empty, Finsupp.support_mul_subset_right, Finset.coe_orderIsoOfFin_apply, Finset.smulAntidiagonal_min_smul_min, UniqueFactorizationMonoid.primeFactors_one, Finset.min_one, Finset.addAntidiagonal_mono_right, Finset.coe_singletonMulHom, Int.divisorsAntidiagonal_three, Equiv.Perm.mem_support_iff_mem_support_of_mem_cycleFactorsFinset, Finset.uIcc_product_uIcc, Finset.Nat.antidiagonal_zero, Finset.memberSubfamily_inter, Finset.attach_affineCombination_coe, Nat.primeFactors_div_gcd, Set.powersetCard.exists_mem_notMem, CategoryTheory.Limits.CoproductsFromFiniteFiltered.liftToFinset_obj_map, eq_affineCombination_of_mem_affineSpan_image, Finset.inf'_one, SimpleGraph.cliqueSet_mono', Finset.covBy_iff_exists_insert, Finset.nonempty_coe_sort, Finset.coe_mul, Option.toFinset_some, isCompact_iff_finite_subcover, Nat.pairwise_coprime_pow_primeFactors_factorization, Polynomial.bUnion_roots_finite, Finset.fiber_nonempty_iff_mem_image, Finset.exists_ne_map_eq_of_card_image_lt, Finset.image_zero, Finset.mulDysonETransform.card, Finset.geomSum_ofColex_strictMono, IsCompact.exists_finite_cover_vadd, Finsupp.coe_neLocus, Finset.powersetCard_card_add, tendsto_mulIndicator_biUnion_finset, ContinuousMultilinearMap.map_piecewise_add, Finset.codisjoint_left, Finset.inf_sub_right, Finset.coe_singletonOneHom, List.nat_divisors_prod, Finset.card_mul_mulConst, SimpleGraph.edgeFinset_replaceVertex_of_not_adj, Finset.compls_subset_iff, Finset.neg_singleton, Equiv.Perm.mem_support_cycleOf_iff', PowerSeries.WithPiTopology.summable_prod_of_tendsto_order_atTop_nhds_top, IsLocalization.finsetIntegerMultiple_image, MeasureTheory.preVariation.Finset.sup_measurableSetSubtype_eq_biUnion, Finset.vadd_union, HahnSeries.SummableFamily.smul_support_subset_prod, Polynomial.Chebyshev.strictAntiOn_node, Finset.nonempty_def, Finset.pure_def, MeasureTheory.IsSetRing.biInter_mem, Finpartition.parts_eq_empty_iff, Finset.filter_subset, Finset.equivBitIndices_apply, Finset.subConst_neg_left, Finset.addDysonETransform_snd, MvPolynomial.vars_sub_subset, Finset.expect_empty, Equiv.Perm.Disjoint.support_mul, Finset.exists_mem_image₂, Finset.subset_compl_singleton, Finset.image_pow, Finset.div_def, Set.pairwiseDisjoint_filter, Finset.univ_eq_empty, Finset.sumLexLift_eq_empty, BoxIntegral.Prepartition.bot_boxes, Finset.filter_false_of_mem, LieAlgebra.IsKilling.instIsCrystallographicSubtypeWeightMemLieSubalgebraFinsetRootDualRootSystem, Finset.vadd_finset_subset_iff, Subgroup.FG.biSup_finset, Finset.subset_range_sup_succ, Finset.offDiag_mono, FreeMonoid.mem_symbols, Finset.singleton_infs, Finset.empty_zpow, Finset.le_card_mul_mul_mulEnergy, Finset.singleton_nonempty, DyckWord.equivTreesOfNumNodesEq_apply_coe, Finset.range_filter_eq, Finset.supIndep_iff_pairwiseDisjoint, Finset.powerset_card_biUnion, Module.le_rank_iff_exists_finset, Finset.ruzsa_triangle_inequality_add_add_negAdd, isLUB_hasProd', Finset.vadd_finset_nonempty, PrimitiveSpectrum.hull_finsetInf, Finset.coe_eq_zero, SSet.stdSimplex.faceSingletonIso_zero_hom_comp_ι_eq_δ_assoc, Finpartition.parts_extendOfLE_of_lt, Finset.mem_mulSpan, Finset.max'_zero, Finset.isGreatest_max', Besicovitch.exist_finset_disjoint_balls_large_measure, Finset.subConst_neg_right, Finset.piecewise_compl, Submodule.mem_span_iff_exists_finset_subset, Function.Commute.finset_image, Finset.max_mem_image_coe, Finset.tendsto_Ioo_neg, Submodule.mem_span_mul_finite_of_mem_mul, Finsupp.mem_neLocus, Cardinal.mk_finset_of_infinite, List.toFinset_eq_empty_iff, Finset.card_mul_cast_subConst, Finset.inclusion_exclusion_sum_inf_compl, Set.powersetCard.eq_empty_iff, Equiv.Perm.support_swap_iff, tendstoUniformlyOn_tsum, Fin.addRothNumber_eq_rothNumberNat, Ideal.Factors.isScalarTower, Set.toFinset_vsub, Equiv.Perm.OnCycleFactors.mem_range_toPermHom'_iff, Finset.uIcc_subset_uIcc_iff_le', Finset.infs_infs_infs_comm, Finset.inter_vsub_subset, Finpartition.bind_parts, UnitsInt.univ, Finset.mem_Icc, Finset.image_mul, MeasureTheory.IsProjectiveLimit.measure_univ_eq, Finset.exists_mem_insert, Finset.smul_finset_inter_subset, Algebra.Presentation.coeffs_relation_subset_core, Equiv.finsetCongr_toEmbedding, Finset.Ico_inter_Ico, Finset.disjoint_or_nonempty_inter, Finset.uIcc_subset_uIcc_iff_le, SSet.horn₃₁.desc.multicofork_π_two_assoc, Finset.mem_one, Finset.product_eq_sprod, Finset.union_left_idem, Finset.exists_subset_card_eq, Finset.coe_inj, Set.Finite.toFinset_vadd_set, GradedAlgebra.exists_finset_adjoin_eq_top_and_homogeneous, Finset.update_eq_piecewise, Finset.coe_image_subset_range, WittVector.wittZSMul_vars, Finset.exists_minimalFor, MeasureTheory.IsSetSemiring.sUnion_disjointOfDiff, Finset.card_mul_inv_eq_convolution_inv, Finset.inf_eq_inter, CategoryTheory.Limits.ProductsFromFiniteCofiltered.finiteSubproductsCocone_π_app_eq_sum, cauchy_davenport_of_isAddTorsionFree, Finset.mem_diag, Finset.Nonempty.ciSup_mem_image, IsExposed.sInter, Fintype.prod_ite_mem, Finset.one_lt_prod_iff_of_one_le, Finset.sdiff_inter_self, BoxIntegral.unitPartition.mem_admissibleIndex_of_mem_box, Finset.image_union, Caratheodory.mem_minCardFinsetOfMemConvexHull, CategoryTheory.Limits.CoproductsFromFiniteFiltered.liftToFinsetColimitCocone_cocone_ι_app, Finset.inter_eq_univ, Polynomial.rootsExpandPowToRoots_apply, Finset.Ici_mul_Ici_subset', Finset.Ici_add_Ioi_subset, Finsupp.frange_single, RootPairing.GeckConstruction.trace_toEnd_eq_zero, Affine.Simplex.mongePlane_def, Finset.card_le_three, DFinsupp.subset_support_tsub, Equiv.Perm.cycleFactorsFinset_one, Set.powersetCard.mem_coe_iff, Equidecomp.IsDecompOn.of_leftInvOn, Finset.card_sdiff_add_card_inter, Finset.smulAntidiagonal_mono_left, Finset.singleton_subset_iff, Finpartition.mem_atomise, SSet.horn₃₁.desc.multicofork_π_zero_assoc, Finset.coe_image, LinearMap.det_eq_det_toMatrix_of_finset, Finset.sum_attach, SimpleGraph.mem_finsetWalkLength_iff, exists_finset_linearIndependent_of_le_finrank, Nat.one_mem_divisors, MeasureTheory.IsSetAlgebra.biUnion_mem, Finset.prod_mul_prod_compl, Finset.ruzsa_triangle_inequality_mul_div_div, Finset.one_mem_inv_mul_iff, IsOfFinOrder.mem_zpowers_iff_mem_range_orderOf, Affine.Simplex.ExcenterExists.excenterWeights_eq_excenterWeights_iff, Finset.vsub_eq_empty, Finset.SupIndep.independent, Ideal.IsMinimalPrimaryDecomposition.minimalPrimes_subset_image_radical, Fintype.prod_eq_prod_compl_mul, SummationFilter.instNeBotFinsetFilterOfNeBot, Finset.prod_coe_sort, Polynomial.mem_support_iff, FreeCommRing.exists_finset_support, Set.toFinset_smul, Finset.union_val_nd, Finset.instIsTransSSubset, Finset.card_le_card_add_left, Finset.shatterer_compress_subset_shatterer, SimpleGraph.IsMaximumIndepSet.isMaximalIndepSet, Finset.vadd_finset_def, UniqueAdd.addHom_preimage, Finset.gc_map_inr_toRight, Finset.symmDiff_nonempty, DFinsupp.mk_zero, Finset.setOf_mem, Finset.sup_empty, Finset.insert_Ioc_succ_left_eq_Ioc, IsPrimitiveRoot.primitiveRootsPowEquiv_symm_apply_coe, Finset.card_le_five, Finset.sup_sub_right, ProbabilityTheory.Kernel.partialTraj_succ_eq_comp, Nat.bijOn_ofDigits', Finset.isCoatom_compl_singleton, Preorder.measurable_frestrictLe₂, Preorder.continuous_frestrictLe, MeasureTheory.IsSetAlgebra.biInter_mem, Fintype.sum_ite_mem, Finset.sups_eq_empty, iSup_eq_iSup_finset, Finset.card_image₂_singleton_right, Submonoid.exists_minimal_closure_eq_top, Cardinal.mk_coe_finset, FixedDetMatrices.reps_entries_le_m', SimpleGraph.neighborFinset_boxProd, Finset.sumLift₂_eq_empty, isNoetherian_adjoin_finset, RootPairing.Base.cartanMatrix_apply_eq_zero_iff_pairing, HallMarriageTheorem.hall_cond_of_restrict, Finset.sup'_eq_csSup_image, Finset.insert_Ioc_right_eq_Ioc_succ_of_not_isMax, Finset.image_add_right', SimpleGraph.mem_indepSetFinset_iff, Finset.sum_card_slice, MulAction.stabilizer_finset_univ, Finpartition.IsEquipartition.card_small_parts_eq_mod, Finset.prod_product_right', DFinsupp.support_tsub, DFinsupp.support_eq_empty, Finset.product_sdiff_diag, SummationFilter.symmetricIco_filter, Finset.disjoint_filter, Nat.disjoint_divisors_filter_isPrimePow, Finset.mem_filterMap, AddMonoid.closure_finset_fg, Finset.card_le_card_add_right, Finset.univ_product_univ, RootPairing.Base.chainBotCoeff_eq_zero, Finset.mem_disjSups, AddGroup.rank_spec, ProbabilityTheory.Kernel.partialTraj_le_def, Finset.univ_unique, Finset.insert_union, Finset.smul_finset_subset_iff₀, Set.powersetCard.coe_ofFinEmb, Finset.sup_attach, DFinsupp.support_inf, Finset.subset_powersetCard_univ_iff, Finsupp.prod_attach_index, Finset.exists_sum_fiber_le_of_sum_fiber_nonneg_of_sum_le_nsmul, SummationFilter.symmetricIoc_filter, Finset.Ioc_diff_Ioo_self, Finset.mem_pimage, Finset.mem_sigmaLift, Real.pow_mul_norm_iteratedFDeriv_fourier_le, Finset.inl_mem_sumLift₂, Finset.Icc_subset_Ico_right, Finset.sups_empty, Polynomial.coeff_mem_coeffs, MvPolynomial.combinatorial_nullstellensatz_exists_eval_nonzero, Finset.sym_union, Finset.Nontrivial.add_left, Finset.inf_product_left, Finset.mem_piDiag, primitiveRoots_zero, Finset.singleton_biUnion, Submodule.fg_span_iff_fg_span_finset_subset, Finset.map_insert, Turing.PartrecToTM2.supports_singleton, FormalMultilinearSeries.compPartialSumTarget_tendsto_atTop, Finset.exists_max_image, Finset.sdiff_insert, Finsupp.card_Icc, Set.definable_finset_biUnion, Finset.card_le_card_sdiff_add_card, Finset.monotone_filter_right, Finset.ruzsa_triangle_inequality_invMul_invMul_invMul, SSet.stdSimplex.face_obj, Affine.Simplex.sign_excenterWeights_singleton_neg, Finset.max_mem_insert_bot_image_coe, Group.rank_spec, AddSubmonoid.exists_minimal_closure_eq_top, Finset.mulEnergy_empty_right, finsum_mem_finset_eq_sum, Polynomial.derivativeFinsupp_derivative, Finset.notMem_of_lt_min, Finset.tendsto_Icc_neg_atTop_atTop, Finset.filter_piFinset_eq_map_consEquiv, Set.Finite.subtypeEquivToFinset_apply_coe, MeasureTheory.IsProjectiveMeasureFamily.eq_zero_of_isEmpty, Finset.mem_sym2_iff, Affine.Simplex.excenterWeights_empty_lt_inv_two, Finset.ofColex_injective, Finset.smul_neg, Finset.none_mem_insertNone, Finset.prod_lt_one_iff_of_le_one, Finset.add_inter_subset, Bornology.isBounded_biUnion_finset, SimpleGraph.incidenceFinset_subset, Finset.image_some_eraseNone, Finset.range_subset, SimpleGraph.cliqueFinset_map_of_equiv, DirectSum.coe_mul_apply, Int.divisorsAntidiagonal_four, Finset.singleton_smul, Finsupp.rangeIcc_apply, Finset.inf_inv, Lagrange.basis_empty, ENNReal.tsum_eq_iSup_sum, MeasureTheory.lmarginal_singleton, Filter.tendsto_finset_prod_atTop, Finset.singleton_injective, Finset.Nonempty.product, MulAction.mem_stabilizer_finset, Finset.Ioc_inter_Ioc, Finset.intervalGapsWithin_surjOn, Finset.isClosed, Ideal.IsPrime.prod_mem_iff, Finset.insert_Ioc_pred_right_eq_Ioc, Finset.mul_prod_eq_prod_insertNone, Finset.measurableSet, Finset.map_sdiff, Finset.inf_attach, Finset.sup'_insert, Finsupp.support_single_ne_zero, Bornology.isCobounded_biInter_finset, Finset.measurableSet_biInter, Equiv.Perm.support_cycleOf_eq_nil_iff, affineIndependent_iff_indicator_eq_of_affineCombination_eq, Multiset.card_uIcc, ruzsaSzemerediNumber_spec, Affine.Simplex.sum_excenterWeightsUnnorm_singleton_pos, Finset.prod_apply_dite, SimpleGraph.TripartiteFromTriangles.is3Clique_iff, Order.exists_orderEmbedding_insert, Finset.tendsto_Ico_atBot_prod_atTop, Finset.asymptoticCone_biUnion, Finset.mulConst_inv_left, Finset.add_subset_iff_right, Algebra.FiniteType.iff_quotient_freeAlgebra, Nat.primeFactors_gcd, Finset.Iic_bot, SimpleGraph.cliqueSet_map, exists_sum_eq_one_iff_pairwise_coprime', Finset.swap_mem_antidiagonal, SummationFilter.instIsCountablyGeneratedFinsetFilterUnconditionalOfCountable, Finset.not_disjoint_iff_nonempty_inter, Finset.right_eq_union, Finset.mem_of_min, Finset.sum_fiberwise_eq_sum_filter, Finset.mem_sigma, DFinsupp.support_rangeIcc_subset, ContinuousMultilinearMap.map_add_univ, SimpleGraph.isNIndepSet_iff, SimpleGraph.CliqueFree.cliqueSet, Affine.Triangle.sOppSide_affineSpan_pair_excenter_singleton_point, Finsupp.card_uIcc, FormalMultilinearSeries.nnnorm_changeOriginSeries_apply_le_tsum, Int.sum_modEq_ite, SimpleGraph.interedges_def, SimpleGraph.IsFiveWheelLike.isNClique_snd_right, Finset.smul_finset_symmDiff₀, Finset.mulConst_empty_left, Finset.smul_union, Affine.Simplex.exradius_empty, Finsupp.card_Ioo, Finset.filter_False, Finset.coe_sups, Finset.truncatedSup_singleton, MvPolynomial.mem_supported, Finset.coe_Ioc, Affine.Simplex.points_mem_affineSpan_face, LocallyFinite.exists_finset_mulSupport, Finsupp.comapDomain_surjective, SimpleGraph.TripartiteFromTriangles.Graph.in₀₂_iff, Finset.inter_inter_inter_comm, RootPairing.GeckConstruction.span_range_h'_eq_top, Sym2.toFinset_mk_eq, Finsupp.comapDomain_mapDomain, Finsupp.support_sum, Finset.powersetCard_map, Finset.sups_union_right, Finset.Nonempty.card_nsmul_mono, Finset.coe_Ioo, Finset.card_union_eq_card_add_card, Finset.singleton_vadd_singleton, Finset.erase_sdiff_distrib, Finset.Nonempty.csSup_mem, Finsupp.mk_mem_graph_iff, Fintype.univ_pempty, SimpleGraph.nonuniformWitnesses_spec, Finset.map_op_add, addRothNumber_spec, Finset.dens_strictMono, SimpleGraph.edgeFinset_sup, tendsto_indicator_biUnion_finset, Finsupp.zero_notMem_frange, MeasureTheory.SimpleFunc.range_zero, Sum.Lex.Icc_inr_inl, SimpleGraph.isClique_map_finset_iff_of_nontrivial, Set.Finite.toFinset_symmDiff, Fin.orderIsoTriple_one, Finset.Icc_eq_empty_of_lt, Finset.map_ssubset_map, hasSumLocallyUniformlyOn_iff_tendstoLocallyUniformlyOn, Tuple.self_comp_sort, Finpartition.mem_part_ofSetoid_iff_rel, Finset.set_biInter_inter, Finset.range_subset_range, ProbabilityTheory.iCondIndepSets_singleton_iff, SkewPolynomial.support_add, Affine.Simplex.range_face_points, Finset.powersetCard_eq_filter, Finset.min_empty, Equiv.Perm.toList_eq_nil_iff, Finset.Icc_ssubset_Icc_left, Finset.filter_infs_le, Finset.diffs_compls_eq_infs, Finset.image_singleton, Finset.Colex.ofColex_top, IicProdIoc_def, Finsupp.mem_toMultiset, Affine.Simplex.mem_interior_face_iff_sbtw, SimpleGraph.right_nonuniformWitnesses_subset, Finset.Nonempty.inl, LocallyFiniteOrderBot.finset_mem_Iio, MvPolynomial.coe_coeffs_map, wittPolynomial_vars_subset, Equiv.Perm.Basis.ofPermHom_mem_centralizer, Finset.not_ssubset_empty, TwoUniqueSums.uniqueAdd_of_one_lt_card, Finset.union_sdiff_right, Set.Finite.coe_toFinset, Filter.tendsto_finset_powerset_atTop_atTop, Finset.range_add_one, MeasureTheory.Measure.pi_prod_map_IicProdIoc, Finset.dens_sdiff_add_dens, Finset.mem_insert, Finset.subset_union_left, Finset.prod_eq_ite, Finset.Ioc_succ_succ, Finsupp.support_update_ne_zero, Finset.card_le_four, MeasureTheory.measurableCylinders_nat, Finset.inf_eq_inter', Finset.antidiagonal_subtype_ext_iff, partialSups_eq_sUnion_image, MulAction.stabilizer_finset_empty, Finset.insert_erase_invOn, Finset.infs_eq_empty, Finset.disjSups_inter_subset_right, SmoothPartitionOfUnity.mem_finsupport, IsPrimitiveRoot.disjoint, Finset.insert_Ioc_right_eq_Ioc_succ, MeasureTheory.SimpleFunc.exists_range_iff, Finset.union_idempotent, DFinsupp.support_mk'_subset, SSet.horn₂₀.sq, Finset.mem_nonMemberSubfamily, SummationFilter.comap_filter, MultilinearMap.map_add_sub_map_add_sub_linearDeriv, Finset.set_ncard_biUnion_le, ContextFreeGrammar.Produces.exists_nonterminal_input_mem, hasProdLocallyUniformly_iff_tendstoLocallyUniformly, Submodule.coe_finsetInf, Finset.compl_insert, Finset.exists_superset_card_eq, ProbabilityTheory.iIndepSet.meas_biInter, Finsupp.support_subset_singleton, SimpleGraph.FarFromTriangleFree.cliqueFinset_nonempty, Submodule.mem_span_set, Finset.sdiff_inter_distrib_right, Set.Finite.toFinset_ssubset_toFinset, Finset.filter_union_right, Finset.singleton_subset_coe, Finset.Iic_mul_Iic_subset', Absorbs.biUnion_finset, Finset.range_orderEmbOfFin, Set.Sized.subsingleton', Fintype.prod_eq_mul_prod_compl, IntermediateField.exists_finset_of_mem_supr'', SSet.stdSimplex.mem_face_iff, YoungDiagram.isLowerSet, Set.powersetCard.coe_map, Finset.disjoint_iff_ne, Finset.card_zero, Finset.prod_sdiff_le_prod_sdiff, Finset.ext_iff, Dynamics.coverEntropy_biUnion_finset, Polynomial.support_C_subset, Finset.image_sub_product, Finset.inv_zero, Finset.fold_union_empty_singleton, Finset.Icc_subset_Ici_self, Multiset.toEnumFinset_mono, Finset.Nonempty.vadd, Finset.pairwiseDisjoint_iff, UniqueAdd.subsingleton, Finset.inf_product_right, Polynomial.support_C_mul_X_pow', Nat.finMulAntidiag_one, Finset.Nonempty.coe_sort, Finset.insert_val', Finset.ssubset_def, SimpleGraph.IsFiveWheelLike.notMem_left, Finset.inter_subset_union, Nat.properDivisors_subset_divisors, Finset.mem_upShadow_iterate_iff_exists_card, Finset.memberSubfamily_nonMemberSubfamily, MeasureTheory.ae_eq_restrict_biUnion_finset_iff, Finset.mem_sup_support_iff, Finset.supIndep_empty, Finset.sup_eq_top_iff, PairReduction.finset_logSizeBallSeq_add_one, ProbabilityTheory.iIndepFun_iff_finset, Finset.inter_union_distrib_left, Finset.sdiff_union_self_eq_union, Finpartition.part_mem, Finset.addAntidiagonal_min_add_min, Finset.mem_vadd_finset, DFinsupp.card_Ioo, Polynomial.support_X, Finset.toLeft_sdiff, Finpartition.exists_enumeration, Profinite.NobelingProof.factors_prod_eq_basis_of_ne, Finset.Colex.lt_iff_exists_filter_lt, SSet.stdSimplex.faceSingletonIso_one_hom_comp_ι_eq_δ, Finset.prod_pow_boole, Topology.CWComplex.cellFrontier_subset_finite_closedCell, Finset.ruzsa_triangle_inequality_div_mul_mul, Finsupp.support_ceilDiv_subset, Finset.singleton_mul_inter, Finset.zsmul_eq_empty, Finset.set_biInter_insert, CategoryTheory.Limits.ProductsFromFiniteCofiltered.liftToFinset_obj_map, mem_powers_iff_mem_range_orderOf, Finpartition.mem_part_iff_exists, Finset.orderEmbOfFin_singleton, MeasureTheory.FinMeasAdditive.map_iUnion_fin_meas_set_eq_sum, Finset.pimage_inter, UniqueAdd.exists_iff_exists_existsUnique, Finset.union_div, Finset.vsub_empty, Fintype.univ_unit, Finset.inf_eq_bot_iff, Submodule.mem_span_finset', Turing.PartrecToTM2.codeSupp'_self, Finset.iInf_biUnion, Finset.compls_subset_compls, Equiv.Perm.support_zpowers_of_mem_cycleFactorsFinset_le, Finset.add_subset_iff, addRothNumber_le_ruzsaSzemerediNumber, Finsupp.prod_indicator_index_eq_prod_attach, iSup_eq_iSup_finset', Finset.union_add, Finset.prod_X_add_C_coeff, Finset.eraseNone_map_some, Finset.pluennecke_ruzsa_inequality_pow_div_pow_mul, IsAddKleinFour.eq_finset_univ, Finset.Nontrivial.add_right, PartitionOfUnity.eventually_finsupport_subset, Finsupp.prod_eq_zero_iff, ProbabilityTheory.Kernel.instIsSFiniteKernelForallValNatMemFinsetIicPartialTraj, Set.Finite.toFinset_diff, Finset.vaddCommClass_finset'', DFinsupp.support_zero, Submodule.IsMinimalPrimaryDecomposition.distinct, not_linearIndependent_iffₒₛ, Finsupp.support_sym2Mul_subset, Polynomial.supp_subset_range_natDegree_succ, List.disjoint_toFinset_iff_disjoint, PairReduction.pairSet_empty_eq_empty, MeasureTheory.disjoint_cylinder_iff, Finset.Colex.toColex_le_toColex, RootPairing.GeckConstruction.instIsLieAbelianSubtypeMatrixSumMemFinsetSupportLieSubalgebraLieAlgebraCartanSubalgebra', Finset.sum_compl_add_sum, Finset.prod_one_add, Finset.equivBitIndices_symm_apply, Finset.powerset_image, Finset.diag_eq_empty, Finset.mem_range, Finset.shatters_empty, Sum.Lex.Ioc_inr_inl, Set.powersetCard.mem_ofFinEmb_iff_mem_range, Finset.symmDiff_subset_sdiff, Finset.coe_coeEmb, Nat.primeFactors_zero, WittVector.mul_polyOfInterest_vars, Set.powersetCard.card_eq, Rel.mem_interedges_iff, Finset.swap_mem_addAntidiagonal, Finset.coe_ssubset, Fintype.piFinset_empty, Finset.mem_piAntidiag, Finset.image_smul_comm, Finset.preimage_compl, Finset.card_eq_two, Finset.le_inf_mul, Finset.add_mem_vadd_finset_iff, Polynomial.roots_expand_image_frobenius_subset, Finset.mem_image₂, Finset.coe_attach, LieAlgebra.IsKilling.instIsRootSystemSubtypeWeightMemLieSubalgebraFinsetRootDualRootSystem, Set.powersetCard.ofFinEmbEquiv_symm_apply, Equiv.Perm.ofSign_disjoint, Finset.filter_piFinset_eq_map_insertNthEquiv, Finset.Ioc_eq_empty, Finset.erase_insert_subset, Finset.Ioi_eq_empty, Finset.continuous_restrict, multipliable_iff_cauchySeq_finset, isProperLinearSet_iff, Finset.eventuallyLE_iUnion, Finset.sup_prodMap, Finset.piDiag_subset_piFinset, List.toFinset_surjective, Affine.Simplex.exsphere_compl, Finset.filter_eq', Finset.mem_image_const_self, Finset.disjSum_mono_right, Finset.sum_dite_eq', Finset.sum_sdiff_sub_sum_sdiff, Finset.ruzsa_triangle_inequality_negAdd_negAdd_negAdd, Finset.card_nsmul_quotient_add_nsmul_inter_addSubgroup_le, Finset.truncatedInf_empty, Finset.univ_fin2, Equiv.Perm.support_zpow_le, Finset.Ico_add_Icc_subset, Finset.inv_filter_univ, Multiset.toEnumFinset_subset_iff, Finset.disjSum_eq_empty, Set.Finite.toFinset_smul_set, Set.powersetCard.mem_compl, MvPolynomial.support_coeff_finSuccEquiv, Filter.tendsto_toLeft_atTop, Finset.disjoint_filter_filter_not, Finset.univ_mul_univ, Finset.instNoZeroDivisors, Finset.union_insert, Finset.card_union_add_card_inter, Polynomial.rootSet_def, HasSumUniformly.tendstoUniformly, Function.Injective.mem_finset_image, Finset.Nonempty.csInf_eq_min', Affine.Simplex.dist_incenter_eq_dist_incenter, Finset.compl_filter, SSet.stdSimplex.faceSingletonComplIso_hom_ι, addRothNumber_empty, MeasureTheory.partialTraj_const, Polynomial.support_add, Finset.card_insert_le, Nat.binomial_one, Affine.Triangle.excenter_eq_incenter_or_excenter_singleton, SimpleGraph.IsNClique.isClique, Finset.diffs_empty, UniqueFactorizationMonoid.primeFactors_mul_eq_union, Finset.card_inter_vadd, NumberField.InfinitePlace.card_isUnramified_compl, Finset.biUnion_union, Equiv.Perm.Basis.mem_support_self, Finset.empty_infs, Finset.biUnion_empty, Finset.addETransformLeft.fst_add_snd_subset, Equiv.Perm.OnCycleFactors.val_centralizer_smul, Finset.union_sdiff_self, DFinsupp.support_update_ne_zero, Finset.preimage_mul_right_one, Finset.inv_product, Finset.dens_empty, Finset.symmDiff_subset_union, Finset.exists_mem_empty_iff, rothNumberNat_def, Finset.toLeft_eq_empty, ProbabilityTheory.Kernel.partialTraj_le, Fin.snoc_mem_piFinset_snoc, MeasureTheory.mem_closedCompactCylinders, Finset.card_le_card_mul_self', Finset.sup_sub_le, AffineIndependent.finrank_vectorSpan_image_finset, Finset.Ico_filter_le_of_right_le, SummationFilter.symmetricIcc_le_Conditional, Subgroup.exists_leftTransversal_of_FiniteIndex, Finset.mem_compl, Finset.card_div_mul_le_card_div_mul_card_mul, Finset.mem_nsmul, Finset.lcm_empty, IsLocalization.map_integerMultiple, Finset.union_vsub, Affine.Simplex.mem_closedInterior_face_iff_wbtw, Finset.sup'_inf_sup', RootPairing.GeckConstruction.span_range_h_le_range_diagonal, Finset.sym_inter, Finset.smul_finset_nonempty, Finset.addDysonETransform_fst, Finset.singleton_union, SkewMonoidAlgebra.sum_ite_eq', Finset.inter_smul_union_subset_union, Finset.min_mem_image_coe, Finset.three_lt_card_iff, Subgroup.rank_closure_finset_le_card, Finset.Ico_union_Ico_eq_Ico, Finset.filter_inter, PMF.support_ofMultiset, Finset.toRight_monotone, Finset.memberSubfamily_union_nonMemberSubfamily, SummationFilter.NeBot.ne_bot, Finset.Nonempty.zero_div, iInf_eq_iInf_finset, Finset.biUnion_op_vadd_finset, Finset.map_op_zero, Finset.sym_zero, Finset.inter_right_idem, Finset.map_op_neg, exteriorPower.ιMultiDual_apply_ιMulti, Finset.disjoint_map_inl_map_inr, Finset.disjoint_Ioi_Iio, Finpartition.exists_equipartition_card_eq, Finset.pi_const_singleton, SimpleGraph.not_isUniform_iff, Finset.erase_ssubset_insert, DFinsupp.Icc_eq, Finset.Colex.toColex_lt_singleton, Finset.zero_subset, not_linearIndependent_iffₛ, Finset.hasSum_iff_compl, AddAction.stabilizer_finset_singleton, Affine.Simplex.exradius_singleton_pos, Finpartition.part_nonempty, Finset.singleton_sub_singleton, Finset.Ioc_subset_Ici_self, Nat.mem_primeFactors_of_ne_zero, Finset.coe_compl, Finset.max'_insert, MonoidAlgebra.exists_finset_adjoin_eq_top, SimpleGraph.IsFiveWheelLike.snd_notMem_left, Equiv.Perm.support_mul_le, Finset.smul_finset_subset_iff, Finpartition.mem_part_self, Finset.sups_right_comm, Finset.centroid_univ, MeasureTheory.IsSetSemiring.diff_eq_sUnion', Affine.Simplex.exradius_compl, SimplexCategory.II.castSucc_mem_finset_iff, WittVector.wittAdd_vars, Filter.mem_iInf_finset, IsUnit.finset, Turing.PartrecToTM2.codeSupp_zero, ProbabilityTheory.Kernel.partialTraj_succ_self, Set.Finite.toFinset_ssubset, finsum_mem_finset_product', Equiv.Perm.card_support_prod_list_of_pairwise_disjoint, Finset.Colex.singleton_lt_singleton, Finset.uIcc_prod_def, Finset.inv_smul_finset_distrib₀, Finset.cast_mulConst_mul_card, Finset.vadd_finset_card_le, CategoryTheory.Limits.CoproductsFromFiniteFiltered.liftToFinsetObj_map, Fintype.all_card_le_filter_rel_iff_exists_injective, exteriorPower.ιMulti_family_eq_coe_comp, Finset.prod_dite_eq, MonoidAlgebra.support_mul_single_subset, Finset.coe_smul_finset, Finset.compl_univ, Finset.card_le_card_mul_self, Finset.union_self, Finset.sup_zero, LieAlgebra.IsKilling.corootForm_rootSystem_eq_killing, Finset.sub_eq_empty, Set.powersetCard.mulActionHom_compl_mulActionHom_compl, Finset.Ioo_self, Finset.filter_union_filter_not_eq, Finset.toRight_insert_inr, Finset.Ioc_eq_empty_iff, Finset.mem_neg_vadd_finset_iff, Fintype.complete, SimpleGraph.TripartiteFromTriangles.cliqueSet_eq_image, Finset.Ioc_self, Finset.card_union_le, not_addDissociated_iff_exists_disjoint, Finset.three_lt_card, Finset.inter_sdiff_left_comm, Set.toFinset_insert, Finset.infs_self, FractionalIdeal.spanFinset_ne_zero, Finset.inl_mem_sumLexLift, Finset.isCentralScalar, rank_span_finset_le, Finset.Ico_mul_Icc_subset', Finset.eventually_cofinite_notMem, Finset.eq_singleton_iff_unique_mem, Finset.sum_pos_iff_of_nonneg, Behrend.sphere_zero_right, biInf_finsetSigma, pi_eq_generateFrom, Finset.expect_dite_eq', Finpartition.card_atomise_le, Finset.Ioc_mul_Ico_subset', Finset.coe_vadd, Finset.inf_insert, Finset.Ioc_subset_Icc_self, Finset.zsmul_singleton, RootPairing.GeckConstruction.ω_mul_h, SimpleGraph.cliqueFinset_map, Finset.mem_ssubsets, Finset.product_eq_empty, ProbabilityTheory.iCondIndepSet_iff, UniqueMul.mulHom_preimage, Finset.dens_le_dens_sdiff_add_dens, Finset.mulDysonETransform.subset, measurable_updateFinset, Finset.card_consEquiv_filter_piFinset, Finset.map_injective, Finset.insert_Ioc_left_eq_Ioc_pred_of_not_isMin, Finset.sum_ite_zero, SmoothPartitionOfUnity.coe_finsupport, DFinsupp.erase_def, Finset.mul_eq_empty, Behrend.sphere_zero_subset, Finset.diag_mem_sym2_mem_iff, Equiv.Perm.card_compl_support_modEq, Finset.convolution_inv, Finset.coe_infsep, Fin.attachFin_uIcc, IsProperSemilinearSet.biUnion_finset, Finset.mem_powerset, Fintype.piFinset_sub, Finset.singleton_add_inter, Set.powersetCard.coe_finset, Geometry.SimplicialComplex.mem_facets, Finset.covBy_iff_card_sdiff_eq_one, Fintype.card_finset, Finset.monotone_filter_left, Finset.image_sdiff_product, Finset.sym2_empty, Set.sized_iUnion₂, MeasureTheory.IsSetSemiring.notMem_disjointOfDiff, Finset.disjoint_insert_right, Finset.image_op_zero, Equiv.Perm.zpow_apply_mem_support, Finset.toColex_injective, cauchySeq_finset_iff_prod_vanishing, Affine.Simplex.excenterWeightsUnnorm_empty_apply, isCompact_iff_finite_subfamily_closed, Finset.compls_inter, ProbabilityTheory.Kernel.iIndepFun.measure_inter_preimage_eq_mul, exists_orthonormalBasis, Finset.image₂_union_inter_subset_union, RootPairing.GeckConstruction.instIsIrreducible, IntermediateField.exists_finset_of_mem_iSup, MeasureTheory.sum_measure_preimage_singleton, Finset.inf_set_eq_iInter, Finset.addConvolution_ne_zero, Finset.inclusion_exclusion_card_biUnion, Finset.neg_product, UniqueFactorizationMonoid.radical_dvd_radical_iff_primeFactors_subset_primeFactors, Sum.Ioo_inr_inl, Finset.Ico_succ_succ, Finset.fold_sup_bot_singleton, Finset.mem_range_iff_mem_finset_range_of_mod_eq', Topology.CWComplex.mapsTo', Down.card_compression, Finsupp.support_eq_singleton, SimpleGraph.TripartiteFromTriangles.cliqueFinset_eq_image, Finset.sup_eq_biUnion, Equiv.Perm.cycleFactorsFinset_eq_singleton_iff, Affine.Simplex.inradius_eq_abs_inv_sum, Equiv.Perm.Basis.toPermHom_apply_toCentralizer, Finset.Colex.toColex_lt_toColex_iff_exists_forall_lt, Set.powersetCard.coe_nonempty_iff, Finset.card_le_two, Polynomial.one_mem_nthRootsFinset, Set.powersetCard.faithfulVAdd, Finset.one_nonempty, MeasureTheory.integral_biUnion_eq_sum_powerset, Finset.union_eq_empty, Nat.divisors_eq_empty, Finset.Icc_subset_Icc_iff, RootPairing.Base.linearIndepOn_root, Finset.card_infs_le, Finset.product_eq_biUnion_right, AbsolutelyContinuousOnInterval.tendsto_volume_restrict_totalLengthFilter_disjWithin_nhds_zero, Finset.mem_convexHull, Set.toFinset_singleton, biInf_finsetSigma', Finset.disjoint_sdiff, SimpleGraph.mk_mem_interedges_iff, Finset.sub_singleton, RootPairing.Base.toCoweightBasis_apply, Set.toFinset_empty, DiscreteQuotient.comp_finsetClopens, Finset.filter_snd_eq_antidiagonal, Finset.fold_empty, MvPolynomial.support_esymm', szemeredi_regularity, Finset.mem_powersetCard, Geometry.SimplicialComplex.empty_notMem, ArithmeticFunction.sum_Ioc_mul_eq_sum_prod_filter, Finset.powerset_nonempty, SimpleGraph.coe_finsetWalkLength_eq, Finset.pairwiseDisjoint_map_sigmaMk, Set.Finite.toFinset_mono, Finset.val_injective, Finset.empty_sups, Finset.canLift, Finset.card_eq_four, Finset.iInf_finset_image, Finpartition.coe_energy, DFinsupp.coe_neLocus, Finset.smul_finset_neg, Finset.mem_addSpan, Module.Basis.mem_span_image, Turing.PartrecToTM2.codeSupp_fix, Finsupp.support_update, YoungDiagram.mem_cellsOfRowLens, Finset.insert_Icc_right_eq_Icc_add_one, Finset.Iic_ssubset_Iic, measurable_IicProdIoc, Finset.image_subset_Iic_sup, Finset.Nonempty.smul, BoxIntegral.Prepartition.pairwiseDisjoint, Submodule.mem_span_mul_finite_of_mem_span_mul, Finset.mapRange_finsuppAntidiag_subset, MvPolynomial.mem_support_coeff_optionEquivLeft, Finset.toRight_eq_univ, SkewMonoidAlgebra.mem_support_iff, Finpartition.biUnion_parts, AddAction.mem_stabilizer_finset', Finpartition.empty_notMem_parts, Finset.disjiUnion_singleton, Finset.nat_divisors_prod, Finset.hasSum, Nat.properDivisors_eq_singleton_one_iff_prime, Finset.op_vadd_finset_add_eq_add_vadd_finset, Finset.max_zero, Finset.card_smul_inter, Finset.sum_product', Finset.vsub_nonempty, MvPolynomial.mem_supported_vars, FormalMultilinearSeries.changeOriginIndexEquiv_apply_fst, Finset.codisjoint_right, Finset.prod_union_eq_right, Finset.compl_empty, Finset.sups_union_left, Seminorm.exists_apply_eq_finset_sup, DFinsupp.notMem_neLocus, Subgroup.finiteIndex_iInf', Finset.card_sq_le_card_mul_mulEnergy, addRothNumber_singleton, Finset.Icc_ssubset_Icc_right, Module.Basis.reindexFinsetRange_repr_self, Finset.zero_notMem_sub_iff, RootPairing.Base.span_int_root_support, PiNat.cylinder_eq_pi, SimpleGraph.edgeDisjointTriangles_iff_mem_sym2_subsingleton, Finset.dens_inv, Finset.inf_add_left, Finset.min'_zero, Finset.sum_insertNone, SummationFilter.support_eq_univ_iff, Finset.product_nsmul, Equiv.Perm.OnCycleFactors.mem_ker_toPermHom_iff, AddMonoidAlgebra.exists_supDegree_mem_support, SkewMonoidAlgebra.support_add, Ideal.iSup_iInf_eq_top_iff_pairwise, MvPolynomial.mem_restrictSupport_iff, FreeAbelianGroup.notMem_support_iff, Equiv.Perm.Basis.ofPermHom_support, Multipliable.prod_mul_tprod_subtype_compl, Finset.add_subset_iff_left, Convex.exists_subset_interior_convexHull_finset_of_isCompact, ProbabilityTheory.iIndepSets.meas_biInter, Finset.Iic_eq_powerset, Finset.smul_nonempty_iff, Nat.divisors_injective, MeasurableEquiv.coe_IicProdIoc, Finset.smul_finset_empty, MeasureTheory.IntegrableOn.finset, Finpartition.card_mod_card_parts_le, Equiv.Perm.IsThreeCycle.eq_swap_mul_swap_iff_mem_support, SimpleGraph.mem_indepSetSet_iff, SubMulAction.fg_iff, Finset.union_sdiff_distrib, SimpleGraph.edgeFinset_strict_mono, MeasureTheory.Measure.haar.addIndex_defined, Finset.erase_insert_of_ne, cauchySeq_finset_iff_tprod_vanishing, MeasureTheory.IsSetSemiring.sUnion_insert_disjointOfDiff, Finset.le_sup_iff, SimpleGraph.unreduced_edges_subset, EMetric.pair_reduction, Monoid.closure_finset_fg, Set.toFinset_subset, Sum.Icc_inl_inr, Finset.image_inv_eq_inv, Finset.prod_prod_Ioi_mul_eq_prod_prod_off_diag, Affine.Simplex.sOppSide_excenter_singleton_point, Finset.pimage_subset, Finset.divConst_empty_left, Finset.mem_map_mk, Finset.coe_neg, ProbabilityTheory.isProjectiveMeasureFamily_map_restrict, Finset.mem_Ioo, Finset.mulDysonETransform_fst, Nat.mem_Ioc_succ', Set.powersetCard.mulActionHom_compl_bijective, Set.definable_biUnion_finset, Finset.subset_def, Finset.sum_singleton, Finset.sups_left_comm, Finset.subset_product_image_fst, Finset.add_nonempty, FormalMultilinearSeries.changeOriginIndexEquiv_symm_apply_snd_fst, Finset.instAntisymmSubset, Finset.vsub_union, Finset.sdiff_eq_sdiff_iff_inter_eq_inter, CategoryTheory.Limits.ProductsFromFiniteCofiltered.finiteSubproductsCone_pt, ProbabilityTheory.cond_iInter, Finset.Nonempty.csSup_eq_max', Submodule.mem_span_finite_of_mem_span, Finset.infs_left_comm, Finset.Nonempty.mul_zero, Finset.mem_sdiff, Nat.sum_divisors_filter_squarefree, Preorder.frestrictLe_apply, Prime.dvd_finsuppProd_iff, isClopen_biUnion_finset, SimplexCategory.II.last_mem_finset, Finset.card_truncatedInf_union_add_card_truncatedInf_sups, biUnion_Iic_disjointed, Finset.image₂_empty_left, Nat.Ico_pred_singleton, Finset.convexHull_eq, Preorder.frestrictLe₂_apply, Set.toFinset_add, Fintype.coe_finsetOrderIsoSet_symm, Finset.default_singleton, Finsupp.support_mapRange, MvPowerSeries.WithPiTopology.summable_prod_of_tendsto_weightedOrder_atTop_nhds_top, RootPairing.GeckConstruction.ωConjLieSubmodule_eq_top_iff, finrank_span_finset_le_card, Finset.singleton_add, SimpleGraph.exists_isFiveWheelLike_of_maximal_cliqueFree_not_isCompleteMultipartite, Finset.union_smul, Part.toFinset_none, RootPairing.Base.toCoweightBasis_repr_coroot, BoxIntegral.Prepartition.sum_disj_union_boxes, Finset.sup_sub_left, Finmap.keys_singleton, Fin.attachFin_Ico, GradedRing.mem_support_iff, MulAction.stabilizer_finset_singleton, Finset.orderEmbOfCardLe_mem, SSet.face_le_horn, finprod_mem_finset_product', Set.Finite.subset_toFinset, Finset.left_mem_uIcc, UV.card_compress, Finset.Ico_union_Ico, Finset.image_vadd, Finset.sum_eraseNone, TopologicalSpace.CompactOpens.coe_finsetSup, Equiv.finsetCongr_apply, MeasureTheory.GridLines.T_empty, Filter.biInter_finset_mem, Finset.card_filter_le_iff, Finset.add_eq_zero_iff, Finset.subset_one_iff_eq, Finset.prod_product_right, SimpleGraph.IsFiveWheelLike.fst_notMem_right, Fintype.expect_ite_mem, finprod_mem_coe_finset, Set.toFinset_strict_mono, Filter.tendsto_finset_preimage_atTop_atTop, Finset.sup_inf, DFinsupp.subtypeSupportEqEquiv_symm_apply_coe, Finset.min_eq_top, Finset.exists_mem_eq_sup, VectorFourier.pow_mul_norm_iteratedFDeriv_fourierIntegral_le, Finset.prod_attach_univ, MvPolynomial.vars_prod, Finset.Icc_eq_singleton_iff, Finset.card_mul_iff, Finset.image_add_product, Finset.pluennecke_ruzsa_inequality_pow_div, Equiv.Perm.cycleFactorsFinset_pairwise_disjoint, SimpleGraph.IsNIndepSet.isIndepSet, Multiset.mem_toEnumFinset, DFinsupp.support_update, Finset.product_eq_univ, Finset.card_le_card_div_self, Finset.sum_product_right', Finset.mem_shadow_iff_insert_mem, Finset.isWF_bUnion, Finset.vadd_finset_union, Finset.singleton_add_singleton, Finset.truncatedInf_singleton, Finset.mem_Ioi, Finset.image_op_mul, Finset.coe_eraseNone, Finset.zero_div_subset, Finset.diffs_inter_subset_left, AddMonoidAlgebra.support_mul, isNilpotent_of_finite_tfae, Finpartition.sparsePairs_mono, Finset.ruzsa_triangle_inequality_add_sub_sub, Finset.expect_product, Finset.orderEmbOfFin_compl_singleton_eq_succAboveOrderEmb, SimpleGraph.swap_mem_interedges_iff, Finset.mulDysonETransform.smul_finset_snd_subset_fst, Nat.roughNumbersUpTo_card_le', Finset.coe_filterMap, SimpleGraph.coe_incidenceFinset, IsCompact.elim_nhds_subcover, List.zipWith_swap_prod_support', Finset.mem_map_equiv, Polynomial.notMem_support_iff, le_mulRothNumber_product, Finset.notMem_uIcc_of_gt, Finset.neg_def, Finset.image₂_inter_union_subset_union, Nat.primesBelow_zero, MeasureTheory.ae_restrict_biUnion_finset_iff, Finset.inv_insert, Equiv.Perm.pairwise_commute_of_mem_zpowers, Finset.notMem_empty, Finset.card_inter_add_card_sdiff, Finset.mem_vsub, Finset.singleton_zero, Finset.Nontrivial.not_subset_singleton, Finset.filterMap_empty, MvPolynomial.coeff_mul_X', mem_primesOverFinset_iff, Finset.mem_div, MeasurableSpace.measurableSet_generateFrom_memPartition_iff, Finsupp.support_mono, IsPrimitiveRoot.primitiveRootsPowEquivOfCoprime_apply_coe, Equiv.Perm.mem_ofSign, Finset.mem_erase, Finset.supIndep_pair, Finset.Colex.toColex_mono, DFinsupp.mem_support_iff, Finset.ssubset_iff, AddSubgroup.leftCoset_cover_const_iff_surjOn, MultilinearMap.map_add_eq_map_add_linearDeriv_add, SimpleGraph.IsMaximumClique.isClique, Equiv.Perm.support_swap_mul_ge_support_diff, wittStructureInt_vars, Finset.wellFoundedLT, ContinuousAlternatingMap.map_add_univ, Polynomial.Chebyshev.isLocalExtr_T_real_iff, Finset.le_card_iff_exists_subset_card, Set.powersetCard.addActionHom_singleton_bijective, SimpleGraph.cliqueFreeOn_of_card_lt, Rel.mk_mem_interedges_iff, hasProdUniformly_iff_tendstoUniformly, Finset.coe_list_prod, Equiv.Perm.Basis.ofPermHomFun_apply_mem_support_cycle_iff, PMF.support_ofFinset, DFinsupp.card_uIcc, Finpartition.part_subset, Equiv.Perm.mem_cycleFactorsFinset_conj', Finset.disjoint_range_addLeftEmbedding, YoungDiagram.mk_mem_col_iff, IsPrimitiveRoot.primitiveRootsPowEquiv_apply_coe, Finset.eventuallyEq_iUnion, List.mem_foldr_sup_support_iff, Finsupp.mem_rangeIcc_apply_iff, PrimitiveSpectrum.preimage_upperClosure_compl_finset, Finset.Iio_subset_Iic_self, Finset.map_comp_coe, Finset.prod_dite_of_false, Finset.fold_insert_idem, SimpleGraph.isNClique_empty, Finset.erase_image_subset_image_erase, Multiset.toEmbedding_coeEquiv_trans, Finset.Icc_subset_Icc, sum_eq_tsum_indicator, Finset.mem_of_max, Finset.Iic_mul_Iio_subset', SmoothPartitionOfUnity.eventually_fintsupport_subset, Set.powersetCard.coe_compl, Finset.instMulRightMono, Finset.hasProd_support, Finset.Nonempty.smul_finset, Finset.Ico_subset_Iic_self, Finset.sups_infs_subset_right, Finset.insert_Icc_succ_left_eq_Icc, Finpartition.mem_bot_iff, Finset.biUnion_singleton_eq_self, Submodule.span_range_natDegree_eq_adjoin, Finset.Nonempty.inv, Set.toFinset_inter, Finset.insert_ne_self, Turing.PartrecToTM2.contSupp_cons₂, Fintype.coe_piFinset, AhlswedeZhang.infSum_compls_add_supSum, List.pairwise_iff_coe_toFinset_pairwise, Set.indicator_pi_one_apply, Finset.inf_add_right, SimpleGraph.isMaximalClique_compl, Finset.strictMono_iff_forall_lt_insert, Finset.image_subset_iff, Finset.SupIndep.union, Finset.sup_union, Finset.coe_eq_univ, SSet.horn.faceι_ι, Finset.gcd_union, AbsolutelyContinuousOnInterval.biUnion_uIoc_subset_of_mem_disjWithin, Finset.addConst_mul_card, SimpleGraph.cycleGraph_neighborFinset, Sym2.mem_toFinset, Finset.Ioc_subset_Ioi_self, FreeAddMonoid.symbols_of, xInTermsOfW_vars_subset, SimpleGraph.IsFiveWheelLike.card_inter, Finset.isCompact_biUnion, Finset.neg_empty, Finset.Nonempty.inf_eq_bot_iff, Finset.shadow_singleton, Polynomial.support_integralNormalization_subset, Finset.product_val, UniqueFactorizationMonoid.mem_primeFactors, Polynomial.map_restriction, Submodule.sum_mem_biSup, Finset.sups_subset_self, Finset.right_notMem_Ico, Finset.coe_injective, Finset.biUnion_insert, Set.powersetCard.mem_iff, Finset.supIndep_singleton, Finset.image_smul, Finset.min_eq_bot, Finset.shadow_singleton_empty, Finset.prod_sdiff_div_prod_sdiff, Finset.prodMap_map_product, SimpleGraph.IsFiveWheelLike.isNClique_left, Finset.coe_covBy_coe, Finset.prodMap_image_product, Finset.ruzsa_triangle_inequality_mulInv_mul_mul, MvPolynomial.coeff_mem_coeffs, Finset.ruzsa_triangle_inequality_mul_mul_mul, AddMonoidAlgebra.support_one_subset, Finset.prod_erase_attach, RootPairing.GeckConstruction.cartanSubalgebra_le_lieAlgebra, Finset.singleton_infs_singleton, Finset.fold_min_le, Finset.image₂_distrib_subset_right, Finset.ssubset_univ_iff, MulAction.mem_stabilizer_finset_iff_smul_finset_subset, ProbabilityTheory.Kernel.partialTraj_comp_partialTraj, Finset.restrict_preimage_univ, IsPrimitiveRoot.injOn_pow_mul, Finset.powerset_injective, PMF.support_uniformOfFinset, SimpleGraph.CliqueFree.mem_of_sup_edge_isNClique, Finset.max'_union, Finset.empty_mem_powerset, Set.Finite.toFinset_empty, Affine.Triangle.affineSpan_pair_eq_orthRadius_insphere, Finset.Iic_subset_Iic, Finset.filter_eq_empty_iff, Finset.sup'_zero, Finset.preimage_neg, BoxIntegral.Prepartition.splitMany_empty, FirstOrder.Language.Theory.isSatisfiable_iUnion_iff_isSatisfiable_iUnion_finset, Set.Finite.toFinset_subset_toFinset, Finset.zpow_eq_empty, Finset.image_nsmul, Finset.compls_sups, Finset.le_dens_sdiff, Finset.image₂_union_left, SkewMonoidAlgebra.support_zero, Equiv.Perm.IsCycle.zpowersEquivSupport_apply, Submodule.isPrimary_decomposition_pairwise_ne_radical, SimpleGraph.componentCompl_finite, Filter.tendsto_finset_range, Set.Finite.toFinset_smul, rel_iSup_prod, WithTop.prod_eq_top_iff, Finsupp.card_pi, exists_finset_linearIndependent_of_le_rank, Ideal.Factors.liesOver, Finset.image₂_inter_subset_right, Finset.card_attach, Affine.Simplex.sign_touchpointWeights_singleton_pos, IsUltrametricDist.exists_norm_finset_sum_le, Finset.isLUB_sup', Finset.sum_sdiff_le_sum_sdiff, Finset.iInf_union, SimpleGraph.is3Clique_iff, AddMonoidAlgebra.exists_finset_adjoin_eq_top, MultilinearMap.map_piecewise_add, MeasureTheory.lintegral_finset, Finset.sigmaAntidiagonalEquivProd_symm_apply_snd_coe, Finset.Colex.isInitSeg_iff_exists_initSeg, Finset.min_pair, Fintype.eval_image_piFinset_subset, Finset.sum_boole_nsmul, exteriorPower.ιMulti_family_span_of_span, Finset.le_card_add_mul_addEnergy, Finset.Iic_disjoint_Ioc, Fin.image_castSucc, MvPolynomial.mem_support_finSuccEquiv, Rel.edgeDensity_empty_left, Finset.commApplicative, Equiv.Perm.OnCycleFactors.cycleType_kerParam_apply_apply, Finset.sups_nonempty, Finset.singletonAddHom_apply, MeasurableSpace.measurableSet_generateFrom_countablePartition_iff, Set.toFinset_ssubset, Finset.max_eq_bot, SimpleGraph.LocallyLinear.le_ruzsaSzemerediNumber, Fintype.piFinset_eq_empty, Polynomial.iterate_derivative_prod_X_sub_C, Finset.sup_eq_iSup, Finset.some_mem_insertNone, ProbabilityTheory.identDistrib_iff_forall_finset_identDistrib, Polynomial.support_smul, Finset.slice_union_shadow_falling_succ, CompositionAsSet.getLast_mem, Multiset.toFinset_zero, Finset.mul_subset_iff_left, Finset.subset_set_image_iff, RootPairing.GeckConstruction.instIsTriangularizableSubtypeMatrixSumMemFinsetSupportLieSubalgebraLieAlgebraCartanSubalgebra'Forall, Finset.div_subset_iff, MeasureTheory.ae_restrict_biUnion_finset_eq, SkewMonoidAlgebra.support_mul_single_subset, mulRothNumber_empty, Finset.Nonempty.card_pow_mono, Submodule.spanRank_toENat_eq_iInf_finset_card, Finset.insert_Icc_add_one_left_eq_Icc, Finset.min'_insert, Finset.card_sq_le_card_mul_addEnergy, Finset.mulETransformRight_inv, Polynomial.X_pow_sub_one_mul_prod_cyclotomic_eq_X_pow_sub_one_of_dvd, SimpleGraph.map_neighborFinset_induce, Fintype.piFinset_smul, RootPairing.GeckConstruction.diagonal_elim_mem_span_h_iff, Finset.not_nontrivial_empty, Geometry.SimplicialComplex.mem_vertices, IsOfFinAddOrder.mem_multiples_iff_mem_range_addOrderOf, Finset.pluennecke_ruzsa_inequality_nsmul_sub_nsmul_sub, Finset.exists_card_fiber_lt_of_card_lt_mul, IsCompact.elim_nhds_subcover_nhdsSet, IsCompact.elim_nhdsWithin_subcover, Finset.Ico_subset_Ico_iff, Finset.image_inter_subset, ProbabilityTheory.iCondIndepSets_iff, Finset.Ici_prod_def, Finset.univ_eq_attach, Sum.Lex.Ico_inr_inl, Finsupp.support_single_add_single_subset, Fintype.piFinset_mul, Finset.mem_toLeft, UniqueAdd.set_subsingleton, RootPairing.GeckConstruction.ωConj_invFun, Finset.image_infs, Finset.card_inter_add_card_union, Finset.mem_inv', Ideal.sum_pow_mem_span_pow, tendstoUniformlyOn_tsum_of_cofinite_eventually, Finset.dens_neg, Finset.Ioo_eq_empty_of_le, Finset.isDirected_le, Finsupp.finite_vaddAntidiagonal, Finset.prod_extend_by_one, Finset.zero_mem_zero, Finset.centroid_mem_convexHull, Real.geom_mean_lt_arith_mean_weighted_iff_of_pos, Int.existsUnique_mem_box, Profinite.NobelingProof.spanFinBasis.span, Infinite.exists_notMem_finset, SimpleGraph.triangle_counting', Finset.untrop_sum, Finset.vadd_finset_insert, Nat.mem_factoredNumbers_iff_primeFactors_subset, Finset.coe_nsmul, Finset.prodMk_inf'_inf', Finset.instLawfulSingleton, Finsupp.support_floorDiv_subset, ProbabilityTheory.iIndep_iff, Finset.sum_powerset_neg_one_pow_card_of_nonempty, Fin.attachFin_Ioo, Nat.Prime.mem_primeFactors_self, Finset.mulAntidiagonal_mono_left, Finset.insert_union_comm, SimpleGraph.TripartiteFromTriangles.Graph.in₁₂_iff', Finset.injective_sym2, Infinite.exists_superset_card_eq, Finset.union_right_idem, Finset.vaddCommClass_finset, LocallyFiniteOrder.finset_mem_Ico, Finset.tendsto_Icc_neg, Finset.subset_iff_eq_of_card_le, Finset.uIcc_subset_uIcc_iff_mem, Finpartition.card_bind, rel_iSup_sum, Nat.pow_mul_mem_factoredNumbers, Set.powersetCard.coe_addActionHom_of_embedding, Topology.RelCWComplex.cellFrontier_subset_finite_openCell, MeasureTheory.Filtration.piFinset_eq_comap_restrict, MeasureTheory.Measure.haar.addIndex_elim, IsCompact.elim_finite_subcover, Finset.insert_Icc_pred_right_eq_Icc, Fintype.coe_finsetOrderIsoSet, Finset.Nat.mem_antidiagonalTuple, Finset.op_smul_finset_smul_eq_smul_smul_finset, Finset.prod_eq_zero_iff, SkewMonoidAlgebra.support_mul, IsNonarchimedean.finset_image_add_of_nonempty, Finsupp.indicator_eq_sum_attach_single, Finset.sub_nonempty, Finset.iSup_insert, Equiv.finsetSubtypeComm_symm_apply, Finset.inv_op_smul_finset_distrib₀, Finset.card_sub_card_eq, exteriorPower.basis_coord, UniqueMul.of_card_le_one, Finset.diag_mem_sym2_iff, FractionalIdeal.mem_span_mul_finite_of_mem_mul, SimpleGraph.TripartiteFromTriangles.Graph.in₂₀_iff', Finset.disjoint_iff_inter_eq_empty, Function.updateFinset_univ_apply, SSet.horn_eq_iSup, FreeAddMonoid.symbols_zero, Finset.Icc_prod_def, Finset.insert_Ico_right_eq_Ico_add_one, Finset.subset_mulSpan, SimpleGraph.mem_interedges_iff, Finset.ssubset_iff_exists_cons_subset, Multiset.toFinset_replicate, Finset.sym_singleton, Equiv.Perm.pow_apply_mem_support, Nat.primesBelow_succ, Nat.primeFactors_one, Finset.union_eq_right, Finset.sum_pow_mul_eq_add_pow, Finset.gcd_singleton, Finset.singleton_mul_singleton, Affine.Simplex.incenter_eq_affineCombination, not_mulDissociated_iff_exists_disjoint, Nat.Prime.mem_primeFactors, Finset.isLUB_sup, Finset.map_inl_subset_iff_subset_toLeft, Finset.image₂_distrib_subset_left, Finset.mul_add_subset, compact_covered_by_add_left_translates, SSet.stdSimplex.obj₀Equiv_symm_mem_face_iff, Finset.product_mul_product_comm, Finset.card_insert_eq_ite, Polynomial.coeffs_one, Fintype.univ_ofIsEmpty, Multiset.mem_sup, Finset.disjoint_singleton, Finset.subset_sdiff, Finset.prod_coe_sort_eq_attach, measurable_updateFinset', Finset.sum_extend_by_zero, IntermediateField.isSplittingField_iSup, Finset.cast_subConst, Finset.sum_neg_iff_of_nonpos, Finpartition.ofSetoid_parts_val, Finset.card_sdiff_eq_card_sdiff_iff, Finset.singleton_inj, SimpleGraph.isNClique_one, SimpleGraph.isNClique_zero, Finset.prod_product, FreeMonoid.symbols_of, MeasureTheory.sum_measureReal_preimage_singleton, Finset.map_op_mul, Finset.prod_insert_one, SimpleGraph.mem_neighborFinset, Finset.max_eq_top, Finset.sup_singleton_apply, Finset.addConvolution_pos, MonomialOrder.degree_mem_support, Finset.prod_attach_eq_prod_dite, Finset.smul_finset_union, Finset.disjoint_filter_filter', Finset.max_empty, Finset.sub_inter_subset, Function.updateFinset_empty, Finset.Nat.antidiagonalTuple_zero_succ, Finset.sub_def, Multiset.disjoint_toFinset, Finset.imageAddHom_apply, Equiv.Perm.isPretransitive_of_isCycle_mem, finsum_mem_finset_product, Finset.Nontrivial.mul, CategoryTheory.Limits.ProductsFromFiniteCofiltered.liftToFinsetLimitCone_cone_pt, SimpleGraph.IsFiveWheelLike.fst_notMem, CategoryTheory.Limits.ProductsFromFiniteCofiltered.liftToFinset_map_app, Finset.card_mul_le, Finset.self_mem_range_succ, Affine.Simplex.sOppSide_point_excenter_singleton, Finset.equitableOn_iff, Finsupp.antidiagonal_zero, pi_generateFrom_eq, MonoidAlgebra.support_gen_of_gen, Finset.smul_univ₀', Turing.TM2.stmts₁_self, Finset.centroidWeightsIndicator_def, MvPolynomial.support_monomial_subset, Finset.Icc_subset_uIcc, Finset.inter_val_nd, Equiv.Perm.OnCycleFactors.coe_toPermHom, IsTopologicalBasis.iInf, SimpleGraph.sdiff_compl_neighborFinset_inter_eq, Finset.HasAntidiagonal.mem_antidiagonal, Finset.MulETransform.card, Finset.Nonempty.empty_ssubset, Finset.centerMass_empty, Finset.biUnion_image_sup_right, PointedCone.mem_span_set, Finset.union_empty, Cardinal.mk_finset_of_fintype, Equiv.Perm.IsThreeCycle.nodup_iff_mem_support, Finset.prod_singleton', Finset.notMem_of_coe_lt_min, DFinsupp.card_pi, Finset.inf_mul_right, Finset.Nonempty.vsub, Tree.mem_treesOfNumNodesEq_numNodes, Finset.exists_mem_ne, WittVector.wittSub_vars, SimpleGraph.IsSRGWith.card_neighborFinset_union_of_not_adj, Finset.toList_empty, Finset.union_biUnion, BoxIntegral.Prepartition.splitMany_insert, Finset.op_vadd_addConvolution_eq_addConvolution_vadd, MeasureTheory.measure_biUnion_finset_le, FreeAddMonoid.mem_symbols, Finset.inter_singleton, FirstOrder.Ring.MvPolynomialSupportLEEquiv_symm_apply_coeff, Cardinal.mk_eq_nat_iff_finset, YoungDiagram.mem_col_iff, Finset.compls_infs, Finset.piFinset_filter_const, exists_isTranscendenceBasis_and_isSeparable_of_perfectField, Finset.sdiff_eq_empty_iff_subset, Finset.piecewise_insert_of_ne, Finset.isPWO_bUnion, Finset.union_mul_inter_subset, List.support_formPerm_le', Finmap.keysLookupEquiv_apply_coe_snd, MvPolynomial.support_X_pow, Finset.upShadow_monotone, Finset.sym_eq_empty, Finset.dependsOn_restrict, FormalMultilinearSeries.changeOriginSeries_summable_aux₁, Finset.smulCommClass, Finset.coe_symmDiff, Finset.mem_sup', Finset.inter_assoc, Finset.SupIndep.insert, Finset.disjoint_product, CompositionAsSet.zero_mem, Finset.isAtom_singleton, Set.ssubset_toFinset, IsCompact.elim_nhds_subcover', Fintype.univ_Prop, Finset.Iio_mul_Iic_subset', Finset.filter_sups_le, DFinsupp.mem_pi, inf_sSup_eq_iSup_inf_sup_finset, Finset.mk_zero, ENNReal.hasSum, isLUB_hasSum', Finset.prod_ite_mem, Finset.inter_mul_union_subset, IsNoetherian.coe_finsetBasisIndex, Finset.Icc_mul_Ico_subset', Finset.sum_anti_set_of_nonpos, Nat.prod_pow_primeFactors_factorization, Nat.multinomial_singleton, Finset.inter_mul_union_subset_union, Affine.Simplex.sign_touchpointWeights_singleton_neg, Finset.inr_mem_sumLift₂, Finset.iInf_singleton, Set.iUnion_eq_iUnion_finset, Finset.disjiUnion_empty, SSet.horn₃₂.desc.multicofork_π_zero_assoc, Finset.measure_zero, addRothNumber_map_add_left, Finset.sum_sum_Ioi_add_eq_sum_sum_off_diag, WithTop.sum_eq_top, Nat.primeFactors_subset_of_mem_factoredNumbers, Finset.erase_insert_eq_erase, Finset.mem_disjSum, Finpartition.IsEquipartition.sum_nonUniforms_lt, Finset.pi_empty, RootPairing.GeckConstruction.isNilpotent_f, Finset.left_eq_union, Finset.ruzsa_triangle_inequality_mulInv_mulInv_mulInv, SimpleGraph.mem_cliqueFinset_iff, Finset.sum_ite_mem_eq, Finset.prod_powerset, Finsupp.notMem_graph_snd_zero, Tree.coe_treesOfNumNodesEq, Finset.Colex.le_def, Finset.compl_eq_univ_iff, BoxIntegral.Prepartition.single_boxes, YoungDiagram.row_eq_prod, Finset.inv_inter, Finset.image₂_singleton_left, Finset.filter_and, SimpleGraph.EdgeDisjointTriangles.mem_sym2_subsingleton, Finset.image_sup_product, Finset.notMem_union, Monoid.exponent_eq_max'_orderOf, Finset.empty_sdiff, isOpen_biInter_finset, Finset.Ioo_insert_right, Finset.min'_singleton, Finset.card_pair_eq_one_or_two, Behrend.box_zero, Finset.sum_dite_of_false, Finset.map_insertNthEquiv_filter_piFinset, Finset.mem_bipartiteBelow, Finset.filter_ssubset, Finset.forall_coe, Fintype.sum_eq_sum_compl_add, Finset.exists_maximal, Finset.Ioo_subset_Ioo_right, Finset.shadow_empty, RootPairing.GeckConstruction.lie_e_f_same, Finset.vadd_finset_empty, Finset.subset_map_iff, Finsupp.subset_support_tsub, SimpleGraph.ComponentCompl.infinite_iff_in_all_ranges, Finset.empty_pow, SkewMonoidAlgebra.support_single_subset, MeasureTheory.Measure.isProjectiveLimit_infinitePiNat, Finset.Colex.initSeg_nonempty, Finset.mem_falling, MeasureTheory.Measure.restrict_finset_biUnion_congr, Finset.Injective2_disjSum, Algebra.FiniteType.iff_quotient_mvPolynomial, Finset.card_add_singleton, Finset.coeAddMonoidHom_apply, AddMonoidAlgebra.mem_grade_iff, Finset.smul_finset_def, Finset.max'_eq_iff, IsPiSystem.tendsto_probabilityMeasure_biUnion, Finsupp.rangeSingleton_apply, Finset.dens_mono, RootPairing.GeckConstruction.ω_mul_ω, AddSubgroup.FG.biSup_finset, WittVector.wittPow_vars, List.toFinset_surj_on, Finset.gcd_insert, MeasureTheory.Measure.count_apply_finset, Finset.Ioo_eq_empty_iff, Finset.sum_powerset, Finset.Ico_eq_empty_of_le, Caratheodory.affineIndependent_minCardFinsetOfMemConvexHull, Finset.mulEnergy_eq_zero_iff, DFinsupp.support_sup_union_support_inf, Nat.prod_modEq_ite, Finset.inf_empty, Set.powersetCard.addAction_faithful, Finset.card_neg, Finset.Ioc_disjoint_Ioc_of_le, Finset.biUnion_inter, Finset.subset_univ_image_iff, Nat.divisors_subset_properDivisors, Finsupp.support_single_disjoint, Finpartition.mem_bind, DFinsupp.lmk_apply, Nat.Prime.divisors, tendsto_tsum_compl_atTop_zero, Finset.erase_union_distrib, Finset.subset_iff, Finset.eraseNone_eq_biUnion, Finset.Ioc_insert_left, Module.exists_nontrivial_relation_sum_zero_of_finrank_succ_lt_card, SSet.horn.faceι_ι_assoc, Finset.preimage_add_right_singleton, Finset.fold_union_inter, Int.Icc_eq_pair, Int.divisorsAntidiagonal_two, AddMonoidAlgebra.mem_adjoin_support, Set.Sized.subsingleton, IsPrimitiveRoot.ntRootsFinset_pairwise_associated_sub_one_sub_of_prime, linearIndependent_iff_finset_linearIndependent, Multiset.nat_divisors_prod, Finset.isPWO, Finset.sdiff_inter_self_right, Finset.disjoint_biUnion_left, Finsupp.support_smul, Finset.cast_mulConst, Finsupp.mem_support_single, List.fixedLengthDigits_zero, Finset.Icc_diff_Ico_self, Finset.card_empty, Finset.image_diag_union_image_offDiag, RootPairing.GeckConstruction.ωConj_toFun, Finset.bddBelow, Ideal.decomposition_erase_inf, Finset.union_right_comm, Finset.inv_univ, Finset.smul_finset_eq_univ, Finsupp.support_update_subset, Finset.UV.toColex_compress_lt_toColex, Finset.coe_zero, Int.divisorsAntidiagonal_one, Finset.op_smul_convolution_eq_convolution_smul, Multiset.toFinset_union, Finset.all_card_le_biUnion_card_iff_exists_injective, Finset.inter_add_singleton, Finset.mem_inf, Finset.smul_def, CategoryTheory.Limits.CoproductsFromFiniteFiltered.liftToFinset_map_app, Finset.mulEnergy_eq_sum_sq, Finset.Icc_diff_both, Finset.Nontrivial.coe, IsLocalRing.primesOverFinset_eq, Finset.Ico_add_Ioc_subset, Finset.piAntidiag_empty_zero, Finset.Icc_self, Finset.addEnergy_self_eq_zero_iff, Equiv.Perm.Disjoint.disjoint_support, Set.image_finset_sum_pi, Finset.insert_union_distrib, SimpleGraph.mk_mem_interedges_comm, Finset.mulSupport_prod, Ideal.sup_iInf_eq_top, Finset.centroid_singleton, isClopen_biInter_finset, Finset.piecewise_singleton, Finset.powerset_inter, Equiv.Perm.support_prod_le, Finset.coe_diffs, IsPrimitiveRoot.primitiveRoots_one, Finset.prod_mono_set', Turing.PartrecToTM2.codeSupp_succ, Finset.subConst_mul_card, SimpleGraph.cliqueSet_eq_empty_iff, Turing.PartrecToTM2.codeSupp_case, TopologicalSpace.Clopens.surjective_finset_sup_prod, SummationFilter.symmetricIcc_filter, Affine.Simplex.sign_signedInfDist_touchpoint_empty, Finset.infs_singleton, Finset.mem_subtype, mem_zmultiples_iff_mem_range_addOrderOf, Behrend.mem_box, Finset.subset_subsetSum, Finset.pow_eq_empty, IsCompact.elim_nhdsWithin_subcover', Finset.smul_finset_card_le, Ideal.Factors.finrank_pow_ramificationIdx, Finset.min'_pair, Finset.dens_inter_add_dens_union, Finset.biUnion_image_inf_right, Finset.notMem_of_max_lt_coe, Finset.mulETransformLeft.card, MeasureTheory.Measure.restrict_biUnion_finset_congr, Finset.Ici_product_Ici, RootPairing.GeckConstruction.ω_mul_e, SimpleGraph.edgeDensity_empty_left, Finset.smul_finset_eq_empty, MeasureTheory.SimpleFunc.mem_restrict_range, Finset.sup_mem_of_nonempty, List.pairwiseDisjoint_consFixedLengthDigits, SimpleGraph.IsMaximumClique.isMaximalClique, SmoothPartitionOfUnity.finsupport_subset_fintsupport, Finset.card_mul_cast_mulConst, RootPairing.GeckConstruction.isNilpotent_e, Dense.diff_finset, Finset.Ioi_subset_Ioi, Finmap.keysLookupEquiv_symm_apply_keys, ProbabilityTheory.Kernel.partialTraj_self, sigmaAntidiagonalEquivProd_symm_apply_fst, Nat.Ico_succ_right_eq_insert_Ico, Finset.filter_or, Set.powersetCard.mem_ofFinEmbEquiv_iff_mem_range, linearIndepOn_finset_iffₛ, Finset.image₂_inter_subset_left, Finset.max_insert, Fin.sum_pow_mul_eq_add_pow, Finsupp.mem_vaddAntidiagonal_of_addGroup, Finset.map_inr_subset_iff_subset_toRight, Nat.primeFactors_eq_empty, Finset.eq_empty_of_isEmpty, Finset.tendsto_Ioo_neg_atTop_atTop, Finset.instIdempotentOpUnion, Topology.CWComplex.cellFrontier_subset_finite_openCell, Finset.inter_right_comm, Affine.Triangle.dist_circumcenter_reflection_orthocenter_finset, Finset.imageMulHom_apply, Finset.iInter_mem_sets, Finset.exists_sum_fiber_lt_of_sum_fiber_nonneg_of_sum_lt_nsmul, Polynomial.support_update, Finset.addConst_neg_left, Finset.card_le_six, Seminorm.zero_or_exists_apply_eq_finset_sup, Finset.prod_inv_index, Finsupp.coe_rangeIcc, Finset.image₂_union_inter_subset, BoxIntegral.Prepartition.disjUnion_boxes, Affine.Simplex.sign_excenterWeights_empty, Finset.toRight_eq_empty, Set.Sized.univ_mem_iff, convexHull_eq_union_convexHull_finite_subsets, union_support_maximal_linearIndependent_eq_range_basis, Equiv.Perm.pow_apply_mem_toList_iff_mem_support, Sym2.filter_image_mk_not_isDiag, MvPolynomial.vars_one, Mathlib.Meta.NormNum.Finset.sum_empty, Finset.filter_insert, SkewPolynomial.support_eq_empty, Finset.isUnit_iff_singleton, Module.FinitePresentation.out, SimplexCategory.II.mem_finset_iff, RootPairing.Base.exists_root_eq_sum_int, MeasureTheory.SimpleFunc.range_eq_empty_of_isEmpty, Finset.instNontrivial, Submodule.exists_finset_span_eq_linearIndepOn, Finset.Ioo_subset_Ioc_self, Set.definable_biInter_finset, IntermediateField.exists_finset_of_mem_adjoin, Finset.one_lt_prod_iff, Finset.disjoint_val, Finset.biUnion_vadd_finset, Finset.Nonempty.attach, ENNReal.sum_add_tsum_compl, Finset.insert_Ioc_left_eq_Ioc_sub_one, Finset.right_mem_Icc, Finset.sumEquiv_apply_snd, RootPairing.GeckConstruction.h_mem_lieAlgebra, IsUltrametricDist.exists_norm_finset_sum_le_of_nonempty, Finset.sigma_eq_empty, IicProdIoc_preimage, univ_eq_singleton_of_card_one, Finset.mem_shadow_iterate_iff_exists_card, Finset.Ioo_subset_Ioo_left, SimpleGraph.IsSRGWith.card_neighborFinset_union_of_adj, Finset.coe_Ioi, Finset.mem_sumLexLift, Equiv.Perm.cycleFactorsFinset_conj_eq, Finset.insert_inter_distrib, Finset.left_notMem_Ioc, Finpartition.nonempty_of_not_uniform, Finset.compls_union, Finset.inter_pow_subset, MvPolynomial.vars_bind₁, Polynomial.support_C_mul_X_pow, Fin.attachFin_Iio, Finset.inter_biUnion, FirstOrder.Language.distinctConstantsTheory_eq_iUnion, Function.updateFinset_univ, Nat.divisorsAntidiagonal_eq_prod_filter_of_le, Finset.dens_singleton, Finset.PiFinsetCoe.canLift, Finset.shadow_iterate_empty, Finset.isUnit_singleton, Finset.le_card_infs_mul_card_sups, SimpleGraph.mem_edgeFinset, SSet.horn.multicoequalizerDiagram, Finset.Colex.lt_iff_max'_mem, Finset.biUnion_image_sup_left, MeasureTheory.IsProjectiveMeasureFamily.measure_univ_eq, FractionalIdeal.spanFinset_coe, Sum.Icc_inr_inl, IntermediateField.adjoin_finset_isCompactElement, Finset.Icc_subset_Ioo_iff, Finset.finsuppAntidiag_empty_zero, Finset.eq_affineCombination_subset_iff_eq_affineCombination_subtype, Polynomial.rootsExpandToRoots_apply, Finset.inter_smul_subset, Multipliable.prod_mul_tprod_compl, RootPairing.Base.root_mem_or_neg_mem, Tree.mem_treesOfNumNodesEq, Finset.card_add_iff, Finset.Icc_diff_Ioo_self, Finset.sum_pi_single', Finset.exists_subset_mulSpan_card_le_of_forall_mulDissociated, Finset.singleton_vsub, RootPairing.Base.toWeightBasis_apply, SimpleGraph.edgeFinset_bot, Fintype.piFinset_smul_finset, Polynomial.coeff_restriction, Finset.Shatters.nonempty, Finset.inter_div_union_subset_union, Finset.eq_weightedVSub_subset_iff_eq_weightedVSub_subtype, Finset.exists_mem_image, MvPolynomial.vars_mul, Finset.card_eq_zero, IntermediateField.exists_finset_of_mem_supr', Set.powersetCard.nontrivial', IsPiSystem.tendsto_measureReal_biUnion, Finset.smul_convolution_eq_convolution_inv_mul, Equiv.Perm.apply_mem_support, FormalMultilinearSeries.changeOriginSeries_summable_aux₂, Finset.mem_shadow_iff_exists_sdiff, Fin.addRothNumber_le_rothNumberNat, ENNReal.exists_le_of_sum_le, Set.piCongrLeft_comp_restrict, Finset.filter_subset_univ, Topology.RelCWComplex.mapsTo, Finset.empty_mem_ssubsets, Finset.notMem_Iio_self, Finset.Iio_add_Iic_subset, Finset.Ici_ssubset_Ici, Finset.mulAntidiagonal_mono_right, Finset.infs_compls_eq_diffs, SimpleGraph.cliqueSet_zero, Finset.isLowerSet_shatterer, Finset.grade_multiset_eq, TopologicalSpace.Clopens.coe_finset_sup, MvPolynomial.mem_coeffsIn_iff_coeffs_subset, Submodule.mem_iSup_finset_iff_exists_sum, ProbabilityTheory.iCondIndepFun_iff, Finset.box_succ_eq_sdiff, Set.powersetCard.nontrivial, SSet.horn₃₁.desc.multicofork_π_three_assoc, exteriorPower.basis_repr_apply, Finset.sdiff_sdiff_self_left, DFinsupp.rangeIcc_apply, Finset.min'_eq_iff, Finset.mem_powersetCard_univ, Finset.subset_compl_comm, Finset.monotone_sym2, Finset.neg_smul_finset, Finset.prod_fiberwise_eq_prod_filter', YoungDiagram.cells_sup, Finset.exists_not_mem_of_card_lt_enatCard, MeasureTheory.SimpleFunc.range_one, Finset.coe_eq_one, MvPolynomial.weightedDecomposition.decompose'_eq, Finset.sum_pi_single, Finset.image₂_subset_iff_left, Finset.sups_comm, Finset.subset_zero_iff_eq, Polynomial.natTrailingDegree_mem_support_of_nonzero, Finset.card_compl_lt_iff_nonempty, Finset.expect_neg_index, Finset.union_left_comm, Finset.isGLB_iff_isLeast, Finset.pairwiseDisjoint_vadd_iff, Finset.symmDiff_subset_sdiff', TopologicalSpace.exists_finite_open_cover_prod_subset_of_mem_nhds_diagonal_of_compact, Finset.map_sups, MvPolynomial.vars_pow, Finset.le_eq_subset, Finset.finsuppAntidiag_empty, AddAction.mem_stabilizer_finset_iff_subset_vadd_finset, Finset.filter_piFinset_eq_map_snocEquiv, Submodule.exists_isInternal_prime_power_torsion, Finset.card_pow_mono, Affine.Simplex.closedInterior_face_eq_affineSegment, Finset.inclusion_exclusion_sum_biUnion, Finset.Nontrivial.nsmul, Finset.exists_card_fiber_le_of_card_le_nsmul, Finset.Icc_mul_Icc_subset', List.support_sum_subset, Finset.attachFin_ssubset_attachFin_iff, FiniteDimensional.exists_relation_sum_zero_pos_coefficient_of_finrank_succ_lt_card, AddSubmonoid.FG.biSup_finset, coe_notMemRangeEquiv, Finset.Ico_subset_Iio_self, Dynamics.netMaxcard_finite_iff, SSet.horn₃₁.desc.multicofork_π_zero, Finset.notMem_sigmaLift_of_ne_left, Finset.multipliable_compl_iff, Finset.empty_covBy_singleton, BoxIntegral.Prepartition.eventually_not_disjoint_imp_le_of_mem_splitMany, PartitionOfUnity.finsupport_subset_fintsupport, Finset.infs_union_right, Finset.disjoint_empty_right, LieAlgebra.IsKilling.rootSystem_pairing_apply, Finpartition.card_filter_equitabilise_small, rank_span_of_finset, Finset.powersetCard_sup, Finset.infs_right_comm, Dynamics.exists_isDynCoverOf_of_isCompact_uniformContinuous, Set.sized_singleton, Set.Finite.toFinset_inter, Finset.nontrivial_prod_iff, IsOfFinAddOrder.multiples_eq_image_range_addOrderOf, Finset.pairwise_subtype_iff_pairwise_finset', DFinsupp.card_Ico, Nat.mem_primeFactors_iff_mem_primeFactorsList, Finset.Iic_add_Iio_subset, Equiv.Perm.OnCycleFactors.mem_range_toPermHom_iff, MvPowerSeries.WithPiTopology.summable_prod_of_tendsto_order_atTop_nhds_top, cauchy_davenport_mul_of_linearOrder_isCancelMul, Finset.mem_smul_finset, Finset.Ioi_add_Ici_subset, BoxIntegral.unitPartition.mem_prepartition_iff, Finset.instAssociativeUnion, Finset.exists_ne_one_of_prod_ne_one, MvPolynomial.exists_finset_rename₂, Finset.disjoint_insert_left, Finset.toList_eq_nil, Finset.prod_eraseNone, Finset.infsep_zero_iff_subsingleton, Fintype.piFinset_inv, MeasureTheory.SimpleFunc.range_const, Function.Semiconj.finset_image, Finpartition.card_bot, Finset.support_prod_subset, Finset.exists_disjoint_union_of_even_card_iff, Finset.sym2_insert, Set.Finite.toFinset_singleton, SimpleGraph.TripartiteFromTriangles.exists_mem_toTriangle, Finset.min'_one, DirectSum.support_of_subset, Finset.eraseNone_image_some, DFinsupp.mk_add, OrthonormalBasis.span_apply, Nat.self_notMem_properDivisors, Finset.mem_pi, Finset.empty_add, Finset.mem_upShadow_iff_exists_sdiff, SimpleGraph.right_nonuniformWitnesses_card, Finset.map_singleton, Finset.filter_inj, Finset.union_sdiff_symm, AddMonoidAlgebra.support_divOf, Finset.inter_eq_right, convexIndependent_iff_finset, Finset.card_inter_smul, Finset.mul_nonempty, Finset.preimage_inv, Finset.card_eq_succ, addRothNumber_le, Finset.smul_finset_insert, prod_indicator, Finset.prod_ite_index, Finset.vadd_finset_inter_subset, Finsupp.sum_attach_index, Polynomial.support_map_subset, Finset.addETransformRight_snd, MvPolynomial.vars_C, Finset.Colex.isInitSeg_empty, BoxIntegral.Prepartition.iUnion_def', RootPairing.EmbeddedG2.indexEquivAllRoots_apply_coe, Equiv.Perm.OnCycleFactors.kerParam_range_eq_centralizer_of_count_le_one, MvPolynomial.support_map_subset, Affine.Simplex.exsphere_empty, Affine.Triangle.sOppSide_affineSpan_pair_point_excenter_singleton, Equiv.Perm.support_refl, Finset.div_singleton, Equiv.Perm.cycleOf_mem_cycleFactorsFinset_iff, Group.fg_iff', Set.iInter_eq_iInter_finset', Finset.card_image_iff, Finset.prod_ite_eq, SimpleGraph.Walk.exists_mem_support_mem_erase_mem_support_takeUntil_eq_empty, ProbabilityTheory.iIndepSet_iff, Finset.inter_nsmul_subset, BoxIntegral.Prepartition.mem_boxes, Finset.le_card_sdiff, Finsupp.support_add, Finset.card_div_le, Finsupp.graph_zero, Finset.inl_mem_disjSum, Finset.image₂_inter_left, Finset.sigma_preimage_mk, finite_cover_nhds_interior, MultilinearMap.support_dfinsuppFamily_subset, SSet.stdSimplex.ofSimplex_yonedaEquiv_δ, Fintype.piFinset_div, mem_primitiveRoots, Finset.union_eq_union_iff_right, Finsupp.support_inf_union_support_sup, Set.encard_coe_eq_coe_finsetCard, Finset.Ioo_eq_empty, Finset.nonempty_iff_eq_singleton_default, Fin.cons_mem_piFinset_cons, Equiv.finsetSubtypeComm_apply_coe, Filter.iInf_sets_eq_finite, WittVector.polyOfInterest_vars, Finset.cast_addConst_mul_card, MvPolynomial.esymm_eq_sum_monomial, Finset.sum_empty', cauchy_davenport_minOrder_add, Equiv.Perm.IsCycle.zpowersEquivSupport_symm_apply, Finset.diag_inter, Finset.mulETransformRight_fst, Real.pow_mul_norm_iteratedFDeriv_fourierIntegral_le, Finset.Ico_diff_Ico_right, Finset.notMem_range_self, Finset.div_empty, List.toFinset_inter, Finset.notMem_of_max_lt, Finset.sup_neg, Finset.instIsEmpty, Finpartition.card_parts_equitabilise, DFinsupp.mem_rangeIcc_apply_iff, Finset.coe_pimage, Finset.card_Iic_finset, Set.powersetCard.isPreprimitive_perm, Finset.zero_smul_finset, SimpleGraph.isMaximumIndepSet_iff, BoxIntegral.TaggedPrepartition.disjUnion_boxes, Set.Finite.disjoint_toFinset, DirectSum.mul_eq_sum_support_ghas_mul, Finset.card_singleton_add, Finset.prod_sdiff_lt_prod_sdiff, MeasureTheory.sum_measure_singleton, Finset.compls_infs_eq_diffs, SimpleGraph.IsFiveWheelLike.isNClique_fst_left, Finset.pimage_empty, UniqueFactorizationMonoid.pairwise_primeFactors_isRelPrime, Finset.subtype_eq_empty, Finsupp.prod_ite_eq, Finset.min_singleton, Submonoid.mem_closure_finset, MeasureTheory.dependsOn_cylinder_indicator_const, Finset.Shatters.exists_superset, Finset.Ici_add_Ici_subset, Finset.insert_nonempty, YoungDiagram.cells_ssubset_iff, Finset.sum_singleton', ProbabilityTheory.map_eq_iff_forall_finset_map_restrict_eq, Finset.card_le_card_pow, Finset.mem_add, Equiv.Perm.mem_cycleFactorsFinset_iff, AlgebraicGeometry.Scheme.OpenCover.finiteSubcover_X, Finset.image_mul_product, SimpleGraph.TripartiteFromTriangles.Graph.in₀₁_iff, Finset.univ_add_univ, Finset.centerMass_pair, Nat.disjoint_primeFactors, Finset.coe_div, Finsupp.support_subset_singleton', Affine.Simplex.touchpointWeights_singleton_neg, MvPolynomial.coeffs_map, LieAlgebra.IsKilling.rootSpace_zsmul_add_ne_bot_iff_mem, Finset.diffs_singleton, Finset.sym2_eq_empty, Finset.exists_lt_of_expect_lt, Finset.inf_sup_inf, Finset.univ_shatters, Finset.card_sups_le, Finset.card_le_card_shatterer, Finset.prod_insertNone, Finset.subConst_empty_right, Finset.product_sdiff_offDiag, Submodule.isInternal_prime_power_torsion, Finset.card_le_card_mul_right, SimpleGraph.TripartiteFromTriangles.card_triangles, Tuple.eq_sort_iff', prod_indicator_const, Finset.univ_sub_univ, Finset.sups_sups_sups_comm, Finset.sum_insert_zero, Set.powersetCard.isPretransitive_of_isMultiplyPretransitive, CategoryTheory.Limits.CoproductsFromFiniteFiltered.finiteSubcoproductsCocone_ι_app, Finset.subset_insert, SimpleGraph.IsUniform.symm, Finset.subset_singleton_iff, Finset.mem_inf', Finset.coe_Iio, Finset.shatterer_eq, Finset.instMulLeftMono, Int.neg_mem_divisorsAntidiag, Finset.mem_compls, Finset.inter_insert, Finset.image_insert_memberSubfamily, Finset.divConst_inv_right, FreeAbelianGroup.support_add, Finset.convolution_eq_zero, Finset.infs_assoc, Polynomial.support_X_pow, Finset.prod_dite, SimpleGraph.TripartiteFromTriangles.Graph.in₂₀_iff, Finset.Ico_subset_Icc_self, Finset.insert_Ico_right_eq_Ico_succ, Finset.mulConst_inv_right, Finset.div_eq_empty, Set.instCanLiftFinsetCoeFinite, Finset.sup_eq_sSup_image, Finset.Nontrivial.pow, Finset.preimage_mul_left_one', AddAction.stabilizer_coe_finset, Finset.cons_empty, Equiv.restrictPreimageFinset_apply_coe, Finset.restrict_preimage, SSet.horn₃₂.desc.multicofork_π_three, Finset.nsmul_singleton, Finset.card_pow_quotient_mul_pow_inter_subgroup_le, Turing.PartrecToTM2.trStmts₁_self, SimpleGraph.edgeFinset_subset_edgeFinset, RootPairing.Base.cartanMatrix_eq_neg_chainTopCoeff, RootPairing.GeckConstruction.lie_h_f, Finset.Ioo_succ_succ, Finset.image_add_left', Ideal.isCoprime_biInf, Finset.image_neg_eq_neg, RootPairing.GeckConstruction.ω_mul_f, UniqueSums.uniqueAdd_of_nonempty, Finset.mulAntidiagonal_min_mul_min, Finset.sub_subset_iff, Finset.subset_singleton_iff', Finset.insert_Ioc_sub_one_right_eq_Ioc, ProbabilityTheory.isProjectiveLimit_map, WithTop.top_mem_insertTop, Finpartition.nonUniforms_bot, Equiv.Perm.Basis.mem_fixedPoints_or_exists_zpow_eq, Finset.exists_min_image, Int.mem_box, SimpleGraph.exists_of_maximal_cliqueFree_not_adj, Finset.powersetCard_nonempty, Affine.Simplex.mongePoint_vsub_face_centroid_eq_weightedVSub_of_pointsWithCircumcenter, Finset.Nontrivial.exists_ne, exteriorPower.map_comp_ιMulti_family, Finset.lawfulFunctor, Finset.shadow_monotone, Polynomial.support_update_ne_zero, MeasureTheory.IsSetRing.biUnion_mem, Finset.addEnergy_empty_right, Finset.range_add_eq_union, CategoryTheory.Limits.ProductsFromFiniteCofiltered.finiteSubproductsCone_π_app, Finset.Iio_bot, IsPrimitiveRoot.embeddingsEquivPrimitiveRoots_apply_coe, Finset.mulConst_empty_right, Equiv.Perm.cycleFactorsFinset_mem_commute, cauchySeq_finset_of_norm_bounded, Finset.centroid_pair, SimpleGraph.IsTuranMaximal.card_parts, DFinsupp.support_single_subset, MeasureTheory.Measure.infinitePiNat_map_restrict, Finset.Colex.toColex_image_ofColex_strictMono, Finset.union_add_inter_subset, Finset.prod_finset_coe, SummationFilter.conditional_filter_eq_map_Ici, summable_iff_cauchySeq_finset, Equiv.Perm.OnCycleFactors.toPermHom_apply, Finset.esymm_map_val, Finset.Ioc_subset_Ioc, Finset.exists_mem_eq_sup', Finset.ruzsa_triangle_inequality_mul_mulInv_mul, SkewMonoidAlgebra.notMem_support_iff, Group.closure_finset_fg, Finset.insertNone_nonempty, ContinuousAlternatingMap.map_piecewise_add, Finsupp.restrictSupportEquiv_symm_single, Finset.prod_inter_mul_prod_diff, Finset.coe_product, Finset.image₂_singleton_left', Set.powersetCard.isPreprimitive_alternatingGroup, Lagrange.interpolate_empty, SimpleGraph.TripartiteFromTriangles.Graph.in₁₀_iff', Finset.range_sdiff_zero, Finset.map_swap_product, Finset.mul_subset_iff, Finset.Nonempty.zpow, MeasureTheory.closedCompactCylinders.isClosed, Finset.card_infs_iff, Finset.univ_inter, Finset.prod_ite_mem_eq, Finset.disjoint_right, Finset.exists_compls_iff, AddSubmonoid.FG.exists_minimal_closure_eq, Finset.inter_eq_left, MvPolynomial.support_divMonomial, Nat.mem_smoothNumbers_iff_primeFactors_subset, cauchySeq_finset_iff_sum_vanishing, Fin.mem_piFinset_iff_last_init, CompositionAsSet.mem_boundaries_iff_exists_blocks_sum_take_eq, Finsupp.cons_support, Finset.sup'_id_eq_csSup, Finset.coe_sym2, Set.toFinset_subset_toFinset, SimpleGraph.left_nonuniformWitnesses_card, RootPairing.Base.toWeightBasis_repr_root, Finset.Ioi_top, Finset.addETransformRight_neg, Finset.ruzsa_triangle_inequality_div_mul_div, SkewMonoidAlgebra.support_single_mul_subset, Preorder.measurable_frestrictLe, Finset.addConst_empty_left, Finset.image₂_singleton_right, Finset.smul_empty, Finset.union_val, Finset.image_inv, Set.iUnion_finset_eq_set, Finset.addETransformLeft_snd, UniqueFactorizationMonoid.primeFactors_eq_empty_iff, Finset.offDiag_empty, SimpleGraph.FarFromTriangleFree.le_card_cliqueFinset, Polynomial.degreeLT_eq_span_X_pow, Finset.one_notMem_inv_mul_iff, SimpleGraph.left_nonuniformWitnesses_subset, Finset.coe_compls, Finset.card_sdiff_comm, Finset.lt_sup_iff, AhlswedeZhang.supSum_singleton, Finset.Ioo_subset_Iic_self, Finpartition.mk_mem_sparsePairs, Finpartition.IsEquipartition.exists_partsEquiv, Function.updateFinset_def, Sum.Ico_inl_inr, Finset.dens_eq_zero, Finset.mem_smulAntidiagonal, CategoryTheory.Limits.ProductsFromFiniteCofiltered.liftToFinsetLimitCone_cone_π_app, PolynomialLaw.range_φ, Multiset.toFinset_subset, Finset.Ioi_subset_Ici_self, List.pairwiseDisjoint_iff_coe_toFinset_pairwise_disjoint, Finset.op_vadd_finset_vadd_eq_vadd_vadd_finset, BoxIntegral.TaggedPrepartition.unionComplToSubordinate_boxes, MeasureTheory.partialTraj_const_restrict₂, SSet.stdSimplex.faceSingletonComplIso_hom_ι_assoc, Finset.supIndep_attach, LatticeHom.birkhoffFinset_injective, Finset.filter_not, Module.Basis.repr_support_subset_of_mem_span, Finset.attach_val, MvPolynomial.support_zero, Fintype.piFinset_singleton, Finsupp.supportedEquivFinsupp_apply_support_val, UniqueMul.set_subsingleton, Finset.coe_inv, RootPairing.Base.coroot_mem_or_neg_mem, RootPairing.GeckConstruction.lie_e_lie_f_apply, Nat.sum_modEq_ite, Finset.card_le_card_sub_self, PairReduction.finset_logSizeBallSeq_add_one_subset, Finset.cast_divConst_mul_card, Finset.mem_inv, PairReduction.antitone_logSizeBallSeq_add_one_subset, Finset.inf'_le_iff, DFinsupp.support_add, Finset.card_le_card_sub_left, Equiv.Perm.mem_finPairsLT, MeasureTheory.Filtration.piLE_eq_comap_frestrictLe, Finset.attachFin_subset_attachFin_iff, PairReduction.finset_logSizeBallSeq_subset_logSizeBallSeq_init, MeasureTheory.OuterMeasure.IsMetric.finset_iUnion_of_pairwise_separated, Finsupp.mem_vaddAntidiagonal_iff, Finset.addDysonETransform.vadd_finset_snd_subset_fst, Finset.SupIndep.pairwiseDisjoint, DFinsupp.mk_apply, Finset.countable_toSet, Finset.diag_mono, Finset.min_insert, Finset.iSup_finset_image, Finset.subset_erase, summable_iff_cauchySeq_finset_and_tsum_mem, Filter.atTop_finset_eq_iInf, Finset.Ico_filter_lt_of_le_left, support_subset_support_matPolyEquiv, Finset.singleton_subset_singleton, Finset.sdiff_idem, Finset.powersetCard_zero, Finset.exists_le_sum_fiber_of_sum_fiber_nonpos_of_nsmul_le_sum, Finset.biUnion_subset, Finset.product_empty, univ_option, Finset.Nonempty.subset_zero_iff, Finset.sum_union_eq_right, Profinite.NobelingProof.spanFunctorIsoIndexFunctor_inv_app, Finset.symmDiff_eq_empty, SimpleGraph.IsNClique.insert, Finset.vsub_card_le, mulRothNumber_le, jacobiSum_eq_sum_sdiff, RootPairing.Base.IsPos.exists_mem_support_pos_pairingIn, Finset.vadd_finset_eq_empty, Finset.measurable_restrict_apply, mem_perms_of_finset_iff, SimpleGraph.componentComplFunctor_finite, Finset.insert_Ioc_left_eq_Ioc_pred, Finset.eraseNone_inter, Submodule.exists_minimal_isPrimary_decomposition_of_isPrimary_decomposition, Finset.Iio_subset_Iio, Finset.sups_subset_iff, CompleteLattice.IsCompactElement.exists_finset_of_le_iSup, YoungDiagram.exists_notMem_col, Affine.Simplex.ExcenterExists.signedInfDist_excenter, Finset.upShadow_compls, linearIndepOn_iff_linearIndepOn_finset, Finset.disjoint_sdiff_inter, SimpleGraph.TripartiteFromTriangles.Graph.in₁₂_iff, MvPolynomial.vars_map, Finset.Nonempty.neg, Turing.PartrecToTM2.supports_insert, Polynomial.support_binomial, MvPolynomial.mem_support_coeff_finSuccEquiv, Finset.Iio_insert, Finset.infs_empty, Turing.TM1.stmts₁_self, Set.powersetCard.card, Finset.disjSups_empty_right, Finset.mem_upShadow_iff_erase_mem, MvPolynomial.support_sub, SimpleGraph.completeBipartiteGraph_isContained_iff, AddGroup.closure_finset_fg, Finset.one_notMem_div_iff, xInTermsOfW_vars_aux, Finset.mem_offDiag, Finset.addETransformLeft_fst, Finset.mem_filter, Finset.Colex.singleton_le_singleton, Finset.mulETransformRight.fst_mul_snd_subset, Finset.inf_eq_sInf_image, DirectSum.support_smul, Finset.Ioc_subset_Ioo_right, Finset.lawfulApplicative, LaurentPolynomial.support_C_mul_T_of_ne_zero, Finset.empty_ssubset_singleton, Finset.Colex.toColex_lt_toColex, Finset.Nonempty.to_subtype, BoxIntegral.Prepartition.disjoint_boxes_of_disjoint_iUnion, MvPolynomial.vars_rename, Finset.inf_eq_iInf, Polynomial.isRoot_prod, Affine.Triangle.sbtw_touchpoint_empty, Set.powersetCard.mulActionHom_singleton_bijective, CategoryTheory.Limits.CoproductsFromFiniteFiltered.liftToFinsetColimitCocone_cocone_pt, Rel.card_interedges_finpartition_left, Equiv.Perm.support_swap, SimpleGraph.isNClique_iff, Finset.addConst_empty_right, not_linearIndepOn_finset_iff, Fintype.finsetOrderIsoSet_toEquiv, SimpleGraph.mem_finsetWalkLengthLT_iff, Finset.card_smul_inter_smul, Polynomial.support_eq_empty, UniqueFactorizationMonoid.radical_dvd_iff_primeFactors_subset, ProbabilityTheory.iIndepSet_iff_meas_biInter, Multiset.coeEquiv_symm_apply_fst, Finset.AddETransform.card, Finset.two_lt_card, Finset.Colex.toColex_image_le_toColex_image, Finset.card_image₂_iff, Finset.Ioo_insert_left, Finset.sup'_union, Finset.Colex.toColex_sdiff_lt_toColex_sdiff', MvPolynomial.support_esymm'', Finset.mem_upShadow_iff_exists_mem_card_add_one, Affine.Simplex.touchpoint_empty_notMem_affineSpan_of_ne, Finset.disjSum_mono_left, cauchy_davenport_of_isMulTorsionFree, Cardinal.mk_set_eq_nat_iff_finset, Finset.set_biUnion_union, Finset.disjoint_biUnion_right, prod_indicator_const_apply, Finset.mem_union, Submodule.CoFG.sInf, Finsupp.restrictSupportEquiv_apply, Finset.mem_map', Finset.mapEmbedding_apply, Finset.expect_dite_eq, Finset.map_infs, Set.toFinset_mul, SSet.boundary_eq_iSup, Finset.card_le_card_nsmul, Finset.Ico_diff_Ioo_self, FiniteDimensional.exists_is_basis_integral, Finset.subset_sups_self, RootPairing.GeckConstruction.f_lie_v_same, MonomialOrder.notMem_support_of_degree_lt, Set.toFinset_one, Finset.union_eq_union_iff_left, not_linearIndependent_iff, SimpleGraph.edgeFinset_eq_empty, Finset.mem_smul, Finset.Icc_eq_empty, SzemerediRegularity.coe_m_add_one_pos, Nat.Ico_succ_singleton, Finset.exists_notMem, Equiv.Perm.Basis.ofPermHomFun_mul, SimpleGraph.disjoint_sdiff_neighborFinset_image, List.toFinset_cons, Finset.image₂_mk_eq_product, Finset.sups_eq_self, Finset.sup_inv, Finset.toLeft_insert_inr, Affine.Simplex.excenterWeights_empty_pos, Finset.ruzsa_triangle_inequality_sub_sub_sub, Finset.mem_toRight, Finsupp.Icc_eq, Finset.card_shatterer_le_sum_vcDim, Finset.shatters_iff, PairReduction.point_mem_finset_logSizeBallSeq, Finset.Icc_add_Icc_subset, Finset.cast_divConst, Finset.dens_smul_finset, Finset.Colex.toColex_empty, Finset.mulETransformLeft_inv, Affine.Simplex.sSameSide_point_excenter_singleton, PMF.uniformOfFinset_apply, Set.exists_finite_iff_finset, Set.powersetCard.mulAction_faithful, Finset.inf'_id_eq_csInf, Finset.subset_map_symm, Polynomial.support_derivativeFinsupp_subset_range, isConnected_iff_sUnion_disjoint_open, Polynomial.natDegree_mem_support_of_nonzero, Finset.hasProd_compl_iff, Multiset.toFinset_inter, Finset.disjoint_singleton_right, sSupIndep_iff_finite, Finset.Nontrivial.sdiff_singleton_nonempty, Finset.image_op_add, Finset.coe_filter_univ, ConvexOn.exists_ge_of_centerMass, exteriorPower.basis_repr, Finset.lcm_union, Finset.Nontrivial.exists_cons_eq, Finset.tendsto_Ico_neg, Finset.val_wcovBy_val, Finsupp.support_eq_empty, Numbering.IsPrefix.subset_of_card_le_card, Finset.mulEnergy_empty_left, Finset.imageOneHom_apply, Polynomial.natDegree_restriction, Finmap.mem_keys, Finset.inf_singleton, Finset.subset_map_inr, UniqueAdd.of_card_le_one, Finset.powerset_card_disjiUnion, Finset.addConvolution_neg, UV.compress_disjoint, Finset.card_smul_le, ClassGroup.finsetApprox.zero_notMem, Finset.inv_smul_mem_iff₀, Polynomial.roots_expand_pow_image_iterateFrobenius_subset, Finset.nonempty_product, Fintype.univ_bool, Finsupp.graph_eq_empty, Finset.Ioc_eq_filter_powerset, Finset.mem_symmDiff, Finset.singleton_inter, Finset.insert_idem, Finset.not_subset, Nat.factoredNumbers_empty, Finset.nodup_map_iff_injOn, IsOfFinOrder.powers_eq_image_range_orderOf, Finset.prod_attach, ProbabilityTheory.map_restrict_eq_of_forall_ae_eq, Affine.Triangle.sSameSide_affineSpan_pair_point_excenter_singleton, Caratheodory.minCardFinsetOfMemConvexHull_subseteq, Set.powersetCard.coe_mulActionHom_compl, Set.powersetCard.instFiniteElemFinset, Finset.zsmul_empty, Finset.vadd_univ, Multiset.mem_sum, Finset.set_biUnion_option_toFinset, Finsupp.rangeIcc_support, Set.toFinset_ssubset_univ, Finset.mulETransformRight_snd, Finset.isGLB_inf_id, Finset.map_subset_iff_subset_preimage, Finset.disjoint_singleton_left, SSet.stdSimplex.face_inter_face, Finsupp.support_mul_subset_left, Finset.sum_apply_dite, Finsupp.support_single_subset, Finset.isAddUnit_coe, Finset.isCoatom_iff, Metric.AreSeparated.finset_iUnion_left, Finset.div_inter_subset, Finset.coe_zpow, Finset.Iio_eq_ssubsets, AffineIndependent.exists_affineCombination_eq_smul_eq, Finset.subset_image_iff, MeasureTheory.Measure.haar.index_defined, Multiset.toFinset_ssubset, Affine.Simplex.touchpointWeights_singleton_pos, Finpartition.parts_top_subsingleton, Finset.restrict_def, DirectSum.support_zero, Finset.union_mul_inter_subset_union, Polynomial.Monic.irreducible_iff_natDegree', Finset.pluennecke_ruzsa_inequality_pow_div_pow_div, SSet.horn₃₂.desc.multicofork_pt, SimpleGraph.is3Clique_triple_iff, Finset.sym_empty, Finset.diffs_subset_iff, Finset.Ioc_add_Ico_subset, Ideal.Factors.finiteDimensional_quotient_pow, Submodule.mem_iSup_iff_exists_finset, Finset.instAddRightMono, Geometry.SimplicialComplex.facets_subset, Finset.sup_inf_sup, Finset.finite_toSet, Finset.mem_uIcc_of_ge, Finset.card_powersetCard, Dynamics.coverMincard_finite_iff, Finset.compls_eq_empty, Finset.hasProd, Nat.mem_factoredNumbers, Finset.sum_attach_univ, Nat.Prime.divisors_sq, Finset.mem_diffs, Nat.mem_divisors_prime_pow, Finset.disjoint_diag_offDiag, Finset.empty_subset, Finset.empty_val, Filter.tendsto_finset_Ici_atBot_atTop, Finmap.keys_union, convexHull_eq_union, Finset.empty_div, Finset.sum_empty, IntermediateField.adjoin_minpoly_coeff_of_exists_primitive_element, RootPairing.Base.span_root_support, AddAction.mem_stabilizer_finset, Finset.inter_univ, Numbering.mem_prefixed, Finset.PiFinsetCoe.canLift', Ideal.eq_inf_of_isPrime_inf, untrop_sum_eq_sInf_image, Finset.strictMono_iff_forall_lt_cons, Nat.primeFactors_mul, AddMonoidAlgebra.support_gen_of_gen, Finset.neg_eq_empty, Fintype.card_filter_piFinset_const, Finset.mulETransformRight.card, Finset.disjoint_empty_left, Finset.tendsto_Ioc_neg, LinearMap.coe_det, Finset.mem_slice, convexHull_eq, Nat.mem_smoothNumbersUpTo, MeasureTheory.IsSetSemiring.pairwiseDisjoint_disjointOfDiff, Finset.range_one, Finset.filter_union, Equiv.Perm.IsCycle.forall_commute_iff, Finset.card_le_card_mul_self₀, MvPolynomial.mem_degrees, Finset.singleton_sups, Finset.exists_lt_sum_fiber_of_sum_fiber_nonpos_of_nsmul_lt_sum, Finset.union_union_union_comm, Polynomial.trinomial_support, Equiv.Perm.cycleType_def, Finset.inv_nonempty_iff, LocallyFiniteOrder.finset_mem_Ioc, Finset.ruzsa_triangle_inequality_add_addNeg_add, Finset.sized_falling, Finset.prod_sum, Finset.disjoint_box_succ_prod, EisensteinSeries.eisensteinSeries_tendstoLocallyUniformlyOn, Submodule.mem_sSup_iff_exists_finset, Finset.coe_singletonAddHom, Submonoid.mem_closure_finset', Finset.mem_memberSubfamily, Finset.inf'_singleton, Finset.Colex.le_iff_sdiff_subset_lowerClosure, YoungDiagram.col_eq_prod, Set.toFinset_vadd, Finset.mem_image₂_iff, MeasureTheory.measureReal_biUnion_finset_le, PairReduction.point_logSizeBallSeq_add_one, SimpleGraph.interedges_biUnion, AddMonoidAlgebra.mem_span_support', MeasureTheory.Measure.infinitePi_map_restrict, Finset.mem_inv_smul_finset_iff₀, Submodule.finset_inf_coe, ProbabilityTheory.Kernel.iIndepFun.meas_biInter, Finset.biUnion_singleton, Polynomial.mem_coeffs_iff, Finset.vaddAssocClass', Finset.subset_inter_iff, WittVector.wittNSMul_vars, SmoothPartitionOfUnity.mem_fintsupport_iff, Equiv.Perm.Basis.cycleOf_eq, Finset.disjoint_filter_and_not_filter, not_linearIndepOn_finset_iffₛ, Finset.inf'_eq_csInf_image, SummationFilter.map_filter, Finset.Icc_add_Ico_subset, Finset.sup_add_right, Set.iUnion_eq_iUnion_finset', Finpartition.sum_card_parts, Ideal.subset_union_prime, Finset.singletonMulHom_apply, Finset.nsmul_univ, Finset.card_sub_le, Module.Finite.span_finset, Affine.Simplex.sum_excenterWeightsUnnorm_empty_pos, Finset.mem_Ioc, Multiset.card_Icc, Finset.prod_dite_eq', Finset.mem_neg, Equiv.Perm.OnCycleFactors.kerParam_range_le_centralizer, SimpleGraph.componentComplFunctor_nonempty_of_infinite, Finset.Nonempty.one_mem_div, Finset.diag_insert, Affine.Simplex.excenterExists_compl, Finset.inter_left_idem, Finset.tprod_subtype, Finpartition.bot_notMem, Equiv.Perm.two_le_length_toList_iff_mem_support, Finset.disjoint_union_left, Finset.card_le_card_div_right, Finset.range_mono, Finset.sub_union, Fintype.univ_punit, Finset.toRight_sdiff, Finset.map_empty, Finset.nullMeasurableSet, Finset.powerset_empty, Finset.card_pair, DirectSum.support_subset, Finset.Nonempty.csInf_mem, Finset.addETransformLeft.card, Finset.finsetCongr_piAntidiag_eq_antidiag, Fin.mem_piFinset_iff_zero_tail, Finset.card_mul_singleton, Finset.isAddUnit_singleton, Finset.notMem_erase, Finset.sup_div_left, Finset.exists_eq_insert_iff, Finset.Nonempty.zero_mul, Finset.Nonempty.sups, IsCompact.elim_nhds_subcover_nhdsSet', MeasureTheory.SimpleFunc.range_const_subset, Finset.singleton_product, Finset.sdiff_empty, Finset.two_lt_card_iff, Int.swap_mem_divisorsAntidiag, Finset.prod_indicator_biUnion_sub_indicator, Finset.Nonempty.subset_singleton_iff, Finset.subset_smul_finset_iff₀, Finset.coe_map, SimpleGraph.compl_neighborFinset_sdiff_inter_eq, Finset.insert_Icc_sub_one_right_eq_Icc, Finset.union_add_inter_subset_union, Finset.isUnit_iff, Set.Finite.toFinset_vadd, Finset.image_add, Finset.image_op_pow, mem_multiples_iff_mem_range_addOrderOf, Nat.Coprime.disjoint_primeFactors, WithTop.Ioc_coe_top, Finset.Nonempty.nsmul, Nat.prod_primeFactors_invOn_squarefree, Tree.treesOfNumNodesEq_zero, Fintype.card_finset_len, SSet.stdSimplex.faceSingletonIso_one_hom_comp_ι_eq_δ_assoc, Set.biUnion_finsetSigma', Finsupp.mem_support_toFun, Nat.mem_properDivisors, Nat.insert_self_properDivisors, Finset.notMem_uIcc_of_lt, algebraicIndependent_finset_map_embedding_subtype, Finset.sdiff_self, Finset.mem_Iio, Finset.Iic_product_Iic, Finset.countable, measurable_IocProdIoc, HallMarriageTheorem.hall_cond_of_compl, Finset.image₂_insert_right, SmoothPartitionOfUnity.eventually_finsupport_subset, Finset.disjoint_left, Finset.Nonempty.mul, Finset.prod_mulIndicator_eq_prod_inter, Polynomial.coeff_restriction', Ideal.Factors.isPrime, FreeMonoid.symbols_one, Equiv.Perm.IsCycle.commute_iff, Finset.strictAnti_iff_forall_cons_lt, List.support_formPerm_of_nodup', PrimeSpectrum.exists_image_comap_of_finite_of_free, Finset.Ioo_subset_Ico_self, Nat.divisorsAntidiagonal_zero, Finset.Nonempty.vadd_finset, Finset.set_biInter_singleton, Behrend.threeAPFree_image_sphere, DFinsupp.mk_sub, CompleteLattice.isCompactElement_iff_exists_le_sSup_of_le_sSup, Finset.image_sups, Finsupp.mem_graph_iff, Finset.sum_dite_of_true, Set.mem_toFinset, linearIndependent_finset_map_embedding_subtype, Finset.vadd_mem_vadd_finset_iff, Finset.coe_add, Finset.sum_powerset_neg_one_pow_card, hasProdUniformlyOn_iff_tendstoUniformlyOn, Equiv.Perm.pairwise_disjoint_of_mem_zpowers, Finset.pluennecke_ruzsa_inequality_pow_mul, Turing.TM1to0.tr_supports, Finset.piecewise_empty, Finset.sum_mono_set_of_nonneg, FormalMultilinearSeries.changeOriginIndexEquiv_apply_snd, Finset.Nontrivial.mul_left, Affine.Simplex.ExcenterExists.signedInfDist_excenter_eq_mul_sum_inv, Finset.union_sub_inter_subset_union, Finset.preimage_map, Ideal.isPrimary_decomposition_pairwise_ne_radical, Finset.sum_ite_index, Finset.union_inter_cancel_left, Finsupp.support_sup, Finset.toLeft_union, Finset.lt_fold_max, Finset.inf_div_left, SkewMonoidAlgebra.support_update, Geometry.SimplicialComplex.facets_bot, Finset.Nat.sigmaAntidiagonalTupleEquivTuple_apply, IsMax.finsetIoi_eq, ProbabilityTheory.Kernel.iIndepSets_singleton_iff, Finset.powerset_mono, PairReduction.point_logSizeBallSeq_zero, Finset.card_le_card_div_left, Finset.toList_eq_singleton_iff, Finset.smul_finset_inter₀, Finset.sumEquiv_apply_fst, Finset.inv_eq_empty, UniqueFactorizationMonoid.disjoint_primeFactors, ClassGroup.mem_finsetApprox, Finset.image_mono, Finset.vaddAntidiagonal_mono_right, FirstOrder.Language.Theory.CompleteType.toList_foldr_inf_mem, AddSubgroup.exists_leftTransversal_of_FiniteIndex, Finsupp.support_subset_iff, Finset.coe_Ici, Int.divisorsAntidiag_zero, Finset.mem_map, Finset.intervalGapsWithin_mapsTo, tendstoUniformly_tsum, Finset.disjSups_union_left, mulIndicator_biUnion_finset_eventuallyEq, ENNReal.hasProd_iInf_prod, Finset.mulSupport_of_fiberwise_prod_subset_image, addDissociated_iff_sum_eq_subsingleton, Finset.mem_infs, Equiv.Perm.CycleType.count_def, Finsupp.support_monotone, Finset.univ_finset_of_isEmpty, Turing.PartrecToTM2.codeSupp_cons, iSupIndep_iff_supIndep, ENNReal.sum_eq_top, AddAction.stabilizer_finset_empty, Finset.compls_empty, exists_sum_eq_one_iff_pairwise_coprime, Finset.card_vadd_inter, MeasureTheory.addContent_biUnion_le, Set.Finite.toFinset_mul, YoungDiagram.mk_mem_row_iff, SummationFilter.symmetricIcc_eq_map_Icc_nat, IsAddUnit.finset, FreeMonoid.symbols_mul, Finset.sdiff_inter_right_comm, Finset.inter_add_union_subset_union, SimpleGraph.Walk.coe_edges_toFinset, Finset.Ico_eq_empty_iff, coe_notMemRangeEquiv_symm, Fintype.sum_extend_by_zero, Finset.covBy_iff_exists_erase, Finset.smul_inter_subset, Seminorm.ball_finset_sup_eq_iInter, Finset.box_zero, Finset.inf_div_right, FreeAddMonoid.symbols_add, SSet.stdSimplex.face_le_face_iff, Finset.card_sdiff_le_card_sdiff_iff, Finset.filter_singleton, Finset.pluennecke_ruzsa_inequality_nsmul_sub, Polynomial.support_restriction, Finset.sum_powerset_apply_card, Submodule.finset_span_isCompactElement, Finset.filter_union_filter_neg_eq, SimpleGraph.card_toFinset_mem_edgeFinset, partialSups_eq_biUnion_range, addRothNumber_Ico, Finset.ruzsa_triangle_inequality_addNeg_addNeg_addNeg, isClosed_biUnion_finset, Polynomial.rootSet_prod, Finset.pair_eq_singleton, WithTop.prod_eq_top_ex_top, Polynomial.coeffs_zero, Finset.map_cast_heq, Finset.wellFoundedOn, Finset.card_le_card_mul_left, FreeAbelianGroup.mem_support_iff, Ideal.IsPrime.prod_mem_iff_exists_mem, LaurentPolynomial.support_C_mul_T, Finmap.keysLookupEquiv_symm_apply_lookup, Mathlib.Meta.Finset.range_zero', Finset.sup'_congr, Affine.Simplex.exists_forall_signedInfDist_eq_iff_excenterExists_and_eq_excenter, Finset.subset_product, Finset.erase_eq_self, Finset.sup'_one, RootPairing.Base.cartanMatrixIn_mul_diagonal_eq, Finset.mem_shadow_iff, Finset.powerset_union, Finset.mul_def, Finset.pi_eq_empty, Finset.preimage_add_left_zero', Polynomial.nthRootsFinset_zero, pairwise_isRelPrime_iff_isRelPrime_prod, Submodule.mem_span_set_iff_exists_finsupp_le_finrank, Finset.sym_succ, Finset.union_singleton, Finset.card_nsmul_le, Nat.divisorsAntidiagonal_one, Finset.ruzsa_triangle_inequality_div_div_div, Finset.inter_vadd_union_subset_union, Finset.disjSups_empty_left, Finset.Ico_subset_Ioo_left, finprod_mem_finset_product₃, Finset.neg_vadd_mem_iff, Finset.mem_inter, Finset.nontrivial_def, Finset.Ioo_subset_Iio_self, Equiv.Perm.ofSubtype_support_disjoint, Finset.sup_toFinset, HasProdUniformlyOn.tendstoUniformlyOn, Finset.inf_neg, Fintype.sum_pow_mul_eq_add_pow, Finset.smul_finset_sdiff₀, UniqueFactorizationMonoid.primeFactors_of_isUnit, PMF.toOuterMeasure_apply_finset, Finset.restrict_comp_piCongrLeft, Nat.finMulAntidiag_zero_left, SummationFilter.LeAtTop.le_atTop, Finset.divConst_inv_left, hasSumUniformlyOn_iff_tendstoUniformlyOn, HasProdUniformly.tendstoUniformly, CategoryTheory.Limits.CoproductsFromFiniteFiltered.finiteSubcoproductsCocone_ι_app_eq_sum, Finsupp.support_sup_union_support_inf, Finset.subset_disjSum, FinEnum.Finset.mem_enum, Equiv.Perm.Disjoint.cycleFactorsFinset_mul_eq_union, Finset.sdiff_inter_self_left, PartitionOfUnity.mem_fintsupport_iff, LocallyFinite.exists_finset_nhds_mulSupport_subset, RootPairing.GeckConstruction.f_mem_lieAlgebra, Finset.sup_mul_left, Equiv.Perm.cycleFactorsFinset_injective, Equidecomp.IsDecompOn.comp', Option.mem_toFinset, NNReal.tendsto_tsum_compl_atTop_zero, isTopologicalBasis_pi, RootPairing.Base.exists_eq_sum_and_forall_sum_mem_of_isPos, Finset.mem_shadow_iterate_iff_exists_mem_card_add, Nat.mem_primesBelow, Finset.Ioc_eq_empty_of_le, Finset.tendsto_Icc_atBot_prod_atTop, Set.toFinset_subset_toFinset_of_subset, Nat.divisors_one, Nat.multinomial_empty, Nat.divisors_filter_squarefree, Set.sized_iUnion, SimpleGraph.cycleGraph_degree_two_le, Finset.subset_of_eq, Fin.orderIsoTriple_two, Finset.Ioc_subset_Ioc_right, Finset.biUnion_op_smul_finset, Multiset.coeEquiv_symm_apply_snd_val, Finset.image₂_union_right, finprod_mem_finset_eq_prod, Finset.filter_attach, Finset.Ioo_subset_Ioi_self, Nat.binomial_spec, Finset.map_eq_empty, Affine.Simplex.excenterExists_empty, Finset.Icc_product_Icc, Finset.coe_zsmul, DFinsupp.eq_mk_support, Finset.Nonempty.infs, Finset.disjSups_subset_sups, List.toFinset_replicate_of_ne_zero, Finset.insert_Ico_pred_right_eq_Ico, Ico_subset_biUnion_Ico, Finset.sum_powersetCard, Finset.sub_empty, Finset.subset_Iic_sup_id, Finset.fiber_card_ne_zero_iff_mem_image, Finset.memberSubfamily_memberSubfamily, Set.Finite.exists_finset_coe, Finset.le_iff_subset, Finset.inter_val, Finset.sum_fiberwise_eq_sum_filter', Finset.finsuppAntidiag_zero, Finset.piAntidiag_empty_of_ne_zero, Finset.forall_mem_not_eq', MvPolynomial.coeffs_C_subset, IsLocalizedModule.map_integerMultiple, Finset.infs_sups_subset_left, Finsupp.mem_frange, Finset.biUnion_smul_finset, Finset.coe_inter, Submodule.mem_set_smul, Metric.AreSeparated.finset_iUnion_right, Finset.attach_map_val, Finset.Nonempty.ciSup_eq_max'_image, le_rank_iff_exists_linearIndependent_finset, Finset.attach_empty, SupPrime.le_finset_sup, MeasureTheory.measureReal_biUnion_eq_sum_powerset, Finset.uIcc_self, RootPairing.GeckConstruction.e_mem_lieAlgebra, Units.mk0_prod, Finset.sum_product_right, Set.Finite.exists_finset, MvPolynomial.esymm_eq_sum_subtype, Polynomial.support_scaleRoots_le, Finset.Ico_subset_Ici_self, Finset.Ioc_disjoint_Ioc, Finset.preimage_add_right_zero, IsDedekindDomain.exists_representative_mod_finset, MeasureTheory.SimpleFunc.mem_range_self, Finset.mem_toList, range_pow_padicValNat_subset_divisors', Finset.singletonOneHom_apply, Finset.infs_self_subset, Finset.lcm_insert, Finset.disjSum_strictMono_right, Finset.inf_one, Finset.card_eq_three, Finset.exists_subset_addSpan_card_le_of_forall_addDissociated, Set.Finite.toFinset_strictMono, Finset.insert_Icc_left_eq_Icc_pred, MeasureTheory.SimpleFunc.support_eq, Finset.set_biUnion_preimage_singleton, Nat.card_pair_lcm_eq, addRothNumber_map_add_right, Finset.exists_lt_of_sum_lt, Nat.Prime.primeFactors, Finset.iSup_option_toFinset, List.zipWith_swap_prod_support, RootPairing.GeckConstruction.lie_h_h, Nat.Prime.mem_primeFactors', Finset.sup_eq_union, ZMod.erdos_ginzburg_ziv, Finsupp.comapDomain_add_of_injective, Finset.erase_empty, MeasureTheory.squareCylinders_eq_iUnion_image, Finset.isGLB_inf', Finset.filter_attach', DFinsupp.support_inf_union_support_sup, Finset.card_eraseNone_eq_card_erase, Finset.vadd_finset_subset_vadd_finset_iff, Finset.map_subset_map, Finset.empty_disjSum, Finset.convolution_pos, Finsupp.support_inf, Polynomial.support_monomial', Finset.subset_vadd_finset_iff, Finset.sum_union_eq_left, Finset.Ioo_subset_Ioo, Finset.Nonempty.to_set, cauchy_davenport_minOrder_mul, Finset.vaddAntidiagonal_min_vadd_min, Finset.image_one, Affine.Triangle.sSameSide_affineSpan_pair_excenter_singleton_point, Finset.vadd_singleton, Topology.CWComplex.mapsTo, Finset.mem_upShadow_iff, Submonoid.FG.biSup_finset, MultilinearMap.map_sub_map_piecewise, exteriorPower.ιMulti_family_linearIndependent_ofBasis, exists_signed_sum, IsNonarchimedean.finset_powerset_image_add, Finset.smul_subset_iff, Finset.one_product_one, Finset.coe_insert, finsum_mem_finset_product₃, Finset.lt_iff_ssubset, Finset.pluennecke_ruzsa_inequality_nsmul_sub_nsmul_add, Finset.addEnergy_eq_card_filter, Finset.mem_shadow_iff_exists_mem_card_add_one, Algebra.essFiniteType_iff, Finset.card_diffs_iff, UV.mem_compression, Finset.mem_finsuppAntidiag', Algebra.EssFiniteType.cond, Finset.exists_maximalFor, FirstOrder.Ring.mvPolynomial_zeroLocus_definable, Finset.sum_coe_sort_eq_attach, SimpleGraph.IsFiveWheelLike.notMem_right, SimpleGraph.CliqueFree.cliqueFinset, Finset.inter_mul_singleton, MvPolynomial.vars_add_subset, WithTop.some_mem_insertTop, HasSumUniformlyOn.tendstoUniformlyOn, Finset.prod_sdiff_eq_prod_sdiff_iff, Finset.union_sdiff_left, Finset.set_biInter_option_toFinset, Set.powersetCard.val_map, Set.toFinset_smul_set, Finset.indicator_biUnion_eq_sum_powerset, Fintype.sum_eq_add_sum_compl, Finset.mem_bipartiteAbove, isLUB_hasSum, Finset.sups_inter_subset_left, Finset.sum_product, Finset.union_eq_sdiff_union_sdiff_union_inter, Set.biUnion_finsetSigma_univ', Finset.empty_toList, GradedAlgebra.mem_support_iff, Finset.subConst_empty_left, Finset.mulEnergy_eq_card_filter, List.toFinset_nil, PartitionOfUnity.exists_finset_nhds', Finset.toRight_insert_inl, Finset.maximal_iff_forall_insert, Finset.imageAddMonoidHom_apply, Set.powersetCard.mem_range_ofFinEmbEquiv_symm_iff_mem, Finset.add_def, Equiv.Perm.mem_conj_support, RootPairing.EmbeddedG2.allRoots_subset_range_root, Finset.exists_lt_of_prod_lt', Finset.Ico_mul_Ioc_subset', SimpleGraph.componentComplFunctor_map, Finset.zero_smul_finset_subset, AddSubgroup.finiteIndex_iInf', Finset.lcm_eq_zero_iff, Polynomial.degreeLE_eq_span_X_pow, Sum.Ioc_inr_inl, AddSubmonoid.mem_closure_finset', Finset.map_union, Finpartition.IsEquipartition.exists_partPreservingEquiv, MvPolynomial.support_symmDiff_support_subset_support_add, LocallyFiniteOrderTop.finset_mem_Ioi, piiUnionInter_singleton_left, PairReduction.pairSet_subset, Set.toFinset_mono, Fin.image_succAbove_univ, Rel.swap_mem_interedges_iff, AlternatingGroup.map_subtype_of_cycleType, BoxIntegral.Prepartition.eventually_splitMany_inf_eq_filter, Nat.mem_divisors_self, WithTop.Icc_coe_top, Finset.noncommProd_singleton, Finset.prod_compl_mul_prod, SimpleGraph.coe_finsetWalkLengthLT_eq, Int.prod_modEq_ite, MvPolynomial.mem_coeffs_iff, Finset.diag_singleton, Finset.subset_compl_iff_disjoint_left, Finset.singletonZeroHom_apply, SummationFilter.conditional_filter, Finset.neg_nonempty_iff, Finset.powerset_univ, Finset.inv_def, Equiv.Perm.disjoint_iff_disjoint_support, MonoidAlgebra.support_single_mul_subset, Nat.primeFactors_prime_pow, ProbabilityTheory.Kernel.iIndepFun.cond_iInter, Finset.powersetCard_eq_empty, Finset.zero_smul_subset, Finset.sdiff_disjoint, IsCompact.elim_finite_subfamily_closed, Finset.addConvolution_op_vadd_eq_addConvolution_add_neg, Finset.univ_finset_eq_singleton_empty_iff, Finset.dens_union_le, Finset.set_biUnion_insert, Finsupp.neLocus_eq_empty, RootPairing.Base.abs_cartanMatrix_apply, Finset.mem_neg', Finset.strictMono_sym2, exteriorPower.ιMulti_family_span, MeasureTheory.IsSetSemiring.exists_finpartition_diff, Finset.singleton_one, Finset.erase_inter, Nat.filter_range_nth_eq_insert_of_infinite, SimpleGraph.IsMaximumIndepSet.isIndepSet, Finset.neg_univ, Finsupp.support_indicator_subset, Finset.uIcc_injective_left, Finset.iInf_option_toFinset, Finset.infs_inter_subset_left, MeasureTheory.SimpleFunc.map_preimage, SimpleGraph.coe_neighborFinset, Finset.Nonempty.div_zero, Finset.insert_Ico_left_eq_Ico_sub_one, Finset.partiallyWellOrderedOn_bUnion, Set.sized_empty, Finset.zero_mem_smul_iff, Affine.Simplex.dist_incenter, PairReduction.finset_logSizeBallSeq_add_one_ssubset, CompactSpace.elim_nhds_subcover, Finset.insert_Ico_right_eq_Ico_succ_of_not_isMax, Finset.filter_mem_eq_inter, Finset.zero_mul_subset, MeasureTheory.lmarginal_empty, Finset.orderIsoColex_symm_apply, Orthonormal.exists_orthonormalBasis_extension, Finset.insert_erase_subset, Finset.coe_smul, Preorder.piCongrLeft_comp_restrictLe, Finset.le_inf_sub, Set.powersetCard.ncard_eq, Finsupp.support_tsub, PairReduction.iSup_edist_pairSet, Finset.sum_dite_eq, DFinsupp.support_single_ne_zero, LocallyFiniteOrderBot.finset_mem_Iic, not_linearIndepOn_finset_iffₒₛ, Finset.mul_eq_one_iff, Equiv.Perm.OnCycleFactors.kerParam_range_eq, RootPairing.GeckConstruction.h_eq_diagonal, Finset.instLawfulAlternative, Finset.vaddCommClass_finset', Finset.subset_union_right, Finset.mem_product, Finset.orderEmbOfFin_mem, Filter.tendsto_finset_Iic_atTop_atTop, Finset.Iic_prod_def, Finset.sum_finset_coe, Affine.Simplex.excenterExists_singleton, Fintype.univ_ofSubsingleton, Finset.gcd_ne_zero_iff, Finset.coe_list_sum, Affine.Simplex.excenterWeightsUnnorm_compl, MeasureTheory.measurableCylinders.measurableSet, mulRothNumber_map_mul_right, Finset.biUnion_image_inf_left, discreteTopology_biUnion_finset, RootPairing.Base.span_int_coroot_support, Finset.disjoint_range_addRightEmbedding, Finset.product_add_product_comm, IsNoetherian.coeSort_finsetBasisIndex, Finset.preimage_mul_right_singleton, Finset.smul_zero_subset, Finset.sum_sdiff_lt_sum_sdiff, Finset.inter_product, Finset.exists_coe, instInfiniteFinset, TopCat.partialSections.directed, isRoot_of_unity_iff, Finset.prod_product', Finset.Nonempty.smul_zero, Finset.div_union, Turing.PartrecToTM2.contSupp_cons₁, MeasureTheory.IsSetSemiring.subset_disjointOfDiff, Finset.image_div, SkewMonoidAlgebra.mem_span_support, SSet.horn₃₂.desc.multicofork_π_zero, Finset.tsum_subtype, Finset.neg_smul, Finset.apply_union_le_sum, HahnSeries.SummableFamily.support_powerSeriesFamily_subset, SimpleGraph.nonuniformWitness_subset, MeasureTheory.mem_measurableCylinders, Finset.prod_anti_set_of_le_one, Equiv.Perm.support_le_prod_of_mem, Fintype.card_coe, CategoryTheory.Limits.CoproductsFromFiniteFiltered.liftToFinset_obj_obj, FormalMultilinearSeries.changeOriginSeriesTerm_changeOriginIndexEquiv_symm, Finset.diag_eq_filter, Finset.union_smul_inter_subset_union, Finset.mul_zero_subset, Finset.expect_ite_eq, SSet.horn₃₂.desc.multicofork_π_three_assoc, Finset.card_nsmul_mono, Finset.isUnit_iff_singleton_aux, MvPolynomial.support_esymm, Finset.exists_ne_zero_of_expect_ne_zero, Nat.succ_mul_binomial, Nat.mul_divisors_filter_prime_pow, Nat.notMem_primesBelow, Ideal.Factors.piQuotientEquiv_mk, Finset.map_inter, CategoryTheory.Limits.ProductsFromFiniteCofiltered.liftToFinset_obj_obj, Finset.prod_insert_of_eq_one_if_notMem, ProbabilityTheory.Kernel.partialTraj_zero, SSet.horn₃₂.desc.multicofork_π_one_assoc, Finset.vadd_finset_sdiff, UniqueMul.subsingleton, SimpleGraph.singleton_disjoint_neighborFinset, Finset.hasSum_compl_iff, Finset.divConst_empty_right, Finset.support_sum, Finset.image_mul_right', Finset.empty_vadd, Set.Finite.subtypeEquivToFinset_symm_apply_coe, FormalMultilinearSeries.mem_compPartialSumTarget_iff, Finset.union_inter_distrib_right, Finset.prod_piecewise, Finset.sup_id_eq_sSup, Finset.fmap_def, Finset.one_lt_card, Multiset.card_Ioo, Finset.sum_mul_boole, Finset.zero_notMem_neg_add_iff, Finset.Nonempty.exists_eq_singleton_or_nontrivial, SimpleGraph.edgeFinset_deleteEdges, Finset.isDirected_subset, IsCompact.elim_finite_subfamily_isClosed_subtype, Module.Basis.mem_span_repr_support, AddMonoidAlgebra.support_gen_of_gen', Submodule.decomposition_erase_inf, Finset.mem_coe, SummationFilter.unconditional_filter, DFinsupp.support_sum, MvPolynomial.coeffs_eq_empty_of_subsingleton, Filter.tendsto_toRight_atTop, Finset.sdiff_subset, Finset.monotone_preimage, CategoryTheory.Limits.CoproductsFromFiniteFiltered.liftToFinsetColimIso_aux, DFinsupp.card_Icc, SimpleGraph.TripartiteFromTriangles.toTriangle_apply, Finset.union_subset_iff, Finset.expect_singleton, Finsupp.supportedEquivFinsupp_apply_apply, Finset.uIcc_subset_uIcc_union_uIcc, Finset.inter_div_subset, Finset.image_op_nsmul, Equiv.Perm.signBijAux_injOn, ENNReal.tprod_eq_iInf_prod, Finset.disjSups_union_right, Finset.filter_product, Submonoid.FG.exists_minimal_closure_eq, Finsupp.nsmul_single_one_image, MonoidAlgebra.support_mul, Finset.product_inter_product, Finset.erase_sdiff_comm, DFinsupp.support_mapRange, Finset.inter_subset_left, Finset.singleton_iff_unique_mem, WittVector.wittNeg_vars, Affine.Triangle.dist_orthocenter_reflection_circumcenter_finset, Finset.pairwiseDisjoint_slice, MvPolynomial.support_smul, Finset.coe_pow, Finset.image_add_left, Equiv.Perm.Basis.ofPermHomFun_one, Finset.vadd_def, Nat.prodMk_mem_divisorsAntidiag, OrderIso.finsetSetFinite_apply_coe, Finset.singleton_div_singleton, RootPairing.GeckConstruction.coe_genWeightSpace_zero_eq_span_range_u, Finset.inter_add_subset, Finset.inv_filter, MulAction.mem_stabilizer_finset', SimpleGraph.TripartiteFromTriangles.map_toTriangle_disjoint, Finset.card_add_neg_eq_addConvolution_neg, Finset.mul_union, Finset.offDiag_inter, Finset.infs_subset_iff, Finsupp.graph_injective, mulRothNumber_union_le, Finsupp.mem_sym2_support_of_mul_ne_zero, Finset.box_succ_union_prod, Finset.erase_singleton, Nat.mod_injOn_Ico, Finset.union_inter_cancel_right, Finset.coe_vsub, Finset.powersetCard_one, tendsto_tprod_compl_atTop_one, Nat.mem_Ioc_succ, one_half_le_sum_primes_ge_one_div, Finset.sum_coe_sort, Finset.preimage_add_right_zero', Finset.filter_product_left, MvPolynomial.support_X, Nat.mem_primeFactors, Finset.range_inter_range, Finset.mem_eraseNone, Finset.measurableSet_biUnion, hasSumLocallyUniformly_iff_tendstoLocallyUniformly, Finsupp.mem_splitSupport_iff_nonzero, Finset.card_univ_diff, Finset.inter_empty, IntermediateField.FG.exists_finset_maximalFor_isTranscendenceBasis_separableClosure, Finset.toLeft_insert_inl, Finset.mem_attachFin, Finset.mem_upShadow_iterate_iff_exists_sdiff, Finset.mem_dfinsupp_iff, Finmap.keys_empty, Finset.exists_lt_of_lt_expect, Finset.union_vadd, Finset.apply_coe_mem_map, Set.powersetCard.mem_map_iff_mem_range, Part.mem_toFinset, Multiset.mem_toFinset, Finset.map_op_pow, Dynamics.exists_isDynCoverOf_of_isCompact_invariant, Finsupp.notMem_neLocus, Set.Finite.toFinset_union, Fintype.not_linearIndependent_iffₒₛ, Affine.Simplex.excenter_compl, Finset.gc_map_inl_toLeft, IsDedekindDomain.quotientEquivPiFactors_mk, SimpleGraph.edgeFinset_inf, Multiset.toFinset_singleton, Equiv.finsetCongr_symm, Finset.sum_add_sum_compl, Finset.image₂_right_identity, Preorder.piCongrLeft_comp_frestrictLe, Finset.Iic_diff_Ioc, Finset.erase_ne_self, Finset.mem_powerset_self, Finset.pi_singletons, Finset.insert_comm, VectorFourier.norm_fourierPowSMulRight_iteratedFDeriv_fourierIntegral_le, Finset.addEnergy_eq_zero_iff, Finset.coe_sum, PMF.mem_support_uniformOfFinset_iff, Finset.univ_of_card_le_two, Finset.filter_union_filter_of_codisjoint, Set.powersetCard.coe_mulActionHom_of_embedding, Finset.univ_filter_card_eq, NonarchimedeanAddGroup.cauchySeq_sum_of_tendsto_cofinite_zero, Finset.sup_id_set_eq_sUnion, Finset.coe_image₂, Finset.sigmaLift_eq_empty, Behrend.exists_large_sphere_aux, Finset.card_singleton_mul, Finset.infs_inter_subset_right, Function.Injective.map_atTop_finset_sum_eq, Finset.mem_biUnion, SummationFilter.conditional_filter_eq_map_Iic, LinearMap.le_rank_iff_exists_linearIndependent_finset, Nat.Coprime.primeFactors_mul, Finsupp.support_zipWith, ZMod.cauchy_davenport, Finset.addETransformRight_fst, Finsupp.prod_ite_eq', Filter.tendsto_finset_image_atTop_atTop, Finset.sum_inv_index, FormalMultilinearSeries.compPartialSumTarget_tendsto_prod_atTop, SSet.horn₃₁.desc.multicofork_π_three, Finset.sort_singleton, Finset.eraseNone_empty, Finset.sdiff_union_inter, Finset.eraseNone_insertNone, Polynomial.support_zero, Finmap.keysLookupEquiv_apply_coe_fst, Finset.toLeft_inter, IntermediateField.finiteDimensional_iSup_of_finset', Finset.insert_Ioc_add_one_left_eq_Ioc, Affine.Simplex.ExcenterExists.excenter_eq_excenter_iff, Finset.compl_subset_compl, Finset.prod_union_inter, Nat.filter_range_nth_eq_insert, AlgebraicGeometry.Scheme.exists_isOpenCover_and_isAffine, DFinsupp.support_subset_iff, Finset.sumEquiv_symm_apply, WithSeminorms.hasBasis_ball, MvPolynomial.coeffs_zero, Finset.mem_sups, Finsupp.restrictSupportEquiv_symm_apply_coe, Finset.card_smul_finset, Nat.binomial_eq_choose, Finset.mulETransformLeft_snd, four_functions_theorem, RootPairing.GeckConstruction.lie_e_f_mul_ω, Behrend.sphere_subset_box, Finset.Ici_subset_Ici, Finset.card_vadd_inter_vadd, Finset.sdiff_union_distrib, MulAction.stabilizer_coe_finset, SimpleGraph.map_edgeFinset_induce, Preorder.continuous_frestrictLe₂, Polynomial.coeffs_ofSubring, Polynomial.lifts_iff_coeffs_subset_range, Set.Finite.toFinset_zero, Finset.sum_ite_eq, Finset.eventually_cocardinal_notMem, Finset.Icc_eq_empty_iff, Finset.card_neg_le, SSet.horn₂₁.sq, Finset.image_vadd_product, cauchySeq_finset_iff_tsum_vanishing, Finset.instAssociativeDisjSups, Finset.smulCommClass_finset', SimpleGraph.card_cliqueFinset_le, Set.powersetCard.mulActionHom_of_embedding_surjective, Lagrange.basis_pair_left, Finsupp.subset_mapRange_neLocus, Finset.sdiff_eq_inter_compl, Affine.Simplex.touchpoint_empty_mem_interior_faceOpposite, Nat.binomial_eq, AhlswedeZhang.infSum_union_add_infSum_sups, Finset.inf'_insert, Finsupp.support_eq_singleton', Equiv.Perm.OnCycleFactors.kerParam_apply, Finset.sup_add_left, Finset.image₂_singleton_inter, Down.mem_compression, MeasureTheory.IsSetSemiring.disjoint_sUnion_disjointOfDiff, Prime.dvd_finset_prod_iff, Finset.Icc_eq_filter_powerset, Finset.antitone_iff_forall_cons_le, Finset.geomSum_injective, SignType.univ_eq, SetTheory.PGame.Domineering.mem_left, Set.sized_powersetCard, range_pow_padicValNat_subset_divisors, Finset.card_mul_cast_divConst, cauchySeq_finset_of_geometric_bound, Finset.union_union_distrib_left, cauchy_davenport_add_of_linearOrder_isCancelAdd, Finset.disjiUnion_Iic_disjointed, Finset.mulETransformLeft_fst, MvPolynomial.vars_sum_subset, Finset.Nat.antidiagonalEquivFin_apply_val, Finset.val_le_iff, Finset.expect_ite_eq', Affine.Simplex.faceOppositeCentroid_eq_affineCombination, mem_generatePiSystem_iUnion_elim', Finpartition.not_isEquipartition, Finset.diffs_inter_subset_right, Finset.sum_eq_ite, Finset.cast_addConst, WittVector.wittPolyProd_vars, List.toFinset_union, Finset.prod_add_one, MonoidAlgebra.support_one, Cardinal.finset_card_lt_aleph0, AddMonoidAlgebra.mem_gradeBy_iff, trop_sInf_image, Matroid.IsRkFinite.exists_finset_isBasis', Submonoid.mem_closure_iff_exists_finset_subset, Finset.erase_subset, Finset.inf'_union, SimpleGraph.TripartiteFromTriangles.Graph.in₂₁_iff, DFinsupp.mk_smul, Finset.mul_singleton, Finset.wcovBy_insert, Tuple.proj_equiv₁', Finset.hasProd_iff_compl, Finset.notMem_map_subtype_of_not_property, Finset.preimage_inl, Finset.vsub_singleton, MvPolynomial.support_C, Finset.disjSups_inter_subset_left, MvPolynomial.supported_eq_vars_subset, Algebra.Presentation.HasCoeffs.coeffs_relation_mem_range, Finset.powersetCard_nonempty_of_le, Behrend.threeAPFree_sphere, Finset.insert_Ioc_left_eq_Ioc_sub_one_of_not_isMin, Finset.max_one, Finset.pairwise_disjoint_powersetCard, Finset.powersetCard_empty_subsingleton, Finset.subset_univ, Finset.mem_val, Finset.image_ssubset_image, Finset.Nonempty.inr, Finset.disjoint_erase_comm, Multiset.toEnumFinset_filter_eq, Finset.attach_image_val, Finset.ruzsa_triangle_inequality_add_add_add, LieAlgebra.IsKilling.rootSystem_root_apply, Set.toFinset_prod, Finset.univ_div_univ, Finset.exists_cycleOn, Finset.strictAnti_iff_forall_lt_insert, Finset.set_biInter_biUnion, Finset.support_prod, Finset.mem_addAntidiagonal, WithBot.some_mem_insertBot, DFinsupp.support_smul, Profinite.NobelingProof.factors_prod_eq_basis, Finset.mem_def, Set.ncard_coe_finset, Finset.filter_inter_distrib, Finset.orderIsoColex_apply, DFinsupp.neLocus_eq_empty, Finset.infs_union_left, Finset.diffs_union_left, Finset.univ_eq_empty_iff, AddMonoidAlgebra.mem_span_support, Finset.empty_sub, Finset.singleton_smul_singleton, Metric.AreSeparated.finset_iUnion_left_iff, Finset.diag_empty, Finpartition.bot_isEquipartition, SimpleGraph.componentCompl_nonempty_of_infinite, Affine.Simplex.excenterWeights_compl, Finset.sup_mul_right, Finset.card_mono, DFinsupp.card_Ioc, biUnion_Ioc_disjointed_of_monotone, Seminorm.closedBall_finset_sup_eq_iInter, Set.powersetCard.coe_smul, Finset.inv_empty, Finset.addAntidiagonal_mono_left, Finset.subset_range, compact_covered_by_mul_left_translates, Finset.image_insert, WithBot.bot_mem_insertBot, Finset.coe_subset_singleton, Finset.piecewise_insert_self, Finset.Ici_top, Set.Sized.isAntichain, Finset.sum_eq_sum_extend, Finset.eq_empty_or_nonempty, Finset.centerMass_singleton, WithBot.Icc_bot_coe, SubAddAction.fg_iff, Finset.map_some_eraseNone, convexHull_range_eq_exists_affineCombination, SimpleGraph.cliqueSet_one, Finset.compls_singleton, Set.powersetCard.coe_nontrivial_iff, SSet.stdSimplex.face_singleton_compl, Finset.Icc_subset_Icc_right, Profinite.NobelingProof.factors_prod_eq_basis_of_eq, MvPolynomial.vars_0, Fintype.finsetEquivSet_symm_apply, Finset.sigmaAntidiagonalEquivProd_apply, Finset.coe_singletonZeroHom, Finset.sym2_eq_image, Finset.exists_mem_eq_inf', Finset.prod_fiberwise_eq_prod_filter, Finpartition.part_surjOn, Finset.compl_eq_empty_iff, Finset.subset_infs_self, Finpartition.exists_subset_part_bijOn, Finset.filter_eq, Finset.expect_product', Lagrange.interpolate_singleton, FormalMultilinearSeries.mem_compPartialSumSource_iff, Finset.zero_mem_box, Finset.exists_le_of_sum_le, Finset.sigmaAntidiagonalEquivProd_symm_apply_fst, MeasureTheory.Measure.sum_coe_finset, Finset.Colex.ofColex_bot, Set.powersetCard.exists_mem_notMem_iff_ne, Equiv.Perm.cycleOf_ne_one_iff_mem_cycleFactorsFinset, Set.Finite.toFinset_one, SummationFilter.instIsCountablyGeneratedFinsetFilterConditionalOfAtTopOfAtBot, MulAction.mem_stabilizer_finset_iff_subset_smul_finset, Finset.instNonemptyElemCoeInsert, Set.Finite.toFinset_insert, Finset.ruzsa_triangle_inequality_negAdd_add_add, mul_eq_mul_prime_prod, Finset.ruzsa_triangle_inequality_addNeg_add_add, Sum.Ico_inr_inl, Finset.Nontrivial.add, Finset.subset_compl_iff_disjoint_right, Finset.Iic_diff_Ioc_self_of_le, OrderEmbedding.birkhoffFinset_sup, RootPairing.GeckConstruction.e_lie_u, Finset.dens_vadd_finset, AddMonoidAlgebra.supDegree_mem_support, MvPolynomial.vars_monomial_single, Finset.image_mul_left, Finset.card_truncatedSup_union_add_card_truncatedSup_infs, Finset.memberSubfamily_union, Fin.orderIsoPair_one, Equiv.Perm.OnCycleFactors.range_toPermHom_eq_range_toPermHom', Finset.image_symmDiff, Polynomial.support_X_empty, Finset.toRight_union, MeasureTheory.isProjectiveLimit_nat_iff', IsKleinFour.eq_finset_univ, IntermediateField.induction_on_adjoin_finset, Finsupp.mem_pi, exteriorPower.basis_repr_self, Finset.exists_nat_subset_range, DFinsupp.sigmaFinsetFunEquiv_apply_fst, RootPairing.GeckConstruction.lie_e_f_ne, Finset.coe_uIcc, Finset.card_sdiff_add_card, Finset.image_op_neg, Equiv.Perm.OnCycleFactors.centralizer_smul_def, DFinsupp.support_sup, Finset.mem_finAntidiagonal, Finset.insert_Ioc_right_eq_Ioc_add_one_of_not_isMax, Polynomial.mem_nthRootsFinset, WittVector.wittPolyProdRemainder_vars, Finset.neg_vadd_finset_distrib, Finset.Ioi_mul_Ici_subset', schnirelmannDensity_finset, Finset.inter_mul_subset, Finset.coe_sigma, Finset.mem_Ico, Finset.isLeast_min', ClassGroup.exists_mem_finset_approx', Finset.singleton_vadd, Finset.fold_op_rel_iff_or, Finset.mem_shatterer, WithSeminorms.hasBasis_zero_ball, Finset.isWF, Finset.sum_dite, Finset.mulETransformLeft.fst_mul_snd_subset, Finset.mem_prod_list_ofFn, Finpartition.parts_inf, Set.biInter_finsetSigma_univ', Finset.piecewise_coe, Finset.not_disjoint_iff, Affine.Simplex.touchpoint_mem_insphere, EisensteinSeries.eisensteinSeries_tendstoLocallyUniformly, Finset.left_mem_Ico, Finset.mem_uIcc, MeasureTheory.SimpleFunc.map_preimage_singleton, Finset.union_div_inter_subset_union, Finset.subset_insert_iff, Finset.exists_mem_notMem_of_card_lt_card, Finset.range_zero, Finset.image_mul_right, Finsupp.support_sub, NonarchimedeanGroup.cauchySeq_prod_of_tendsto_cofinite_one, ProbabilityTheory.iIndepSets_singleton_iff, AddMonoidAlgebra.support_one, Finset.image₂_singleton, Finset.toRight_inter, DFinsupp.support_monotone, Finset.empty_smul, Nat.divisors_zero, Ideal.Factors.piQuotientEquiv_map, ClassGroup.exists_mem_finsetApprox, Finset.vaddCommClass, Finset.singleton_div, Set.image_finset_prod_pi, Fin.attachFin_Ioc, Finset.vsub_def, Finset.notMem_compl, YoungDiagram.cells_inf, Finset.Nonempty.div, Finset.cast_card_inter, Finset.iSup_union, Set.powersetCard.coe_vadd, Finset.Ioc_subset_Ioc_left, Finset.sum_neg_index, mulDissociated_iff_sum_eq_subsingleton, Finset.notMem_sigmaLift_of_ne_right, biSup_finsetSigma, AddSemigroupIdeal.fg_iff, MvPolynomial.decomposition.decompose'_eq, Equiv.Perm.commute_ofSubtype_noncommPiCoprod, PairReduction.radius_logSizeBallSeq_zero, Set.coe_toFinset, Finset.mem_insertNone, IsTopologicalBasis.iInf_induced, Finset.imageZeroHom_apply, AddAction.mem_stabilizer_finset_iff_vadd_finset_subset, Finset.min_mem_insert_top_image_coe, Finset.powersetCard_self, mulRothNumber_singleton, Finset.card_powerset, Finset.insert_inj_on', LieAlgebra.IsKilling.instIsIrreducibleSubtypeWeightMemLieSubalgebraFinsetRootDualRootSystemOfIsSimple, Set.powersetCard.ofFinEmbEquiv_apply, Finset.toList_singleton, RootPairing.Base.chainTopCoeff_eq_of_ne, Finset.inter_add_union_subset, Finset.nsmul_piAntidiag_univ, Finset.mem_sum_list_ofFn, Finset.vsub_inter_subset, WittVector.wittMul_vars, Finset.Iio_eq_empty, Finset.ruzsa_triangle_inequality_sub_add_add, Finset.sym2_singleton, Finset.prod_mono_set_of_one_le', MultilinearMap.map_add_univ, Finpartition.IsEquipartition.card_interedges_sparsePairs_le', Finset.univ_pow, Finset.image_inf_product, Finset.val_covBy_val, DFinsupp.subset_mapRange_neLocus, Finpartition.atomise_empty, CategoryTheory.Limits.ProductsFromFiniteCofiltered.liftToFinsetObj_map, WithSeminorms.finset_sups, Finset.coe_union, Finset.Ico_subset_Ico, Finset.val_eq_singleton_iff, Equiv.Perm.OnCycleFactors.sign_kerParam_apply_apply, Finset.coe_map_subset_range, Set.powersetCard.eq_iff_subset, Finset.card_singleton, Set.Finite.toFinset_compl, Finset.prod_dite_of_true, Finset.isLUB_iff_isGreatest, DFinsupp.sigmaFinsetFunEquiv_apply_snd_coe, Multiset.toFinset_eq_singleton_iff, Finset.smul_eq_empty, Submodule.spanFinrank_eq_iInf, Finset.sdiff_sdiff_left', Holor.sum_unitVec_mul_slice, SimpleGraph.mem_cliqueSet_iff, Finset.tsum_subtype', Finset.convolution_op_smul_eq_convolution_mul_inv, eq_sUnion_finset_of_isTopologicalBasis_of_isCompact_open, Finset.shatters_univ, Finset.powerset_eq_univ, Finset.coe_subset, Finsupp.image_pow_eq_finsuppProd_image, PMF.toMeasure_apply_finset, Finset.interior_iInter, Finset.addETransformRight.card, SimpleGraph.edgeFinset_ssubset_edgeFinset, PartitionOfUnity.mem_finsupport, Finsupp.sym2_support_eq_preimage_support_mul, Finpartition.ofSetSetoid_parts, Finset.nsmul_piAntidiag, Finset.mem_upShadow_iterate_iff_exists_mem_card_add, Finset.id_traverse, Finset.inter_inter_distrib_right, Finset.coe_singletonMonoidHom, Finset.insert_inter, SkewMonoidAlgebra.support_single_ne_zero, Finset.mem_mul, Set.sized_union, HilbertBasis.finite_spans_dense, Polynomial.toSubring_one, ProbabilityTheory.Kernel.iIndepFun_iff_measure_inter_preimage_eq_mul, Finset.image_sdiff, SimpleGraph.Walk.exists_mem_support_forall_mem_support_imp_eq, Set.definable_iff_finitely_definable, Turing.PartrecToTM2.codeSupp_comp, List.mem_fixedLengthDigits_iff

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