Lattice

📁 Source: Mathlib/Order/Lattice.lean

Statistics

Metric	Count
Definitions instDistribLattice, instPartialOrder, DistribLattice, ofInfSupLe, toLattice, distribLattice, lattice, semilatticeInf, semilatticeSup, inf, mk', toLinearOrder, toSemilatticeInf, toSemilatticeSup, toLattice, instDistribLattice, instLattice, instSemilatticeInf, instSemilatticeSup, instDistribLattice, instLattice, instMaxForall_mathlib, instMinForall_mathlib, instSemilatticeInf, instSemilatticeSup, instDistribLattice, instLattice, instMax_mathlib, instMin_mathlib, instSemilatticeInf, instSemilatticeSup, SemilatticeInf, inf, mk', toMin, toPartialOrder, SemilatticeSup, mk', sup, toMax, toPartialOrder, lattice, semilatticeInf, semilatticeSup, instDistribLattice, instLattice, instLinearOrder, instSemilatticeInf, instSemilatticeSup, instDistribLatticeNat, instDistribLatticeOfLinearOrder, instLatticeInt	52
Theorems inf, le_map_inf, map_inf, map_sup, map_sup_le, max, min, sup, inf, map_inf, map_sup, max, min, of_map_inf, of_map_sup, sup, le_sup_inf, update_inf, update_sup, ext, inf_le_left, inf_le_right, le_inf, inf, le_map_sup, map_inf, map_inf_le, map_sup, max, min, of_le_map_sup, of_left_le_map_sup, of_map_inf, of_map_inf_le, of_map_inf_le_left, of_map_sup, sup, inf, map_inf, map_sup, max, min, of_map_inf, of_map_sup, sup, inf_lt_or_inf_lt, lt_sup_or_lt_sup, of_gt, of_lt, inf_apply, inf_def, sup_apply, sup_def, fst_inf, fst_sup, inf_def, mk_inf_mk, mk_sup_mk, snd_inf, snd_sup, sup_def, swap_inf, swap_sup, dual_dual, ext, ext_inf, inf_le_left, inf_le_right, le_inf, dual_dual, ext, ext_sup, le_sup_left, le_sup_right, sup_le, coe_inf, coe_sup, mk_inf_mk, mk_sup_mk, eq_of_inf_eq_sup_eq, exists_and_iff_of_antitone, exists_and_iff_of_monotone, exists_ge_and_iff_exists, exists_le_and_iff_exists, inf_assoc, inf_comm, inf_congr_left, inf_congr_right, inf_eq_and_sup_eq_iff, inf_eq_iff_sup_eq, inf_eq_inf_iff_left, inf_eq_inf_iff_right, inf_eq_left, inf_eq_minDefault, inf_eq_right, inf_eq_sup, inf_idem, inf_ind, inf_inf_distrib_left, inf_inf_distrib_right, inf_inf_inf_comm, inf_le_iff, inf_le_inf, inf_le_inf_left, inf_le_inf_right, inf_le_ite, inf_le_left, inf_le_of_left_le, inf_le_of_right_le, inf_le_right, inf_le_sup, inf_left_comm, inf_left_idem, inf_left_le_sup_left, inf_left_le_sup_right, inf_left_right_swap, inf_lt_iff, inf_lt_left, inf_lt_left_or_right, inf_lt_of_left_lt, inf_lt_of_right_lt, inf_lt_right, inf_lt_sup, inf_of_le_left, inf_of_le_right, inf_right_comm, inf_right_idem, inf_right_le_sup_left, inf_right_le_sup_right, inf_sup_le, inf_sup_left, inf_sup_right, inf_sup_self, instAssociativeMax_mathlib, instAssociativeMin_mathlib, instCommutativeMax_mathlib, instCommutativeMin_mathlib, instIdempotentOpMax_mathlib, instIdempotentOpMin_mathlib, ite_le_sup, le_iff_exists_inf, le_iff_exists_sup, le_inf, le_inf_iff, le_inf_sup, le_of_inf_eq, le_of_inf_eq', le_of_inf_le_sup_le, le_of_sup_eq, le_of_sup_eq', le_sup_iff, le_sup_inf, le_sup_left, le_sup_of_le_left, le_sup_of_le_right, le_sup_right, left_eq_inf, left_eq_sup, left_lt_sup, left_or_right_lt_sup, lt_inf_iff, lt_sup_iff, lt_sup_of_lt_left, lt_sup_of_lt_right, max_max_max_comm, min_min_min_comm, ofDual_inf, ofDual_max, ofDual_min, ofDual_sup, pairwise_iff_gt, pairwise_iff_lt, right_eq_inf, right_eq_sup, right_lt_sup, semilatticeSup_mk'_partialOrder_eq_semilatticeInf_mk'_partialOrder, sup_assoc, sup_comm, sup_congr_left, sup_congr_right, sup_eq_and_inf_eq_iff, sup_eq_iff_inf_eq, sup_eq_inf, sup_eq_left, sup_eq_maxDefault, sup_eq_right, sup_eq_sup_iff_left, sup_eq_sup_iff_right, sup_idem, sup_ind, sup_inf_le, sup_inf_left, sup_inf_right, sup_inf_self, sup_le, sup_le_iff, sup_le_inf, sup_le_sup, sup_le_sup_left, sup_le_sup_right, sup_left_comm, sup_left_idem, sup_left_right_swap, sup_lt_iff, sup_of_le_left, sup_of_le_right, sup_right_comm, sup_right_idem, sup_sup_distrib_left, sup_sup_distrib_right, sup_sup_sup_comm, toDual_inf, toDual_max, toDual_min, toDual_sup	215
Total	267

Antitone

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
inf 📖	mathematical	Antitone PartialOrder.toPreorder SemilatticeInf.toPartialOrder	Pi.instMinForall_mathlib SemilatticeInf.toMin	—	inf_le_inf
le_map_inf 📖	mathematical	Antitone PartialOrder.toPreorder SemilatticeInf.toPartialOrder SemilatticeSup.toPartialOrder	Preorder.toLE SemilatticeSup.toMax SemilatticeInf.toMin	—	Monotone.map_inf_le dual_right
map_inf 📖	mathematical	Antitone PartialOrder.toPreorder SemilatticeInf.toPartialOrder Lattice.toSemilatticeInf DistribLattice.toLattice instDistribLatticeOfLinearOrder SemilatticeSup.toPartialOrder	SemilatticeInf.toMin SemilatticeSup.toMax	—	Monotone.map_inf dual_right
map_sup 📖	mathematical	Antitone PartialOrder.toPreorder SemilatticeInf.toPartialOrder Lattice.toSemilatticeInf DistribLattice.toLattice instDistribLatticeOfLinearOrder	SemilatticeSup.toMax Lattice.toSemilatticeSup SemilatticeInf.toMin	—	Monotone.map_sup dual_right
map_sup_le 📖	mathematical	Antitone PartialOrder.toPreorder SemilatticeSup.toPartialOrder SemilatticeInf.toPartialOrder	Preorder.toLE SemilatticeSup.toMax SemilatticeInf.toMin	—	Monotone.le_map_sup dual_right
max 📖	mathematical	Antitone PartialOrder.toPreorder SemilatticeInf.toPartialOrder Lattice.toSemilatticeInf DistribLattice.toLattice instDistribLatticeOfLinearOrder	SemilatticeSup.toMax Lattice.toSemilatticeSup	—	sup
min 📖	mathematical	Antitone PartialOrder.toPreorder SemilatticeInf.toPartialOrder Lattice.toSemilatticeInf DistribLattice.toLattice instDistribLatticeOfLinearOrder	SemilatticeInf.toMin	—	inf
sup 📖	mathematical	Antitone PartialOrder.toPreorder SemilatticeSup.toPartialOrder	Pi.instMaxForall_mathlib SemilatticeSup.toMax	—	sup_le_sup

AntitoneOn

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
inf 📖	mathematical	AntitoneOn PartialOrder.toPreorder SemilatticeInf.toPartialOrder	Pi.instMinForall_mathlib SemilatticeInf.toMin	—	dual sup
map_inf 📖	mathematical	AntitoneOn PartialOrder.toPreorder SemilatticeInf.toPartialOrder Lattice.toSemilatticeInf DistribLattice.toLattice instDistribLatticeOfLinearOrder SemilatticeSup.toPartialOrder Set Set.instMembership	SemilatticeInf.toMin SemilatticeSup.toMax	—	map_sup dual
map_sup 📖	mathematical	AntitoneOn PartialOrder.toPreorder SemilatticeInf.toPartialOrder Lattice.toSemilatticeInf DistribLattice.toLattice instDistribLatticeOfLinearOrder Set Set.instMembership	SemilatticeSup.toMax Lattice.toSemilatticeSup SemilatticeInf.toMin	—	le_total sup_of_le_right inf_of_le_right sup_of_le_left inf_of_le_left
max 📖	mathematical	AntitoneOn PartialOrder.toPreorder SemilatticeInf.toPartialOrder Lattice.toSemilatticeInf DistribLattice.toLattice instDistribLatticeOfLinearOrder	SemilatticeSup.toMax Lattice.toSemilatticeSup	—	sup
min 📖	mathematical	AntitoneOn PartialOrder.toPreorder SemilatticeInf.toPartialOrder Lattice.toSemilatticeInf DistribLattice.toLattice instDistribLatticeOfLinearOrder	SemilatticeInf.toMin	—	inf
of_map_inf 📖	mathematical	SemilatticeInf.toMin SemilatticeSup.toMax	AntitoneOn PartialOrder.toPreorder SemilatticeInf.toPartialOrder SemilatticeSup.toPartialOrder	—	sup_eq_left inf_eq_left
of_map_sup 📖	mathematical	SemilatticeSup.toMax SemilatticeInf.toMin	AntitoneOn PartialOrder.toPreorder SemilatticeSup.toPartialOrder SemilatticeInf.toPartialOrder	—	dual of_map_inf
sup 📖	mathematical	AntitoneOn PartialOrder.toPreorder SemilatticeSup.toPartialOrder	Pi.instMaxForall_mathlib SemilatticeSup.toMax	—	sup_le_sup

Bool

Definitions

Name	Category	Theorems
instDistribLattice 📖	CompOp	—
instPartialOrder 📖	CompOp	1 math math: wcovBy_iff

DistribLattice

Definitions

Name	Category	Theorems
ofInfSupLe 📖	CompOp	—
toLattice 📖	CompOp	4438 math math: countable_image_lt_image_Ioi_within, max_choice, SuccOrder.hasBasis_nhds_Ioc, max_sub_min_eq_abs', PredOrder.nhdsGT_eq_nhdsNE, HahnSeries.order_lt_iff_exists, Affine.Simplex.sSameSide_affineSpan_faceOpposite_point_left_iff, units_inv_smul, Function.Embedding.encard_le, LinearOrder.isSuccArchimedean_iff_isPredArchimedean, le_iff_forall_lt_one_mul_le, RingCone.nonneg.isMaxCone, Set.finite_diff_iUnion_Ioo, tsub_lt_self_iff, HurwitzZeta.hasSum_int_hurwitzZetaOdd, Multiset.Ico_sub_Ico_right, AddUnits.orderEmbeddingVal_apply, one_le_div_iff, AffineSubspace.sOppSide_iff_exists_right, GenContFract.IntFractPair.nth_stream_fr_nonneg_lt_one, Int.ceil_lt_iff, Mathlib.Meta.NormNum.isNNRat_lt_false, ENat.add_lt_top, HahnSeries.SummableFamily.powerSeriesFamily_add, continuousOn_ceil, PNat.bot_eq_one, Valuation.IsRankOneDiscrete.generator_lt_one, mul_self_nonneg, nhds_basis_one_mabs_lt, sign_intCast, Cardinal.natCast_lt_toENat_iff, hasSum_mellin_pi_mul_sq', Ordinal.toNimber_eq_zero, mul_nonpos_iff_neg_imp_nonneg, IsCompact.bddBelow, Finset.min'_union, Finset.sup_add_sup, Filter.Tendsto.max_left, AddCircle.coe_equivIco_mk_apply, PNat.addLeftMono, DistLat.hom_inv_apply, WithTop.coe_max, ENat.toENNReal_lt_top, Set.Ioo_subset_Ioo_union_Ico, Valued.isOpen_closedball, emultiplicity_le_emultiplicity_of_dvd_left, DivisibleHull.archimedeanClassMk_mk_eq, continuous_mabs, Set.Iio_union_Ici, Affine.Simplex.wOppSide_affineSpan_faceOpposite_point_left_iff, nsmul_nonneg_iff, abs_sub_abs_le_abs_add, HahnEmbedding.IsPartial.baseEmbedding_le, Rat.intCast_lt_cast, DFinsupp.toMultiset_sup, Valuation.IsTrivialOn.valuation_algebraMap_le_one, ArchimedeanClass.FiniteResidueField.mk_ratCast, Irreducible.maximalIdeal_eq_setOf_le_v_coe, IsPreconnected.intermediate_value_Ico, RootPairing.coxeterWeight_nonneg, NNRat.coe_floor, ProbabilityTheory.gaussianReal_map_const_mul, Continuous.strictMono_of_inj_boundedOrder', IsDedekindDomain.HeightOneSpectrum.adicValued.has_uniform_continuous_const_smul', SignType.neg_one_lt_iff, Set.Ici_add_one_eq_Ioi, min_eq_bot, Int.lt_succ_floor, MvPolynomial.isWeightedHomogeneous_zero_iff_weightedTotalDegree_eq_zero, Finsupp.Colex.addLeftStrictMono, Measurable.max, ENat.top_pos, Mathlib.Meta.NormNum.IsNNRat.natFloor, Finset.max_union, strictConvexOn_iff_slope_strict_mono_adjacent, CauSeq.lt_irrefl, closure_interior_Icc, Order.Ioo_succ_right, NNRat.cast_strictMono, Fin.addNatOrderEmb_toEmbedding, LinearOrderedAddCommGroup.wellFoundedOn_setOf_le_lt_iff_nonempty_discrete, Mathlib.Tactic.Order.ToInt.toInt_sup_toInt_eq_toInt, Dense.exists_ge, ValuationSubring.valuation_lt_one_iff, OrderIso.pnatIsoNat_symm_apply, Set.notMem_Ioi, Valuation.FiniteField.algebraMap_le_one, Finset.le_fold_min, LinearOrderedAddCommGroupWithTop.sub_pos, ArchimedeanClass.FiniteElement.instIsStrictOrderedRing, tendsto_inv_atTop_zero, Int.lt_ceil, min_sub_sub_left, Units.min_val, neg_le_self_iff, tendsto_const_mul_pow_nhds_iff', Valuation.HasExtension.val_map_le_iff, Set.compl_ordConnectedSection_ordSeparatingSet_mem_nhdsGE, ENat.lt_add_one_iff', OrderEmbedding.birkhoffFinset_inf, Orientation.ne_iff_eq_neg, Valuation.isEquiv_iff_val_sub_one_lt_one, Summable.abs, HahnSeries.mem_cardSuppLTSubfield, Valuation.one_apply_lt_one_iff, nhds_bot_basis, Finset.exists_mem_eq_inf, dense_iff_exists_between, countable_image_gt_image_Ioi_within, sign_mul_self, Finset.exists_one_lt_of_prod_one_of_exists_ne_one', quasiconcaveOn_iff_min_le, not_isCofinal_iff, AbsoluteValue.isEquiv_trivial_iff_eq_trivial, Set.toENat_cardinalMk_subtype, convexHull_insert, Set.Ioi_subset_Ioo_union_Ici, Set.Infinite.exists_gt, ENat.self_le_mul_left, ValuationSubring.integralClosure_algebraMap_injective, PNat.map_subtype_embedding_Ico, MeasureTheory.aecover_Ioi_of_Ici, Cardinal.toENat_eq_natCast_iff, cocompact_le_atBot, Matrix.abs_det_reindex, tsub_add_min, MeasureTheory.stoppedProcess_stoppedProcess, PowerSeries.heval_C, inv_atBot₀, MonomialOrder.degree_add_of_ne, Polynomial.isEquivalent_atBot_div, ENat.card_le_card_of_injective, tendsto_ceil_right', covBy_iff_le_iff_lt_right, Valuation.mem_maximalIdeal_iff, LinOrd.ofHom_apply, convex_iff_ordConnected, RootPairing.RootPositiveForm.zero_lt_posForm_apply_root, Finset.sup'_add', MeasureTheory.integrable_iff_integrableAtFilter_atBot, convexHull_multiset_sum, FiniteArchimedeanClass.mem_addSubgroup_iff, abs_sub_round, partialSups_succ', WellOrderExtension.wellFoundedLT, Valuation.mem_leSubmodule_iff, isPiSystem_image_Iic, abs_add_eq_add_abs_iff, Multiset.Ico_sub_Ico_left, Left.pow_lt_one_iff', ArchimedeanClass.mk_intCast, Set.uIcc_injective_left, ofDual_max, Set.disjoint_or_nonempty_inter, Finset.prod_one_sub_ordered, PredOrder.isOpen_iff, Cardinal.ofENat_lt_ofNat, add_max, ProbabilityTheory.gaussianReal_const_mul, Mathlib.Meta.Positivity.pos_of_isNNRat, Finset.le_fold_max, deriv_abs, Finset.Ioi_disjUnion_Iio, NumberField.FinitePlace.mk_apply, isOpen_lt_prod, NNRat.le_def, CauSeq.sup_inf_distrib_right, IsCompact.exists_isLeast, MeasureTheory.aecover_Ioi_of_Ioi, NNRat.not_cast_lt_zero, Finset.Icc_add_one_left_eq_Ioc, WithTop.continuousOn_untopD, MulArchimedeanClass.subgroup_strictAntiOn, nsmul_neg_iff, concaveOn_iff_slope_anti_adjacent, strictConvex_Iic, sub_le_neg_add_iff, Finset.disjSups_right_comm, Filter.Tendsto.mabs, min_bot_left, nhdsSet_Ioo, right_lt_lineMap_iff_one_lt, AffineSubspace.setOf_sSameSide_eq_image2, List.sortedLE_mergeSort, Hyperreal.epsilon_lt_of_pos, Finset.Ico_subset_Ico_union_Ico, min_mul_mul_left, OrderEmbedding.mulRight_apply, Nat.succPNat_mono, List.getD_max?_eq_unbotD_maximum, IsNonarchimedean.multiset_powerset_image_add, Set.Ioc_union_Ioc_left, Set.Iio_succ_eq_Iic, Padic.withValUniformEquiv_norm_le_one_iff, Int.cast_one_le_of_pos, Valued.toNormedField.norm_le_one_iff, HeytAlg.hasForgetToLat_forget₂_map, Rat.padicValuation_cast, nullMeasurableSet_Ioc, Finset.image_orderEmbOfFin_univ, ProbabilityTheory.Kernel.partialTraj_succ_of_le, Int.preimage_Ioc, CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.ofComposableArrows_incl_app, PNat.find_le, Finset.Iio_filter_lt, one_le_pow_mul_abs_eval_div, Set.tsub_encard_le_encard_diff, IsCauSeq.bounded', Finset.inf'_sup_inf', ConvexCone.canLift, Matrix.eRank_le_card_width, Ordinal.liftOnWellOrder_type, finSumEquivOfFinset_inr, MeasureTheory.ae_le_const_iff_forall_gt_measure_zero, Seminorm.finset_sup_apply, Polynomial.div_tendsto_atTop_leadingCoeff_div_of_degree_eq, AddCircle.card_torsion_le_of_isSMulRegular, min_lt_min_right_iff, Finset.dens_map_le, Order.succ_lt_succ_iff, inf_inf_sdiff, SuccOrder.limitRecOn_succ, List.maximum_cons, Finset.Colex.toColex_univ, Ordinal.iSup_typein_succ, Affine.Simplex.sign_excenterWeights_singleton_pos, HahnSeries.leadingCoeff_mul, ENat.card_lt_top, Set.range_IciExtend, LinearOrderedCommGroup.tendsto_nhds, Finset.le_sup'_iff, Int.cast_abs, ArchimedeanClass.closedBallAddSubgroup_top, ValuationSubring.valuation_le_iff, List.foldr_max_of_ne_nil, ArchimedeanClass.addSubgroup_antitone, Nat.succPNat_le_succPNat, Finset.min_eq_inf_withTop, Nat.ceil_pos, Set.iUnion_Ioc_eq_Ioi_self_iff, mabs_le, add_right_strictMono_of_ne_top, instCommutativeMax, mapClusterPt_leftLim, le_mabs', abs_dvd, Finset.addConst_le_inv_dens, convex_iff_sum_mem, Finset.card_Ico_mul_right, Finset.fold_min_lt, MvPowerSeries.le_order_mul, FinBddDistLat.ofHom_comp, OrderRingHom.eq_id, mem_nhdsLT_iff_exists_Ico_subset, Cardinal.ofENat_le_ofNat, Matrix.abs_det_submatrix_equiv_equiv, QuadraticMap.linMulLinSelfPosDef, abs_eq_iff_mul_self_eq, Cardinal.toENat_ofENat, PNat.Icc_eq_finset_subtype, Valuation.IsRankOneDiscrete.exists_generator_lt_one', Function.support_max, signHom_apply, Polynomial.div_tendsto_atBot_leadingCoeff_div_of_degree_eq, Set.infs_sups_subset_right, Ordinal.toNatOrdinal_eq_one, Set.ncard_le_encard, List.max_prod_le, CategoryTheory.Limits.MultispanIndex.toLinearOrderMultispanIso_inv_app, HahnSeries.instIsStrictOrderedRingLexOfIsDomain, continuousOn_floor, Finset.Icc_min_max, LaurentSeries.LaurentSeriesRingEquiv_def, Field.Emb.Cardinal.directed_filtration, Set.Ioc_union_Ioc_right, abs_smul, AbsoluteValue.map_units_intCast, instIsCountablyGenerated_atBot, tendsto_one_iff_mabs_tendsto_one, Polynomial.eventually_atBot_not_isRoot, Set.OrdConnected.uIcc_subset, HahnEmbedding.Partial.orderTop_eq_archimedeanClassMk, Set.OrdConnected.IicExtend, Finset.uIcc_eq_union, Continuous.upperSemicontinuous, tendsto_smul_comp_nat_floor_of_tendsto_mul, List.minimum_of_length_pos_le_iff, Field.Emb.Cardinal.instInverseSystemWithTopToTypeOrdRankAlgHomSubtypeMemIntermediateFieldCoeOrderEmbeddingFiltrationAlgebraicClosureEmbFunctor, exists_seq_strictMono_tendsto_nhdsWithin, Hyperreal.neg_lt_of_tendsto_zero_of_pos, nhdsWithin_Ioi_isMeasurablyGenerated, HahnSeries.SummableFamily.powers_zero, min_add_distrib', Module.length_of_free, Set.image_const_mul_uIcc, isLocallyClosed_Ioi, PNat.Ioo_eq_finset_subtype, lowerClosure_eq_top_iff, WithZeroTopology.nhds_zero, Set.Icc_succ_left_eq_Ioc, Field.Emb.Cardinal.filtration_succ, Set.unit_eq, ArchimedeanClass.FiniteResidueField.ofArchimedean_apply, Finset.inf_lt_iff, AddCircle.equivIccQuot_comp_mk_eq_toIcoMod, Set.IciExtend_self, Valuation.mem_ltIdeal_iff, CauSeq.abv_pos_of_not_limZero, mabs_pow, Valuation.val_le_one_or_val_inv_lt_one, Mathlib.Tactic.Order.ToInt.toInt_le_toInt, Matrix.eRank_le_card_height, Padic.instCompatibleWithZeroMultiplicativeIntMulValuation, emultiplicity_add_eq_min, Nonneg.nontrivial, Module.End.independent_genEigenspace, NumberField.FinitePlace.norm_def', ENat.card_pos, max_neg_neg, smulPosStrictMono_iff_SMulPosReflectLE, IsCoprime.abs_right_iff, Valuation.leSubmodule_monotone, Int.fract_add_fract_le, sum_div_card_sq_le_sum_sq_div_card, Set.Icc_min_max, PredOrder.isPredLimit_of_mem_frontier, two_mul_le_add_sq, SetTheory.PGame.grundyValue_eq_iff_equiv_nim, interior_Ici, ENat.toENNReal_strictMono, Int.cast_le_neg_one_of_neg, FunctionField.inftyValuation.X_inv, Set.Icc_subset_Ico_union_Icc, LinOrd.hom_id, Set.Ioo_inter_Iio, CategoryTheory.Limits.MultispanIndex.toLinearOrderMultispanIso_hom_app, WithBot.le_of_forall_lt_iff_le, Set.Ioi_diff_Ici, Int.padicValuation_lt_one_iff, HahnSeries.single_zero_ofScientific, Filter.Tendsto.uIcc, Finset.set_encard_biUnion_le, Nat.floor_div_natCast, ENat.one_lt_card_iff_nontrivial, IsDedekindDomain.HeightOneSpectrum.intValuation_if_neg, Set.projIic_surjective, monotone_transfiniteIterate, invOf_pos, PNat.instIsOrderedCancelMonoid, NumberField.FinitePlace.embedding_apply, min_lt_min_left_iff, Ordinal.toNimber_symm_eq, IsDedekindDomain.HeightOneSpectrum.valuation_of_algebraMap, Set.disjoint_union_right, min_mul, nhds_basis_Icc_pos, nullMeasurableSet_Ioo, Valuation.Integers.isPrincipal_iff_exists_isGreatest, Set.encard_preimage_val_le_encard_left, nhds_basis_abs_sub_lt, Finset.one_le_mulConst_self, instWellQuasiOrderedLEOfWellFoundedLT, Set.strictMonoOn_projIic, inv_atTop₀, LinearOrderedCommGroupWithZero.inl_mul_inr_eq_coe_toLex, LaurentSeries.valuation_le_iff_coeff_lt_eq_zero, instIsDiscreteValuationRingSubtypeMemSubringIntegerWithZeroMultiplicativeIntValuation, Finpartition.IsEquipartition.card_biUnion_offDiag_le', OrderIso.isNormal, exists_seq_strictAnti_tendsto, CategoryTheory.Functor.WellOrderInductionData.Extension.map_zero, lowerSemicontinuous_iff_isClosed_preimage, Set.ordConnected_iff_uIcc_subset_left, lt_tsub_iff_right, NatOrdinal.toOrdinal_min, LaurentSeries.valuation_single_zpow, FiniteArchimedeanClass.mk_lt_mk, infPrime_iff_not_isMax, max_add_add_le_max_add_max, tendsto_fract_left', AbsoluteValue.abs_abv_sub_le_abv_sub, CauSeq.sup_idem, monovary_iff_mul_rearrangement, SetTheory.PGame.grundyValue_nim_add_nim, NNRat.instStarOrderedRing, Nimber.succ_def, sbtw_midpoint_of_ne, IsDedekindDomain.HeightOneSpectrum.intValuation_le_one, sameRay_or_ne_zero_and_sameRay_neg_iff_not_linearIndependent, le_iff_forall_rat_lt_imp_le, Affine.Simplex.wSameSide_affineSpan_faceOpposite_iff, smul_nonneg_iff_neg_imp_nonpos, Affine.Simplex.wOppSide_affineSpan_faceOpposite_point_right_iff, WeierstrassCurve.valuation_Δ_aux_eq_of_isIntegral, Nat.preimage_Iio, AEMeasurable.max, Finset.Nonempty.sup_eq_top_iff, MonomialOrder.degree_sub_le, Orientation.eq_or_eq_neg, IsNonarchimedean.apply_sum_le_sup_of_isNonarchimedean, le_of_toZ_le, Finset.inf'_lt_iff, CategoryTheory.TransfiniteCompositionOfShape.fac_assoc, Polynomial.exists_min_root, Hyperreal.infinitesimal_def, isPiSystem_Ioi, ContFract.convs_eq_convs', MeasureTheory.Filtration.rightCont_eq_self, min_mul_min_le_min_mul_mul', ArchimedeanClass.FiniteResidueField.mk_eq_zero, le_zero_iff, Finset.lubell_yamamoto_meshalkin_inequality_sum_card_div_choose, convexJoin_segments, Affine.Simplex.sign_signedInfDist_lineMap_incenter_touchpoint, Finset.Colex.toColex_lt_toColex_iff_max'_mem, Nat.measurable_floor, StieltjesFunction.measure_Ioo, EReal.sign_eq_and_abs_eq_iff_eq, starConvex_iff_ordConnected, Order.pred_injective, AddGroupSeminormClass.toNonnegHomClass, Valuation.Compatible.srel_iff_lt, one_lt_mabs, exists_pos_right_iff_sameRay, Finset.lt_sup'_iff, NNRat.cast_le, Valuation.IsEquiv.valuedCompletion_le_one_iff, antivaryOn_comm, codisjoint_inf_right, instAssociativeMax, AddMonoidAlgebra.Monic.supDegree_mul_of_ne_zero_right, MvPowerSeries.min_lexOrder_le, NNRat.floor_coe, Order.Ioo_eq_empty_iff_le_succ, mul_self_le_one_iff, Set.Iic_diff_Iio, OrderEmbedding.preimage_uIoc, CategoryTheory.Functor.WellOrderInductionData.surjective, Module.End.genEigenspace_directed, Valuation.isEquiv_iff_val_lt_val, Finset.subConst_le_addConst_sq, le_iff_forall_pos_le_add, lt_emultiplicity_of_lt_multiplicity, ENat.monotone_map_iff, mul_nonpos_iff_pos_imp_nonpos, InnerProductSpace.gramSchmidt_bot, Set.Ioc_subset_uIoc', Set.disjoint_singleton_right, Submodule.spanRank_toENat_eq_iInf_encard, nhdsWithin_uIcc_isMeasurablyGenerated, Set.neg_uIcc, SimpleGraph.hasse_preconnected_of_pred, max_lt_max_left_iff, variationOnFromTo.antitoneOn, Finset.sortedGT_sort, Finset.mem_uIcc', sign_nonneg_iff, min_abs_abs_le_abs_min, SimpleGraph.regularityReduced_adj, Hyperreal.coe_lt_omega, Finset.card_Ico_add_right, LinOrd.dual_map, nhds_basis_Ioo_one_lt, Pi.instNoMinOrderLexForallOfWellFoundedLTOfNonempty, OrderIso.sumLexIioIci_symm_apply_Ici, Finsupp.Lex.addLeftMono, Ioo_subset_closure_interior, Set.bounded_gt_inter_ge, AbsoluteValue.abs_isEuclidean, Zsqrtd.instIsStrictOrderedRingCastInt, pow_le_pow_iff_left, Finsupp.Lex.single_strictAnti, Valuation.isNontrivial_iff_exists_lt_one, ArchimedeanClass.mk_pow, abs_dvd_abs, ArchimedeanClass.isAddRegular_mk, nullMeasurableSet_Ioi, IsDedekindDomain.HeightOneSpectrum.instIsNontrivialWithZeroMultiplicativeIntValuation, Valuation.Integers.valuation_irreducible_lt_one, Finset.min_union, WithZeroTopology.nhds_zero_of_units, Set.Ico_subset_Icc_union_Ico, AddValuation.map_add', mem_nhdsGT_iff_exists_Ioc_subset, borel_eq_generateFrom_Ici, Topology.RelCWComplex.coe_skeletonLT, Num.cast_le, invOf_nonneg, Filter.tendsto_mabs_atTop_atTop, DistLat.dual_map, min_choice, BooleanAlgebra.sdiff_eq, strictConvex_Icc, antivary_iff_smul_rearrangement, Nonneg.mk_nnratCast, Set.Ioo_inter_Ioi, zpow_two_nonneg, GenContFract.succ_nth_fib_le_of_nth_den, Module.End.maxGenEigenspace_eq, one_le_mul_self_iff, List.coe_maximum_of_length_pos, Finset.Colex.le_iff_max'_mem, lt_inv_self_iff, ArchimedeanClass.mk_le_mk, NNRat.lt_def, exists_lub_Iio, Polynomial.div_tendsto_zero_iff_degree_lt, tendsto_floor_right_pure, MeasureTheory.aecover_Iio_of_Iic, Nat.preimage_Ici, upperSemicontinuousAt_iff_frequently, Finsupp.Colex.isStrictOrder, Int.padicValuation_eq_one_iff, smul_nonpos_iff, WithTop.untop₀_min, mabs_div_le, segment_eq_uIcc, Nat.count_le_setENCard, Nat.one_div_le_one_div, IsPreconnected.intermediate_value_Ioo, MvPowerSeries.le_weightedOrder_mul, FinBddDistLat.ofHom_apply, max_inv_one, Set.unbounded_gt_inter_gt, RootPairing.RootPositiveForm.zero_lt_posForm_iff, Finset.inf_sup_distrib_right, MvPolynomial.supDegree_esymmAlgHomMonomial, partialSups_add_one', ofDual_min, LinearOrderedField.lt_inducedMap_iff, Finset.max_sum_le, MvPolynomial.schwartz_zippel_totalDegree, isGLB_Ioi, Finset.max'_le_iff, Right.pow_lt_one_iff, isOpen_lt, PowerSeries.coeff_heval, continuousOn_fract, Cardinal.toENat_eq_zero, Affine.Simplex.sign_touchpointWeights_empty, HahnSeries.ofSuppBddBelow_zero, ProbabilityTheory.HasSubgaussianMGF.const_mul, Tropical.min_eq_add, StieltjesFunction.mono', MvPowerSeries.le_order_prod, CategoryTheory.Functor.WellOrderInductionData.sectionsMk_val_op_bot, BoundedLENhdsClass.of_closedIciTopology, MulArchimedeanClass.top_eq_mk_iff, Ioc_subset_biUnion_Ioc, OrderRingHom.apply_eq_self, Topology.CWComplex.iUnion_openCell_eq_skeletonLT, CategoryTheory.SmallObject.SuccStruct.Iteration.mkOfLimit.inductiveSystem_obj, Hyperreal.InfiniteNeg.lt_zero, Sym2.sortEquiv_apply_coe, Finset.orderIsoOfFin_symm_apply, tsub_pos_iff_lt, emultiplicity_lt_iff_not_dvd, Cardinal.toENat_eq_ofNat, CauSeq.const_lt, CanonicallyOrderedAdd.toOrderedSub, exists_nonneg_left_iff_sameRay, Valuation.Integers.map_le_one, emultiplicity_le_emultiplicity_of_dvd_right, InnerProductSpace.gramSchmidt_def, Orientation.map_eq_neg_iff_det_neg, neg_abs_le_neg, IsDedekindDomain.HeightOneSpectrum.intValuation_le_pow_iff_mem, Finset.mulConst_le_card, Int.preimage_Ioi, MonomialOrder.degree_reduce_lt, IsNonarchimedean.finset_image_add, tendsto_zero_iff_abs_tendsto_zero, Archimedean.embedReal_apply, Order.Ici_pred, Polynomial.abs_div_tendsto_atTop_of_degree_gt, IsDedekindDomain.HeightOneSpectrum.intValuation_singleton, Module.End.maxGenEigenspace_eq_genEigenspace_finrank, Ordinal.toNimber_min, emultiplicity_pos_of_dvd, CategoryTheory.TransfiniteCompositionOfShape.iic_isoBot, HahnEmbedding.Partial.archimedeanClassMk_eq_iff, exists_rat_gt, LinearOrderedCommGroup.Subgroup.genLTOne_lt_one, Module.End.mapsTo_genEigenspace_of_comm, HahnSeries.support_abs, ValuativeRel.ValueGroupWithZero.mk_pos, MonoidWithZeroHom.fst_mono, le_mabs, Odd.pow_nonneg_iff, Topology.IsUpper.isTopologicalBasis_insert_univ_subbasis, IsNonarchimedean.apply_natCast_le_one_of_isNonarchimedean, NNRat.cast_mono, PowerSeries.order_mul_ge, SimpleGraph.farFromTriangleFree_iff, Nat.lt_succ_floor, MonomialOrder.zero_le, Finset.Colex.lt_iff_exists_forall_lt, sbtw_iff_left_ne_and_right_mem_image_Ioi, FunctionField.instIsNontrivialRatFuncWithZeroMultiplicativeIntInftyValuation, MultilinearMap.map_piecewise_sub_map_piecewise, Set.notMem_Iic, ArchimedeanClass.mk_natCast, CategoryTheory.TransfiniteCompositionOfShape.ofArrowIso_isoBot, CategoryTheory.Limits.HasIterationOfShape.hasColimitsOfShape, Nat.ceil_eq_zero, BddDistLat.hom_id, Even.pow_nonneg, zpow_neg_two_nonneg, Int.floor_eq_zero_iff, MeasureTheory.meas_le_ae_eq_meas_lt, Set.uIoo_eq_union, AffineBasis.convexHull_eq_nonneg_coord, Even.zpow_abs, Nat.floor_sub_one, AffineSubspace.sSameSide_iff_exists_left, CauSeq.inf_comm, Fin.map_valEmbedding_uIcc, InitialSeg.isNormal, NNRat.coe_max, pos_add_self_iff, mfderivWithin_projIcc_one, ENat.forall_natCast_le_iff_le, WithBot.lt_add_one_iff, Finset.min'_le, Set.Infinite.exists_lt, Cardinal.ofENat_mono, tendsto_ceil_left_pure_ceil, measurable_lt, Valuation.ltAddSubgroup_monotone, Rat.padicValuation_self, apply_abs_le_mul_of_one_le, hasBasis_nhdsSet_Ici_Ioi, Polynomial.tendsto_atTop_iff_leadingCoeff_nonneg, Polynomial.IsDistinguishedAt.degree_eq_coe_lift_order_map, Set.encard_preimage_val_le_encard_right, apply_abs_le_mul_of_one_le', Set.Iio_inj, MeasureTheory.aecover_Ioo_of_Ioc, max_inv_inv', HahnEmbedding.Seed.baseEmbedding_strictMono, PNat.le_of_dvd, Mathlib.Meta.NormNum.isRat_lt_true, Mathlib.Tactic.Order.ToInt.toInt_nle_toInt, CategoryTheory.TransfiniteCompositionOfShape.ofOrderIso_incl, HasStrictFDerivAt.abs, PowerSeries.le_order_smul, convexHull_toCone_eq_sInf, le_iff_forall_one_lt_lt_mul', max_bot_left, CategoryTheory.TransfiniteCompositionOfShape.isWellOrderContinuous, Valued.isClopen_ball, frontier_Ici, tendsto_ceil_atTop, Finset.max_mono, NonemptyFinLinOrd.epi_iff_surjective, ValuativeRel.ValueGroupWithZero.embed_strictMono, AffineSubspace.wOppSide_iff_exists_wbtw, Valuation.IsEquiv.pos_iff, PNat.card_Icc, Fin.castSuccOrderEmb_toEmbedding, negPart_max, Set.monotone_projIic, List.mem_argmin_iff, exists_lt_mul_self, MonomialOrder.toSyn_strictMono, inf_sup_le, Function.locallyFinsuppWithin.nsmul_posPart, PowerSeries.order_finite_iff_ne_zero, Finset.Ico_diff_Ico_left, FiniteArchimedeanClass.val_mk, min_sub_sub_right, inf_sdiff_inf, Int.self_le_zpow_clog, Polynomial.isEquivalent_atTop_lead, Order.IsNormal.monotone, SimpleGraph.posSemidef_lapMatrix, le_sup_inf, Polynomial.le_trailingDegree_C, Finset.card_div_choose_le_card_shadow_div_choose, max_mul_min, mabs_zpow, MonomialOrder.div_single, LinearOrder.supConvergenceClass, LinOrd.hom_inv_apply, exists_isLocalExtr_Ioo, Polynomial.isLittleO_atTop_of_degree_lt, Set.unbounded_le_inter_le, Nimber.toOrdinal_max, BddDistLat.coe_id, Nonneg.segment_eq_uIcc, mabs_eq_mabs, Finset.Colex.mem_initSeg, abs_eq_max_neg, ArchimedeanClass.mk_add_lt_mk_left_iff, HeytAlg.hasForgetToLat_forget₂_obj_str, pow_two_nonneg, Tuple.monotone_proj, FiniteArchimedeanClass.mem_ballAddSubgroup_iff, Finset.mem_convexHull', MulArchimedeanClass.mk_eq_mk, MvPowerSeries.le_weightedOrder_prod, closure_uIoo, MeasureTheory.aecover_Ioc_of_Ioo, Set.indicator_le_indicator_nonneg, Finset.orderEmbOfFin_eq_orderEmbOfFin_iff, Hyperreal.infinite_abs_iff, div_neg_iff, Int.cast_min, intermediate_value_Icc', BddDistLat.ofHom_id, AffineSubspace.sOppSide_iff_exists_left, Tropical.untrop_max, Polynomial.abs_div_tendsto_atBot_atTop_of_degree_gt, Finsupp.disjoint_iff, measurableSet_Ico, Valuation.Integers.le_of_dvd, geom_sum_pos_iff, NumberField.FinitePlace.norm_embedding_eq, OrderRingIso.eq_refl, div_le_one_iff, GenContFract.abs_sub_convergents_le', isClosed_Ioc_iff, abs_sub_le, NNRat.num_pos, partialSups_add_one, AddMonoidAlgebra.supDegree_mem_range, FinBddDistLat.hom_inv_apply, eVariationOn.nonempty_monotone_mem, intermediate_value_Ioo', Polynomial.valuation_of_mk, Mathlib.Tactic.Qify.nnratCast_le, Valuation.leIdeal_map_algebraMap_eq_leSubmodule_min, isOpen_Ioo, Rat.intCast_le_cast, HeytAlg.hasForgetToLat_forget₂_obj_carrier, MulArchimedeanClass.mk_left_le_mk_mul_iff, Field.Emb.Cardinal.two_le_deg, RootPairing.exists_ge_zero_eq_rootForm, AbsoluteValue.isEquiv_iff_lt_one_iff, Int.le_ceil, MulArchimedeanClass.mem_subgroup_iff, AddSubmonoid.closure_image_isAddIndecomposable_baseOf, HahnSeries.order_mul, Nat.Prime.emultiplicity_le_emultiplicity_choose_add, tendsto_zpow_atTop_zero, Valuation.val_lt_one_iff, Quaternion.normSq_le_zero, MulArchimedeanClass.subsemigroup_strictAnti, Finset.local_lubell_yamamoto_meshalkin_inequality_div, abs_le, Set.preimage_add_const_uIcc, Odd.zpow_nonpos_iff, Int.fract_pos, oneLePart_min, Multiset.untrop_sum, GroupSeminormClass.toNonnegHomClass, strictConvex_uIcc, nhds_basis_zero_abs_lt, nhds_eq_iInf_abs_sub, Valuation.val_le_one_or_val_inv_le_one, himp_eq, Fin.natAddOrderEmb_toEmbedding, measurableSet_Iio, WithTop.tendsto_untop, Valuation.map_add_of_distinct_val, RootPairing.RootPositiveForm.posForm_apply_root_root_le_zero_iff, ArchimedeanClass.mk_left_le_mk_sub_iff, CauSeq.not_limZero_of_pos, ENat.map_natCast_strictMono, Nimber.toOrdinal_min, Polynomial.abs_div_tendsto_atTop_atTop_of_degree_gt, leOnePart_lt, Field.Emb.Cardinal.isLeast_leastExt, sub_half_lt_round, ValuativeRel.nonempty_orderIso_withZeroMul_int_iff, Finset.divConst_le_card, Finset.one_le_mulConst, LaurentSeries.inducing_coe, Set.Ioc_disjoint_Ioc, cmp_add_left, exists_isExtrOn_Ioo_of_tendsto, Ordinal.enum_le_enum', Set.Ioo_subset_Ioc_union_Ico, Valuation.map_add, Set.disjoint_left, ArchimedeanClass.mk_le_mk_smul, CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.ofComposableArrows_isColimit_desc, MulArchimedeanClass.mk_lt_mk, pred_min, div_le_inv_mul_iff, Set.disjoint_singleton_left, LaurentSeries.continuous_coe, PNat.factorMultiset_le_iff, convexJoin_segment_singleton, Finset.Colex.toColex_le_toColex_iff_max'_mem, min_eq_right_iff, HahnEmbedding.Partial.toOrderAddMonoidHom_apply, Set.disjoint_right, monovaryOn_comm, Valuation.HasExtension.val_map_lt_iff, PNat.tendsto_comp_val_iff, Order.IsNormal.ext, openSegment_eq_Ioo', cocompact_le_atTop, MvPowerSeries.lexOrder_def_of_ne_zero, MonomialOrder.degree_add_le, Valued.is_topological_valuation, exists_birkhoff_representation, CategoryTheory.TransfiniteCompositionOfShape.ici_F, HahnEmbedding.Seed.strictMono_coeff, abs_nnqsmul, interior_Iio, min_le_max, one_le_mul_mabs, Nat.floor_div_ofNat, Set.Ioi_diff_Ioi, negPart_pos_iff, isPiSystem_image_Ioi, AddMonoidAlgebra.supDegree_mul, Order.Iio_succ_eq_insert, IsValuativeTopology.isOpen_ball, NatOrdinal.succ_def, continuous_iff_lower_upperSemicontinuous, Topology.RelCWComplex.iUnion_openCell_eq_skeleton, convexJoin_singleton_segment, MvPowerSeries.le_weightedOrder_map, inf_sdiff_self_left, Hyperreal.not_infinite_iff_exist_lt_gt, AffineSubspace.wOppSide_self_iff, le_emultiplicity_map, Dense.Iio_eq_biUnion, ENNReal.bot_eq_zero, CauSeq.coe_sup, Stream'.Seq.length'_le_iff, Hyperreal.archimdeanClassMk_coe, Int.floor_lt, mul_nonneg_iff, IsAbsoluteValue.abs_isAbsoluteValue, Pi.toLex_update_lt_self_iff, Ideal.span_singleton_abs, Order.lt_succ_iff_eq_or_gt, max_div_min_eq_mabs, Field.Emb.Cardinal.succEquiv_coherence, hasDerivWithinAt_abs, NNRat.floor_cast, NNRat.coe_pos, FinBddDistLat.ext_iff, Cardinal.noMaxOrder, abs_sub, Sym2.inf_eq_inf_and_sup_eq_sup, Cardinal.ofENat_lt_aleph0, fn_min_add_fn_max, Hyperreal.tendsto_iff_forall, MvPowerSeries.nat_le_order, Valuation.one_lt_val_iff, Orientation.map_eq_iff_det_pos, smul_nonpos_iff_pos_imp_nonpos, archimedean_iff_nat_le, Mathlib.Meta.NormNum.isNNRat_abs_neg, SuccOrder.nhdsLE_eq_nhds, le_iff_forall_neg_add_le, HahnEmbedding.ArchimedeanStrata.ball_sup_stratum_eq, abs_inv, DFinsupp.lt_of_forall_lt_of_lt, generateFrom_Icc_mem_le_borel, Quaternion.normSq_nonneg, Nat.le_floor_iff', countable_setOf_isolated_right, OrderRingIso.subsingleton_right, Padic.norm_eq_zpow_log_mulValuation, mabs_mul_three, ENat.one_le_card_iff_nonempty, disjoint_sup_right, ValuationSubring.valuation_lt_one_or_eq_one, Set.uIcc_injective_right, Set.Icc_subset_Icc_union_Ioc, HahnSeries.instIsCancelMulZeroOfIsCancelAdd, Set.unbounded_lt_inter_le, PowerSeries.intValuation_eq_of_coe, Set.Ico_succ_succ_eq_Ioc, LocallyFiniteOrder.orderAddMonoidHom_bijective, HahnSeries.orderTop_mul_of_nonzero, Finset.max_pair, List.minimum_of_length_pos_le_of_mem, Nat.ceil_mono, Tuple.sort_eq_refl_iff_monotone, convexHull_add, Set.Ioo_add_one_right_eq_Ioc, Finset.divConst_le_mulConst_sq, FiniteMulArchimedeanClass.withTopOrderIso_apply_coe, WithTop.instBorelSpace, Finsupp.Lex.isStrictOrder, Finset.inf_sup, EReal.abs_mul_sign, Set.Iio_subset_Iic_iff, Finsupp.Colex.addRightMono, OrderEmbedding.coe_birkhoffFinset, PNat.lt_add_right, RootPairing.zero_lt_pairingIn_iff', Nat.preimage_floor_of_ne_zero, Set.Ioc_subset_Ioc_union_Icc, HahnEmbedding.Partial.isWF_support_evalCoeff, Set.projIci_eq_self, Set.antitone_setOf, Filter.Tendsto.abs, CategoryTheory.OrthogonalReflection.iteration_map_succ, HahnEmbedding.Partial.orderTop_eq_iff, Mathlib.Meta.Positivity.nonneg_of_isNNRat, CauSeq.mul_pos, Polynomial.tendsto_atBot_iff_leadingCoeff_nonpos, List.coe_le_maximum_iff, Mathlib.Tactic.ENatToNat.not_lt_top, Finset.lubell_yamamoto_meshalkin_inequality_sum_inv_choose, PNat.find_mono, Order.pred_le_iff_eq_or_le, Order.lt_succ_iff_eq_or_lt, Continuous.exists_forall_le_of_hasCompactSupport, Finset.inf_sup_distrib_left, ArchimedeanClass.top_eq_mk_iff, IsDedekindDomain.HeightOneSpectrum.equivHeightOneSpectrum_symm_apply, LowerSet.total_le, Finset.sups_infs_subset_left, OrderMonoidWithZeroHom.mul_comp, AddValuation.map_add_of_distinct_val, Nat.uIcc_eq_range', tendsto_ceil_right_pure_add_one, ENat.card_le_one_iff_subsingleton, Finset.sup'_inf_distrib_right, ArchimedeanClass.instIsOrderedAddMonoid, Hyperreal.isSt_iff_abs_sub_lt_delta, nhds_top_basis_Ici, Cardinal.toENat_lt_natCast_iff, abs_max_sub_max_le_abs, Finsupp.DegLex.single_lt_iff, Set.projIic_surjOn, LaurentSeries.val_le_one_iff_eq_coe, Filter.Tendsto.min_left, DistLat.ext_iff, ProbabilityTheory.Kernel.HasSubgaussianMGF.const_mul, DistLat.Iso.mk_inv, Polynomial.le_trailingDegree_monomial, Function.Periodic.image_uIcc, ContinuousOn.strictMonoOn_of_injOn_Icc', MonomialOrder.le_degree, Set.Iio_diff_Iio, nhds_basis_Icc_one_lt, Module.Basis.orientation_eq_iff_det_pos, sq_le_sq, List.sum_min_le, LinOrd.inv_hom_apply, max_lt_max_right_iff, ArchimedeanClass.mk_ofNat, mul_nonneg_iff_pos_imp_nonneg, Polynomial.degree_comp, Finset.pluennecke_ruzsa_inequality_nsmul_add, ADEInequality.lt_six, IsDedekindDomain.HeightOneSpectrum.valuation_exists_uniformizer, Finset.abs_sum_le_sum_abs, Finsupp.Colex.addRightStrictMono, Function.locallyFinsuppWithin.posPart_add, frontier_Ioi, Set.Finite.encard_lt_top, invOf_lt_zero, FloorRing.gc_ceil_coe, IsDiscreteValuationRing.isRankOneDiscrete, Set.image_neg_uIcc, instIsStrictOrderedRingNNRat, ENat.card_lt_top_of_finite, ENat.lift_one, apply_abs_le_add_of_nonneg, PredOrder.nhdsGE_eq_nhds, continuousWithinAt_iff_lower_upperSemicontinuousWithinAt, Submodule.inf_genEigenspace, abs_pow_eq_one, Int.ceil_eq_iff, FinBddDistLat.coe_id, ArchimedeanClass.mk_lt_mk, Set.disjoint_singleton, add_left_strictMono_of_ne_top, abs_neg_one_pow, neg_abs_le, oneLePart_eq_ite_lt, MvPowerSeries.nat_le_weightedOrder, Rat.toNNRat_lt_toNNRat_iff', upperBounds_Iio, Set.encard_union_le, MeasureTheory.aecover_Icc_of_Ioc, PrimeMultiset.prod_dvd_iff', ValuativeExtension.mapValueGroupWithZero_strictMono, borel_eq_generateFrom_Icc, Module.End.genEigenspace_top_eq_maxUnifEigenspaceIndex, Set.encard_strictMono, Polynomial.trailingDegree_le_trailingDegree, IsDedekindDomain.HeightOneSpectrum.adicCompletionIntegers.integers, Ordinal.toNatOrdinal_min, exists_wellOrder, unitInterval.symm_projIcc, Rat.preimage_cast_Ioi, cocompact_eq_atTop, ArchimedeanClass.FiniteElement.not_isUnit_iff_mk_pos, exists_lt_add_iff_lt_left, Hyperreal.archimedeanClassMk_neg_of_tendsto_atBot, HahnSeries.order_single_mul_of_isRegular, Polynomial.abs_tendsto_atTop_iff, Order.Ideal.coe_sup_eq, Finset.min_le, Finset.infs_sups_subset_right, Cardinal.toENat_lift, PNat.Ico_eq_finset_subtype, CategoryTheory.SmallObject.SuccStruct.restrictionLTOfCoconeIso_inv_app, hasDerivAt_iff_tendsto_slope_left_right, Finset.inf'_sup_distrib_right, MeasureTheory.stoppedProcess_eq_stoppedValue_apply, sign_zero, Function.Lex.wellFoundedLT, min_le_iff, disjoint_partialSups_right, tendsto_floor_right_pure_floor, Finset.Ioc_sub_one_left_eq_Icc, IsOpen.exists_Ioo_subset, CauSeq.bounded', CauSeq.add_pos, convexHull_basis_eq_stdSimplex, Hyperreal.isSt_sSup, Filter.tendsto_const_mul_atBot_iff, Field.Emb.Cardinal.noMaxOrder_rank_toType, Order.Ioo_pred_left, Set.biUnion_Ico_eq_Iio_self_iff, Convex.radon_partition, Finset.Ico_add_one_left_eq_Ioo, Units.orderEmbeddingVal_apply, Continuous.exists_forall_ge_of_hasCompactSupport, HahnSeries.SummableFamily.hsum_powerSeriesFamily_mul, NNRat.one_le_cast, Finset.max'_subset, List.minimum_append, FinBddDistLat.inv_hom_apply, Set.preimage_mul_const_uIcc, max_add_add_left, PosSMulMono.nnrat_of_rat, List.le_maximum_of_length_pos_of_mem, MeasureTheory.aecover_Ioc_of_Icc, OrderMonoidIso.withZeroUnits_symm_apply, ENat.add_one_le_iff, Set.Ioi_inj, ArchimedeanClass.orderHom_zero, Int.preimage_Iio, FunctionField.valuedFqtInfty.def, Polynomial.exists_max_root, Int.floor_le_iff, Rat.preimage_cast_Icc, LinOrd.Iso.mk_hom, Set.Ico_subset_Ico_union_Ico, Finset.prod_sub_ordered, MonoidWithZeroHom.inl_strictMono, PowerSeries.heval_apply, ENat.instOrderTopology, generateFrom_Ico_mem_le_borel, units_smul_eq_self_iff, NormedSpace.normalize_smul, MvPowerSeries.one_le_order_iff_constCoeff_eq_zero, Nonneg.coe_nnratCast, Multiset.toFinsupp_union, sign_mul_abs, HahnSeries.addVal_le_of_coeff_ne_zero, Set.Icc_pred_right_eq_Ico, SimpleGraph.farFromTriangleFree.le_card_sub_card, min_eq_iff, Set.Ici_subset_Icc_union_Ici, Finset.sup_inf_distrib_left, WithBot.ge_of_forall_gt_iff_ge, max_top_right, Affine.Simplex.ExcenterExists.sign_signedInfDist_touchpoint, nhdsGT_basis, MulArchimedeanClass.liftOrderHom_mk, ArchimedeanClass.mem_ball_iff, Finset.max_eq_sup_coe, PNat.sub_coe, SimpleGraph.isUniform_singleton, IsNonarchimedean.multiset_image_add_of_nonempty, Int.floor_le_sub_one_iff, abs_mul, OrderMonoidIso.withZeroUnits_apply, CategoryTheory.TransfiniteCompositionOfShape.ofComposableArrows_F, Cardinal.toENat_le_ofNat, Asymptotics.isEquivalent_nat_ceil, InverseSystem.PEquivOn.nat, units_smul_eq_neg_iff, isPiSystem_Ioc, nonempty_orderEmbedding_of_finite_infinite, abs_one_div, Profinite.NobelingProof.Products.eval_eq, succ_min, ArchimedeanClass.mk_monotoneOn, isCompact_uIcc, WithBot.succ_eq_bot, Int.floor_nonneg, Valuation.IsEquiv.one_lt_iff_one_lt, ArchimedeanClass.mk_sub_lt_mk_right_iff, Polynomial.div_tendsto_atBot_zero_of_degree_lt, Filter.Tendsto.max, DistLat.hom_id, Order.pred_top_le_iff, IsDedekindDomain.HeightOneSpectrum.intValuation_le_pow_iff_dvd, Set.ncard_uIcc_nat, Iio_mem_nhdsSet_Iic_iff, Finset.max'_pair, PNat.addLeftReflectLT, max_one_div_max_inv_one_eq_self, abs_sub_le_iff, finBddDistLat_dual_comp_forget_to_bddDistLat, max_sub_sub_left, abs_div, nhdsWithinLE_sup_nhdsWithinGT, midpoint_le_right, Set.projIic_coe, GenContFract.IntFractPair.nth_stream_fr_lt_one, AddGroupCone.nonneg.hasMemOrNegMem, SMulPosMono.toSMulPosReflectLT, Set.unbounded_inter_ge, covBy_iff_lt_iff_le_left, LipschitzWith.projIcc, min_lt_iff, Set.image_div_const_uIcc, abs_sub_round_div_natCast_eq, MvPowerSeries.le_weightedOrder_pow, Ordinal.toType_noMax_of_succ_lt, RootPairing.zero_lt_pairingIn_iff, IsDedekindDomain.HeightOneSpectrum.valuation_def, le_emultiplicity_of_le_multiplicity, Order.Ioi_pred, Polynomial.abs_tendsto_atTop, MvPolynomial.leadingCoeff_esymmAlgHomMonomial, CategoryTheory.Limits.MultispanIndex.toLinearOrder_fst, MeasureTheory.Measure.pi_prod_map_IocProdIoc, Set.Ioi_subset_Ioc_union_Ioi, Rat.cast_min, lineMap_lt_right_iff_lt_one, Finset.uIcc_injective_right, tendsto_fract_right', Set.vadd_Icc, ValuationClass.map_add_le_max, Matrix.IsIrreducible.nonneg, closure_uIoc, sign_pos, isPiSystem_Ico_mem, smul_min_of_nonneg, Set.Ioo_min_max, IsCompact.exists_isLUB, ValuationSubring.valuation_le_one, CategoryTheory.Limits.MultispanIndex.toLinearOrder_snd, PNat.natPred_monotone, SuccOrder.nhds_eq_pure, PowerSeries.le_order_map, Affine.Simplex.wSameSide_affineSpan_faceOpposite_point_left_iff, toDual_max, CategoryTheory.Limits.instHasIterationOfShapeElemIic, lineMap_le_lineMap_iff_of_lt', inv_le_self_iff, monovaryOn_iff_forall_smul_nonneg, Finset.dens_le_one, ArchimedeanClass.FiniteElement.mk_intCast, distLat_dual_comp_forget_to_Lat, Int.ceil_eq_zero_iff, max_add_min, Finset.le_prod_max_one, CategoryTheory.TransfiniteCompositionOfShape.iic_isColimit, HahnEmbedding.IsPartial.strictMono, MonomialOrder.lex_lt_iff_of_unique, emultiplicity_le_emultiplicity_iff, Finset.le_max_of_eq, max_min_distrib_left, isLocallyClosed_Ico, frontier_lt_subset_eq, add_min, not_bddBelow_iff, Fin.preimage_val_uIcc_val, Nat.floor_natCast, iUnion_Icc_intCast, Set.coe_projIci, MvPowerSeries.min_weightedOrder_le_add, SignType.neg_one_lt_one, Set.eq_empty_or_encard_eq_top_or_encard_diff_singleton_lt, max_div_min_eq_mabs', Nat.one_le_floor_iff, PNat.ofNat_lt_ofNat, RootPairing.zero_le_rootForm, ZNum.isOrderedAddMonoid, Dense.exists_le', MonomialOrder.degLex_le_iff, fn_max_add_fn_min, Filter.tendsto_zpow_atTop_atTop, Set.Ico_inter_Ico, instMulArchimedeanNNRat, tendsto_PNat_val_atTop_atTop, Tuple.graphEquiv₂_apply, denselyOrdered_units_iff, Nat.measurable_ceil, FinBddDistLat.forget_map, HahnSeries.cardSuppLTSubfield_carrier, AffineSubspace.wOppSide_iff_exists_left, OrderIso.withZeroUnits_symm_apply, max_zero_add_max_neg_zero_eq_abs_self, Finset.sup'_pow, ENat.eq_top_iff_forall_gt, Finset.coe_orderIsoOfFin_apply, NNRat.coe_lt_coe, Valuation.nonempty_rankOne_iff_mulArchimedean, QuadraticMap.toBilin_apply, Order.Ideal.IsMaximal.isPrime, MulArchimedeanClass.min_le_mk_mul, atBot_atTop_le_cocompact, tendsto_floor_atTop, MonomialOrder.bot_eq_zero, Function.support_min, Set.ordConnected_iff_disjoint_Ioo_empty, Function.locallyFinsuppWithin.instIsOrderedAddMonoid, ValuativeRel.IsDiscrete.has_maximal_element, Int.floor_mono, ArchimedeanClass.mk_add_lt_mk_right_iff, LinearMap.finrank_genEigenspace_le, FunctionField.InftyValuation.map_add_le_max', MulArchimedeanClass.mem_closedBallSubgroup_iff, FiniteMulArchimedeanClass.mem_ballSubgroup_iff, Finsupp.lt_of_forall_lt_of_lt, Polynomial.natDegree_sum_eq_of_disjoint, WithTop.isOpenEmbedding_coe, inv_mabs_le, MonomialOrder.toSyn_lt_iff_ne_zero, Mathlib.Tactic.Order.ToInt.toInt_inf_toInt_eq_toInt, tendsto_inv_nhdsGT_zero, abs_sub_lt_iff, HasFDerivAt.abs, supPrime_iff_not_isMin, ArchimedeanClass.stdPart_eq_sInf, AffineSubspace.setOf_wOppSide_eq_image2, iUnion_Ioc_add_intCast, LinearOrderedField.cutMap_coe, AbsoluteValue.abs_apply, Finset.sup'_lt_iff, Hyperreal.stdPart_coe, HasFDerivWithinAt.abs, NatOrdinal.toOrdinal_max, Odd.pow_neg_iff, OrderEmbedding.birkhoffSet_inf, Nonneg.instNontrivialSubtypeLeOfNatOfAddLeftMono, Filter.Tendsto.max_right, DistLat.forget_map, Module.End.iSup_genEigenspace_eq, smul_max_of_nonneg, projIcc_eq_one, HasSSubset.SSubset.lt, Hyperreal.infinitePos_iff_infinite_and_pos, Finset.lt_fold_min, strictConvex_Ioo, Set.sup_eq_union, ArchimedeanClass.ballAddSubgroup_top, LaurentSeries.exists_ratFunc_val_lt, sameRay_smul_left_iff, AffineSubspace.wSameSide_and_wOppSide_iff, min_top_left, List.exists_map_eq_of_sorted_nonempty_iff_sbtw, Int.lt_floor_add_one, Multiset.Ico_filter_lt, LinOrd.id_apply, BddDistLat.coe_comp, Module.End.genEigenspace_inf_le_add, interior_Icc, FiniteArchimedeanClass.liftOrderHom_mk, Finset.addConst_le_subConst_sq, Field.Emb.Cardinal.instIsSeparableSubtypeMemIntermediateFieldAdjoinImageToTypeOrdRankCompCoeBasisWellOrderedBasisLeastExtIioSingletonSet, HahnSeries.embDomainOrderEmbedding_apply, ArchimedeanClass.mk_map_nonneg_of_archimedean, Finset.subset_range_sup_succ, LinearOrderedCommMonoidWithZero.toIsOrderedMonoid, ENat.coe_toNat_le_self, Finset.disjSups_left_comm, Set.IicExtend_apply, Module.End.eigenspace_le_genEigenspace, LocallyFiniteOrder.orderAddMonoidHom_strictMono, Order.isGLB_Ioi_iff_isPredPrelimit, Multiset.toFinsupp_inter, FiniteMulArchimedeanClass.mem_closedBallSubgroup_iff, Valued.hasBasis_nhds_zero, Finset.supIndep_iff_pairwiseDisjoint, MonomialOrder.degree_le_iff, ArchimedeanClass.FiniteResidueField.ofArchimedean_inj, Affine.Simplex.wOppSide_affineSpan_faceOpposite_iff, Set.indicator_nonpos_le_indicator, abs_sq, Hyperreal.epsilon_lt_pos, abs_lt_iff_mul_self_lt, NonemptyFinLinOrd.hom_comp, Hyperreal.coe_nonneg, Finset.isGreatest_max', GenContFract.zero_le_of_den, Nat.cast_finsetSup', OrderIso.sumLexIioIci_symm_apply_Iio, Finset.fold_max_add, HahnEmbedding.ArchimedeanStrata.disjoint_ball_stratum, lowerSemicontinuous_iff_frequently, comap_mabs_nhds_one, HahnEmbedding.ArchimedeanStrata.archimedeanClassMk_of_mem_stratum, PUnit.isOrderedCancelAddMonoid, WithTop.continuous_coe, smul_min_of_nonpos, Nat.one_div_cast_pos, Set.Ioc_subset_Ioc_union_Ioc, Finset.Ico_inter_Ico, Padic.mulValuation_toFun, Finset.uIcc_subset_uIcc_iff_le, Order.pred_le_pred_iff, zpow_two_pos_of_ne_zero, SimpleGraph.FarFromTriangleFree.nonpos, Finset.inf'_pow, IsDedekindDomain.HeightOneSpectrum.valuation_div_le_one_iff, CategoryTheory.SmallObject.SuccStruct.Iteration.mkOfLimit.inductiveSystem_map, Cardinal.one_le_ofENat, Int.sub_one_lt_floor, Set.projIci_surjective, Ideal.height_le_spanRank_toENat_of_mem_minimal_primes, ArchimedeanClass.stdPart_map_real, Finset.prod_one_add_ordered, Tropical.add_eq_left_iff, instModuleFinite, Hyperreal.infinitePos_iff_infinitesimal_inv_pos, IsValuativeTopology.mem_nhds_iff', HahnEmbedding.IsPartial.truncLT_mem_range, IsDedekindDomain.HeightOneSpectrum.valuation_lt_one_iff_dvd, NNRat.cast_nonneg, SignType.not_one_lt, ContinuousOn.strictMonoOn_of_injOn_Ioo, LinOrd.ofHom_id, WithZero.withZeroUnitsEquiv_symm_strictMono, iUnion_Ico_add_intCast, mapClusterPt_rightLim, Affine.Simplex.wSameSide_affineSpan_faceOpposite_point_right_iff, AffineMap.lineMap_mono, isLUB_Iio, Nat.cast_max, Set.Icc_succ_pred_eq_Ioo, IsDedekindDomain.HeightOneSpectrum.intValuation.map_add_le_max', exists_isLocalExtr_Ioo_of_tendsto, Set.right_mem_uIoc, ENat.epow_right_mono, Finsupp.Colex.wellFoundedLT_of_finite, Rat.cast_lt_natCast, LinearOrderedAddCommGroupWithTop.neg_pos, min_one, WithBot.coe_min, Valuation.isEquiv_iff_val_le_one, Padic.comap_mulValuation_eq_padicValuation, CategoryTheory.SmallObject.SuccStruct.Iteration.obj_bot, Set.exists_min_image, disjointed_add_one, Polynomial.abs_tendsto_atBot_iff, DivisibleHull.instIsStrictOrderedModuleNNRat, Filter.tendsto_const_mul_pow_atTop_iff, Order.pred_lt_iff_eq_or_lt, PowerSeries.le_order_mul, Finset.disjoint_sup_left, wellQuasiOrderedLE_iff_wellFoundedLT, Set.image_sub_const_uIcc, Mathlib.Meta.NormNum.IsNat.natCeil, Set.sups_infs_subset_left, NumberField.FinitePlace.norm_lt_one_iff_mem, posSMulStrictMono_iff_PosSMulReflectLE, lowerSemicontinuous_iff_isClosed_epigraph, hasBasis_nhdsSet_Iic_Iic, PNat.find_le_iff, CategoryTheory.instIsCardinalFilteredToTypeOrd, Valuation.Integers.not_denselyOrdered_of_isPrincipalIdealRing, isCompact_Ioo_iff, Module.Basis.orientation_eq_or_eq_neg, tendsto_ceil_right_pure_floor_add_one, Rat.preimage_cast_Ico, Set.Ioc_subset_uIoc, quasiconvexOn_iff_le_max, HahnSeries.order_abs, Set.encard_lt_top_iff, Valuation.HasExtension.val_map_le_one_iff, AddCircle.equivIccQuot_comp_mk_eq_toIocMod, sup_inf_right, le_iff_forall_pos_lt_add', Valuation.map_sub, Hyperreal.coe_pos, Rat.valuation_le_one_iff_den, supIrred_iff_not_isMin, PosSMulReflectLT.toPosSMulMono, EReal.sign_mul, Hyperreal.archimedeanClassMk_neg_of_tendsto_atTop, MulArchimedeanClass.mk_mul_lt_mk_left_iff, min_mul_distrib', Tropical.trop_min, Nat.floor_div_eq_div, Valuation.mem_valuationSubring_iff, Rat.cast_max, Complementeds.codisjoint_coe, LinearOrderedAddCommGroupWithTop.sub_left_strictMono_of_ne_top, List.argmax_cons, Set.IicExtend_coe, tendsto_ceil_left, continuousWithinAt_iff_continuous_left'_right', ArchimedeanClass.mk_natCast_nonneg, Finset.orderEmbOfFin_zero, WithZero.le_max_iff, Set.encard_le_card, SimpleGraph.hasse_preconnected_of_succ, segment_eq_Icc', latticeClosure_prod, Order.PartialIso.exists_across, ProbabilityTheory.Kernel.partialTraj_le_def, NNRat.nonpos_iff_eq_zero, leOnePart_eq_ite_lt, Ioc_subset_closure_interior, Valuation.Integers.isIntegral_iff_v_le_one, partialSups_succ, Set.monotoneOn_or_antitoneOn_iff_uIcc, sbtw_iff_right_ne_and_left_mem_image_Ioi, ArchimedeanClass.mk_right_le_mk_sub_iff, upperSemicontinuous_iff_frequently, tendsto_pow_div_pow_atTop_zero, Multiset.max_sum_le, IsCauSeq.bounded, Set.not_disjoint_iff_nonempty_inter, Valuation.Integers.isPrincipalIdealRing_iff_not_denselyOrdered, isOpen_Iio, PNat.factorMultiset_gcd, WeierstrassCurve.isGoodReduction_iff, max_idem, Rat.toNNRat_lt_toNNRat_iff_of_nonneg, nhds_basis_Ioo_pos, nullMeasurableSet_le, min_div_div_left', NNRat.preimage_cast_Iic, BooleanAlgebra.inf_compl_le_bot, ArchimedeanClass.FiniteResidueField.ofArchimedean_injective, HasProd.abs, lineMap_le_left_iff_nonpos, Finset.exists_max_image, lt_tsub_comm, Set.Finite.encard_lt_encard, EReal.sign_coe, AddCircle.continuous_equivIoc_symm, Ordinal.toNatOrdinal_one, Affine.Simplex.sign_excenterWeights_singleton_neg, NonemptyFinLinOrd.Iso.mk_inv, SSet.stdSimplex.nonDegenerateEquiv_apply_apply, Rat.cast_lt_intCast, Continuous.abs, Valuation.RankOne.strictMono, tendsto_inv_atBot_nhdsLT_zero, Nat.floor_lt', Valuation.Integers.le_iff_dvd, SimpleGraph.IsUniform.pos, CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.instIsIsoAppIncl, Set.uIoc_subset_uIcc, self_dvd_abs, four_mul_le_sq_add, ContinuousOn.surjOn_uIcc, Set.Icc_diff_pi_univ_Ioc_subset, LaurentSeries.exists_Polynomial_intValuation_lt, LinearOrderedAddCommGroupWithTop.top_pos, Hyperreal.infiniteNeg_iff_infinite_and_neg, MonomialOrder.degree_sum_le, tendsto_ceil_atBot, inf_Prop_eq, PNat.card_fintype_uIcc, sdiff_eq, Max.left_comm, Ioc_diff_botSet, round_le, LinearOrderedCommGroup.wellFoundedOn_setOf_ge_gt_iff_nonempty_discrete, LinearOrderedField.inducedOrderRingHom_toFun, ValuationSubring.valuation_le_one_iff, abs_sub_round_eq_min, Field.Emb.Cardinal.strictMono_leastExt, NNRat.natCast_le_cast, ArchimedeanClass.mk_zero, intermediate_value_uIcc, Finset.Ioc_inter_Ioc, Finset.max'_eq_sup', Set.image_mul_const_uIcc, CategoryTheory.TransfiniteCompositionOfShape.map_isoBot, Set.Ioc_diff_Iic, mem_segment_iff_sameRay, Set.exists_max_image, Set.disjoint_insert_left, tsub_eq_tsub_min, IsDedekindDomain.HeightOneSpectrum.valuedAdicCompletion_eq_valuation', mem_extremePoints_iff_forall_segment, Nat.preimage_ceil_of_ne_zero, Orientation.map_eq_det_inv_smul, PNat.map_subtype_embedding_Icc, MeasureTheory.integrable_iff_integrableAtFilter_atBot_atTop, HahnSeries.orderTop_le_of_coeff_ne_zero, Finset.Ioi_sub_one_eq_Ici, Order.exists_orderEmbedding_insert, NNRat.coe_ceil, Hyperreal.lt_of_tendsto_atTop, NNRat.preimage_cast_Ioi, Rat.natCast_le_cast, isCompact_Ioc_iff, Finset.nonneg_addConst, Set.exists_lower_bound_image, lowerSemicontinuousOn_iff_isClosed_epigraph, mabs_mem_iff, OrderType.type_eq_type, toIcoDiv_zero_one, concaveOn_iff_div, lt_add_iff_lt_left_or_exists_lt, Dense.exists_ge', Set.uIcc_subset_uIcc_union_uIcc, grade_le_grade_iff, Tropical.add_eq_iff, DistLat.id_apply, AEMeasurable.min, ValuationSubring.instIsScalarTowerSubtypeMemValuationSubringWithZeroMultiplicativeInt, continuous_min, max_eq_top, Set.Iic_diff_Ioc, Int.orderedSMul, Valuation.map_add_le_max', inf_sdiff_self_right, minimal_iff_isLeast, add_abs_nonneg, inv_nhdsGT_zero, Rat.cast_lt, Finset.Ioc_sub_one_right_eq_Ioo, Finset.Icc_succ_pred_eq_Ioo, Hyperreal.archimedeanClassMk_pos_of_tendsto, Finsupp.DegLex.single_antitone, PNat.uIcc_eq_finset_subtype, WithTop.pred_eq_top, Finsupp.Lex.single_lt_iff, Nimber.add_nat, Complementeds.coe_inf, RootPairing.posRootForm_posForm_pos_of_ne_zero, tendsto_abs_nhdsNE_zero, monovary_iff_forall_smul_nonneg, exists_isExtrOn_uIoo_of_tendsto, closure_openSegment, Affine.Simplex.ExcenterExists.sign_signedInfDist_lineMap_excenter_touchpoint, min_add_add_right, SimpleGraph.nonuniformWitnesses_spec, Polynomial.isBigO_atBot_of_degree_le, CategoryTheory.TransfiniteCompositionOfShape.fac, Finset.prod_add_ordered, lt_abs, Set.not_monotoneOn_not_antitoneOn_iff_exists_le_le, Finset.dens_strictMono, eventually_nhdsWithin_sign_eq_of_deriv_neg, Rat.preimage_cast_uIcc, OrderRingIso.subsingleton_left, exists_abs_lt, LinearOrderedAddCommGroupWithTop.strictMono_add_left_of_ne_top, borel_eq_generateFrom_Ioc, Valued.isClosed_ball, BddDistLat.forget_map, covBy_iff_le_iff_lt_left, WithZero.exists_ne_zero_and_le_and_le, Tuple.self_comp_sort, max_div_div_left', StieltjesFunction.measurableSet_Ioi, Finset.Ioo_succ_right_eq_Ioc, List.sortedLE_insertionSort, IsCompact.bddAbove, Set.bounded_ge_inter_ge, Even.pow_pos, sup_sdiff_inf, le_abs, sameRay_smul_left_iff_of_ne, Finset.Colex.ofColex_top, IicProdIoc_def, PNat.ofNat_le_ofNat, Finset.orderEmbOfFin_last, strictConvex_Iio, HahnSeries.order_mul_of_nonzero, Set.lt_eq_ssubset, List.exists_map_eq_of_sorted_nonempty_iff_wbtw, FiniteMulArchimedeanClass.withTopOrderIso_symm_apply, FiniteArchimedeanClass.mem_closedBallAddSubgroup_iff, OrderHomClass.to_lattice_hom_apply, not_bddAbove_iff_isCofinal, Int.cast_max, Set.Icc_diff_pi_univ_Ioo_subset, PseudoMetric.IsUltra.isTransitiveRel_ball, HahnModule.coeff_smul_order_add_order, Module.Basis.orientation_ne_iff_eq_neg, Valuation.srel_iff_lt, abs_mul_sign, MeasureTheory.Measure.pi_prod_map_IicProdIoc, Set.iUnion_Ico_eq_Iio_self_iff, LinearOrderedAddCommGroup.discrete_iff_not_denselyOrdered, MulArchimedeanOrder.instTotalLe, ENat.natCast_lt_succ, upperSemicontinuousOn_iff_preimage_Iio, FiniteArchimedeanClass.mem_ball_iff, not_isCofinal_iff_bddAbove, PNat.equivNonZeroDivisorsNat_symm_apply_coe, grade_eq_grade_iff, WithZero.exists_ne_zero_and_lt_and_lt, CategoryTheory.TransfiniteCompositionOfShape.map_isColimit, PowerSeries.one_le_order_iff_constCoeff_eq_zero, continuousAt_iff_continuous_left'_right', abs_by_cases, IsCoprime.abs_right, OrderIso.subsingleton_of_wellFoundedGT', Profinite.NobelingProof.Products.eval_πs_image', MulArchimedeanClass.mk_le_mk_iff_lt, Filter.tendsto_mabs_atBot_atTop, OrderIso.sumLexIicIoi_symm_apply_Iic, Nat.succPNat_lt_succPNat, HahnSeries.SummableFamily.powerSeriesFamily_hsum_zero, HahnSeries.archimedeanClassMk_eq_archimedeanClassMk_iff, LinearOrderedAddCommGroupWithTop.add_lt_top, Affine.Simplex.face_points, min_max_distrib_right, Filter.tendsto_abs_atBot_atTop, Finset.range_orderEmbOfFin, tendsto_nat_floor_div_atTop, Units.mem_posSubgroup, FiniteMulArchimedeanClass.liftOrderHom_mk, fn_min_mul_fn_max, Int.abs_fract, tendsto_inv_atTop_nhdsGT_zero, Filter.comap_abs_atTop, Tropical.trop_sup_def, ValuativeRel.ValueGroupWithZero.mk_lt_mk, ENat.toENNRealOrderEmbedding_apply, NNRat.natCast_lt_cast, monovaryOn_iff_exists_monotoneOn, strictConvex_iff_convex, intermediate_value_Ioo, Set.Ioc_pred_right_eq_Ioo, DivisibleHull.mk_le_mk, max_le_iff, one_lt_div_iff, Continuous.bddBelow_range_of_hasCompactSupport, HurwitzZeta.hasSum_int_completedHurwitzZetaOdd, CategoryTheory.SimplicialThickening.functor_map, Polynomial.degree_sum_le, MonomialOrder.degree_mul_lt_iff_left_lt_of_ne_zero, Field.Emb.Cardinal.equivSucc_coherence, NNRat.cast_le_one, Finset.Iio_add_one_eq_Iic, Finset.sup_eq_top_iff, LinearOrderedCommGroupWithZero.inl_eq_coe_inlₗ, Nat.emultiplicity_two_factorial_lt, convexJoin_assoc, MonomialOrder.degree_smul_le, Rat.comap_cast_atBot, max_eq_left_iff, Finset.Colex.lt_iff_exists_filter_lt, Polynomial.cyclotomic_pos_and_nonneg, max_lt_iff, Set.Ioc_sub_one_right_eq_Ioo, le_emultiplicity_of_pow_dvd, Finset.orderEmbOfFin_singleton, IsDedekindDomain.HeightOneSpectrum.intValuation.le_max_iff_min_le, Tuple.antitone_pair_of_not_sorted, tendsto_inv_atBot_zero, ContinuousOn.upperSemicontinuousOn, MvPolynomial.weightedTotalDegree_eq_zero_iff, nhdsLT_sup_nhdsGE, Multiset.trop_inf, IsNonarchimedean.nmul_le, Finset.inf_eq_bot_iff, right_mem_openSegment_iff, Finset.Icc_sub_one_right_eq_Ico, sup_inf_left, Order.isSuccLimitRecOn_succ, antivaryOn_iff_exists_monotoneOn_antitoneOn, HahnSeries.leadingCoeff_pos_iff, abs_max_sub_max_le_max, MeasureTheory.stoppedValue_stoppedProcess_apply, countable_image_lt_image_Iio_within, CategoryTheory.Limits.MultispanShape.ofLinearOrder_L, MvPowerSeries.le_weightedOrder_smul, Finset.sup_inf_distrib_right, Polynomial.isBigO_of_degree_le, lt_subset_interior_le, Finset.pluennecke_ruzsa_inequality_pow_div_pow_mul, HahnSeries.instNoZeroDivisors, HasCountableSeparatingOn.range_Ioi, IsDedekindDomain.HeightOneSpectrum.valuation_of_mk', HasCountableSeparatingOn.range_Iio, toDual_min, untrop_sum, HahnSeries.leadingCoeff_mul_of_ne_zero, Set.Ioo_subset_uIoo, isLocallyClosed_Ioc, Finset.Ioc_sub_one_sub_one_eq_Ico, not_linearIndependent_iffₒₛ, Multiset.exists_max_image, ArchimedeanClass.mk_abs, ArchimedeanClass.min_le_mk_add, HahnSeries.order_le_of_coeff_ne_zero, Polynomial.le_trailingDegree_mul, Finset.addConst_le_card, div_nonpos_iff, sameRay_of_mem_orbit, Units.inv_pos, Set.Ioi_sub_one_eq_Ici, ArchimedeanClass.mk_le_mk_iff_lt, tendsto_floor_right, Hyperreal.infinitePos_abs_iff_infinite_abs, WithVal.lt_def, Order.isNormal_iff_strictMono_and_continuous, WithTop.ge_of_forall_gt_iff_ge, PNat.factorMultiset_le_iff', antivary_iff_exists_monotone_antitone, Set.bounded_gt_inter_gt, HahnSeries.order_ofForallLtEqZero, Set.powersetCard.ofFinEmbEquiv_symm_apply, one_min, IsValuativeTopology.mem_nhds_zero_iff, max_add_add_right, Finset.one_le_divConst, abs_mul_self, HahnSeries.coeff_mul_order_add_order, HahnEmbedding.Partial.eval_smul, fn_max_mul_fn_min, nsmul_le_nsmul_iff_right, min_idem, Order.Ico_succ_right, Int.le_ceil_iff, Finset.Iic_pred_eq_Iio, MulArchimedeanClass.mk_antitoneOn, MulArchimedeanClass.mk_monotoneOn, Nat.ceil_le_floor_add_one, Tropical.untrop_add, MonomialOrder.degree_mul_le, NNRat.preimage_cast_uIcc, Valuation.apply_posSubmonoid_pos, hasStrictDerivAt_abs, one_le_sq_iff_one_le_abs, Valuation.one_srel_iff, Pi.Colex.isStrictOrder, midpoint_le_left, RatFunc.valuation_eq_LaurentSeries_valuation, CategoryTheory.SmallObject.ιFunctorObj_eq, monovary_iff_smul_rearrangement, List.minimum_cons, sum_Ioo_inv_sq_le, negPart_eq_ite, Nat.succPNat_strictMono, Set.compl_Ioi, Ordinal.le_enum_succ, monovary_comm, FiniteArchimedeanClass.subsemigroup_eq_addSubgroup, HahnSeries.orderTop_mul_of_ne_zero, Stream'.Seq.at_least_as_long_as_coind, Finite.exists_max, NNRat.preimage_cast_Icc, exists_Ioo_extr_on_Icc, max_mul_mul_right, continuousOn_iff_lower_upperSemicontinuousOn, toZ_iterate_pred_ge, MeasureTheory.partialTraj_const, monovary_iff_exists_antitone, Set.left_mem_uIoc, Filter.Tendsto.min_right, Module.End.disjoint_genEigenspace, MvPolynomial.supDegree_esymm, Set.mem_Icc_iff_abs_le, ENat.lift_zero, FloorRing.archimedean, Int.gc_coe_floor, ProbabilityTheory.gaussianReal_mul_const, PosSMulStrictMono.toPosSMulReflectLE, ENat.one_le_iff_ne_zero_withTop, add_le_add_iff_left_of_ne_top, Set.image_const_add_uIcc, WithZeroTopology.isClosed_iff, List.minimum_of_length_pos_le_getElem, strictConvex_Ici, Units.max_val, Hyperreal.archimedeanClassMk_nonneg_of_tendsto, mul_pos_iff, Order.not_isMin_succ, Continuous.if_le, Mathlib.Meta.NormNum.IsRat.natFloor, Function.isMinimalFor_argminOn, Nat.choose_lt_pow_div, ArchimedeanClass.mem_addSubgroup_iff, Function.isMinimalFor_argmin, WithZeroTopology.hasBasis_nhds_zero, ArchimedeanClass.addSubgroup_eq_bot, Hyperreal.epsilon_lt_of_neg, Finset.sup'_inf_sup', Nat.factorization_lcm, Valuation.mem_leAddSubgroup_iff, Submodule.inf_iSup_genEigenspace, tendsto_nat_ceil_atTop, Nat.floor_ofNat, Polynomial.trailingDegree_le_of_ne_zero, MeasureTheory.integrable_iff_integrableAtFilter_atTop, exists_nonneg_right_iff_sameRay, MonomialOrder.le_add_right, FiniteMultiplicity.emultiplicity_le_of_multiplicity_le, AddCircle.coe_image_Icc_eq, Finset.max_le_iff, Polynomial.isEquivalent_atTop_div, isLocallyClosed_Iio, FinBddDistLat.comp_apply, RelHomClass.map_inf, Archimedean.embedReal_injective, IsPreconnected.ordConnected, min_abs_abs_le_abs_max, abs_sub_abs_le_abs_sub, exteriorPower.ιMultiDual_apply_ιMulti, nonemptyFinLinOrd_dual_comp_forget_to_linOrd, Topology.IsLower.tendsto_nhds_iff_lt, List.getD_min?_eq_untopD_minimum, LinearOrderedField.coe_mem_cutMap_iff, Valuation.vle_iff_le, Module.End.genEigenspace_eq_genEigenspace_maxUnifEigenspaceIndex_of_le, Order.Ioi_pred_eq_insert, SimpleGraph.not_isUniform_iff, OrderIso.sumLexIicIoi_symm_apply_Ioi, MonomialOrder.degree_pow_le, Finset.max_eq_sup_withBot, cmp_mul_right', mul_self_pos, ValuationSubring.monotone_mapOfLE, List.exists_map_eq_of_sorted_iff_sbtw, Finset.max'_insert, measurableSet_Ioi, PNat.add_one_le_iff, Int.preimage_Iic, Finset.nsmul_inf', Valued.toNormedField.norm_le_iff, Valuation.map_add', WithTop.untop₀_max, map_pos_of_ne_zero, Orientation.oangle_sign_smul_left, exists_isLocalExtr_uIoo_of_tendsto, iUnion_Icc_add_intCast, Cardinal.ofENat_le_ofENat, BddDistLat.dual_map, ProbabilityTheory.Kernel.partialTraj_succ_self, ENat.toENNReal_lt, MulArchimedeanClass.ballSubgroup_antitone, IsDedekindDomain.HeightOneSpectrum.valuation_lt_one_iff_mem, countable_image_gt_image_Iio_within, Mathlib.Meta.Positivity.nonneg_of_isRat, bot_eq_one', Polynomial.le_trailingDegree_C_mul_X_pow, DivisibleHull.instIsOrderedCancelAddMonoid, Valuation.ltSubmodule_monotone, Pi.lt_toColex_update_self_iff, Cardinal.ofNat_lt_ofENat, MeasureTheory.stoppedValue_stoppedProcess, Cardinal.card_typein_toType_lt, AffineMap.image_uIcc, Finset.dens_biUnion_le, HahnSeries.finiteArchimedeanClassOrderIsoLex_apply_snd, instArchimedeanNNRat, Module.Basis.orientation_comp_linearEquiv_eq_iff_det_pos, PNat.card_Ico, sameRay_neg_smul_left_iff_of_ne, sub_one_lt, continuousAt_iff_continuous_left_right, HahnSeries.cardSupp_div_le, CategoryTheory.SmallObject.instIsIsoRightAppArrowMapToTypeOrdFunctorIterationFunctor, NumberField.RingOfIntegers.HeightOneSpectrum.adicAbv_def, Fin.castLEOrderEmb_toEmbedding, Orientation.oangle_sign_smul_add_smul_smul_add_smul, ValuativeRel.RankLeOneStruct.strictMono, associated_abs_left_iff, IsNonarchimedean.add_eq_max_of_ne, GroupCone.oneLE.hasMemOrInvMem, Finset.Ici_succ_eq_Ioi, MonomialOrder.toSyn_monotone, Valued.integer.mulArchimedean_mrange_of_isCompact_integer, eventually_nhdsWithin_sign_eq_of_deriv_pos, SimpleGraph.extremalNumber_of_fintypeCard_eq, Valuation.Integers.dvdNotUnit_iff_lt, RelHomClass.map_sup, nhds_eq_iInf_mabs_div, exists_le_mul_self, Padic.valuation_p_lt_one, Finset.dens_le_dens_sdiff_add_dens, LaurentSeries.intValuation_le_iff_coeff_lt_eq_zero, Tropical.addLeftMono, min_neg_neg, PointedCone.tmul_subset_maxTensorProduct, Fin.attachFin_uIcc, MvPowerSeries.weightedOrder_mul_ge, Valuation.IsEquiv.lt_iff_lt, convexJoin_convexJoin_convexJoin_comm, MvPowerSeries.le_order, Nat.ceil_intCast, Finset.dens_lt_dens, Function.argminOn_le, RootPairing.zero_le_posForm, StieltjesFunction.mono, Finset.Iio_succ_eq_Iic, Set.one_le_encard_insert, min_max_distrib_left, PNat.map_subtype_embedding_Ioo, Set.Nonempty.encard_pos, Set.compl_ordConnectedSection_ordSeparatingSet_mem_nhdsLE, convexHull_sum, PowerSeries.le_order_pow_of_constantCoeff_eq_zero, LinearOrderedSemiring.toOrderedSMul, Set.monotone_or_antitone_iff_uIcc, MonomialOrder.degLex_single_le_iff, ArchimedeanClass.mk_mul, strictConcaveOn_iff_slope_strict_anti_adjacent, Continuous.mabs, HahnSeries.addVal_apply_of_ne, tendsto_ratCast_atBot_iff, isLeast_pair, MeasureTheory.aecover_Icc_of_Icc, LinearOrderedCommGroup.wellFoundedOn_setOf_le_lt_iff_nonempty_discrete, posPart_pos_iff, Order.Iio_succ, Nimber.instWellFoundedLT, MvPolynomial.leadingCoeff_toLex_C, AddCircle.coe_image_Ioc_eq, leOnePart_max, Filter.tendsto_mul_const_atTop_iff, interior_Ioc, ArchimedeanClass.map_mk_eq, max_sub_min_eq_abs, Set.Ioi_pred_eq_Ici, MvPowerSeries.order_le, Multiset.Ico_inter_Ico, Finset.Colex.toColex_lt_toColex_iff_exists_forall_lt, Rat.preimage_cast_Iic, Finset.max'_eq_sorted_last, ENat.toENNReal_min, Finset.min'_subset, LinearLocallyFiniteOrder.instIsPredArchimedeanOfLocallyFiniteOrder, PredOrder.nhds_eq_pure, add_lt_add_iff_left_of_ne_top, hasBasis_nhdsSet_Iic_Iio, NatOrdinal.toOrdinal_natCast, Set.Ioc_pred_left_eq_Icc, Module.End.mem_genEigenspace_top, continuousOn_uIcc_extendFrom_uIoo, Valued.closure_coe_completion_v_lt, List.minimum_eq_coe_iff, Module.Basis.orientation_adjustToOrientation, MulArchimedeanClass.mk_div_lt_mk_left_iff, mul_max, OrderHomClass.toLatticeHomClass, Pi.Lex.wellFoundedLT, sign_mul, grade_lt_grade_iff, countable_setOf_covBy_left, posPart_eq_ite, Polynomial.isEquivalent_atBot_lead, Module.End.injOn_genEigenspace, Finset.mem_convexHull, LinearOrder.infClosed, OrderEmbedding.preimage_uIcc, ZNum.cast_le, max_zero_sub_max_neg_zero_eq_self, IsDiscreteValuationRing.addVal_add, SetTheory.PGame.equiv_nim_grundyValue, Mathlib.Meta.NormNum.isRat_lt_false, Nonneg.coe_nnqsmul, Module.Basis.orientation_comp_linearEquiv_eq_neg_iff_det_neg, mul_neg_iff, Finset.nonneg_addConst_self, Finset.Icc_pred_right_eq_Ico, AbsoluteValue.map_units_int_smul, Module.End.genEigenspace_one, Profinite.NobelingProof.Products.lt_iff_lex_lt, Int.padicValuation_self, mabs_div, Valued.closure_coe_completion_v_mul_v_lt, LinearOrder.isSublattice, Set.encard_iUnion_le_of_finite, mul_self_lt_one_iff, Multipliable.abs, Nat.ceil_one, RootPairing.RootPositiveForm.rootLength_pos, measurable_IicProdIoc, Hyperreal.infinitesimal_neg_iff_infiniteNeg_inv, Set.uIcc_eq_union, mabs_by_cases, HahnSeries.isUnit_iff, Hyperreal.infiniteNeg_def, MulArchimedeanClass.mk_right_le_mk_mul_iff, IsMulIndecomposable.baseOf_subset_one_lt, smul_nonpos_iff_neg_imp_nonneg, Set.Ico_diff_Iio, Set.unbounded_ge_iff_unbounded_inter_ge, inf_sup_right, isPiSystem_Ico, Valued.cauchy_iff, AffineSubspace.wSameSide_iff_exists_left, Nat.ceil_ofNat, MvPolynomial.schwartz_zippel_sup_sum, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.map_f', Asymptotics.IsEquivalent.tendsto_atBot_iff, Valuation.one_apply_le_one, Cardinal.toENatAux_gc, AddCircle.card_torsion_le_of_isSMulRegular_int, EReal.sign_bot, LinearOrderedAddCommGroup.Subgroup.negGen_neg, HahnSeries.min_order_le_order_add, sbtw_pointReflection_of_ne, PointedCone.minTensorProduct_le_maxTensorProduct, transfiniteIterate_bot, AddMonoidAlgebra.exists_supDegree_mem_support, CategoryTheory.TransfiniteCompositionOfShape.ici_isoBot, Set.compl_Iic, Nat.ceil_sub_natCast, Filter.comap_mabs_atTop, nhdsWithin_Iio_isMeasurablyGenerated, comap_coe_nhdsLT_eq_atTop_iff, Cardinal.toNat_toENat, PNat.Ioc_eq_finset_subtype, ArchimedeanClass.mk_left_le_mk_add_iff, Finset.sort_sorted_lt, Finset.le_card_falling_div_choose, MulArchimedeanClass.mk_one, Finset.Ioc_pred_right_eq_Ioo, exists_pos_left_iff_sameRay, MvPolynomial.monic_esymm, Finset.prod_min_le, Set.Ico_succ_left_eq_Ioo, Int.floor_eq_iff, subsingleton_floorSemiring, ArchimedeanClass.FiniteResidueField.mk_eq_mk, ArchimedeanClass.stdPart_monotoneOn, abs_nonpos_iff, Ordinal.toNimber_one, Convex.min_le_combo, monovaryOn_iff_smul_rearrangement, Odd.strictMono_pow, NNRat.instCanonicallyOrderedAdd, IsDedekindDomain.HeightOneSpectrum.adicValued_apply, Finset.prod_prod_Ioi_mul_eq_prod_prod_off_diag, InnerProductSpace.gramSchmidt_def', closure_Iio, Set.not_disjoint_iff, RootPairing.pairingIn_le_zero_iff, CategoryTheory.SmallObject.SuccStruct.extendToSucc.obj_eq, NumberField.FinitePlace.norm_def_int, WithTop.tendsto_untopA, CategoryTheory.TransfiniteCompositionOfShape.iic_F, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.w, Set.disjoint_iff_inter_eq_empty, Finset.expect_mul_sq_le_sq_mul_sq, NNRat.coe_le_coe, CategoryTheory.SmallObject.SuccStruct.restrictionLTOfCoconeIso_hom_app, tendsto_ceil_left_pure, self_mul_sign, ContinuousWithinAt.lowerSemicontinuousWithinAt, Set.uIcc_subset_uIcc_iff_le, convexHullAddMonoidHom_apply, cocompact_eq_atBot, RingSeminormClass.toNonnegHomClass, vectorSpan_segment, HahnSeries.binomial_power, ENat.toENNReal_mono, OrderTopology.to_orderClosedTopology, Ordinal.cof_eq_cof_toType, RootPairing.pairingIn_lt_zero_iff, LinearLocallyFiniteOrder.succFn_spec, List.argmax_eq_some_iff, MonoidWithZeroHom.inr_mono, IsValuativeTopology.hasBasis_nhds_zero', CauSeq.le_sup_left, Finset.convexHull_eq, Mathlib.Meta.NormNum.isRat_le_false, Set.Infinite.exists_lt_map_eq_of_mapsTo, Set.Iic_sub_one_eq_Iio, isSquare_mabs, Polynomial.div_tendsto_leadingCoeff_div_of_degree_eq, BddDistLat.inv_hom_apply, abs_choice, max_mul_mul_left, PNat.find_lt_iff, Filter.not_tendsto_pow_atTop_atBot, Set.Ioc_union_Ioc_symm, le_neg_self_iff, upperSemicontinuousOn_iff_frequently, min_right_comm, Finset.orderEmbOfCardLe_mem, Tropical.trop_max_def, exists_isLocalExtr_uIoo, pow_dvd_iff_le_emultiplicity, ENat.epow_left_mono, Nat.cast_min, Dense.borel_eq_generateFrom_Ico_mem, Mathlib.Meta.NormNum.isNNRat_le_true, DistLat.ofHom_apply, PointedCone.tmul_subset_minTensorProduct, Nonneg.coe_inv, Polynomial.eventually_atTop_not_isRoot, Finset.fold_max_le, Order.lt_succ_iff, LinearOrderedField.inducedMap_mono, Polynomial.natTrailingDegree_le_trailingDegree, DFinsupp.toMultiset_inf, ValuativeRel.isRankLeOne_iff_mulArchimedean, Valuation.Integers.maximalIdeal_eq_setOf_le_v_algebraMap, nhdsSet_Iic, Finset.sup_inf, exteriorPower.pairingDual_apply_apply_eq_one, OrderIso.sumLexIicIoi_apply_inr, ArchimedeanClass.mk_ratCast, Order.isLUB_Iio_iff_isSuccPrelimit, Finset.exists_mem_eq_sup, LinearOrderedAddCommGroup.wellFoundedOn_setOf_ge_gt_iff_nonempty_discrete, pred_max, Set.exists_upper_bound_image, tendsto_floor_left', RootPairing.coxeterWeightIn_le_four, Finset.pluennecke_ruzsa_inequality_pow_div, Set.antitone_bforall, Order.succ_injective, MulArchimedeanClass.map_mk_eq, ProbabilityTheory.gaussianReal_map_mul_const, MeasureTheory.stoppedProcess_eq'', Nat.orderedSMul, Set.Iic_union_Ioi, MeasureTheory.integrableOn_Ioi_iff_integrableAtFilter_atTop_nhdsWithin, PowerSeries.min_order_le_order_add, CategoryTheory.OrthogonalReflection.iteration_map_succ_assoc, cmp_sub_zero, ValuationSubring.isIntegral_of_mem_ringOfIntegers', inf_compl_eq_bot', max_min_distrib_right, Rat.preimage_cast_Ici, Set.disjoint_insert_right, Prime.abs, ArchimedeanClass.ballAddSubgroup_antitone, AddCircle.openPartialHomeomorphCoe_source, sign_apply, HahnSeries.embDomainOrderAddMonoidHom_injective, PosNum.cast_le, sq_lt_one_iff_abs_lt_one, GeneralizedBooleanAlgebra.inf_inf_sdiff, Finite.exists_min, Profinite.NobelingProof.Products.lt_nil_empty, sq_sum_le_card_mul_sum_sq, tendsto_nat_floor_atTop, ValuativeRel.instIsOrderedMonoidValueGroupWithZero, Order.pred_top_lt_iff, Nimber.toOrdinal_eq_one, Tuple.comp_sort_eq_comp_iff_monotone, Set.Ici_diff_Ioi, Finset.Ico_add_one_right_eq_Icc, Sym2.sortEquiv_symm_apply, Ico_mem_nhds_iff, PrimeMultiset.prod_inf, intermediate_value_Ioc', toENat_rank_span_set, le_sup_inf, Polynomial.degree_add_le_of_le, Finset.min'_lt_max', GenContFract.of_den_mono, SuccOrder.isOpen_iff, DivisibleHull.qsmul_def, MvPolynomial.supDegree_toLex_C, Finset.mulConst_le_inv_dens, Finset.Ioc_pred_pred_eq_Ico, ArchimedeanClass.out_top, sign_one, ValuativeRel.uniformizer_inv_le_iff, Valuation.one_vlt_iff, neg_lt_self_iff, IsValuativeTopology.isClopen_ball, IsValuativeTopology.hasBasis_nhds, Set.Iic_pred_eq_Iio, Set.encard_mono, abs_cases, Polynomial.tendsto_nhds_iff, Affine.Simplex.sSameSide_affineSpan_faceOpposite_iff, dvd_iff_emultiplicity_pos, AddCircle.measurePreserving_equivIoc, Rat.castOrderEmbedding_apply, ENat.add_lt_add_iff_left, ArchimedeanClass.subsemigroup_strictAnti, Set.encard_singleton_inter, Matrix.IsIrreducible.exists_pos, QuotientAddGroup.btw_coe_iff, Finset.add_sup, Finset.sum_card_slice_div_choose_le_one, IsDedekindDomain.HeightOneSpectrum.intValuation_lt_one_iff_dvd, Filter.Eventually.exists_Ioo_subset, wbtw_iff_right_eq_or_left_mem_image_Ici, Mathlib.Meta.NormNum.isRat_le_true, CauSeq.const_le, FiniteMulArchimedeanClass.mk_le_mk, archimedean_iff_nat_lt, Rat.toNNRat_pos, tendsto_pow_neg_atTop, Finset.sups_infs_subset_right, Asymptotics.IsEquivalent.tendsto_atTop_iff, WithZero.denselyOrdered_set_iff_subsingleton, Set.Iic_subset_Iic_union_Icc, summable_abs_iff, Finset.disjSups_disjSups_disjSups_comm, IsConnected.Icc_subset, abs_pos, Set.subsingleton_Icc_iff, Set.bounded_lt_inter_lt, aemeasurable_uIoc_iff, abs_unit_intCast, infIrred_iff_not_isMax, IsDiscreteValuationRing.map_algebraMap_eq_valuationSubring, LinearLocallyFiniteOrder.instIsSuccArchimedeanOfLocallyFiniteOrder, OrderIso.subsingleton_of_wellFoundedLT', Valuation.one_vle_iff, ENat.one_le_epow, lowerSemicontinuousOn_iff_frequently, Filter.tendsto_const_mul_pow_atBot_iff, wbtw_iff_left_eq_or_right_mem_image_Ici, Ioo_subset_openSegment, Set.unbounded_lt_iff, abs_sub_map_le_div, convex_uIcc, convexHull_pi, ArchimedeanClass.ball_top, Cardinal.toENat_strictMonoOn, InnerProductSpace.span_gramSchmidt_Iic, Function.mulSupport_min, HahnSeries.pow_add, Fin.castAddOrderEmb_toEmbedding, Set.Nontrivial.exists_lt, SimpleGraph.FarFromTriangleFree.lt_half, Finset.Nonempty.inf_eq_bot_iff, round_eq_zero_iff, BddDistLat.ofHom_apply, NNRat.preimage_cast_Ici, Finset.min_eq_bot, map_abs, Order.isPredLimitRecOn_pred, FiniteArchimedeanClass.mk_le_mk, CategoryTheory.SmallObject.iterationFunctorMapSuccAppArrowIso_hom_right_right_comp_assoc, HahnSeries.orderTop_mul, Ordinal.ToType.mk_symm_apply_coe, MonomialOrder.wf, ArchimedeanClass.FiniteElement.isUnit_iff_mk_eq_zero, Finset.fold_min_le, Hyperreal.instIsStrictOrderedRing, frontier_Ici_subset, Set.projIic_self, Valued.toNormedField.one_lt_norm_iff, LinOrd.forget_map, Filter.Germ.const_abs, Set.uIoo_subset_uIcc, Finset.max'_union, Field.Emb.Cardinal.filtration_apply, PrimeMultiset.prod_dvd_iff, Set.Ioc_pred_pred_eq_Ico, measurableSet_uIcc, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.sq, Finset.Ioo_pred_left_eq_Ioc, Affine.Simplex.ExcenterExists.sign_touchpointWeights, Rat.cast_mono, NNRat.ceil_coe, IsDedekindDomain.HeightOneSpectrum.intValuation_zero_lt, sq_lt_sq, Int.lt_zpow_succ_log_self, Set.infs_sups_subset_left, add_sq_le, Finset.le_dens_sdiff, strictConvex_Ioc, Finset.min'_lt_max'_of_card, toZ_iterate_succ, IsValuativeTopology.hasBasis_nhds_zero, AffineMap.lineMap_anti, nhdsWithinLT_sup_nhdsWithinGT, IsDedekindDomain.HeightOneSpectrum.valuedAdicCompletion_eq_valuation, posSMulMono_iff_posSMulReflectLT, AddSubmonoid.mem_closure_image_pos_iff, Valuation.IsNontrivial_iff_exists_one_lt, Tropical.trop_add_def, ContinuousOn.abs, Matroid.ExchangeProperty.encard_diff_le_aux, LinOrd.ext_iff, isOpen_Ioi, Affine.Simplex.sign_touchpointWeights_singleton_pos, NonemptyFinLinOrd.hom_hom_id, Padic.toEquiv_withValUniformEquiv_eq_toEquiv_withValRingEquiv, nhdsSet_Ici, instCommutativeMin, isCompact_Ico_iff, AddCircle.eq_coe_Ico, Set.Iio_subset_Iio_iff, Orientation.oangle_sign_smul_right, Finset.min_pair, Odd.zpow_nonneg_iff, Finset.Ioi_pred_eq_Ici, Asymptotics.isEquivalent_nat_floor, Module.End.genEigenspace_eq_iSup_genEigenspace_nat, trop_iInf, Finset.min'_lt_of_mem_erase_min', Valuation.mem_ltAddSubgroup_iff, le_iff_forall_pos_lt_add, mabs_mabs_div_mabs_le_mabs_div, Cardinal.ofNat_le_ofENat, CategoryTheory.TransfiniteCompositionOfShape.ici_isColimit, IsCompact.bddAbove_image, PNat.succ_eq_add_one, Ordinal.enum_succ_eq_top, Set.uIoo_subset_uIcc_self, Nimber.toOrdinal_one, doublyStochastic_eq_convexHull_permMatrix, HeytAlg.hasForgetToLat_forget₂_obj_isBoundedOrder, mul_smul_one_lt_iff, PNat.factorMultiset_mono, LaurentSeries.valuation_LaurentSeries_equal_extension, cocompact_eq_atBot_atTop, floorDiv_le_ceilDiv, Set.disjoint_univ, ENat.addLECancellable_coe, max_one_mul_max_inv_one_eq_mabs_self, CauSeq.sup_comm, SetLike.coe_strictMono, nhdsLT_basis, Submodule.spanRank_toENat_eq_iInf_finset_card, Finset.min'_insert, PNat.map_subtype_embedding_uIcc, Order.succ_le_succ_iff, LucasLehmer.two_lt_q, HahnSeries.orderTop_nsmul_le_orderTop_pow, variationOnFromTo.sub_self_monotoneOn, min_add_max, Finset.pluennecke_ruzsa_inequality_nsmul_sub_nsmul_sub, CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.instIsIsoMapF, Set.Iio_ssubset_Iio_iff, trichotomy_of_mul_eq_mul, Dense.borel_eq_generateFrom_Ico_mem_aux, RatFunc.v_def, abs_nsmul, DFinsupp.Lex.wellFoundedLT_of_finite, Function.locallyFinsuppWithin.negPart_add, ArchimedeanClass.FiniteResidueField.mk_ne_zero, Nat.one_sub_one_div_cast_nonneg, map_pos_of_ne_one, mul_min, Set.Icc_add_one_left_eq_Ioc, Rat.padicValuation_eq_zero_iff, Set.OrdConnected.IciExtend, NNRat.cast_min, Int.floor_toNat, NonemptyFinLinOrd.dual_map, Finset.nsmul_sup', Set.preimage_const_mul_uIcc, LaurentSeries.LaurentSeries_coe, strictConvex_Ico, MeasureTheory.integrableOn_Iio_iff_integrableAtFilter_atBot_nhdsWithin, PNat.addLeftReflectLE, ENat.pow_lt_top_iff, CategoryTheory.SimplicialThickening.Path.left_le, max_top_left, CategoryTheory.SmallObject.SuccStruct.ofCocone_obj_eq_pt, Finsupp.DegLex.single_le_iff, Finset.centroid_mem_convexHull, IsDedekindDomain.HeightOneSpectrum.intValuation_eq_one_iff, Set.Iio_add_one_eq_Iic, map_mabs, min_top_right, HahnSeries.archimedeanClassOrderIsoWithTop_apply, Finset.untrop_sum, max_eq_bot, Set.OrdConnected.restrict, FiniteMulArchimedeanClass.mem_subgroup_iff, CategoryTheory.TransfiniteCompositionOfShape.ofOrderIso_isoBot, Set.Ico_add_one_left_eq_Ioo, Hyperreal.coe_min, Valuation.Integers.wfDvdMonoid_iff_wellFounded_gt_on_v, Set.encard_le_coe_iff_finite_ncard_le, Rat.preimage_cast_Iio, Finset.Ico_filter_le, Set.unbounded_gt_iff, Rat.cast_nonneg, MvPowerSeries.le_order_smul, NNRat.toNNRat_mono, WithTop.isEmbedding_coe, Set.monotone_setOf, oneTangentSpaceIcc_def, Set.unit_valuation_eq_one, Set.Ioc_inter_Ioc, Finset.min'_eq_sorted_zero, PowerSeries.le_order_pow, Polynomial.isBoundedUnder_abs_atBot_iff, OrderEmbedding.addRight_apply, negPart_lt, IsNonarchimedean.finset_image_add_of_nonempty, DivisibleHull.coeOrderAddMonoidHom_apply, PosSMulStrictMono.nnrat_of_rat, emultiplicity_prime_le_emultiplicity_image_by_factor_orderIso, BddDistLat.id_apply, stdSimplex.barycenter_apply, mul_nonpos_iff, Nat.floor_le_ceil, Finset.min'_le_max', Int.one_le_ceil_iff, Finset.disjSups_assoc, MulArchimedeanClass.mk_mabs, Hyperreal.lt_neg_of_pos_of_infinitesimal, Set.Iio_union_Ioi, abs_mem_iff, Ordinal.iSup_typein_limit, nhdsSet_Iio, IsNonarchimedean.nsmul_le, AbsoluteValue.hasBasis_uniformity, squarefree_iff_emultiplicity_le_one, ArchimedeanClass.mk_le_mk_iff_ratCast, InnerProductSpace.gramSchmidtOrthonormalBasis_inv_blockTriangular, sup_compl_eq_top, NNRat.one_lt_cast, geom_sum_neg_iff, Set.Ico_disjoint_Ico, Set.image_const_sub_uIcc, ValuativeRel.IsNontrivial.exists_lt_one, Set.unbounded_le_iff, zpowers_mabs, Order.lt_add_one_iff, Rat.toNNRat_add_le, Tuple.eq_sort_iff, MeasureTheory.stoppedProcess_eq_of_mem_finset, sign_neg, Cardinal.continuum_toENat, inv_nhdsLT_zero, OrderIso.sumLexIicIoi_apply_inl, IsPreconnected.intermediate_value_Ioc, SuccOrder.nhdsGT, ValuativeRel.le_uniformizer_iff, LinearOrderedCommGroupWithZero.inr_eq_coe_inrₗ, Ioc_mem_nhds_iff, Finset.Icc_succ_left_eq_Ioc, Field.Emb.Cardinal.deg_lt_aleph0, CategoryTheory.Functor.IsWellOrderContinuous.restriction_setIci, tendsto_const_mul_pow_nhds_iff, isPiSystem_image_Iio, DFinsupp.Lex.isStrictOrder, Mathlib.Meta.NormNum.isNNRat_abs_nonneg, signedDist_smul, max_sub_max_le_max, iUnion_Ico_intCast, GenContFract.le_of_succ_succ_get?_contsAux_b, Finset.max_eq_top, ProbabilityTheory.gaussianPDFReal_inv_mul, nhdsGE_basis_Icc, Valuation.integer.v_irreducible_pos, Set.Ioo_subset_Ioc_union_Ioo, StieltjesFunction.measure_Icc, Finsupp.Lex.addRightStrictMono, Set.Ioi_subset_Ioi_iff, Rat.cast_abs, ConvexCone.isGenerating_iff_isReproducing, CauSeq.inf_le_right, Valuation.leIdeal_mono, Set.Ioc_diff_Ioi, FunctionField.inftyValuation.X_zpow, PNat.card_fintype_Ioo, Complementeds.instComplementedLattice, CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.ofComposableArrows_F, FiniteMulArchimedeanClass.congrOrderIso_symm, Int.ceil_le, Set.strictMonoOn_projIci, Tuple.antitone_pair_of_not_sorted', Polynomial.trailingDegree_lt_wf, le_iff_forall_one_lt_lt_mul, Set.finite_diff_iUnion_Ioo', antivaryOn_iff_smul_rearrangement, sq_eq_sq_iff_abs_eq_abs, mabs_div_pos, OrderEmbedding.birkhoffSet_sup, Set.Iic_subset_Iic_union_Ioc, Finset.subConst_le_card, NNRat.cast_max, PredOrder.nhdsLT, PNat.Prime.one_lt, Finset.disjoint_sup_right, Topology.RelCWComplex.iUnion_openCell_eq_skeletonLT, SignType.neg_lt_neg_iff, sq_nonpos_iff, Set.Ioo_pred_left_eq_Ioc, Int.fract_add_le, Finset.trop_inf, HahnSeries.orderTop_add_le_mul, Set.range_projIic, LinOrd.Iso.mk_inv, CategoryTheory.TransfiniteCompositionOfShape.ofArrowIso_incl, Module.End.genEigenspace_le_genEigenspace_maxUnifEigenspaceIndex, HurwitzZeta.hasSum_nat_hurwitzZetaOdd, inf_sup_left, MeasureTheory.ae_restrict_uIoc_iff, LinearOrderedCommGroupWithZero.fst_comp_inl, upperClosure_eq_bot_iff, ENat.le_coe_iff, IsCompact.exists_isMinOn, abs_pow_sub_pow_le, Int.ceil_lt_add_one, HahnEmbedding.ArchimedeanStrata.isInternal_stratum', BddDistLat.forget_bddLat_lat_eq_forget_distLat_lat, Dense.borel_eq_generateFrom_Ioc_mem_aux, Int.image_fract, Multiset.exists_min_image, OrderRingIso.apply_eq_self, Nimber.instZeroLEOneClass, Set.Iic_union_Ici, Fin.succAboveOrderEmb_toEmbedding, PrincipalSeg.isNormal, inv_mabs_le_inv, Positive.coe_inv, Rat.cast_nonpos, Finset.sortedLT_sort, IsCoprime.abs_left_iff, Hyperreal.lt_of_pos_of_infinitesimal, archimedean_iff_rat_le, one_lt_sq_iff_one_lt_abs, ArchimedeanClass.FiniteResidueField.mk_le_mk, OrderIso.subsingleton_of_wellFoundedLT, Filter.tendsto_pow_atTop_iff, Set.encard_le_encard_iff_encard_diff_le_encard_diff, mem_nhdsGE_iff_exists_Ico_subset, Affine.Simplex.sign_touchpointWeights_singleton_neg, PNat.card_uIcc, Set.Ico_add_one_add_one_eq_Ioc, MvPowerSeries.map_iterateFrobenius_expand, Polynomial.supDegree_eq_degree, Order.succ_eq_succ_iff, Finset.sum_sum_Ioi_add_eq_sum_sum_off_diag, Valuation.IsNontrivial.exists_one_lt, IsDedekindDomain.HeightOneSpectrum.intValuation_def, CategoryTheory.Limits.WalkingMultispan.inclusionOfLinearOrder_obj, OrderIso.pnatIsoNat_apply, LocallyFiniteOrder.orderAddMonoidHom_apply, IsCoprime.abs_left, not_lt_zero', Module.Basis.abs_det_adjustToOrientation, SimpleGraph.le_card_nonuniformWitness, CategoryTheory.SmallObject.SuccStruct.transfiniteCompositionOfShapeιIteration_incl, FunctionField.inftyValuation.X, InnerProductSpace.gramSchmidt_def'', Finset.add_sup', RingCone.nonneg.hasMemOrNegMem, Set.unbounded_ge_inter_gt, StieltjesFunction.length_eq, Nat.cast_finsetInf', mem_nhdsLT_iff_exists_Ioo_subset, FiniteMulArchimedeanClass.min_le_mk_mul, MonomialOrder.degree_prod_le, min_mul_distrib, LinearOrderedSemifield.toPosSMulStrictMono_rat, Module.End.genEigenspace_zero_nat, antivary_iff_mul_rearrangement, MeasureTheory.Filtration.rightCont_eq, Set.infinite_iff_exists_gt, comap_abs_nhds_zero, CauSeq.exists_lt, FiniteMultiplicity.emultiplicity_lt_of_multiplicity_lt, HahnSeries.leadingCoeff_nonneg_iff, WithZeroTopology.isOpen_iff, Order.pred_lt_pred_iff, Measurable.nat_floor, toZ_iterate_pred, CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.ofComposableArrows_isoBot_inv, ENat.lt_add_one_iff, ENat.addLECancellable_of_ne_top, List.prod_min_le, Nimber.instNoMaxOrder, ArchimedeanClass.archimedean_of_mk_eq_mk, Finset.max'_eq_iff, tendsto_nat_ceil_div_atTop, Finsupp.DegLex.isStrictOrder, Cardinal.ofENat_lt_ofENat, Finset.dens_mono, ArchimedeanClass.mk_eq_mk, NNRat.instOrderedSub, EReal.sign_top, Matrix.IsPrimitive.exists_pos_pow, Valuation.srel_one_iff, max_mul_mul_le_max_mul_max', LinearOrder.isSuccArchimedean_of_isPredArchimedean, Continuous.strictMono_of_inj, MonomialOrder.div_set, List.mem_argmax_iff, MulArchimedeanClass.mk_mul_lt_mk_right_iff, MeasureTheory.Lp.coe_posPart, right_le_lineMap_iff_one_le, MonoidWithZeroHom.snd_mono, nullMeasurableSet_lt', Set.inv_uIcc, Module.End.genEigenspace_top, Ordinal.toNatOrdinal_zero, CategoryTheory.SmallObject.iterationFunctorMapSuccAppArrowIso_hom_left, HahnEmbedding.Partial.orderTop_eq_finiteArchimedeanClassMk, Valuation.IsUniformizer.val_pos, Set.Ioi_subset_Ici_iff, Finset.orderEmbOfFin_apply, supPrime_iff_supIrred, MeasureTheory.aecover_Ioo_of_Ioo, intermediate_value_Ico', List.exists_map_eq_of_sorted_iff_wbtw, Odd.pow_pos_iff, PointedCone.minTensorProduct_comm, fderiv_norm_smul, Set.disjoint_iff_forall_ne, abs_add', LinOrd.ofHom_comp, HasFDerivAt.hasFDerivAt_norm_smul, NNRat.cast_pos, borel_eq_generateFrom_Ico, Set.coe_projIic, NatOrdinal.toOrdinal_eq_zero, tendsto_floor_atBot, QuotientAddGroup.btw_coe_iff', Multiset.Ico_filter_le, BooleanAlgebra.toComplementedLattice, CategoryTheory.IsGrothendieckAbelian.generatingMonomorphisms.functorToMonoOver_map, List.le_maximum_of_mem', Polynomial.degree_sub_le, abs_neg_one_zpow, MeasureTheory.aecover_Ioc_of_Ioc, PNat.instWellFoundedLT, Order.isNormal_iff', Cardinal.ofENat_strictMono, Pi.lt_toLex_update_self_iff, Int.preimage_Ioo, mabs_eq_one, OrderType.type_le_type_iff, FunctionField.inftyValuedFqt.def, one_lt_oneLePart_iff, CategoryTheory.SmallObject.πFunctorObj_eq, isPiSystem_Iio, Mathlib.Tactic.Qify.nnratCast_lt, NonemptyFinLinOrd.id_apply, tendsto_ceil_left', hahnEmbedding_isOrderedModule_rat, AddValuation.map_sub, Affine.Simplex.sign_signedInfDist_touchpoint_empty, Finsupp.Lex.addLeftStrictMono, FiniteArchimedeanClass.congrOrderIso_symm, Valuation.RankOne.strictMono', mabs_mul_eq_mul_mabs_iff, mabs_div_mabs_le_mabs_mul, PNat.lt_add_left, SimpContFract.of_isContFract, tendsto_const_mul_zpow_atTop_zero, AffineIndependent.convexHull_inter', Finset.min'_pair, Set.Ioi_inter_Ioo, AffineSubspace.sOppSide_pointReflection, max_eq_right_iff, Set.Ici_subset_Icc_union_Ioi, Finset.le_max', PredOrder.hasBasis_nhds_Ioc, Filter.tendsto_Ioc_uIcc_uIcc, Finset.sup_mem_of_nonempty, GenContFract.of_one_le_get?_partDen, Valuation.vle_one_iff, sign_nonpos_iff, Set.Finite.exists_lt_map_eq_of_forall_mem, disjoint_partialSups_left, smul_nonneg_iff, Cardinal.toENat_le_iff_of_le_aleph0, PNat.sub_le, Finset.intervalGapsWithin_snd_of_lt, Valuation.IsEquiv.val_sub_one_lt_one_iff, Nat.one_div_cast_nonneg, Set.Icc_sub_one_right_eq_Ico, ENat.coe_lt_coe, sign_pow, Set.powersetCard.mem_ofFinEmbEquiv_iff_mem_range, Finset.max_insert, PowerSeries.order_le, measurableSet_Ioo, Valuation.Integers.coe_span_singleton_eq_setOf_le_v_algebraMap, LinearOrderedAddCommGroup.discrete_or_denselyOrdered, MonomialOrder.degLex_lt_iff, IsDedekindDomain.HeightOneSpectrum.adicValued.uniformContinuousConstSMul, IsValuativeTopology.hasBasis_nhds', LinearOrder.infConvergenceClass, ContinuousOn.surjOn_Icc, emultiplicity_lt_top, Finset.Ioo_add_one_right_eq_Ioc, Multiset.max_prod_le, AddMonoidAlgebra.Monic.supDegree_mul_of_ne_zero_left, abs_eq_zero, Set.preimage_const_sub_uIcc, HahnModule.orderTop_vAdd_le_orderTop_smul, strictConvex_iff_ordConnected, Multiset.count_finset_sup, NNRat.ofNat_le_cast, Cardinal.toENat_eq_top, sameRay_smul_right_iff_of_ne, extremePoints_doublyStochastic, Valuation.Integers.valuation_pos_iff_ne_zero, hasDerivAt_abs, Valued.isOpen_closedBall, Finset.lt_inf'_iff, lineMap_le_right_iff_le_one, Int.floor_le_neg_one_iff, invOf_nonpos, exists_square_le, Affine.Simplex.sign_excenterWeights_empty, IsPreconnected.mapsTo_Ioi_or_Iio, Finset.intervalGapsWithin_succ_fst_of_lt, Field.Emb.Cardinal.strictMono_filtration, convexHull_eq_union_convexHull_finite_subsets, tendsto_fract_left, Finset.sort_sorted_gt, PNat.card_Ioo, BooleanAlgebra.himp_eq, GenContFract.fib_le_of_contsAux_b, Continuous.max, Finset.le_min_iff, ENat.coe_le_coe, OrderHomClass.coe_to_lattice_hom, upperSemicontinuous_iff_isClosed_preimage, AddMonoidAlgebra.Monic.supDegree_pow, Hyperreal.lt_of_tendsto_atBot, max_bot_right, Nat.one_sub_one_div_cast_le_one, MvPowerSeries.weightedOrder_le, Mathlib.Meta.NormNum.IsRat.natCeil, Finset.Ioc_pred_left_eq_Icc, Valuation.IsEquiv.one_le_iff_one_le, Set.Ioo_succ_right_eq_Ioc, Int.ceil_toNat, min_mul_max, SignType.not_lt_neg_one, HahnEmbedding.Seed.truncLT_mem_range_baseEmbedding, NNRat.ceil_cast, Finset.sup'_add, Nat.cast_div_le, Set.Iio_diff_Iic, Positive.isOrderedCancelMonoid, Finset.untrop_sum', Int.floor_pos, Valued.mem_nhds_zero, Odd.zpow_pos_iff, abs_eq_neg_self, sign_eq_zero_iff, sameRay_neg_smul_right_iff_of_ne, associated_abs_right_iff, HahnSeries.orderTop_le_orderTop_smul, Finset.le_card_infs_mul_card_sups, PNat.equivNonZeroDivisorsNat_apply_coe, Int.preimage_Ici, PseudoMetric.IsUltra.isTrans_ball, Finset.Colex.lt_iff_max'_mem, Valued.isOpen_ball, ENat.add_one_pos, HahnSeries.orderTop_lt_iff_exists, AddCircle.liftIoc_eq_lift_Icc, Nimber.lt_wf, abs_sub_nonpos, ArchimedeanClass.mk_map_of_archimedean, CategoryTheory.IsGrothendieckAbelian.generatingMonomorphisms.instIsWellOrderContinuousFunctor, CauSeq.le_total, Dense.exists_le, SuccOrder.isOpen_singleton_iff, ValuationSubring.mem_principalUnitGroup_iff, Set.image_add_const_uIcc, LocallyBoundedVariationOn.exists_monotoneOn_sub_monotoneOn, monovary_iff_forall_mul_nonneg, pow_lt_one_iff, ArchimedeanClass.FiniteResidueField.instArchimedean, Valued.mem_nhds, Mathlib.Meta.Positivity.abs_pos_of_ne_zero, Ordinal.lsub_typein, OrderMonoidWithZeroHom.coe_mul, abs_sub_map_le_sub, Set.Ico_inter_Iio, punctured_nhds_eq_nhdsWithin_sup_nhdsWithin, Nat.one_div_pos_of_nat, FiniteArchimedeanClass.withTopOrderIso_symm_apply, Archimedean.exists_orderAddMonoidHom_real_injective, Finset.abs_expect_le, finBoolAlg_dual_comp_forget_to_finBddDistLat, Order.embedding_from_countable_to_dense, HahnEmbedding.Partial.mem_domain, Ordinal.toNatOrdinal_eq_zero, Cardinal.one_lt_ofENat, Even.add_pow_le, intermediate_value_univ, Filter.tendsto_Icc_uIcc_uIcc, Topology.CWComplex.iUnion_openCell_eq_skeleton, Finset.Ioo_filter_lt, sq_pos_iff, abs_sub_sq, Hyperreal.infinite_iff_abs_lt_abs, EReal.le_iff_sign, FloorSemiring.eventually_mul_pow_lt_factorial_sub, WithTop.tendsto_untopD, Finset.nonneg_subConst_self, Pi.Colex.wellFoundedLT, max_cases, Ordinal.enum_zero_eq_bot, Polynomial.isBoundedUnder_abs_atTop_iff, IsDedekindDomain.HeightOneSpectrum.valuationOfNeZero_eq, Finset.min'_eq_iff, LinOrd.coe_id, Nat.ceil_sub_ofNat, Multipliable.abs_tprod, Function.argmin_le, HahnSeries.embDomainOrderAddMonoidHom_apply, Set.Ici_diff_Ici, MulArchimedeanClass.out_top, NNRat.coe_mono, sq_nonneg, MeasureTheory.stoppedProcess_stoppedProcess', convexOn_pow, HahnEmbedding.Seed.mem_domain_baseEmbedding, one_le_pow_iff, MulArchimedeanClass.mk_left_le_mk_div_iff, Finset.isGLB_iff_isLeast, Nat.ceil_sub_one, Finsupp.Lex.single_antitone, Topology.RelCWComplex.skeleton_monotone, sameRay_neg_smul_right_iff, RootPairing.RootPositiveForm.exists_pos_eq, Valued.integer.locallyFiniteOrder_units_mrange_of_isCompact_integer, AffineSubspace.sSameSide_iff_exists_right, NNRat.preimage_cast_Ico, SMulPosReflectLT.toSMulPosMono, FiniteDimensional.exists_relation_sum_zero_pos_coefficient_of_finrank_succ_lt_card, mem_convexHull_iff_exists_fintype, Nat.sup_divisors_id, ContinuousWithinAt.mabs, Hyperreal.ofSeq_le_ofSeq, Ico_subset_closure_interior, MeasureTheory.Measure.measure_Ioo_eq_zero, Set.mem_uIoc, Set.Ioc_union_Ioc_union_Ioc_cycle, SuccOrder.isSuccLimit_of_mem_frontier, Set.univ_disjoint, le_iff_forall_lt_rat_imp_le, toZ_iterate_succ_le, Finset.sup'_inf_distrib_left, tsub_min, PNat.card_fintype_Ioc, LaurentSeries.instLaurentSeriesComplete, round_le_add_half, Cardinal.ofENat_lt_nat, LinearOrderedCommGroup.to_noMinOrder, Odd.zpow_neg_iff, AbsoluteValue.map_units_int, nullMeasurableSet_Iio, Set.encard_image_le, convexHull_toCone_isLeast, sameRay_or_sameRay_neg_iff_not_linearIndependent, Nat.cast_finsetSup, IsDedekindDomain.HeightOneSpectrum.valuation_surjective, NNRat.cast_nonpos, Set.Ioc_sub_one_sub_one_eq_Ico, Int.le_floor, Hyperreal.omega_pos, Valuation.rel_one_iff, Rat.cast_lt_zero, MvPowerSeries.weightedOrder_add_of_weightedOrder_ne, Int.fract_eq_self, List.minimum_anti, Set.Ico_add_one_right_eq_Icc, lowerSemicontinuousAt_iff_frequently, CategoryTheory.TransfiniteCompositionOfShape.ofComposableArrows_isoBot, Set.projIci_self, Continuous.integrableOn_uIcc, Rat.cast_strictMono, convex_iff_div, HahnSeries.single_div_single, exists_pred_iterate_or, LinearOrderedCommGroupWithZero.wellFoundedOn_setOf_ge_gt_iff_nonempty_discrete_of_ne_zero, FinBddDistLat.hom_comp, Padic.withValUniformEquiv_cast_apply, Module.End.generalized_eigenvec_disjoint_range_ker, NonemptyFinLinOrd.comp_apply, Cardinal.ofENat_le_one, SimpleGraph.right_nonuniformWitnesses_card, Hyperreal.infiniteNeg_iff_infinitesimal_inv_neg, ArchimedeanClass.mk_intCast_nonneg, countable_image_lt_image_Ioi, tendsto_inv_nhdsLT_zero, DFinsupp.Colex.wellFoundedLT_of_finite, convexIndependent_iff_finset, pow_div_pow_eventuallyEq_atTop, Finset.mul_sup', HahnSeries.archimedeanClassMk_le_archimedeanClassMk_iff, LaurentSeries.valuation_coe_ratFunc, DivisibleHull.archimedeanClassOrderIso_apply, Int.fract_lt_one, Hyperreal.archimedeanClassMk_omega_neg, frontier_le_subset_eq, posPart_lt, Valuation.Integers.isPrincipal_iff_exists_eq_setOf_valuation_le, zsmul_lt_zsmul_iff_right, PNat.card_fintype_Ico, Hyperreal.archimedeanClassMk_coe_nonneg, Matrix.mem_glpos, CategoryTheory.TransfiniteCompositionOfShape.iic_incl_app, IsValuativeTopology.isClosed_ball, min_add_min_le_min_add_add, AddCircle.continuous_equivIco_symm, nhdsWithinLE_sup_nhdsWithinGE, HahnSeries.inv_def, intermediate_value_Icc, Cardinal.ofENat_pos, Padic.coe_withValRingEquiv, Valuation.Integer.not_isUnit_iff_valuation_lt_one, CategoryTheory.TransfiniteCompositionOfShape.ofOrderIso_F, CauSeq.le_sup_right, Matrix.IsPrimitive.nonneg, Finset.Ioo_sub_one_left_eq_Ioc, Max.right_comm, Padic.comap_mulValuation_eq_int_padicValuation, Nat.floor_sub_natCast, Finset.one_le_divConst_self, Int.preimage_Icc, MeasureTheory.ae_const_le_iff_forall_lt_measure_zero, AffineSubspace.wSameSide_iff_exists_right, instIsModularLattice, continuousAt_sign_of_neg, Affine.Simplex.sSameSide_affineSpan_faceOpposite_point_right_iff, isPiSystem_Ioc_mem, div_pos_iff, measurableSet_lt, AddCircle.continuousAt_equivIoc, ENat.add_le_add_iff_right, OrderEmbedding.addLeft_apply, Iic_mem_nhdsSet_Iic_iff, Rat.cast_pos_of_pos, Nat.Prime.emultiplicity_factorial_le_div_pred, UniqueFactorizationMonoid.le_emultiplicity_iff_replicate_le_normalizedFactors, LinearOrderedCommGroupWithZero.fst_apply, variationOnFromTo.monotoneOn, Cardinal.toENat_le_natCast_iff, Set.toENat_cardinalMk, NumberField.FinitePlace.norm_eq_one_iff_notMem, MulArchimedeanClass.ballSubgroup_top, grade_injective, Finset.Ico_diff_Ico_right, ArchimedeanClass.mem_closedBall_iff, Polynomial.div_tendsto_atBot_zero_iff_degree_lt, disjoint_inf_sdiff, Set.bounded_le_inter_lt, countable_of_isolated_left', Dense.exists_seq_strictAnti_tendsto, Set.range_projIci, Set.Ici_subset_Ico_union_Ici, Valuation.vlt_one_iff, multipliable_mabs_iff, Finset.le_min'_iff, Set.Finite.latticeClosure, abs_abs_sub_abs_le_abs_sub, extremePoints_convexHull_subset, DistLat.ofHom_id, ENat.mul_left_strictMono, sup_inf_sdiff, Finset.intervalGapsWithin_fst_of_lt_lt, Module.End.mem_genEigenspace_one, mabs_mul', LaurentSeries.valuation_compare, mem_segment_iff_div, Cardinal.enat_gc, Padic.isUniformInducing_cast_withVal, MeasureTheory.aecover_Ico_of_Ioo, ArchimedeanClass.mk_ratCast_nonneg, Hyperreal.tendsto_atBot_iff, FiniteArchimedeanClass.addSubgroup_strictAnti, Nat.one_le_ceil_iff, PowerSeries.le_order, leOnePart_eq_ite, Orientation.someBasis_orientation, min_div_div_right', Even.zpow_pos_iff, HahnEmbedding.ArchimedeanStrata.archimedean_stratum, exposedPoints_subset_extremePoints, SimpleGraph.nonuniformWitness_spec, Right.nsmul_neg_iff, Set.isPWO_iff_isWF, two_mul_le_add_pow_two, Filter.Germ.const_max, PNat.find_min', Int.ceil_pos, Finset.inf_sup_inf, PointedCone.maxTensorProduct_comm, Finset.fold_max_lt, WithTop.tendsto_coe_atTop, Set.disjoint_empty, Tuple.eq_sort_iff', abs_lt, Set.one_lt_encard_iff, Set.Icc_add_one_sub_one_eq_Ioo, min_zero, MvPowerSeries.order_mul_ge, FiniteMulArchimedeanClass.ballSubgroup_strictAnti, Polynomial.degree_sum_eq_of_disjoint, max_mul, HahnSeries.lt_iff, HahnSeries.instIsOrderedAddMonoidLex, instIsCountablyGenerated_atTop, Module.End.IsFinitelySemisimple.genEigenspace_eq_eigenspace, ArchimedeanClass.mk_le_mk_add_of_archimedean, Fin.image_val_uIcc, DivisibleHull.mk_lt_mk, Submonoid.closure_image_isMulIndecomposable_baseOf, Rat.toNNRat_le_toNNRat_iff, IsCompact.exists_isGLB, Rat.le_toNNRat_iff_coe_le, Cardinal.toENatAux_le_nat, Finsupp.Colex.addLeftMono, Hyperreal.lt_of_tendsto_zero_of_pos, Finset.Icc_add_one_sub_one_eq_Ioo, Cardinal.toENat_le_nat, Rat.toNNRat_le_iff_le_coe, Set.inf_eq_inter, DistLat.coe_id, FinBddDistLat.coe_comp, Rat.cast_le_intCast, Complex.UnitDisc.tendsto_pow_atTop_nhds_zero, Set.encard_pos, mem_nhdsLE_iff_exists_Icc_subset, NNRat.instOrderTopology, Int.preimage_floor_singleton, pow_abs, Int.abs_one_sub_fract, tsub_tsub_eq_min, Finset.map_orderEmbOfFin_univ, closure_Ico, Polynomial.degree_add_le, LaurentSeries.tendsto_valuation, abs_max_le_max_abs_abs, ENat.toENNReal_max, HahnSeries.SummableFamily.powers_toFun, Tropical.add_eq_right_iff, nhdsLT_eq_bot_iff, left_le_midpoint, Hyperreal.coe_max, Module.End.genEigenspace_div, Finset.exists_min_image, Set.unbounded_le_inter_lt, List.Perm.maximum_eq, Ordinal.typein_lt_self, LocallyConvexSpace.convex_open_basis_zero, Valuation.IsEquiv.le_one_iff_le_one, Set.encard_le_coe_iff, countable_setOf_isolated_left_within, Set.Iic_diff_Iic, isPiSystem_Icc, Order.isPredPrelimitRecOn_pred, Zsqrtd.instIsOrderedAddMonoidCastInt, PowerSeries.heval_unit, List.maximum_mono, Units.inv_neg, Ioi_mem_nhdsSet_Ici_iff, MeasureTheory.Measure.measure_Ioo_pos, hasBasis_nhdsSet_Ici_Ici, not_bddAbove_iff, pos_invOf_of_invertible_cast, Polynomial.abs_tendsto_atBot, List.foldr_min_of_ne_nil, Set.infinite_iff_exists_lt, Valuation.integer.coe_span_singleton_eq_setOf_le_v_coe, Nat.choose_le_pow_div, dvd_abs, DFinsupp.Colex.total_le, Valuation.Integers.wellFounded_gt_on_v_iff_discrete_mrange, oneLePart_lt, PUnit.canonicallyOrderedAdd, Order.pred_eq_pred_iff, StieltjesFunction.measure_Ioc, Finset.exists_mem_eq_sup', MeasureTheory.AEEqFun.coeFn_posPart, LinearOrder.bot_topologicalSpace_eq_generateFrom, strictConvex_iff_div, PNat.natPred_strictMono, pow_div_pow_eventuallyEq_atBot, ContinuousOn.lowerSemicontinuousOn, LaurentSeries.coe_range_dense, CategoryTheory.Limits.MultispanShape.ofLinearOrder_fst, InnerProductSpace.span_gramSchmidt_Iio, Odd.pow_lt_pow, Field.Emb.Cardinal.iSup_adjoin_eq_top, MeasureTheory.integrableOn_Ici_iff_integrableAtFilter_atTop, toWellOrderExtension_strictMono, Set.notMem_Iio, FiniteArchimedeanClass.coe_congrOrderIso_apply, MeasureTheory.integrableOn_Iic_iff_integrableAtFilter_atBot, Nat.nth_eq_orderEmbOfFin, zero_le', MvPowerSeries.le_weightedOrder, Module.End.genEigenspace_eq_genEigenspace_finrank_of_le, NonemptyFinLinOrd.hom_hom_comp, nhdsLE_basis_Icc, tendsto_floor_left_pure_ceil_sub_one, Set.compl_Iio, SimpleGraph.FarFromTriangleFree.lt_one, abs_mul_abs_self, Ordinal.toNatOrdinal_natCast, HahnSeries.orderTop_self_sub_one_pos_iff, min_cases, SimpleGraph.left_nonuniformWitnesses_card, AbsoluteValue.map_prod, Finset.lt_min'_iff, BooleanAlgebra.top_le_sup_compl, PowerSeries.intValuation_X, mabs_eq_inv_self, IsSumSq.nonneg, pow_two_pos_of_ne_zero, Set.Ioc_subset_Ioo_union_Icc, AddCircle.continuousAt_equivIco, isCofinal_setOf_imp_lt, SimplexCategory.toCat_obj, Finset.lt_sup_iff, Set.projIci_surjOn, Finpartition.mk_mem_sparsePairs, continuousAt_sign_of_pos, Int.floor_lt_self_iff, NatOrdinal.toOrdinal_symm_eq, CategoryTheory.SmallObject.SuccStruct.iterationCocone_pt, Polynomial.div_tendsto_atTop_zero_of_degree_lt, LocallyFiniteOrder.denselyOrdered_iff_subsingleton, toIcoMod_zero_one, IsDedekindDomain.HeightOneSpectrum.adicValued_apply', Hyperreal.stdPart_of_tendsto, ContinuousWithinAt.abs, OrderRingHom.subsingleton, MulArchimedeanClass.mem_ballSubgroup_iff, LatticeHom.birkhoffFinset_injective, PredOrder.nhdsLE, Finset.min_le_of_eq, midpoint_mem_segment, Set.encard_lt_encard_iff_encard_diff_lt_encard_diff, isLocallyClosed_Ioo, strictConcaveOn_iff_div, Int.gc_ceil_coe, LocallyFiniteOrder.orderAddMonoidHom_toAddMonoidHom, trichotomy_of_add_eq_add, ArchimedeanClass.mk_eq_top_iff, NatOrdinal.toOrdinal_one, ArchimedeanClass.mk_le_add_mk_of_archimedean, Pi.instNoMaxOrderColexForallOfWellFoundedGTOfNonempty, Order.isNormal_iff, Finset.inf'_le_iff, PowerSeries.IsWeierstrassFactorization.degree_eq_coe_lift_order_map, isGreatest_pair, supClosure_infClosure, OrderIso.subsingleton_of_wellFoundedGT, ArchimedeanClass.mk_right_le_mk_add_iff, Rat.cast_le_natCast, mabs_max_le_max_mabs_mabs, archimedean_iff_int_lt, Set.Ico_succ_right_eq_Icc, ArchimedeanClass.FiniteResidueField.mk_lt_mk, Function.mulSupport_max, Finset.min_insert, stdSimplex.barycenter_eq_centerMass, NNRat.Nonneg.coe_ofScientific, tendsto_const_mul_zpow_atTop_nhds_iff, HahnSeries.min_orderTop_le_orderTop_sub, Ordinal.toNimber_zero, CategoryTheory.SmallObject.iterationFunctorObjObjRightIso_ιIteration_app_right, Polynomial.div_tendsto_zero_of_degree_lt, cocompact_le_atBot_atTop, nhdsGT_eq_bot_iff, IsPreconnected.Icc_subset, Finsupp.DegLex.instIsOrderedCancelAddMonoidDegLexNat, cmp_mul_left', Mathlib.Meta.Positivity.pos_of_isRat, min_lt_max, NatOrdinal.toOrdinal_toNatOrdinal, FiniteMulArchimedeanClass.subgroup_eq_bot, interior_Ico, SMulPosStrictMono.toSMulPosReflectLE, RootPairing.rootForm_pos_of_ne_zero, Finset.sup_eq_zero, Set.ordConnected_iff_uIcc_subset_right, OrderIso.withZeroUnits_apply, Function.locallyFinsuppWithin.nsmul_negPart, LinOrd.hom_comp, AffineSpace.asymptoticNhds_eq_smul, smul_max_of_nonpos, exteriorPower.pairingDual_apply_apply_eq_one_zero, exists_seq_strictMono_tendsto, IsRealClosed.nonneg_iff_isSquare, MulArchimedeanClass.subgroup_antitone, WithZeroTopology.Iio_mem_nhds_zero, AddCircle.openPartialHomeomorphCoe_symm_apply, lt_mabs, GenContFract.IntFractPair.succ_nth_stream_b_le_nth_stream_fr_inv, SignType.pos_iff, SuccOrder.prelimitRecOn_succ, BddDistLat.ofHom_comp, frontier_Iic, Finset.subConst_le_inv_dens, upperSemicontinuous_iff_IsClosed_hypograph, NatOrdinal.instWellFoundedLT, Nat.preimage_floor_zero, Module.End.genEigenspace_nat, Affine.Simplex.ExcenterExists.signedInfDist_excenter, Icc_mem_nhds_iff, antivaryOn_iff_forall_mul_nonpos, IsSquare.nonneg, Padic.coe_withValRingEquiv_symm, MulArchimedeanClass.closedBallSubgroup_top, Dense.exists_lt, SuccOrder.nhdsGE, HahnSeries.leadingCoeff_mul_of_nonzero, Mathlib.Tactic.Order.ToInt.toInt_nlt_toInt, LinearOrder.supClosed, Int.abs_sub_lt_one_of_floor_eq_floor, frontier_Iic_subset, archimedean_iff_rat_lt, mabs_min_le_max_mabs_mabs, Valuation.HasExtension.mk_smul_mk, Nat.floor_eq_zero, WithTop.denselyOrdered_set_iff_subsingleton, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.w_assoc, ValuationSubring.mem_nonunits_iff, min_mul_mul_right, Cardinal.toENat_comp_ofENat, one_lt_leOnePart_iff, Real.Angle.sign_toReal, IsAbsoluteValue.abs_abv_sub_le_abv_sub, Valued.toNormedField.norm_lt_iff, MeasureTheory.aecover_Ioc_of_Ico, PseudoMetric.coe_finsetSup, NNRat.preimage_cast_Ioo, Int.floor_le, PowerSeries.IsWeierstrassFactorizationAt.degree_eq_coe_lift_order_map_of_ne_top, Set.sups_infs_subset_right, Valuation.rel_iff_le, sq_le_one_iff_abs_le_one, Polynomial.abs_isBoundedUnder_iff, HahnSeries.order_pow, MulArchimedeanClass.mk_le_mk, StieltjesFunction.iInf_Ioi_eq, segment_subset_uIcc, Set.Ici_succ_eq_Ioi, quasilinearOn_iff_mem_uIcc, lt_add_iff_lt_right_or_exists_lt, sign_eq_sign_or_eq_neg, Hyperreal.lt_of_st_lt, MulArchimedeanClass.mk_eq_top_iff, OrderEmbedding.birkhoffSet_apply, Pi.instNoMaxOrderLexForallOfWellFoundedLTOfNonempty, LocallyFiniteOrder.orderMonoidHom_strictMono, Rat.toNNRat_lt_iff_lt_coe, Set.Ico_subset_Icc_union_Ioo, Asymptotics.superpolynomialDecay_iff_superpolynomialDecay_abs, countable_image_gt_image_Ioi, ENat.strictMono_map_iff, MonomialOrder.lex_lt_iff, Nat.lt_ceil, FloorRing.gc_coe_floor, CategoryTheory.TransfiniteCompositionOfShape.ofArrowIso_isColimit, Hyperreal.coe_abs, MonomialOrder.eq_zero_iff, mabs_choice, PNat.natPred_lt_natPred, Filter.tendsto_div_const_atBot_iff, ENat.one_lt_top, Valuation.Integers.valuation_irreducible_pos, Module.End.genEigenspace_le_maximal, nhdsLE_sup_nhdsGT, LaurentSeries.comparePkg_eq_extension, NumberField.toNNReal_valued_eq_adicAbv, HahnSeries.finiteArchimedeanClassOrderIsoLex_apply_fst, Valuation.vlt_iff_lt, Cardinal.toENat_le_iff_of_lt_aleph0, lowerSemicontinuousOn_iff_preimage_Iic, MonoidWithZeroHom.inr_strictMono, nullMeasurableSet_Ico, convexJoin_left_comm, FiniteArchimedeanClass.ballAddSubgroup_strictAnti, min_add_add_left, one_lt_pow_iff, codisjoint_inf_left, CategoryTheory.HasLiftingProperty.transfiniteComposition.sqFunctor_obj, Nat.sub_one_lt_floor, Order.iso_of_countable_dense, disjoint_disjointed, Rat.preimage_cast_Ioo, DivisibleHull.archimedeanClassOrderIso_symm_apply, Ordinal.ToType.mk_apply, even_abs, Nonneg.coe_div, borel_eq_generateFrom_Ioc_le, iInter_Iic_eq_empty_iff, Valued.hasBasis_uniformity, LinearOrderedField.coe_lt_inducedMap_iff, Set.exists_lt_mem_inter_of_not_pairwiseDisjoint, ArchimedeanClass.addSubgroup_strictAntiOn, isCompl_compl, Nat.floor_mono, ArchimedeanClass.FiniteResidueField.ordConnected_preimage_mk, Valuation.mem_ltSubmodule_iff, nhds_basis_Ioo, MeasureTheory.stoppedValue_stoppedProcess_ae_eq, one_lt_mul_self_iff, StieltjesFunction.outer_Ioc, Module.End.mem_genEigenspace_nat, IsPreconnected.intermediate_value, Set.Iio_inter_Iio, List.minimum_le_of_mem', Nat.le_ceil, ContinuousAt.abs, PNat.instNoMaxOrder, isPiSystem_Ici, Set.preimage_sub_const_uIcc, FiniteArchimedeanClass.submodule_strictAnti, MeasureTheory.aecover_Ioo_of_Ico, PNat.lt_add_one_iff, ArchimedeanClass.mk_one, HahnSeries.orderTop_abs, Set.compl_Ici, DistLat.coe_comp, NNRat.cast_lt_one, Polynomial.degree_update_le, abs_dvd_self, Field.Emb.Cardinal.adjoin_image_leastExt, Complementeds.isCompl_coe, div_nonneg_iff, mul_nonneg_iff_neg_imp_nonpos, borel_eq_generateFrom_Ioi, LaurentSeries.valuation_def, BddDistLat.ext_iff, OrderIso.sumLexIioIci_apply_inl, zero_lt_iff, Set.projIci_coe, Mathlib.Tactic.Order.ToInt.exists_translation, HahnSeries.le_order_iff_forall, Valuation.integer.v_irreducible_lt_one, Cardinal.ofENat_toENat_le, sum_Ioc_inv_sq_le_sub, EReal.sign_mul_inv_abs, Left.pow_lt_one_iff, Nat.ceil_zero, Ordinal.typein_one_toType, MeasureTheory.aecover_Iio_of_Iio, disjoint_sup_left, mabs_eq_max_inv, NNRat.floor_def, PNat.card_Ioc, ArchimedeanClass.mem_ballAddSubgroup_iff, HahnSeries.forallLTEqZero_supp_BddBelow, Convex.combo_le_max, convexHull_prod, Set.bounded_le_inter_le, Filter.isBoundedUnder_le_abs, PNat.natPred_le_natPred, LinearOrderedCommMonoidWithZero.toMulPosStrictMono, zero_min, Rat.cast_pos, MvPowerSeries.order_add_of_order_ne, Set.encard_insert_le, Nat.pow_le_choose, FunctionField.inftyValuation.C, EisensteinSeries.tendsto_tsum_one_div_linear_sub_succ_eq, OrderTopology.of_discreteTopology, NNRat.preimage_cast_Ioc, Valuation.IsNontrivial.exists_lt_one, HahnSeries.instIsOrderedRingLexOfNoZeroDivisors, GeneralizedBooleanAlgebra.sup_inf_sdiff, Even.zpow_nonneg, mem_nhds_iff_exists_Ioo_subset, Set.encard_le_one_iff, Ordinal.toNimber_toOrdinal, Cardinal.toENat_le_one, interior_Ioo, Field.Emb.Cardinal.instFiniteDimensionalSubtypeMemIntermediateFieldAdjoinImageToTypeOrdRankCompCoeBasisWellOrderedBasisLeastExtIioSingletonSet, neg_one_lt_zero, Affine.Simplex.sign_signedInfDist_incenter, Affine.Simplex.ExcenterExists.sign_signedInfDist_excenter, LinearOrderedAddCommGroup.to_noMaxOrder, Finsupp.Colex.single_le_iff, MeasureTheory.aecover_Icc_of_Ioo, Ordinal.cof_type_lt, Nat.ceil_natCast, LinearOrderedAddCommGroup.isAddCyclic_iff_not_denselyOrdered, round_eq_iff, PNat.lt_find_iff, FiniteMulArchimedeanClass.subsemigroup_eq_subgroup, Set.Iio_subset_Iio_union_Ico, Finset.pluennecke_ruzsa_inequality_pow_div_pow_div, Ordinal.toNimber_max, mem_segment_add_sub, OrderTopology.of_linearLocallyFinite, Fin.finsetImage_val_uIcc, Filter.tendsto_div_const_atTop_iff, isClosed_Ico_iff, MeasureTheory.countable_meas_le_ne_meas_lt, Finset.sup_inf_sup, Set.encard_le_encard_of_injOn, min_eq_left_iff, ArchimedeanOrder.instTotalLe, Set.Iio_subset_Iic_union_Ico, frontier_Iio, IsCoprime.abs_abs_iff, Hyperreal.IsSt.lt, denselyOrdered_set_iff_subsingleton, NNRat.cast_lt, infClosure_supClosure, Set.encard_tsub_one_le_encard_diff_singleton, pow_pos_iff, ENat.mul_le_mul_right_iff, HomotopicalAlgebra.RelativeCellComplex.Cells.hj, convexHull_eq_union, Set.preimage_div_const_uIcc, EReal.sign_mul_abs, Order.Ioo_eq_empty_iff_pred_le, DistLat.Iso.mk_hom, Cardinal.toENat_injOn, ArchimedeanClass.min_le_mk_sub, PredOrder.isOpen_singleton_iff, untrop_sum_eq_sInf_image, LinearIndepOn.encard_le_toENat_rank, Ordinal.sup_typein_limit, Int.preimage_ceil_singleton, antivary_iff_forall_mul_nonpos, pow_le_one_iff, Rat.HeightOneSpectrum.valuation_equiv_padicValuation, DivisibleHull.instIsStrictOrderedModuleRat, le_inv_self_iff, LaurentSeries.valuation_le_iff_coeff_lt_log_eq_zero, convexHull_eq, GenContFract.le_of_succ_get?_den, RootPairing.RootPositiveForm.zero_lt_apply_root_root_iff, Cardinal.toENat_eq_nat, exists_seq_strictAnti_tendsto_nhdsWithin, Pi.instNoMinOrderColexForallOfWellFoundedGTOfNonempty, convexJoin_assoc_aux, isPiSystem_Ioo, Orientation.oangle_sign_smul_add_smul_right, boolAlg_dual_comp_forget_to_bddDistLat, MeasureTheory.aecover_Ico_of_Ioc, borel_eq_generateFrom_Iio, Rat.lt_toNNRat_iff_coe_lt, div_le_div_flip, CategoryTheory.HasLiftingProperty.transfiniteComposition.sqFunctor_map, Set.one_lt_encard_iff_nontrivial, LaurentSeries.uniformContinuous_coeff, CategoryTheory.MorphismProperty.IsCardinalForSmallObjectArgument.preservesColimit, GenContFract.zero_le_of_contsAux_b, Mathlib.Meta.NormNum.IsInt.natCeil, Finsupp.DegLex.wellFoundedLT, WithBot.coe_max, LinearOrderedAddCommGroup.Subgroup.exists_neg_generator, AddSubgroup.isLeast_of_closure_iff_eq_abs, ArchimedeanClass.eq_zero_or_top_of_archimedean, tendsto_pow_div_pow_atTop_atTop, mabs_lt, LinearLocallyFiniteOrder.le_succFn, CategoryTheory.IsGrothendieckAbelian.generatingMonomorphisms.functorToMonoOver_obj, HasStrictFDerivAt.hasStrictFDerivAt_norm_smul, min_le_emultiplicity_add, Polynomial.signVariations_eq_eraseLead_add_ite, List.sortedGE_mergeSort, Ordinal.toNimber_eq_one, Filter.Germ.const_min, Multiset.toDFinsupp_inter, Valuation.mem_leIdeal_iff, WithZeroTopology.tendsto_zero, LinearOrderedAddCommGroupWithTop.sub_le_sub_iff_left_of_ne_top, IsNonarchimedean.multiset_image_add, apply_abs_le_add_of_nonneg', Padic.norm_rat_le_one_iff_padicValuation_le_one, emultiplicity_pos_iff, LinearOrderedSemiring.toLocallyConvexSpace, Finset.exists_pos_of_sum_zero_of_exists_nonzero, Nonneg.Icc_subset_segment, Set.nontrivial_iff_exists_lt, Set.bounded_ge_inter_gt, Set.notMem_Ici, Valued.isClosed_closedBall, SignType.lt_one_iff, ENat.succ_def, mem_nhdsGT_iff_exists_Ioo_subset, Cardinal.nat_le_ofENat, Set.smul_Icc, Finset.Ico_succ_left_eq_Ioo, Set.integer_valuation_le_one, grade_covBy_grade_iff, sq_abs, CategoryTheory.SmallObject.SuccStruct.instIsWellOrderContinuousIterationFunctor, interior_Iic, Filter.Tendsto.min, Valuation.coe_ltAddSubgroup, Cardinal.ofENat_toENat_eq_self, AddCircle.coe_image_Ico_eq, Finset.sum_sym2_filter_not_isDiag, Finset.Iic_sub_one_eq_Iio, Order.le_succ_bot_iff, IsDedekindDomain.HeightOneSpectrum.coe_smul_adicCompletion, List.max_sum_le, Finsupp.DegLex.le_iff, Rat.surjective_padicValuation, interior_Ioi, WithTop.le_of_forall_lt_iff_le, Real.smoothTransition.projIcc, Set.Finite.convexHull_eq_image, MonoidWithZeroHom.inl_mono, BooleanAlgebra.le_top, convexJoin_right_comm, nhdsWithinLT_sup_nhdsWithinGE, Affine.Simplex.sOppSide_affineSpan_faceOpposite_point_right_iff, antivaryOn_iff_exists_antitoneOn_monotoneOn, FinBddDistLat.id_apply, Matrix.isIrreducible_iff, MvPolynomial.schwartz_zippel_sum_degreeOf, Mathlib.Meta.NormNum.IsInt.natFloor, FiniteMulArchimedeanClass.val_mk, Set.range_injOn_strictMono, FiniteArchimedeanClass.ball_strictAnti, right_le_midpoint, Int.ceil_mono, CategoryTheory.TransfiniteCompositionOfShape.ofComposableArrows_incl_app, Continuous.exists_forall_le_of_hasCompactMulSupport, ArchimedeanClass.orderHom_top, ENat.exists_nat_gt, Topology.IsLower.isTopologicalBasis_insert_univ_subbasis, mem_openSegment_iff_div, MeasureTheory.AEEqFun.posPart_mk, HahnEmbedding.Partial.eval_zero, CauSeq.lt_total, Finset.sup_add, max_neg_zero, nhdsGE_basis, measurable_IocProdIoc, Cardinal.ofENat_toENat, Ordinal.typein_le_typein', StieltjesFunction.measure_Ico, Hyperreal.abs_omega, Left.nsmul_neg_iff, IsNonarchimedean.apply_intCast_le_one_of_isNonarchimedean, BddDistLat.comp_apply, Set.ordConnected_iff_uIcc_subset, NNRat.cast_le_natCast, antivaryOn_iff_forall_smul_nonpos, List.minimum_concat, tendsto_floor_left, CategoryTheory.Limits.MultispanIndex.toLinearOrder_left, Multiset.sum_min_le, OrderEmbedding.isEmbedding_of_ordConnected, LinearOrderedCommGroup.to_noMaxOrder, convexHull_rangle_single_eq_stdSimplex, Hyperreal.InfinitePos.pos, Function.Injective.encard_range, Set.biUnion_Ioc_eq_Ioi_self_iff, BddDistLat.hom_comp, instAssociativeMin, Set.encard_le_one_iff_eq, sameRay_smul_right_iff, HahnSeries.finiteArchimedeanClassOrderIso_apply, LaurentSeries.ratfuncAdicComplRingEquiv_apply, LinearOrderedAddCommGroupWithTop.strictMono_add_right_of_ne_top, WithTop.tendsto_nhds_top_iff, Polynomial.isLittleO_atBot_of_degree_lt, min_mabs_mabs_le_mabs_max, AffineSpace.asymptoticNhds_eq_smul_vadd, MonomialOrder.div, Finset.pluennecke_ruzsa_inequality_pow_mul, Nimber.toOrdinal_symm_eq, convexHull_union, sq_pos_of_ne_zero, convexHull_sub, Hyperreal.infinitePos_def, Associated.abs_right, Topology.RelCWComplex.skeletonLT_I, Cardinal.aleph_toENat, maximal_iff_isGreatest, cmp_div_one', WithZeroTopology.orderClosedTopology, Finsupp.support_sup, Int.cast_le_neg_one_or_one_le_cast_of_ne_zero, Irreducible.maximalIdeal_pow_eq_setOf_le_v_coe_pow, Finset.lt_fold_max, tendsto_ceil_right, PowerSeries.coeff_heval_zero, Subgroup.HasDetPlusMinusOne.abs_det, MeasureTheory.Measure.measure_Ioi_pos, smul_nonneg_iff_pos_imp_nonneg, MonomialOrder.lex_le_iff, exists_pos_left_iff_sameRay_and_ne_zero, HahnSeries.instIsDomainOfIsCancelAdd, abs_add_three, bddDistLat_dual_comp_forget_to_distLat, sameRay_neg_smul_left_iff, DistLat.comp_apply, Nat.floor_zero, CategoryTheory.SmallObject.prop_iterationFunctor_map_succ, Rat.cast_le, Multiset.toDFinsupp_union, Order.not_isMax_pred, zsmul_le_zsmul_iff_right, antivary_iff_forall_smul_nonpos, Finset.Ico_filter_lt, FiniteArchimedeanClass.min_le_mk_add, Finset.min_mono, Set.lt_iff_ssubset, IsDedekindDomain.HeightOneSpectrum.intValuation_exists_uniformizer, Continuous.bddBelow_range_of_hasCompactMulSupport, antivaryOn_iff_mul_rearrangement, Set.Ioo_sub_one_left_eq_Ioc, Nat.inv_pos_of_nat, HahnSeries.min_le_min_add, convexHull_list_sum, Set.not_monotoneOn_not_antitoneOn_iff_exists_lt_lt, Nat.floor_one, gauge_smul_left, Nat.floor_sub_ofNat, exists_Icc_mem_subset_of_mem_nhds, measurableSet_Ioc, MonomialOrder.degree_sPolynomial_le, OrderEmbedding.range_inj, AffineSubspace.wOppSide_iff_exists_right, EReal.sign_neg, LinearOrderedField.cutMap_self, add_self_nonpos_iff, GroupCone.oneLE.isMaxMulCone, WithVal.le_def, HasCountableSeparatingOn.range_Ici, Finset.pluennecke_ruzsa_inequality_nsmul_sub, Hyperreal.stdPart_omega, Set.Ioc_inter_Ioi, Nat.floor_eq_iff', List.argmin_eq_some_iff, IsDiscreteValuationRing.addVal_le_iff_dvd, Mathlib.Meta.NormNum.isNNRat_le_false, isPiSystem_Icc_mem, ArchimedeanClass.liftOrderHom_mk, Valuation.HasExtension.val_map_lt_one_iff, abs_one, LinearOrderedAddCommGroupWithTop.sub_self_nonneg, Finset.inf'_sup_distrib_left, LinearOrderedField.cutMap_bddAbove, CategoryTheory.TransfiniteCompositionOfShape.map_incl, ArchimedeanClass.orderHom_mk, zmultiples_abs, covBy_iff_lt_iff_le_right, WithBot.denselyOrdered_set_iff_subsingleton, Set.Ici.subtype_functor_final, Set.ordConnectedProj_eq, Metric.isBounded_of_abs_le, Set.Iic_subset_Iio_union_Icc, IicProdIoc_comp_restrict₂, CategoryTheory.SimplicialThickening.Path.le_right, StieltjesFunction.length_Ioc, Order.lt_succ_bot_iff, Continuous.lowerSemicontinuous, Order.pred_lt_iff, MvPolynomial.IsSymmetric.antitone_supDegree, Set.encard_le_encard, ENat.toENNReal_le, Valuation.one_le_val_iff, Cardinal.toENat_eq_iff_of_le_aleph0, FiniteMulArchimedeanClass.mk_lt_mk, Submonoid.closure_image_one_lt_and_isMulIndecomposable, WithTop.coe_min, Set.Ioo_disjoint_Ioo, MulArchimedeanClass.mk_right_le_mk_div_iff, IsCompact.bddBelow_image, four_mul_le_pow_two_add, Valuation.Compatible.vle_iff_le, Mathlib.Tactic.PNatToNat.coe_le_coe, SetTheory.PGame.nim_grundyValue, Iotop_subset_Ioc, PNat.le_one_iff, atTop_le_cocompact, WithZeroTopology.isOpen_Iio, NNRat.floor_natCast_div_natCast, Finsupp.Lex.addRightMono, max_zero_sub_eq_self, Int.fract_nonneg, MonomialOrder.degree_sub_leadingTerm_lt_degree, CauSeq.exists_gt, projIcc_eq_zero, nhds_bot_basis_Iic, Set.integer_eq, mabs_div_lt_iff, measurableSet_lt', Ici_mem_nhdsSet_Ici_iff, Positive.coe_zpow, WithTop.continuousOn_untopA, nhds_top_basis, Hyperreal.abs_lt_real_iff_infinitesimal, Int.preimage_fract, zpow_le_zpow_iff_left, inv_lt_self_iff, instLawfulOrderSup_mathlib, AffineIndependent.not_wbtw_of_injective, Hyperreal.infinitesimal_pos_iff_infinitePos_inv, Multiset.abs_sum_le_sum_abs, AddGroupCone.nonneg.isMaxCone, oneLePart_eq_ite, PowerSeries.order_add_of_order_ne, Module.End.hasGenEigenvector_iff, MulArchimedeanClass.orderHom_mk, Module.Basis.orientation_neg_single, IsCompact.exists_isGreatest, MvPolynomial.leadingCoeff_toLex, Measurable.min, LinearOrder.isPredArchimedean_of_isSuccArchimedean, Ico_subset_biUnion_Ico, ArchimedeanClass.mk_div, abs_le_one_iff_mul_self_le_one, nullMeasurableSet_lt, odd_abs, Set.range_IicExtend, CategoryTheory.TransfiniteCompositionOfShape.map_F, antivary_comm, HahnSeries.leadingCoeff_neg_iff, CategoryTheory.SimplicialThickening.Path.le, ENat.tendsto_nhds_top_iff_natCast_lt, Filter.Germ.min_def, Order.IsNormal.strictMono, iUnion_Ioc_intCast, convexOn_iff_div, Finset.infs_sups_subset_left, Nonneg.coe_zpow, left_mem_openSegment_iff, MonomialOrder.degree_monomial_le, CategoryTheory.SimplicialThickening.functor_id, HahnSeries.order_mul_of_ne_zero, Units.zero_lt, Set.range_injOn_strictAnti, OrderMonoidWithZeroHom.comp_mul, AffineSubspace.setOf_sOppSide_eq_image2, AddValuation.map_add, Finsupp.toMultiset_sup, Module.End.mem_genEigenspace_zero, Finset.Ioc_disjoint_Ioc, Valuation.ltIdeal_mono, Valuation.IsEquiv.lt_one_iff_lt_one, Set.encard_iUnion_le_of_fintype, ProbabilityTheory.gaussianPDFReal_mul, Even.convexOn_pow, abs_sub_pos, Set.one_le_encard_iff_nonempty, Int.sign_eq_sign, Ideal.height_le_spanRank_toENat, Archimedean.embedReal_one, borel_eq_generateFrom_Iic, MonomialOrder.degLex_single_lt_iff, CategoryTheory.OrthogonalReflection.iteration_map_succ_surjectivity, Set.unbounded_ge_iff, strictConvexOn_iff_div, CauSeq.trichotomy, nhdsLE_sup_nhdsGE, ContinuousAt.mabs, NNRat.bddAbove_coe, CategoryTheory.Limits.WalkingMultispan.inclusionOfLinearOrder_map, PointedCone.mem_maxTensorProduct, MeasureTheory.aecover_Ico_of_Icc, List.getElem_le_maximum_of_length_pos, lineMap_lt_lineMap_iff_of_lt', Int.padicValuation_le_one, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.w₁, Finsupp.support_inf, max_left_commutative, ArchimedeanClass.addValuation_apply, MeasureTheory.aecover_Ico_of_Ico, Valuation.isEquiv_iff_val_lt_one, Cardinal.natCast_eq_toENat_iff, le_max_iff, IsDedekindDomain.HeightOneSpectrum.embedding_mul_absNorm, nsmul_pos_iff, Set.not_equitableOn, AffineSubspace.not_sOppSide_self, HahnSeries.inv_single, BooleanAlgebra.bot_le, Valuation.IsUniformizer.val_lt_one, ENat.eq_top_iff_forall_ge, MultilinearMap.map_sub_map_piecewise, Cardinal.ofENat_le_nat, Finsupp.Colex.single_lt_iff, ContinuousAt.lowerSemicontinuousAt, segment_subset_closure_openSegment, CategoryTheory.SmallObject.iterationFunctorMapSuccAppArrowIso_hom_right_right_comp, IsNonarchimedean.finset_powerset_image_add, ringHom_monotone, SMulPosReflectLE.toSMulPosStrictMono, Mathlib.Tactic.PNatToNat.coe_lt_coe, monovaryOn_iff_exists_antitoneOn, MonomialOrder.degree_sub_LTerm_lt, HahnModule.instIsTorsionFree, wbtw_pointReflection, NNRat.cast_lt_natCast, linOrd_dual_comp_forget_to_Lat, continuous_abs, instNonemptySeedRatReal, abs_min_sub_min_le_max, countable_setOf_isolated_left, Finset.pluennecke_ruzsa_inequality_nsmul_sub_nsmul_add, Hyperreal.coe_le_coe, MulArchimedeanClass.min_le_mk_div, CategoryTheory.TransfiniteCompositionOfShape.ofComposableArrows_isColimit, LocallyFiniteOrder.orderMonoidWithZeroHom_strictMono, Nimber.toOrdinal_zero, monovaryOn_iff_mul_rearrangement, ENat.mul_le_mul_left_iff, AffineSubspace.setOf_wSameSide_eq_image2, NatOrdinal.toOrdinal_zero, mul_nonneg_of_three, Module.End.genEigenspace_le_genEigenspace_finrank, MonomialOrder.sPolynomial_lt_of_degree_ne_zero_of_degree_eq, mabs_div_mabs_le_mabs_div, NumberField.FinitePlace.norm_le_one, min_mabs_mabs_le_mabs_min, CategoryTheory.Limits.MultispanShape.ofLinearOrder_snd, Order.Iic_succ, PseudoMetric.finsetSup_apply, add_self_neg_iff, Dense.exists_seq_strictMono_tendsto, Module.End.mem_genEigenspace, FinBddDistLat.hom_id, Collinear.wbtw_or_wbtw_or_wbtw, Valuation.mem_integer_iff, FinBddDistLat.dual_map, Nat.cast_mul_floor_div_cancel, Units.mulArchimedean_iff, infPrime_iff_infIrred, Nat.mul_cast_floor_div_cancel, Set.powersetCard.mem_range_ofFinEmbEquiv_symm_iff_mem, nsmul_nonpos_iff, Finsupp.DegLex.monotone_degree, le_emultiplicity_iff_replicate_subperm_primeFactorsList, ArchimedeanClass.mk_antitoneOn, partialSups_add_one_eq_sup_disjointed, Rat.toNNRat_lt_toNNRat_iff, isPiSystem_Iic, Affine.Simplex.face_points', Finset.codisjoint_inf_left, nhdsGT_sup_nhdsWithin_singleton, abs_eq_abs, HahnSeries.addVal_apply, tendsto_fract_right, Cardinal.toENat_nat, tendsto_floor_left_pure_sub_one, Hyperreal.coe_lt_coe, LinearOrderedCommGroup.Subgroup.exists_generator_lt_one, Tropical.trop_inf, HahnEmbedding.Partial.exists_domain_eq_top, cmp_add_right, Topology.RelCWComplex.skeletonLT_monotone, div_lt_one_iff, FiniteMulArchimedeanClass.subgroup_strictAnti, PowerSeries.nat_le_order, WeierstrassCurve.IsGoodReduction.goodReduction, LinearOrderedCommGroupWithZero.discrete_iff_not_denselyOrdered, NNRat.coe_min, Order.pred_lt_iff_eq_or_gt, LinearOrderedCommGroup.discrete_or_denselyOrdered, Finset.dens_union_le, Polynomial.roots_countP_pos_le_signVariations, Valued.isClopen_closedBall, ArchimedeanClass.mk_eq_zero_of_archimedean, PNat.map_subtype_embedding_Ioc, SimplexCategory.toCat_map, Dense.Ioi_eq_biUnion, upperSemicontinuousOn_iff_isClosed_hypograph, Nimber.toOrdinal_toNimber, HahnSeries.cardSupp_hsum_powers_le, min_inv_inv', Finset.uIcc_injective_left, abs_eq_self, NonemptyFinLinOrd.mono_iff_injective, lt_neg_self_iff, Finset.sup'_mul, nhdsLT_sup_nhdsGT, DistLat.hom_comp, Rat.preimage_cast_Ioc, iUnion_Iio_eq_univ_iff, LinearOrderedCommGroupWithZero.inl_apply, Set.bounded_lt_inter_le, nhdsLT_neBot, ArchimedeanClass.mk_sub_lt_mk_left_iff, WithTop.continuous_untop, CategoryTheory.SmallObject.preservesColimit, FinBddDistLat.ofHom_id, Filter.tendsto_abs_atTop_atTop, Orientation.eq_or_eq_neg_of_isEmpty, Valuation.leAddSubgroup_monotone, DistLat.inv_hom_apply, LinearOrderedCommGroupWithZero.inr_apply, Finsupp.Lex.single_le_iff, isPiSystem_Ioo_mem, Orientation.oangle_sign_smul_add_smul_left, Dense.exists_gt, convexOn_zpow, RootPairing.posRootForm_rootFormIn_posDef, abs_zsmul, Polynomial.degree_sub_le_of_le, Module.End.genEigenspace_zero, not_linearIndepOn_finset_iffₒₛ, Polynomial.le_trailingDegree_X_pow, continuousWithinAt_iff_continuous_left_right, Matroid.toENat_cRank_eq, Polynomial.supDegree_eq_natDegree, List.minimum_le_coe_iff, Polynomial.degree_add_eq_of_leadingCoeff_add_ne_zero, measurableSet_bddBelow_range, ValuationSubring.algebraMap_injective, Hyperreal.st_eq_sSup, Nonneg.toNonneg_lt, PosSMulMono.toPosSMulReflectLT, abs_min_le_max_abs_abs, Finset.orderEmbOfFin_mem, Ordinal.toNatOrdinal_toOrdinal, Set.Finite.encard_biUnion_le, Finset.max_prod_le, Hyperreal.infinitePos_abs_iff_infinite, ContinuousWithinAt.upperSemicontinuousWithinAt, MvPowerSeries.le_order_pow, MeasureTheory.aecover_Icc_of_Ico, Nat.factorization_gcd, Set.projIic_eq_self, continuousAt_sign_of_ne_zero, AffineSubspace.wOppSide_pointReflection, tendsto_floor_right', IsValuativeTopology.mem_nhds_iff, PowerSeries.heval_mul, Int.lt_floor_iff, lowerSemicontinuousWithinAt_iff_frequently, MulArchimedeanClass.subgroup_eq_bot, nhds_basis_mabs_div_lt, Valuation.pos_iff, LinearOrderedCommGroup.discrete_iff_not_denselyOrdered, Valued.norm_pos_iff_valuation_pos, wbtw_midpoint, Nat.ceil_eq_iff, exists_zero_lt, List.maximum_eq_coe_iff, Rat.natCast_lt_cast, HahnSeries.SummableFamily.support_powerSeriesFamily_subset, PredOrder.prelimitRecOn_pred, Ordinal.enum_zero_le', HahnSeries.zero_ofSuppBddBelow, smulPosMono_iff_smulPosReflectLT, MeasureTheory.IsSetSemiring.Ioc, List.sortedGE_insertionSort, tsub_add_eq_max, LocallyFiniteOrder.orderAddMonoidEquiv_apply, Right.sign_neg, List.le_maximum_of_length_pos_iff, Set.compl_Ioc, AffineIndependent.convexHull_inter, List.coe_minimum_of_length_pos, CauSeq.sup_inf_distrib_left, exists_le_add_iff_le_right, LinOrd.comp_apply, NatOrdinal.toOrdinal_eq_one, Finset.Ici_add_one_eq_Ioi, abs_zpow, isPiSystem_image_Ici, ArchimedeanClass.FiniteElement.mk_natCast, Odd.geom_sum_pos, LinOrd.coe_comp, IsDedekindDomain.HeightOneSpectrum.valuation_le_one, ENat.one_lt_card, ENat.self_le_mul_right, ENat.add_le_add_iff_left, PosSMulMono.toPosSMulReflectLE, tendsto_pow_atTop_nhds_zero_iff, Set.Ioi_inter_Ioi, Dense.borel_eq_generateFrom_Ioc_mem, ENat.mul_right_strictMono, CategoryTheory.SmallObject.iterationFunctorObjObjRightIso_ιIteration_app_right_assoc, instIsPrincipalIdealRingSubtypeMemSubringIntegerWithZeroMultiplicativeIntValuation, Finset.max'_lt_iff, comap_coe_nhdsGT_eq_atBot_iff, MeasureTheory.uIoc_ae_eq_interval, Finset.listMap_orderEmbOfFin_finRange, strictConvex_Ioi, Ordinal.familyOfBFamily_enum, Polynomial.div_tendsto_atTop_zero_iff_degree_lt, Valued.toNormedField.norm_lt_one_iff, le_min_iff, CauSeq.inf_idem, CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.ofComposableArrows_isoBot_hom, Cardinal.power_le_max_power_one, UpperSet.total_le, instLawfulOrderInf_mathlib, Nat.add_one_le_ceil_iff, HahnSeries.mem_orderTopSubOnePos_iff, Continuous.exists_forall_ge_of_hasCompactMulSupport, denselyOrdered_iff_denselyOrdered_units_and_nontrivial_units, Measurable.nat_ceil, Continuous.min, SuccOrder.nhdsLT_eq_nhdsNE, compl_sup_eq_top, CategoryTheory.TransfiniteCompositionOfShape.ici_incl, IsDedekindDomain.HeightOneSpectrum.valuationOfNeZeroToFun_eq, Finset.uIcc_subset_uIcc_union_uIcc, Order.sub_one_lt_iff, ZSpan.mem_fundamentalDomain, exists_succ_iterate_or, MeasureTheory.aecover_Ioo_of_Icc, Set.Iio_subset_Iic_union_Ioo, Set.Ici_eq_singleton_iff_isTop, Real.log_of_ne_zero, Set.disjoint_range_iff, ArchimedeanClass.mk_map_of_archimedean', Filter.tendsto_uIcc_of_Icc, Module.End.genEigenspace_le_smul, CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.mem_map, Order.lt_one_iff_nonpos, Subgroup.isLeast_of_closure_iff_eq_mabs, MvPowerSeries.min_order_le_add, Nonneg.orderedSub, AddCircle.liftIco_eq_lift_Icc, PNat.card_fintype_Icc, MeasureTheory.ae_restrict_uIoc_eq, Finset.Nonempty.dens_pos, succ_max, FiniteArchimedeanClass.addSubgroup_eq_bot, WithZero.min_le_iff, mabs_div_le_iff, WithZeroTopology.nhds_eq_update, ValuativeRel.uniformizer_lt_one, nhdsGT_neBot, continuous_max, archimedean_iff_int_le, min_eq_top, Finset.add_sup'', countable_setOf_covBy_right, PowerSeries.le_order_prod, ValuativeRel.uniformizer_pos, HahnEmbedding.Partial.exists_isMax, Archimedean.mkRat_mem_ratLt, CauSeq.bounded, NNRat.cast_le_ofNat, exists_uIoo_isExtrOn_uIcc, Ordinal.type_toType, le_add_iff_lt_right_or_exists_le, LinearOrderedAddCommGroup.isAddCyclic_iff_nonempty_equiv_int, HahnSeries.orderTop_embDomain, Valuation.IsRankOneDiscrete.exists_generator_lt_one, SignType.neg_iff, Ordinal.nmul_eq_mul, PowerSeries.order_add_of_order_eq, Set.preimage_const_add_uIcc, Set.Finite.convexHull_eq, BoundedGENhdsClass.of_closedIicTopology, Archimedean.embedRealFun_strictMono, HahnSeries.cardSupp_inv_le, MeasureTheory.Measure.measure_Iio_pos, Hyperreal.stdPart_epsilon, min_add, Set.IsPWO.of_linearOrder, Profinite.NobelingProof.Products.instWellFoundedLT, mabs_div_le_one, ZNum.isStrictOrderedRing, MulArchimedeanClass.mk_div_lt_mk_right_iff, Matrix.eRank_submatrix_le, Finset.dens_le_dens, DFinsupp.Lex.total_le, Complex.sum_div_factorial_le, Set.empty_disjoint, Hyperreal.ofSeq_lt_ofSeq, Module.End.genEigenspace_restrict, ContinuousAt.upperSemicontinuousAt, orderTopology_of_ordConnected, finSumEquivOfFinset_inl, exists_one_lt', CategoryTheory.TransfiniteCompositionOfShape.ofOrderIso_isColimit, exists_rat_lt, CategoryTheory.SimplicialThickening.functor_obj_as, Set.Ioo_subset_uIoo', Set.Ioc_sub_one_left_eq_Icc, Archimedean.of_locallyFiniteOrder, LinearOrder.topologicalLattice, FunctionField.inftyValuation_apply, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.w₂, IsCompact.exists_isMaxOn, MulArchimedeanClass.mulArchimedean_of_mk_eq_mk, Order.Ioc_pred_left, isClosed_Ioo_iff, Fintype.not_linearIndependent_iffₒₛ, min_add_distrib, nonneg_add_self_iff, zpow_lt_zpow_iff_left, sub_le_sub_flip, Odd.pow_nonpos_iff, Polynomial.cyclotomic_pos, Dense.borel_eq_generateFrom_Icc_mem, Finset.Iic_diff_Ioc, Set.disjoint_union_left, ValuativeRel.instMulArchimedeanValueGroupWithZeroOfIsRankLeOne, ArchimedeanClass.ball_antitone, Set.Ioo_inter_Ioo, Finset.Ico_succ_succ_eq_Ioc, starConvex_iff_div, nhdsSet_Ioi, Finset.sup'_eq_zero, Mathlib.Meta.NormNum.IsNat.natFloor, Left.sign_neg, Affine.Simplex.sOppSide_affineSpan_faceOpposite_iff, measurableSet_bddAbove_range, Finset.le_max, HahnSeries.min_orderTop_le_orderTop_add, Profinite.NobelingProof.Products.eval_πs_image, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.w₁_assoc, PNat.one_le_find, Valuation.val_le_one_iff, max_sub_sub_right, Filter.tendsto_mul_const_atBot_iff, HahnSeries.leadingCoeff_nonpos_iff, StieltjesFunction.right_continuous, sdiff_inf_sdiff, Odd.pow_le_pow, Set.instOrdConnectedOrdConnectedComponent, sup_Prop_eq, Filter.Germ.max_def, LaurentSeries.exists_ratFunc_eq_v, HahnSeries.SummableFamily.powerSeriesFamily_smul, Cardinal.natCast_le_toENat_iff, Polynomial.trailingDegree_one_le, Set.Ioi_subset_Ioc_union_Ici, min_bot_right, Valued.toNormedField.one_le_norm_iff, Pi.Lex.isStrictOrder, Even.pow_abs, EReal.sign_mul_inv_abs', countable_image_gt_image_Iio, Stream'.Seq.lt_length'_iff, Set.Finite.encard_strictMonoOn, le_iff_forall_one_lt_le_mul, Set.mem_ordConnectedComponent, ENat.add_lt_add_iff_right, wellFoundedLT_toType, one_lt_ltOnePart_iff, openSegment_subset_union, Nat.cast_inv_le_one, Finset.divConst_le_inv_dens, multiplicity_le_emultiplicity, Hyperreal.gt_of_neg_of_infinitesimal, LinearOrderedCommGroupWithZero.wellFoundedOn_setOf_le_lt_iff_nonempty_discrete_of_ne_zero, Finset.instAssociativeDisjSups, Int.add_one_le_ceil_iff, Nat.lt_floor_add_one, Finsupp.Lex.wellFoundedLT_of_finite, OrderIso.sumLexIioIci_apply_inr, Rat.comap_cast_atTop, MonomialOrder.degree_sPolynomial_lt_sup_degree, Padic.isDenseInducing_cast_withVal, left_lt_lineMap_iff_pos, add_lt_add_iff_right_of_ne_top, Set.encard_le_one_iff_subsingleton, HahnEmbedding.Seed.domain_baseEmbedding, NNRat.cast_lt_ofNat, Nat.one_div_lt_one_div, Finsupp.toMultiset_inf, Set.monotone_powerset, abs_le_iff_mul_self_le, Finset.abs_prod, PNat.mod_le, Continuous.bddAbove_range_of_hasCompactSupport, ArchimedeanClass.mem_closedBallAddSubgroup_iff, Finset.disjiUnion_Iic_disjointed, sign_eq_neg_one_iff, FiniteArchimedeanClass.withTopOrderIso_apply_coe, CategoryTheory.SimplicialThickening.functor_comp, LinearOrderedField.mem_cutMap_iff, Module.End.pos_finrank_genEigenspace_of_hasEigenvalue, Set.Iio_injective, Finset.orderEmbOfFin_compl_singleton_apply, BddDistLat.hom_inv_apply, ENat.lt_coe_add_one_iff, Dense.borel_eq_generateFrom_Icc_mem_aux, Dense.topology_eq_generateFrom, Asymptotics.isLittleO_pow_pow_atTop_of_lt, DFinsupp.Colex.isStrictOrder, Metric.isBounded_of_abs_lt, Finset.mulConst_le_divConst_sq, ENat.card_le_one, trop_sInf_image, negPart_eq_ite_lt, Polynomial.le_trailingDegree_X, Module.length_eq_rank, WithTop.nhds_coe, min_left_commutative, FiniteMulArchimedeanClass.coe_congrOrderIso_apply, SetTheory.PGame.nim_add_nim_equiv, intermediate_value_Ioc, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.w₂_assoc, NNRat.preimage_cast_Iio, CauSeq.const_pos, PseudoMetric.nonneg, Ioo_subset_Iotop, intermediate_value_Ico, Tropical.untrop_sup, MonomialOrder.degree_sub_leadingTerm_lt_iff, NNRat.ofNat_lt_cast, sign_eq_one_iff, exists_le_add_iff_le_left, Set.Ioi_injective, Set.unbounded_lt_inter_lt, Subfield.toIsStrictOrderedRing, ArchimedeanClass.FiniteResidueField.instIsOrderedRing, Cardinal.toENat_lt_top, MonomialOrder.degree_sub_leadingTerm_le, Valuation.exists_div_eq_of_surjective, le_abs', Valuation.Integers.maximalIdeal_pow_eq_setOf_le_v_algebraMap_pow, Submonoid.mem_closure_image_one_lt_iff, Finset.mul_sup₀, IsDedekindDomain.HeightOneSpectrum.intValuation_apply, IsCoprime.abs_abs, Finset.min'_eq_inf', nhdsLE_basis, Cardinal.lift_min, Int.preimage_Ico, Filter.Germ.abs_def, le_add_iff_lt_left_or_exists_le, HahnSeries.le_orderTop_iff_forall, SetLike.coe_mono, MvPowerSeries.le_order_pow_of_constantCoeff_eq_zero, posPart_min, ArchimedeanClass.mk_inv, Valuation.Integers.isPrincipalIdealRing_iff_not_denselyOrdered_mrange, Asymptotics.superpolynomialDecay_iff_abs_tendsto_zero, Complementeds.disjoint_coe, Finsupp.DegLex.single_strictAnti, List.trop_minimum, Set.Icc_subset_Icc_union_Icc, Finset.lt_max'_of_mem_erase_max', Ordinal.toNatOrdinal_max, upperSemicontinuousWithinAt_iff_frequently, Set.IciExtend_apply, Set.uIoc_eq_union, Set.IicExtend_self, convexHull_range_eq_exists_affineCombination, mabs_le_one, Matrix.isPrimitive_iff, Real.arcsin_projIcc, wbtw_iff_sameRay_vsub, NonemptyFinLinOrd.Iso.mk_hom, LaurentSeries.valuation_X_pow, exists_glb_Ioi, Set.ordConnected_uIoc, Order.le_succ_iff_eq_or_le, Nimber.toOrdinal_eq_zero, lowerBounds_Ioi, countable_setOf_isolated_right_within, tendsto_mabs_nhdsNE_one, Tropical.inf_eq_add, Nat.card_uIcc, lt_max_iff, abs_pow, HahnSeries.le_order_smul, Finset.sum_mul_sq_le_sq_mul_sq, Finset.exists_mem_eq_inf', IsDedekindDomain.HeightOneSpectrum.intValuation_lt_one_iff_mem, mem_ideal_sup_principal, Set.monotone_projIci, Int.padicValuation_eq_zero_iff, Valuation.Integers.dvd_iff_le, List.maximum_concat, Cardinal.toENat_congr, CategoryTheory.Limits.instIsWellOrderContinuousCompOfPreservesWellOrderContinuousOfShape, OrderMonoidWithZeroHom.mul_apply, ENat.range_natCast, Finset.sum_min_le, Polynomial.eventually_no_roots, NumberField.FinitePlace.norm_def, CauSeq.coe_inf, lt_min_iff, FiniteArchimedeanClass.mem_closedBall_iff, antivary_iff_exists_antitone_monotone, Even.pow_pos_iff, Finset.sup_mul₀, Complementeds.coe_sup, discreteTopology_iff_orderTopology_of_pred_succ, toZ_le_iff, AddUnits.min_val, Valuation.one_rel_iff, MulArchimedeanClass.orderHom_top, Valuation.le_one_of_subsingleton, NonnegSpectrumClass.iff_spectrum_nonneg, Finset.codisjoint_inf_right, mabs_cases, Nat.preimage_Ico, GenContFract.abs_sub_convs_le, CategoryTheory.Functor.WellOrderInductionData.Extension.zero_val, OrderEmbedding.birkhoffFinset_sup, NNRat.castOrderEmbedding_apply, continuousAt_iff_lower_upperSemicontinuousAt, AddMonoidAlgebra.supDegree_mem_support, ArchimedeanClass.closedBall_top, PosSMulStrictMono.toPosSMulReflectLT, ENat.one_le_iff_ne_zero, Finsupp.Colex.single_strictMono, NonarchimedeanHomClass.map_add_le_max, PNat.addLeftStrictMono, countable_image_lt_image_Iio, Cardinal.lift_max, mem_segment_sub_add, monovary_iff_exists_monotone, Pi.toColex_update_lt_self_iff, Subgroup.hasDetPlusMinusOne_iff_abs_det, WithZero.withZeroUnitsEquiv_strictMono, LinearOrderedAddCommGroupWithTop.sub_lt_sub_iff_left_of_ne_top, hahnEmbedding_isOrderedAddMonoid, List.maximum_append, ENat.lt_one_iff_eq_zero, Matroid.toENat_cRk_eq, HasCountableSeparatingOn.range_Iic, CauSeq.inf_le_left, exists_lt_mem_inter_of_not_pairwise_disjoint, LinearOrderedCommGroupWithZero.discrete_or_denselyOrdered, GenContFract.IntFractPair.nth_stream_fr_nonneg, Finset.isLeast_min', List.argmin_cons, Tuple.monotone_sort, Set.Ioi_ssubset_Ioi_iff, Set.encard_le_encard_diff_add_encard, ProbabilityTheory.Kernel.partialTraj_eq_prod, Set.image_subtype_val_uIcc, Finpartition.parts_inf, ContinuousOn.mabs, Icc_subset_segment, LinearOrderedAddCommGroup.to_noMinOrder, Filter.tendsto_const_mul_atTop_iff, DistLat.ofHom_comp, PNat.le_find_iff, contMDiffOn_projIcc, Mathlib.Meta.NormNum.isNNRat_lt_true, Cardinal.toENat_eq_one, Order.isSuccPrelimitRecOn_succ, Ordinal.toNatOrdinal_symm_eq, NonemptyFinLinOrd.hom_id, Associated.abs_left, MonomialOrder.iocam, posPart_eq_ite_lt, Finset.max_abv_sum_one_le, mem_nhdsLE_iff_exists_Ioc_subset, ENat.not_lt_zero, MonomialOrder.degree_sub_LTerm_le, Rat.padicValuation_le_one_iff, Finset.Ico_succ_right_eq_Icc, HahnSeries.leadingCoeff_abs, left_le_lineMap_iff_nonneg, exists_lt_add_iff_lt_right, MonomialOrder.lex_le_iff_of_unique, max_add, lineMap_lt_left_iff_neg, LinearOrderedCommGroup.isCyclic_iff_nonempty_equiv_int, max_div_div_right', Measurable.lt, tendsto_ratCast_atTop_iff, Set.disjoint_iff, PredOrder.colimitRecOn_pred, ArchimedeanClass.stdPart_eq_sSup, OrderEmbedding.mulLeft_apply, max_eq_iff, bot_eq_zero', tendsto_smul_comp_nat_floor_of_tendsto_nsmul, Hyperreal.gt_of_tendsto_zero_of_neg, Cardinal.mk_Iio_ord_toType, Hyperreal.epsilon_pos, PosSMulReflectLE.toPosSMulStrictMono, Multiset.prod_min_le, Set.IciExtend_coe, LinearOrderedCommGroup.isCyclic_iff_not_denselyOrdered, instDenselyOrderedUnits, upperSemicontinuousOn_iff_preimage_Ici, Hyperreal.archimedeanClassMk_epsilon_pos, Finset.dens_pos, Set.mem_uIcc, Profinite.NobelingProof.Products.head_lt_ord_of_isGood, disjoint_sdiff_sdiff, Finset.nonneg_subConst, NNRat.cast_lt_zero, CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.mem_incl_app, Set.Nonempty.not_disjoint, Ordinal.sup_typein_succ, exists_pos_right_iff_sameRay_and_ne_zero, Hyperreal.tendsto_atTop_iff, IsAddIndecomposable.baseOf_subset_pos, Set.powersetCard.ofFinEmbEquiv_apply, LinearOrderedCommMonoidWithZero.toZeroLeOneClass, Set.notMem_uIoc, Topology.IsUpper.tendsto_nhds_iff_lt, Mathlib.Tactic.Order.ToInt.toInt_lt_toInt, LinearOrderedField.toPosSMulStrictMono_rat, ENat.coe_lt_top, MonomialOrder.degree_sPolynomial, Polynomial.isBigO_atTop_of_degree_le, Nat.preimage_ceil_zero, nhdsGE_basis_Ico, Ordinal.nadd_eq_add, AddMonoidAlgebra.apply_supDegree_add_supDegree, HahnSeries.BddBelow_zero, Continuous.bddAbove_range_of_hasCompactMulSupport, Cardinal.nat_lt_ofENat, polynomialFunctions.comap_compRightAlgHom_iccHomeoI, Polynomial.valuation_X_eq_neg_one, hahnEmbedding_isOrderedModule, Ordinal.one_toType_eq, List.Perm.minimum_eq, LinearOrderedAddCommGroup.tendsto_nhds, Nat.ceil_add_le, AbsoluteValue.eq_trivial_of_isEquiv_trivial, closure_Ioc, Finset.Ico_add_one_add_one_eq_Ioc, Set.Iio_inter_Ioo, restrict₂_comp_IicProdIoc, Finset.isLUB_iff_isGreatest, ProbabilityTheory.Kernel.traj_eq_prod, MonomialOrder.degree_X_le_single, NatOrdinal.lt_wf, PNat.lt_succ_self, WithBot.add_one_le_iff, tendsto_zero_geometric_tsum_pnat, AddUnits.max_val, IsNonarchimedean.add_pow_le, MeasureTheory.stoppedProcess_eq_stoppedValue, Int.fract_eq_iff, closure_Ioi, abs_two, convexOn_iff_slope_mono_adjacent, ArchimedeanClass.mk_zpow, lt_tsub_iff_left, add_tsub_eq_max, Set.ordConnected_uIcc, mem_nhdsGE_iff_exists_Icc_subset, Affine.Simplex.sOppSide_affineSpan_faceOpposite_point_left_iff, mabs_eq_self, MeasureTheory.AEStronglyMeasurable.aestronglyMeasurable_uIoc_iff, add_le_add_iff_right_of_ne_top, closure_Ioo, MvPowerSeries.le_order_map, atBot_le_cocompact, MulArchimedean.of_locallyFiniteOrder, Hyperreal.coeRingHom_toFun, Even.zpow_pos, Nat.floor_pos, StieltjesFunction.right_continuous', HahnEmbedding.Partial.toOrderAddMonoidHom_injective, monovaryOn_iff_forall_mul_nonneg

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
le_sup_inf 📖	mathematical	—	Preorder.toLE PartialOrder.toPreorder SemilatticeSup.toPartialOrder Lattice.toSemilatticeSup toLattice SemilatticeInf.toMin Lattice.inf Lattice.inf_le_left Lattice.inf_le_right Lattice.le_inf SemilatticeSup.toMax	—	—

Function

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
update_inf 📖	mathematical	—	update SemilatticeInf.toMin Pi.instMinForall_mathlib	—	eq_or_ne update_self update_of_ne inf_of_le_left le_refl
update_sup 📖	mathematical	—	update SemilatticeSup.toMax Pi.instMaxForall_mathlib	—	eq_or_ne update_self update_of_ne sup_of_le_left

Function.Injective

Definitions

Name	Category	Theorems
distribLattice 📖	CompOp	—
lattice 📖	CompOp	—
semilatticeInf 📖	CompOp	—
semilatticeSup 📖	CompOp	—

Lattice

Definitions

Name	Category	Theorems
inf 📖	CompOp	17 math math: BooleanAlgebra.sdiff_eq, DistribLattice.le_sup_inf, CompleteBooleanAlgebra.sdiff_eq, BooleanAlgebra.inf_compl_le_bot, CompleteBooleanAlgebra.le_sup_inf, Order.Frame.le_himp_iff, CompleteLinearOrder.le_himp_iff, CompletelyDistribLattice.le_himp_iff, GeneralizedBooleanAlgebra.inf_inf_sdiff, GeneralizedHeytingAlgebra.le_himp_iff, inf_le_left, le_inf, GeneralizedBooleanAlgebra.sup_inf_sdiff, Order.Frame.MinimalAxioms.inf_sSup_le_iSup_inf, CompleteBooleanAlgebra.inf_compl_le_bot, CompleteDistribLattice.MinimalAxioms.inf_sSup_le_iSup_inf, inf_le_right
mk' 📖	CompOp	—
toLinearOrder 📖	CompOp	—
toSemilatticeInf 📖	CompOp	5443 math math: countable_image_lt_image_Ioi_within, SuccOrder.hasBasis_nhds_Ioc, max_sub_min_eq_abs', PredOrder.nhdsGT_eq_nhdsNE, HahnSeries.order_lt_iff_exists, RatFunc.instFaithfulSMulPolynomialLaurentSeries, Affine.Simplex.sSameSide_affineSpan_faceOpposite_point_left_iff, units_inv_smul, Function.Embedding.encard_le, LinearOrder.isSuccArchimedean_iff_isPredArchimedean, le_iff_forall_lt_one_mul_le, RingCone.nonneg.isMaxCone, Set.finite_diff_iUnion_Ioo, tsub_lt_self_iff, HurwitzZeta.hasSum_int_hurwitzZetaOdd, Multiset.Ico_sub_Ico_right, AddUnits.orderEmbeddingVal_apply, one_le_div_iff, oneLePart_mono, AffineSubspace.sOppSide_iff_exists_right, GenContFract.IntFractPair.nth_stream_fr_nonneg_lt_one, Int.ceil_lt_iff, negPart_nonpos, isCompl_toDual_iff, Mathlib.Meta.NormNum.isNNRat_lt_false, sub_sup, ENat.add_lt_top, HahnSeries.SummableFamily.powerSeriesFamily_add, instPosSMulStrictMonoIntOfIsOrderedAddMonoid, continuousOn_ceil, PNat.bot_eq_one, Set.pairwiseDisjoint_range_iff, Valuation.IsRankOneDiscrete.generator_lt_one, mul_self_nonneg, Subalgebra.LinearDisjoint.inf_eq_bot, nhds_basis_one_mabs_lt, Nat.iInf_le_succ', sign_intCast, Cardinal.natCast_lt_toENat_iff, hasSum_mellin_pi_mul_sq', Ordinal.toNimber_eq_zero, mul_nonpos_iff_neg_imp_nonneg, IsCompact.bddBelow, Finset.min'_union, AddCircle.coe_equivIco_mk_apply, mapClusterPt_atTop_pow_tfae, PNat.addLeftMono, Order.Frame.MinimalAxioms.iSup_inf_eq, ENat.toENNReal_lt_top, Set.Ioo_subset_Ioo_union_Ico, AlgebraicGeometry.descendsAlong_isOpenImmersion_surjective_inf_flat_inf_quasicompact', AffineSubspace.direction_inf, Valued.isOpen_closedball, biSup_inf_le_inf_biSup, emultiplicity_le_emultiplicity_of_dvd_left, DivisibleHull.archimedeanClassMk_mk_eq, Set.pairwise_disjoint_Ioc_zpow, codisjoint_iff_compl_le_right, Set.Iio_union_Ici, oneLePart_eq_one, Affine.Simplex.wOppSide_affineSpan_faceOpposite_point_left_iff, nsmul_nonneg_iff, abs_sub_abs_le_abs_add, Set.Iic.coe_sInf, HahnEmbedding.IsPartial.baseEmbedding_le, Finpartition.empty_parts, Set.pairwise_disjoint_Ioo_add_zsmul, CategoryTheory.ObjectProperty.InheritedFromTarget.instMin, Rat.intCast_lt_cast, iInf_inf, CompositionSeries.le_last, zpow_right_strictAnti, Valuation.IsTrivialOn.valuation_algebraMap_le_one, ArchimedeanClass.FiniteResidueField.mk_ratCast, Irreducible.maximalIdeal_eq_setOf_le_v_coe, IsPreconnected.intermediate_value_Ico, CompositionSeries.last_eraseLast_le, RootPairing.coxeterWeight_nonneg, sup_div_inf_eq_mabs_div, NNRat.coe_floor, ProbabilityTheory.gaussianReal_map_const_mul, Continuous.strictMono_of_inj_boundedOrder', IsDedekindDomain.HeightOneSpectrum.adicValued.has_uniform_continuous_const_smul', SignType.neg_one_lt_iff, Set.Ici_add_one_eq_Ioi, min_eq_bot, Int.lt_succ_floor, Finsupp.Colex.addLeftStrictMono, ENat.top_pos, Mathlib.Meta.NormNum.IsNNRat.natFloor, strictConvexOn_iff_slope_strict_mono_adjacent, Set.functorToTypes_obj, closure_interior_Icc, Order.Ioo_succ_right, NNRat.cast_strictMono, Fin.addNatOrderEmb_toEmbedding, LinearOrderedAddCommGroup.wellFoundedOn_setOf_le_lt_iff_nonempty_discrete, Set.Finite.inf_of_right, Dense.exists_ge, ValuationSubring.valuation_lt_one_iff, continuousMul_inf, TopCat.Sheaf.interUnionPullbackCone_snd, Set.Finite.einfsep, OrderIso.pnatIsoNat_symm_apply, Heyting.isRegular_top, IntermediateField.LinearDisjoint.iff_inf_eq_bot, iInf_sum, AlgebraicGeometry.Scheme.Hom.image_preimage_eq_opensRange_inter, IntermediateField.normal_inf, Set.notMem_Ioi, Valuation.FiniteField.algebraMap_le_one, AlgebraicGeometry.descendsAlong_universallyClosed_surjective_inf_flat_inf_quasicompact, Finset.le_fold_min, LinearOrderedAddCommGroupWithTop.sub_pos, ArchimedeanClass.FiniteElement.instIsStrictOrderedRing, Polynomial.cardPowDegree_zero, tendsto_inv_atTop_zero, Int.lt_ceil, min_sub_sub_left, Units.min_val, neg_le_self_iff, tendsto_const_mul_pow_nhds_iff', himp_inf_distrib, LatticeCon.r_inf_sup_iff, Valuation.HasExtension.val_map_le_iff, Set.compl_ordConnectedSection_ordSeparatingSet_mem_nhdsGE, StarSubalgebra.map_inf, ENat.lt_add_one_iff', OrderEmbedding.birkhoffFinset_inf, Orientation.ne_iff_eq_neg, CategoryTheory.Limits.Types.binaryCofan_isColimit_iff, Valuation.isEquiv_iff_val_sub_one_lt_one, HahnSeries.mem_cardSuppLTSubfield, Valuation.one_apply_lt_one_iff, nhds_bot_basis, Finset.exists_mem_eq_inf, dense_iff_exists_between, countable_image_gt_image_Ioi_within, AlgebraicGeometry.RingedSpace.basicOpen_res, sign_mul_self, Finset.exists_one_lt_of_prod_one_of_exists_ne_one', quasiconcaveOn_iff_min_le, Set.abs_sub_right_of_mem_uIcc, not_isCofinal_iff, Sym2.disjoint_diagSet_fromRel, AbsoluteValue.isEquiv_trivial_iff_eq_trivial, Set.toENat_cardinalMk_subtype, convexHull_insert, Set.Ioi_subset_Ioo_union_Ici, Set.einfsep_of_fintype, Set.Infinite.exists_gt, ENat.self_le_mul_left, ValuationSubring.integralClosure_algebraMap_injective, PNat.map_subtype_embedding_Ico, MeasureTheory.aecover_Ioi_of_Ici, Cardinal.toENat_eq_natCast_iff, cocompact_le_atBot, Set.disjoint_compl_left_iff_subset, tsub_add_min, MeasureTheory.stoppedProcess_stoppedProcess, PowerSeries.heval_C, AddGroupTopology.toTopologicalSpace_inf, inv_atBot₀, CovBy.inf_of_sup_of_sup_right, Polynomial.isEquivalent_atBot_div, inv_le_mabs, bihimp_left_involutive, ENat.card_le_card_of_injective, tendsto_ceil_right', Valuation.mem_maximalIdeal_iff, LinOrd.ofHom_apply, convex_iff_ordConnected, RootPairing.RootPositiveForm.zero_lt_posForm_apply_root, le_sdiff_right, MeasureTheory.integrable_iff_integrableAtFilter_atBot, convexHull_multiset_sum, FiniteArchimedeanClass.mem_addSubgroup_iff, abs_sub_round, partialSups_succ', WellOrderExtension.wellFoundedLT, Valuation.mem_leSubmodule_iff, isPiSystem_image_Iic, abs_add_eq_add_abs_iff, Multiset.Ico_sub_Ico_left, Left.pow_lt_one_iff', Set.pairwise_disjoint_Ico_zsmul, ArchimedeanClass.mk_intCast, ofDual_max, WithBot.orderIsoPUnitSumLex_symm_inl, Set.disjoint_or_nonempty_inter, Finset.prod_one_sub_ordered, PredOrder.isOpen_iff, disjoint_sdiff_self_right, Cardinal.ofENat_lt_ofNat, ProbabilityTheory.gaussianReal_const_mul, Mathlib.Meta.Positivity.pos_of_isNNRat, Finset.le_fold_max, deriv_abs, Finset.Ioi_disjUnion_Iio, CategoryTheory.MorphismProperty.universally_inf, Submodule.toConvexCone_inf, Nucleus.himp_apply, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivInverse_obj_π_app, NumberField.FinitePlace.mk_apply, isOpen_lt_prod, NNRat.le_def, IsCompact.exists_isLeast, inf_right_le_sup_left, bihimp_bihimp_cancel_right, MeasureTheory.aecover_Ioi_of_Ioi, lt_compl_self, NNRat.not_cast_lt_zero, Finset.Icc_add_one_left_eq_Ioc, WithTop.continuousOn_untopD, MulArchimedeanClass.subgroup_strictAntiOn, nsmul_neg_iff, concaveOn_iff_slope_anti_adjacent, strictConvex_Iic, sub_le_neg_add_iff, Finset.inf_id_set_eq_sInter, min_bot_left, sInf_pair, nhdsSet_Ioo, right_lt_lineMap_iff_one_lt, AffineSubspace.setOf_sSameSide_eq_image2, CategoryTheory.ObjectProperty.instIsClosedUnderIsomorphismsMin, Nat.Ioc_filter_modEq_cast, supClosed_preimage_ofDual, List.sortedLE_mergeSort, HasSolidNorm.continuousInf, Hyperreal.epsilon_lt_of_pos, Finset.uIcc_toDual, Finset.Ico_subset_Ico_union_Ico, min_mul_mul_left, BicartSq.commSq, AffineSubspace.direction_inf_of_mem, OrderEmbedding.mulRight_apply, Nat.succPNat_mono, List.getD_max?_eq_unbotD_maximum, IsNonarchimedean.multiset_powerset_image_add, Set.Ioc_union_Ioc_left, Set.Iio_succ_eq_Iic, IntermediateField.relrank_comap_comap_eq_relrank_inf, Filter.bliminf_inf_not, Finset.inf'_univ_eq_ciInf, Filter.blimsup_and_le_inf, Padic.withValUniformEquiv_norm_le_one_iff, Int.cast_one_le_of_pos, Valued.toNormedField.norm_le_one_iff, ArchimedeanOrder.le_def, Nucleus.map_himp_apply, Rat.padicValuation_cast, bihimp_eq_left, nullMeasurableSet_Ioc, Finset.image_orderEmbOfFin_univ, ProbabilityTheory.Kernel.partialTraj_succ_of_le, Int.preimage_Ioc, CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.ofComposableArrows_incl_app, PNat.find_le, symmDiff_eq', Finset.Iio_filter_lt, one_le_pow_mul_abs_eval_div, Set.tsub_encard_le_encard_diff, IsCauSeq.bounded', Finset.inf'_sup_inf', ConvexCone.canLift, Matrix.eRank_le_card_width, Ordinal.liftOnWellOrder_type, finSumEquivOfFinset_inr, MeasureTheory.ae_le_const_iff_forall_gt_measure_zero, Seminorm.finset_sup_apply, Polynomial.div_tendsto_atTop_leadingCoeff_div_of_degree_eq, Set.pairwise_disjoint_Ioo_mul_zpow, AddCircle.card_torsion_le_of_isSMulRegular, min_lt_min_right_iff, TopologicalLattice.toContinuousInf, Finset.dens_map_le, Order.succ_lt_succ_iff, inf_inf_sdiff, SuccOrder.limitRecOn_succ, List.maximum_cons, Finset.Colex.toColex_univ, Ordinal.iSup_typein_succ, Affine.Simplex.sign_excenterWeights_singleton_pos, CompleteLattice.MulticoequalizerDiagram.eq_inf, CauSeq.le_lim, Int.instIsStrictOrderedRing, HahnSeries.leadingCoeff_mul, ENat.card_lt_top, Finset.uIcc_map_sectR, Set.range_IciExtend, LinearOrderedCommGroup.tendsto_nhds, Finset.le_sup'_iff, ArchimedeanClass.closedBallAddSubgroup_top, ValuationSubring.valuation_le_iff, sup_inf_inf_compl, List.foldr_max_of_ne_nil, ArchimedeanClass.addSubgroup_antitone, Nat.succPNat_le_succPNat, Finset.min_eq_inf_withTop, Nat.ceil_pos, Set.iUnion_Ioc_eq_Ioi_self_iff, Polynomial.exists_partition_polynomial, mabs_le, add_right_strictMono_of_ne_top, mapClusterPt_leftLim, le_mabs', Finset.addConst_le_inv_dens, convex_iff_sum_mem, sdiff_le_iff', Finset.card_Ico_mul_right, Finset.fold_min_lt, MvPowerSeries.le_order_mul, Sublattice.map_equiv_eq_comap_symm, OrderRingHom.eq_id, mem_nhdsLT_iff_exists_Ico_subset, inf_symmDiff_distrib_right, sInf_union, Cardinal.ofENat_le_ofNat, biSup_inf_le_biSup_inf, QuadraticMap.linMulLinSelfPosDef, sup_compl_le_himp, Cardinal.toENat_ofENat, PNat.Icc_eq_finset_subtype, Valuation.IsRankOneDiscrete.exists_generator_lt_one', Finset.supIndep_univ_fin_two, signHom_apply, Set.sdiff_singleton_wcovBy, Polynomial.div_tendsto_atBot_leadingCoeff_div_of_degree_eq, Set.infs_sups_subset_right, Ordinal.toNatOrdinal_eq_one, Set.ncard_le_encard, himp_triangle, List.max_prod_le, CategoryTheory.Limits.MultispanIndex.toLinearOrderMultispanIso_inv_app, Opens.pretopology_toGrothendieck, HahnSeries.instIsStrictOrderedRingLexOfIsDomain, continuousOn_floor, Finset.Icc_min_max, LaurentSeries.LaurentSeriesRingEquiv_def, Field.Emb.Cardinal.directed_filtration, Set.Ioc_union_Ioc_right, sdiff_symmDiff, MeasureTheory.hittingBtwn_univ, AbsoluteValue.map_units_intCast, AlgebraicGeometry.IsAffineOpen.isCompact_pullback_inf, instIsCountablyGenerated_atBot, Polynomial.eventually_atBot_not_isRoot, Complementeds.coe_le_coe, HahnEmbedding.Partial.orderTop_eq_archimedeanClassMk, Set.OrdConnected.IicExtend, inf_eq_sub_posPart_sub, Int.strictAntiOn_natAbs, Finset.uIcc_eq_union, Continuous.upperSemicontinuous, IsLeast.insert, OrderEmbedding.infIrredUpperSet_surjective, tendsto_smul_comp_nat_floor_of_tendsto_mul, List.minimum_of_length_pos_le_iff, Field.Emb.Cardinal.instInverseSystemWithTopToTypeOrdRankAlgHomSubtypeMemIntermediateFieldCoeOrderEmbeddingFiltrationAlgebraicClosureEmbFunctor, induced_inf, scottContinuous_inf_right, GroupTopology.toTopologicalSpace_inf, exists_seq_strictMono_tendsto_nhdsWithin, Hyperreal.neg_lt_of_tendsto_zero_of_pos, nhdsWithin_Ioi_isMeasurablyGenerated, HahnSeries.SummableFamily.powers_zero, min_add_distrib', Module.length_of_free, isLocallyClosed_Ioi, IsCompactlyGenerated.BooleanGenerators.sSup_inter, PNat.Ioo_eq_finset_subtype, lowerClosure_eq_top_iff, WithZeroTopology.nhds_zero, codisjoint_bihimp_sup, Set.Icc_succ_left_eq_Ioc, Field.Emb.Cardinal.filtration_succ, Set.unit_eq, ArchimedeanClass.FiniteResidueField.ofArchimedean_apply, Finset.inf_lt_iff, AddCircle.equivIccQuot_comp_mk_eq_toIcoMod, NonUnitalAlgebra.coe_inf, Set.IciExtend_self, Valuation.mem_ltIdeal_iff, CauSeq.abv_pos_of_not_limZero, Valuation.val_le_one_or_val_inv_lt_one, Mathlib.Tactic.Order.ToInt.toInt_le_toInt, Matrix.eRank_le_card_height, Padic.instCompatibleWithZeroMultiplicativeIntMulValuation, emultiplicity_add_eq_min, bihimp_bihimp_sup, toBoolRing_inf, Nonneg.nontrivial, inf_covBy_of_covBy_sup_of_covBy_sup_right, inf_eq_iInf, Module.End.independent_genEigenspace, NumberField.FinitePlace.norm_def', negPart_eq_zero', ENat.card_pos, max_neg_neg, BoundedLatticeHom.coe_comp_sup_hom', smulPosStrictMono_iff_SMulPosReflectLE, Valuation.leSubmodule_monotone, Int.fract_add_fract_le, compl_inf, LocallyConvexSpace.inf, sum_div_card_sq_le_sum_sq_div_card, Sublattice.inf_mem, Set.Icc_min_max, PredOrder.isPredLimit_of_mem_frontier, two_mul_le_add_sq, IsDedekindDomain.HeightOneSpectrum.mem_adicCompletionIntegers, SetTheory.PGame.grundyValue_eq_iff_equiv_nim, interior_Ici, ENat.toENNReal_strictMono, inf_mul, Int.cast_le_neg_one_of_neg, FunctionField.inftyValuation.X_inv, Set.Icc_subset_Ico_union_Icc, LinOrd.hom_id, Set.Ioo_inter_Iio, CategoryTheory.Limits.MultispanIndex.toLinearOrderMultispanIso_hom_app, WithBot.le_of_forall_lt_iff_le, Set.Ioi_diff_Ici, Finset.disjoint_coe, posPart_eq_self, Int.padicValuation_lt_one_iff, HahnSeries.single_zero_ofScientific, Finset.pairwiseDisjoint_coe, Finset.set_encard_biUnion_le, Nat.floor_div_natCast, Filter.cardinalInterFilter_sup, ENat.one_lt_card_iff_nontrivial, isCompl_ofDual_iff, IsDedekindDomain.HeightOneSpectrum.intValuation_if_neg, Set.projIic_surjective, monotone_transfiniteIterate, invOf_pos, le_abs_self, PNat.instIsOrderedCancelMonoid, NumberField.FinitePlace.embedding_apply, min_lt_min_left_iff, Ordinal.toNimber_symm_eq, Finset.Icc_succ_succ, IsDedekindDomain.HeightOneSpectrum.valuation_of_algebraMap, Set.disjoint_union_right, min_mul, StarSubalgebra.inf_toSubalgebra, nhds_basis_Icc_pos, Finset.prod_Icc_eq_prod_Ico_mul, nullMeasurableSet_Ioo, Valuation.Integers.isPrincipal_iff_exists_isGreatest, Set.disjoint_of_subset_iff_left_eq_empty, VertexOperator.of_coeff_apply_coeff, Set.encard_preimage_val_le_encard_left, nhds_basis_abs_sub_lt, meromorphicOrderAt_add_of_ne, Finset.one_le_mulConst_self, instWellQuasiOrderedLEOfWellFoundedLT, ConvexCone.coe_inf, inf_covBy_of_covBy_sup_of_covBy_sup_left, csInf_insert, Set.strictMonoOn_projIic, inv_atTop₀, LinearOrderedCommGroupWithZero.inl_mul_inr_eq_coe_toLex, LaurentSeries.valuation_le_iff_coeff_lt_eq_zero, instIsDiscreteValuationRingSubtypeMemSubringIntegerWithZeroMultiplicativeIntValuation, Finpartition.IsEquipartition.card_biUnion_offDiag_le', BoundedLatticeHom.dual_id, OrderIso.isNormal, exists_seq_strictAnti_tendsto, CategoryTheory.Functor.WellOrderInductionData.Extension.map_zero, BicartSq.le₁₂, Int.card_Ioo, orderBornology_isBounded, sSup_inf_sSup, lowerSemicontinuous_iff_isClosed_preimage, Set.ordConnected_iff_uIcc_subset_left, lt_tsub_iff_right, CategoryTheory.MorphismProperty.ContainsIdentities.inf, NatOrdinal.toOrdinal_min, LaurentSeries.valuation_single_zpow, leOnePart_eq_inv_inf_one, FiniteArchimedeanClass.mk_lt_mk, infPrime_iff_not_isMax, inf_himp_bihimp, SetRel.core_mono, sdiff_sdiff_sup_sdiff', max_add_add_le_max_add_max, Finset.sum_Ico_le_sum, tendsto_fract_left', AbsoluteValue.abs_abv_sub_le_abv_sub, monovary_iff_mul_rearrangement, SetTheory.PGame.grundyValue_nim_add_nim, NNRat.instStarOrderedRing, Nimber.succ_def, sbtw_midpoint_of_ne, IsDedekindDomain.HeightOneSpectrum.intValuation_le_one, sameRay_or_ne_zero_and_sameRay_neg_iff_not_linearIndependent, le_iff_forall_rat_lt_imp_le, Affine.Simplex.wSameSide_affineSpan_faceOpposite_iff, smul_nonneg_iff_neg_imp_nonpos, Affine.Simplex.wOppSide_affineSpan_faceOpposite_point_right_iff, WeierstrassCurve.valuation_Δ_aux_eq_of_isIntegral, Nat.preimage_Iio, Finset.Nonempty.sup_eq_top_iff, MonomialOrder.degree_sub_le, Orientation.eq_or_eq_neg, negPart_eq_neg', IsNonarchimedean.apply_sum_le_sup_of_isNonarchimedean, le_of_toZ_le, Finset.inf'_lt_iff, CategoryTheory.TransfiniteCompositionOfShape.fac_assoc, Polynomial.exists_min_root, Hyperreal.infinitesimal_def, isPiSystem_Ioi, Finset.sum_Ico_int_sub, ContFract.convs_eq_convs', Topology.IsLower.toContinuousInf, MeasureTheory.Filtration.rightCont_eq_self, min_mul_min_le_min_mul_mul', ArchimedeanClass.FiniteResidueField.mk_eq_zero, le_zero_iff, Finset.lubell_yamamoto_meshalkin_inequality_sum_card_div_choose, convexJoin_segments, Affine.Simplex.sign_signedInfDist_lineMap_incenter_touchpoint, Coheyting.boundary_top, Finset.Colex.toColex_lt_toColex_iff_max'_mem, Nat.measurable_floor, StieltjesFunction.measure_Ioo, Finset.compl_inf, EReal.sign_eq_and_abs_eq_iff_eq, FiniteGaloisIntermediateField.instFiniteDimensionalSubtypeMemIntermediateFieldMin_1, starConvex_iff_ordConnected, continuous_inf_dom_left₂, AddGroupSeminormClass.toNonnegHomClass, Valuation.Compatible.srel_iff_lt, one_lt_mabs, exists_pos_right_iff_sameRay, Finset.lt_sup'_iff, AlgebraicGeometry.isPullback_opens_inf, NNRat.cast_le, Frm.Iso.mk_hom, Valuation.IsEquiv.valuedCompletion_le_one_iff, antivaryOn_comm, codisjoint_inf_right, CovBy.inf_of_sup_left, MvPowerSeries.min_lexOrder_le, hnot_le_iff_codisjoint_left, NNRat.floor_coe, Order.Ioo_eq_empty_iff_le_succ, mul_self_le_one_iff, WithBot.orderIsoPUnitSumLex_symm_inr, Set.Iic_diff_Iio, Order.Ideal.IsProper.notMem_or_compl_notMem, Coheyting.boundary_le_hnot, ENNReal.iInf_ennreal, OrderEmbedding.preimage_uIoc, CategoryTheory.Functor.WellOrderInductionData.surjective, LieModule.genWeightSpaceChain_def', Module.End.genEigenspace_directed, Valuation.isEquiv_iff_val_lt_val, Finset.subConst_le_addConst_sq, Polynomial.exists_partition_polynomial_aux, le_iff_forall_pos_le_add, lt_emultiplicity_of_lt_multiplicity, ENat.monotone_map_iff, leOnePart_le_one, sup_inf_inf_sdiff, mul_nonpos_iff_pos_imp_nonpos, InnerProductSpace.gramSchmidt_bot, CovBy.inf_of_sup_right, himp_inf_le, Set.Ioc_subset_uIoc', Set.isCompl_range_some_none, Set.disjoint_singleton_right, Submodule.spanRank_toENat_eq_iInf_encard, isLeast_sdiff, SimpleGraph.hasse_preconnected_of_pred, max_lt_max_left_iff, variationOnFromTo.antitoneOn, Nat.ceil_int, Finset.sortedGT_sort, Finset.mem_uIcc', sign_nonneg_iff, min_abs_abs_le_abs_min, SimpleGraph.regularityReduced_adj, Hyperreal.coe_lt_omega, Finset.card_Ico_add_right, LinOrd.dual_map, nhds_basis_Ioo_one_lt, Pi.instNoMinOrderLexForallOfWellFoundedLTOfNonempty, OrderIso.sumLexIioIci_symm_apply_Ici, Finsupp.Lex.addLeftMono, Ioo_subset_closure_interior, Set.bounded_gt_inter_ge, AbsoluteValue.abs_isEuclidean, Zsqrtd.instIsStrictOrderedRingCastInt, pow_le_pow_iff_left, Finsupp.Lex.single_strictAnti, Valuation.isNontrivial_iff_exists_lt_one, ArchimedeanClass.mk_pow, ArchimedeanClass.isAddRegular_mk, nullMeasurableSet_Ioi, IsDedekindDomain.HeightOneSpectrum.instIsNontrivialWithZeroMultiplicativeIntValuation, Valuation.Integers.valuation_irreducible_lt_one, Finset.min_union, WithZeroTopology.nhds_zero_of_units, AlgebraicGeometry.isImmersion_eq_inf, Set.Ico_subset_Icc_union_Ico, AddValuation.map_add', mem_nhdsGT_iff_exists_Ioc_subset, borel_eq_generateFrom_Ici, Topology.RelCWComplex.coe_skeletonLT, Num.cast_le, invOf_nonneg, Filter.tendsto_mabs_atTop_atTop, min_choice, Finpartition.disjoint, strictConvex_Icc, antivary_iff_smul_rearrangement, Nonneg.mk_nnratCast, Ideal.comap_finsetInf, Set.Ioo_inter_Ioi, zpow_two_nonneg, Submodule.colon_finsetInf, GenContFract.succ_nth_fib_le_of_nth_den, Module.End.maxGenEigenspace_eq, one_le_mul_self_iff, List.coe_maximum_of_length_pos, Finset.Colex.le_iff_max'_mem, negPart_anti, lt_inv_self_iff, Nat.iInf_lt_succ', ArchimedeanClass.mk_le_mk, NNRat.lt_def, exists_lub_Iio, Polynomial.div_tendsto_zero_iff_degree_lt, tendsto_floor_right_pure, MeasureTheory.aecover_Iio_of_Iic, Nat.preimage_Ici, upperSemicontinuousAt_iff_frequently, Finsupp.Colex.isStrictOrder, Int.padicValuation_eq_one_iff, smul_nonpos_iff, WithTop.untop₀_min, isClosed_nonneg, mabs_div_le, segment_eq_uIcc, Nat.count_le_setENCard, Nat.one_div_le_one_div, IsPreconnected.intermediate_value_Ioo, MvPowerSeries.le_weightedOrder_mul, inf_eq_sup, PowerSeries.coe_add, Set.unbounded_gt_inter_gt, RootPairing.RootPositiveForm.zero_lt_posForm_iff, Finset.inf_sup_distrib_right, MvPolynomial.supDegree_esymmAlgHomMonomial, partialSups_add_one', sup_le_inf, pairwise_disjoint_fiber, LinearOrderedField.lt_inducedMap_iff, Finset.max_sum_le, MvPolynomial.schwartz_zippel_totalDegree, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivCounitIso_hom_app_hom, Finset.max'_le_iff, Finset.compl_sup, OrderHom.gfp_const_inf_le, Right.pow_lt_one_iff, isOpen_lt, Sublattice.infClosed', Finset.inclusion_exclusion_card_inf_compl, PowerSeries.coeff_heval, continuousOn_fract, Cardinal.toENat_eq_zero, bihimp_right_surjective, Affine.Simplex.sign_touchpointWeights_empty, HahnSeries.ofSuppBddBelow_zero, AlgebraicGeometry.descendsAlong_isomorphisms_surjective_inf_flat_inf_quasicompact, ProbabilityTheory.HasSubgaussianMGF.const_mul, iSup₂_inf_eq, Tropical.min_eq_add, continuousAdd_inf, Finset.inter_mem_infs, StieltjesFunction.mono', hnot_hnot_le, inf_biInf, MvPowerSeries.le_order_prod, CategoryTheory.Functor.WellOrderInductionData.sectionsMk_val_op_bot, BoundedLENhdsClass.of_closedIciTopology, MulArchimedeanClass.top_eq_mk_iff, Ioc_subset_biUnion_Ioc, OrderRingHom.apply_eq_self, Topology.CWComplex.iUnion_openCell_eq_skeletonLT, ofBoolAlg_inf, CategoryTheory.SmallObject.SuccStruct.Iteration.mkOfLimit.inductiveSystem_obj, Hyperreal.InfiniteNeg.lt_zero, Sym2.sortEquiv_apply_coe, Finset.orderIsoOfFin_symm_apply, tsub_pos_iff_lt, emultiplicity_lt_iff_not_dvd, CategoryTheory.GrothendieckTopology.arrow_intersect, Cardinal.toENat_eq_ofNat, CauSeq.const_lt, CategoryTheory.GrothendieckTopology.intersection_covering_iff, CanonicallyOrderedAdd.toOrderedSub, Nat.image_cast_int_Icc, exists_nonneg_left_iff_sameRay, continuous_inf_dom_right₂, Valuation.Integers.map_le_one, TopCat.Sheaf.interUnionPullbackCone_fst, emultiplicity_le_emultiplicity_of_dvd_right, iInf_ite, Nat.image_cast_int_Iic, leOnePart_eq_one', Nucleus.restrict_toFun, InnerProductSpace.gramSchmidt_def, Orientation.map_eq_neg_iff_det_neg, NonUnitalSubalgebra.prod_inf_prod, neg_abs_le_neg, Finset.inf_id_eq_sInf, IsDedekindDomain.HeightOneSpectrum.intValuation_le_pow_iff_mem, Finset.mulConst_le_card, Finset.Icc_subset_uIcc', AlgebraicGeometry.IsSeparated.eq_valuativeCriterion, Int.preimage_Ioi, generateFrom_union, MonomialOrder.degree_reduce_lt, IsNonarchimedean.finset_image_add, Archimedean.embedReal_apply, Order.Ici_pred, Set.covBy_iff_exists_sdiff_singleton, le_himp_comm, Polynomial.abs_div_tendsto_atTop_of_degree_gt, LaurentSeries.ofPowerSeries_powerSeriesPart, instWellFoundedLTSubtypeSetFinite, IsDedekindDomain.HeightOneSpectrum.intValuation_singleton, Module.End.maxGenEigenspace_eq_genEigenspace_finrank, Ordinal.toNimber_min, emultiplicity_pos_of_dvd, CategoryTheory.TransfiniteCompositionOfShape.iic_isoBot, LaurentSeries.single_order_mul_powerSeriesPart, HahnEmbedding.Partial.archimedeanClassMk_eq_iff, exists_rat_gt, LinearOrderedCommGroup.Subgroup.genLTOne_lt_one, Module.End.mapsTo_genEigenspace_of_comm, HahnSeries.support_abs, ValuativeRel.ValueGroupWithZero.mk_pos, MonoidWithZeroHom.fst_mono, Nucleus.map_himp_le, le_mabs, Odd.pow_nonneg_iff, Topology.IsUpper.isTopologicalBasis_insert_univ_subbasis, IsNonarchimedean.apply_natCast_le_one_of_isNonarchimedean, NNRat.cast_mono, disjoint_compl_right_iff, inf_left_le_sup_left, AlgebraicGeometry.IsClosedImmersion.eq_proper_inf_monomorphisms, PowerSeries.order_mul_ge, SimpleGraph.farFromTriangleFree_iff, Nat.lt_succ_floor, MonomialOrder.zero_le, CompositionSeries.lt_last_of_mem_eraseLast, Finset.Colex.lt_iff_exists_forall_lt, sbtw_iff_left_ne_and_right_mem_image_Ioi, Complementeds.mk_bot, FunctionField.instIsNontrivialRatFuncWithZeroMultiplicativeIntInftyValuation, MultilinearMap.map_piecewise_sub_map_piecewise, Set.notMem_Iic, ArchimedeanClass.mk_natCast, CategoryTheory.TransfiniteCompositionOfShape.ofArrowIso_isoBot, CategoryTheory.Limits.HasIterationOfShape.hasColimitsOfShape, Nat.ceil_eq_zero, SetRel.prod_comp_prod, Even.pow_nonneg, zpow_neg_two_nonneg, Int.floor_eq_zero_iff, MeasureTheory.meas_le_ae_eq_meas_lt, Set.uIoo_eq_union, AffineBasis.convexHull_eq_nonneg_coord, lt_inf_iff, Nat.floor_sub_one, codisjoint_iff_compl_le_left, AffineSubspace.sSameSide_iff_exists_left, IsModularLattice.complementedLattice_Ici, Subalgebra.prod_inf_prod, Set.disjoint_image_left, HeytAlg.Iso.mk_inv, InitialSeg.isNormal, pos_add_self_iff, mfderivWithin_projIcc_one, ENat.forall_natCast_le_iff_le, WithBot.lt_add_one_iff, Finset.min'_le, Set.Infinite.exists_lt, Cardinal.ofENat_mono, TopCat.pullback_topology, tendsto_ceil_left_pure_ceil, CategoryTheory.MorphismProperty.IsMultiplicative.inf, Int.comap_cast_atTop, le_himp_himp, measurable_lt, IntermediateField.inf_toSubalgebra, Valuation.ltAddSubgroup_monotone, Rat.padicValuation_self, OrderIso.infIrredUpperSet_symm_apply, hasBasis_nhdsSet_Ici_Ioi, Polynomial.tendsto_atTop_iff_leadingCoeff_nonneg, BoundedLatticeHom.symm_dual_comp, Polynomial.IsDistinguishedAt.degree_eq_coe_lift_order_map, Set.encard_preimage_val_le_encard_right, Set.Iio_inj, MeasureTheory.aecover_Ioo_of_Ioc, max_inv_inv', HahnEmbedding.Seed.baseEmbedding_strictMono, PNat.le_of_dvd, Mathlib.Meta.NormNum.isRat_lt_true, Booleanisation.comp_lt_comp, Mathlib.Tactic.Order.ToInt.toInt_nle_toInt, iInf_option, CategoryTheory.TransfiniteCompositionOfShape.ofOrderIso_incl, HasStrictFDerivAt.abs, RatFunc.coe_X, PowerSeries.le_order_smul, convexHull_toCone_eq_sInf, le_iff_forall_one_lt_lt_mul', max_bot_left, CategoryTheory.TransfiniteCompositionOfShape.isWellOrderContinuous, PowerSeries.coeff_coe, Valued.isClopen_ball, frontier_Ici, Set.sdiff_singleton_covBy, tendsto_ceil_atTop, Heyting.IsRegular.disjoint_compl_right_iff, BooleanSubalgebra.inf_mem, bihimp_himp_left, Finset.max_mono, NonemptyFinLinOrd.epi_iff_surjective, ValuativeRel.ValueGroupWithZero.embed_strictMono, AffineSubspace.wOppSide_iff_exists_wbtw, Valuation.IsEquiv.pos_iff, PNat.card_Icc, Types.monoOverEquivalenceSet_inverse_map, Fin.castSuccOrderEmb_toEmbedding, CategoryTheory.MorphismProperty.IsLocalAtSource.inf, inf_iInf_nat_succ, negPart_max, Set.monotone_projIic, List.mem_argmin_iff, disjoint_symmDiff_inf, exists_lt_mul_self, MonomialOrder.toSyn_strictMono, NonUnitalAlgebra.mem_inf, inf_sup_le, complementedLattice_iff, PowerSeries.order_finite_iff_ne_zero, Finset.Ico_diff_Ico_left, FiniteArchimedeanClass.val_mk, min_sub_sub_right, inf_sdiff_inf, Int.self_le_zpow_clog, Polynomial.isEquivalent_atTop_lead, Order.IsNormal.monotone, SimpleGraph.posSemidef_lapMatrix, Polynomial.le_trailingDegree_C, Finset.card_div_choose_le_card_shadow_div_choose, max_mul_min, MonomialOrder.div_single, SSet.Subcomplex.degenerate_eq_top_iff, LinearOrder.supConvergenceClass, LinOrd.hom_inv_apply, LaurentSeries.coe_algebraMap, exists_isLocalExtr_Ioo, Polynomial.isLittleO_atTop_of_degree_lt, Set.unbounded_le_inter_le, Nimber.toOrdinal_max, Nonneg.segment_eq_uIcc, codisjoint_hnot_right, Nat.image_cast_int_Ioc, Finset.Colex.mem_initSeg, ArchimedeanClass.mk_add_lt_mk_left_iff, pow_two_nonneg, Tuple.monotone_proj, FiniteArchimedeanClass.mem_ballAddSubgroup_iff, Finset.mem_convexHull', MulArchimedeanClass.mk_eq_mk, MvPowerSeries.le_weightedOrder_prod, RatFunc.coe_coe, Ideal.isPrimary_finsetInf, MeasureTheory.aecover_Ioc_of_Ioo, Set.indicator_le_indicator_nonneg, Finset.orderEmbOfFin_eq_orderEmbOfFin_iff, div_neg_iff, Int.cast_min, intermediate_value_Icc', AffineSubspace.sOppSide_iff_exists_left, Polynomial.abs_div_tendsto_atBot_atTop_of_degree_gt, Finsupp.disjoint_iff, measurableSet_Ico, Valuation.Integers.le_of_dvd, geom_sum_pos_iff, NumberField.FinitePlace.norm_embedding_eq, OrderRingIso.eq_refl, div_le_one_iff, GenContFract.abs_sub_convergents_le', isClosed_Ioc_iff, Finpartition.mem_avoid, abs_sub_le, NNRat.num_pos, partialSups_add_one, sdiff_sup, eVariationOn.nonempty_monotone_mem, intermediate_value_Ioo', Polynomial.valuation_of_mk, Mathlib.Tactic.Qify.nnratCast_le, Valuation.leIdeal_map_algebraMap_eq_leSubmodule_min, isOpen_Ioo, Rat.intCast_le_cast, mabs_le', topologicalGroup_inf, CategoryTheory.Subfunctor.Subpresheaf.min_obj, MulArchimedeanClass.mk_left_le_mk_mul_iff, sub_inf, Field.Emb.Cardinal.two_le_deg, RootPairing.exists_ge_zero_eq_rootForm, AbsoluteValue.isEquiv_iff_lt_one_iff, Int.le_ceil, MulArchimedeanClass.mem_subgroup_iff, AddSubmonoid.closure_image_isAddIndecomposable_baseOf, HahnSeries.order_mul, Nat.Prime.emultiplicity_le_emultiplicity_choose_add, tendsto_zpow_atTop_zero, Valuation.val_lt_one_iff, Set.pairwise_disjoint_Ioc_zsmul, Quaternion.normSq_le_zero, Set.Finset.coe_einfsep, MulArchimedeanClass.subsemigroup_strictAnti, Finset.local_lubell_yamamoto_meshalkin_inequality_div, abs_le, Filter.inf_limsup, Odd.zpow_nonpos_iff, isCoatom_compl, Int.fract_pos, oneLePart_min, sdiff_symmDiff', topologicalAddGroup_inf, Finpartition.parts_map, Multiset.untrop_sum, GroupSeminormClass.toNonnegHomClass, nhds_basis_zero_abs_lt, nhds_eq_iInf_abs_sub, AlgebraicGeometry.Scheme.Hom.image_preimage_eq_opensRange_inf, Valuation.val_le_one_or_val_inv_le_one, Set.Icc_subset_uIcc, Fin.natAddOrderEmb_toEmbedding, measurableSet_Iio, WithTop.tendsto_untop, mabs_inf_div_inf_le_mabs, RootPairing.RootPositiveForm.posForm_apply_root_root_le_zero_iff, ArchimedeanClass.mk_left_le_mk_sub_iff, bihimp_eq_right, SSet.Subcomplex.preimage_min, bihimp_himp_eq_inf, Set.subset_compl_iff_disjoint_right, ENat.map_natCast_strictMono, Nimber.toOrdinal_min, Ideal.prod_le_inf, Polynomial.cardPowDegree_isEuclidean, Polynomial.abs_div_tendsto_atTop_atTop_of_degree_gt, leOnePart_lt, Field.Emb.Cardinal.isLeast_leastExt, sub_half_lt_round, ValuativeRel.nonempty_orderIso_withZeroMul_int_iff, Finset.divConst_le_card, Finset.one_le_mulConst, LaurentSeries.inducing_coe, ScottContinuous.inf₂, Set.Ioc_disjoint_Ioc, Submodule.mem_finset_inf, Finset.iInf_insert, cmp_add_left, le_hnot_inf_hnot, exists_isExtrOn_Ioo_of_tendsto, biSup_inf_biSup, Ordinal.enum_le_enum', PowerSeries.coe_smul, Set.Ioo_subset_Ioc_union_Ico, Valuation.map_add, sdiff_inf_self_left, sdiff_le_hnot, Set.disjoint_left, ArchimedeanClass.mk_le_mk_smul, CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.ofComposableArrows_isColimit_desc, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivInverseObj_π_app, MulArchimedeanClass.mk_lt_mk, pred_min, div_le_inv_mul_iff, Set.disjoint_singleton_left, LaurentSeries.continuous_coe, PNat.factorMultiset_le_iff, convexJoin_segment_singleton, Finset.Colex.toColex_le_toColex_iff_max'_mem, min_eq_right_iff, HahnEmbedding.Partial.toOrderAddMonoidHom_apply, Set.disjoint_right, monovaryOn_comm, AhlswedeZhang.supSum_union_add_supSum_infs, Valuation.HasExtension.val_map_lt_iff, LaurentSeries.algebraMap_C_mem_adicCompletionIntegers, PNat.tendsto_comp_val_iff, Order.IsNormal.ext, openSegment_eq_Ioo', cocompact_le_atTop, MvPowerSeries.lexOrder_def_of_ne_zero, MonomialOrder.degree_add_le, Valued.is_topological_valuation, IntermediateField.inf_relrank_right, CategoryTheory.TransfiniteCompositionOfShape.ici_F, HahnEmbedding.Seed.strictMono_coeff, iSup_inf_le_inf_iSup, interior_Iio, min_le_max, one_le_mul_mabs, Nat.floor_div_ofNat, Set.Ioi_diff_Ioi, negPart_pos_iff, isPiSystem_image_Ioi, Order.Iio_succ_eq_insert, IsValuativeTopology.isOpen_ball, NatOrdinal.succ_def, min_min_min_comm, continuous_iff_lower_upperSemicontinuous, Topology.RelCWComplex.iUnion_openCell_eq_skeleton, convexJoin_singleton_segment, CompositionSeries.lt_succ, MvPowerSeries.le_weightedOrder_map, inf_sdiff_self_left, Hyperreal.not_infinite_iff_exist_lt_gt, AffineSubspace.wOppSide_self_iff, le_emultiplicity_map, Dense.Iio_eq_biUnion, ENNReal.bot_eq_zero, Stream'.Seq.length'_le_iff, Hyperreal.archimdeanClassMk_coe, Int.floor_lt, mul_nonneg_iff, IsAbsoluteValue.abs_isAbsoluteValue, Pi.toLex_update_lt_self_iff, Order.lt_succ_iff_eq_or_gt, max_div_min_eq_mabs, Field.Emb.Cardinal.succEquiv_coherence, PrimeSpectrum.basicOpen_mul, top_bihimp, hasDerivWithinAt_abs, NNRat.floor_cast, NNRat.coe_pos, Cardinal.noMaxOrder, abs_sub, Sym2.inf_eq_inf_and_sup_eq_sup, compl_symmDiff, Cardinal.ofENat_lt_aleph0, fn_min_add_fn_max, Hyperreal.tendsto_iff_forall, mapClusterPt_atTop_nsmul_tfae, MvPowerSeries.nat_le_order, Valuation.one_lt_val_iff, Orientation.map_eq_iff_det_pos, smul_nonpos_iff_pos_imp_nonpos, LatticeHom.withTopWithBot'_toFun, archimedean_iff_nat_le, SetRel.image_core_gc, SuccOrder.nhdsLE_eq_nhds, le_iff_forall_neg_add_le, HahnEmbedding.ArchimedeanStrata.ball_sup_stratum_eq, compl_sup_compl_le, DFinsupp.lt_of_forall_lt_of_lt, generateFrom_Icc_mem_le_borel, Set.disjoint_sdiff_inter, Quaternion.normSq_nonneg, Nat.le_floor_iff', countable_setOf_isolated_right, OrderRingIso.subsingleton_right, sup_strictMonoOn_Icc_inf, Padic.norm_eq_zpow_log_mulValuation, RingCon.inf_iff_and, continuousNeg_inf, mabs_mul_three, ENat.one_le_card_iff_nonempty, disjoint_sup_right, infClosed_preimage_toDual, Order.Frame.MinimalAxioms.sSup_inf_eq, Nat.image_cast_int_Ici, CategoryTheory.MorphismProperty.DescendsAlong.inf, ValuationSubring.valuation_lt_one_or_eq_one, abs_sub_sup_add_abs_sub_inf, TopCat.prod_topology, CategoryTheory.MorphismProperty.CodescendsAlong.inf, Set.Icc_subset_Icc_union_Ioc, compl_anti, HahnSeries.instIsCancelMulZeroOfIsCancelAdd, Set.unbounded_lt_inter_le, Set.pairwise_disjoint_Ioo_add_intCast, PowerSeries.intValuation_eq_of_coe, Set.Ico_succ_succ_eq_Ioc, Heyting.Regular.coe_sdiff, LocallyFiniteOrder.orderAddMonoidHom_bijective, HahnSeries.orderTop_mul_of_nonzero, List.minimum_of_length_pos_le_of_mem, Nat.ceil_mono, CircleDeg1Lift.inf_apply, Tuple.sort_eq_refl_iff_monotone, le_iff_posPart_negPart, FiniteGaloisIntermediateField.instFiniteDimensionalSubtypeMemIntermediateFieldMin, convexHull_add, Set.Ioo_add_one_right_eq_Ioc, Finset.divConst_le_mulConst_sq, FiniteMulArchimedeanClass.withTopOrderIso_apply_coe, WithTop.instBorelSpace, Finsupp.Lex.isStrictOrder, Finset.inf_sup, EReal.abs_mul_sign, Set.Iio_subset_Iic_iff, Finsupp.Colex.addRightMono, OrderEmbedding.coe_birkhoffFinset, CategoryTheory.Subfunctor.max_min, PNat.lt_add_right, RootPairing.zero_lt_pairingIn_iff', Nat.preimage_floor_of_ne_zero, Set.Ioc_subset_Ioc_union_Icc, HahnEmbedding.Partial.isWF_support_evalCoeff, Set.projIci_eq_self, Set.antitone_setOf, CategoryTheory.MorphismProperty.IsStableUnderBaseChange.inf, CategoryTheory.OrthogonalReflection.iteration_map_succ, Set.covBy_insert, HahnEmbedding.Partial.orderTop_eq_iff, Mathlib.Meta.Positivity.nonneg_of_isNNRat, Sublattice.coe_inf, Polynomial.tendsto_atBot_iff_leadingCoeff_nonpos, List.coe_le_maximum_iff, Con.coe_inf, Mathlib.Tactic.ENatToNat.not_lt_top, Finset.lubell_yamamoto_meshalkin_inequality_sum_inv_choose, disjoint_sdiff_comm, le_himp_iff_left, PNat.find_mono, Order.lt_succ_iff_eq_or_lt, Continuous.exists_forall_le_of_hasCompactSupport, Finset.inf_sup_distrib_left, ArchimedeanClass.top_eq_mk_iff, inv_sup, IsDedekindDomain.HeightOneSpectrum.equivHeightOneSpectrum_symm_apply, LowerSet.total_le, Finset.sups_infs_subset_left, OrderMonoidWithZeroHom.mul_comp, compl_lt_self, AddValuation.map_add_of_distinct_val, tendsto_ceil_right_pure_add_one, ENat.card_le_one_iff_subsingleton, Finset.sup'_inf_distrib_right, Ideal.IsPrime.inf_le', ArchimedeanClass.instIsOrderedAddMonoid, Hyperreal.isSt_iff_abs_sub_lt_delta, meromorphicOrderAt_add, nhds_top_basis_Ici, Cardinal.toENat_lt_natCast_iff, abs_max_sub_max_le_abs, Finsupp.DegLex.single_lt_iff, Set.projIic_surjOn, inf_sub, LaurentSeries.val_le_one_iff_eq_coe, HasSubset.Subset.disjoint_compl_right, Filter.Tendsto.min_left, zpow_right_strictMono, ProbabilityTheory.Kernel.HasSubgaussianMGF.const_mul, disjoint_compl_compl_left_iff, DistLat.Iso.mk_inv, Polynomial.le_trailingDegree_monomial, sdiff_le_iff_left, ContinuousOn.strictMonoOn_of_injOn_Icc', MonomialOrder.le_degree, Set.Iio_diff_Iio, nhds_basis_Icc_one_lt, Module.Basis.orientation_eq_iff_det_pos, sq_le_sq, List.sum_min_le, TopologicalSpace.Opens.mem_inf, LinOrd.inv_hom_apply, max_lt_max_right_iff, ArchimedeanClass.mk_ofNat, mul_nonneg_iff_pos_imp_nonneg, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquiv_counitIso, Polynomial.degree_comp, Finset.pluennecke_ruzsa_inequality_nsmul_add, ADEInequality.lt_six, IsDedekindDomain.HeightOneSpectrum.valuation_exists_uniformizer, Finset.abs_sum_le_sum_abs, Finpartition.ofErase_parts, Order.krullDim_int, Finsupp.Colex.addRightStrictMono, Function.locallyFinsuppWithin.posPart_add, Nucleus.mem_toSublocale, frontier_Ioi, Set.Finite.encard_lt_top, invOf_lt_zero, FloorRing.gc_ceil_coe, IsDiscreteValuationRing.isRankOneDiscrete, instIsStrictOrderedRingNNRat, disjoint_of_sSup_disjoint, ENat.card_lt_top_of_finite, leOnePart_le_one', AlgebraicGeometry.instDescendsAlongSchemeMinMorphismPropertySurjectiveFlatLocallyOfFinitePresentationOfQuasiCompactOfIsZariskiLocalAtTarget, PredOrder.nhdsGE_eq_nhds, continuousWithinAt_iff_lower_upperSemicontinuousWithinAt, Submodule.inf_genEigenspace, Int.ceil_eq_iff, TopologicalSpace.IsTopologicalBasis.inf_induced, ArchimedeanClass.mk_lt_mk, posPart_nonneg, Pi.bihimp_apply, Pi.bihimp_def, Set.disjoint_singleton, ZMod.valMinAbs_mem_Ioc, himp_bihimp_left, add_left_strictMono_of_ne_top, AlgebraicGeometry.HasAffineProperty.affineAnd_eq_of_propertyIsLocal, neg_abs_le, oneLePart_eq_ite_lt, MvPowerSeries.nat_le_weightedOrder, Rat.toNNRat_lt_toNNRat_iff', upperBounds_Iio, Set.encard_union_le, MeasureTheory.aecover_Icc_of_Ioc, PrimeMultiset.prod_dvd_iff', ValuativeExtension.mapValueGroupWithZero_strictMono, borel_eq_generateFrom_Icc, Module.End.genEigenspace_top_eq_maxUnifEigenspaceIndex, Set.encard_strictMono, Polynomial.trailingDegree_le_trailingDegree, IsDedekindDomain.HeightOneSpectrum.adicCompletionIntegers.integers, AlgebraicGeometry.Etale.instHasOfPostcompPropertySchemeMinMorphismPropertyLocallyOfFiniteTypeFormallyUnramified, Ordinal.toNatOrdinal_min, CategoryTheory.Triangulated.TStructure.le_monotone, exists_wellOrder, PowerSeries.coe_mul, unitInterval.symm_projIcc, Rat.preimage_cast_Ioi, sdiff_lt_left, cocompact_eq_atTop, ArchimedeanClass.FiniteElement.not_isUnit_iff_mk_pos, exists_lt_add_iff_lt_left, Hyperreal.archimedeanClassMk_neg_of_tendsto_atBot, HahnSeries.order_single_mul_of_isRegular, Polynomial.abs_tendsto_atTop_iff, Order.Ideal.coe_sup_eq, Finset.min_le, Finset.infs_sups_subset_right, Cardinal.toENat_lift, PNat.Ico_eq_finset_subtype, CategoryTheory.SmallObject.SuccStruct.restrictionLTOfCoconeIso_inv_app, Int.instIsSuccArchimedean, bihimp_left_comm, hasDerivAt_iff_tendsto_slope_left_right, Finset.inf'_sup_distrib_right, MeasureTheory.stoppedProcess_eq_stoppedValue_apply, sign_zero, Function.Lex.wellFoundedLT, min_le_iff, disjoint_partialSups_right, tendsto_floor_right_pure_floor, biInf_le_eq_inf, Finset.Ioc_sub_one_left_eq_Icc, Subfield.extendScalars_inf, IsOpen.exists_Ioo_subset, Finset.inf_himp_right, inf_sup_assoc_of_le, WithZero.lt_mul_exp_iff_le, CauSeq.bounded', AlgebraicGeometry.IsFinite.eq_proper_inf_locallyQuasiFinite, SimpleGraph.edgeSet_eq_iff, convexHull_basis_eq_stdSimplex, Hyperreal.isSt_sSup, Filter.tendsto_const_mul_atBot_iff, Field.Emb.Cardinal.noMaxOrder_rank_toType, Order.Ioo_pred_left, Set.biUnion_Ico_eq_Iio_self_iff, Convex.radon_partition, Finset.Ico_add_one_left_eq_Ioo, Units.orderEmbeddingVal_apply, Continuous.exists_forall_ge_of_hasCompactSupport, HahnSeries.SummableFamily.hsum_powerSeriesFamily_mul, NNRat.one_le_cast, Finset.max'_subset, List.minimum_append, PosSMulMono.nnrat_of_rat, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivFunctorObj_π_app, List.le_maximum_of_length_pos_of_mem, MeasureTheory.aecover_Ioc_of_Icc, Set.pairwise_disjoint_Ioc_add_zsmul, OrderMonoidIso.withZeroUnits_symm_apply, ENat.add_one_le_iff, Set.Ioi_inj, Int.card_Ioc, ArchimedeanClass.orderHom_zero, Int.preimage_Iio, sup_eq_iff_inf_eq, FunctionField.valuedFqtInfty.def, Polynomial.exists_max_root, Int.floor_le_iff, Rat.preimage_cast_Icc, LinOrd.Iso.mk_hom, Set.Ico_subset_Ico_union_Ico, Finset.prod_sub_ordered, MonoidWithZeroHom.inl_strictMono, PowerSeries.heval_apply, mapClusterPt_atTop_zsmul_iff_nsmul, ENat.instOrderTopology, generateFrom_Ico_mem_le_borel, units_smul_eq_self_iff, NormedSpace.normalize_smul, MvPowerSeries.one_le_order_iff_constCoeff_eq_zero, Nonneg.coe_nnratCast, sign_mul_abs, HahnSeries.addVal_le_of_coeff_ne_zero, Set.Icc_pred_right_eq_Ico, SimpleGraph.farFromTriangleFree.le_card_sub_card, PowerSeries.coe_sub, min_eq_iff, Set.Ici_subset_Icc_union_Ici, Finset.sup_inf_distrib_left, WithBot.ge_of_forall_gt_iff_ge, Affine.Simplex.ExcenterExists.sign_signedInfDist_touchpoint, WithZeroMulInt.toNNReal_lt_one_iff, nhdsGT_basis, CategoryTheory.ObjectProperty.IsLocal.inf, inf_covBy_of_covBy_sup_right, DirectedOn.sSup_inf_eq, MulArchimedeanClass.liftOrderHom_mk, ArchimedeanClass.mem_ball_iff, PNat.sub_coe, SimpleGraph.isUniform_singleton, SupClosed.infClosure, IsNonarchimedean.multiset_image_add_of_nonempty, Int.floor_le_sub_one_iff, OrderMonoidIso.withZeroUnits_apply, MeasurableSpace.map_inf, compl_inf_eq_bot, CategoryTheory.TransfiniteCompositionOfShape.ofComposableArrows_F, Cardinal.toENat_le_ofNat, Asymptotics.isEquivalent_nat_ceil, InverseSystem.PEquivOn.nat, units_smul_eq_neg_iff, isPiSystem_Ioc, nonempty_orderEmbedding_of_finite_infinite, Profinite.NobelingProof.Products.eval_eq, WithTop.orderIsoSumLexPUnit_toLex, succ_min, ArchimedeanClass.mk_monotoneOn, WithBot.succ_eq_bot, Set.disjoint_powerset_insert, LaurentSeries.algebraMap_apply, Int.floor_nonneg, Valuation.IsEquiv.one_lt_iff_one_lt, ArchimedeanClass.mk_sub_lt_mk_right_iff, Polynomial.div_tendsto_atBot_zero_of_degree_lt, IsDedekindDomain.HeightOneSpectrum.intValuation_le_pow_iff_dvd, Iio_mem_nhdsSet_Iic_iff, PNat.addLeftReflectLT, abs_sub_le_iff, max_sub_sub_left, Set.disjoint_toFinset, bihimp_left_surjective, nhdsWithinLE_sup_nhdsWithinGT, continuousInv_inf, midpoint_le_right, Int.cast_strictMono, Set.projIic_coe, GenContFract.IntFractPair.nth_stream_fr_lt_one, AddGroupCone.nonneg.hasMemOrNegMem, SMulPosMono.toSMulPosReflectLT, Set.unbounded_inter_ge, covBy_iff_lt_iff_le_left, LipschitzWith.projIcc, min_lt_iff, MvPowerSeries.le_weightedOrder_pow, bihimp_le_iff_left, iSupIndep.supIndep', Ordinal.toType_noMax_of_succ_lt, RootPairing.zero_lt_pairingIn_iff, IsDedekindDomain.HeightOneSpectrum.valuation_def, le_emultiplicity_of_le_multiplicity, iInf_option_elim, Order.Ioi_pred, Polynomial.abs_tendsto_atTop, Filter.bliminf_or_le_inf, MvPolynomial.leadingCoeff_esymmAlgHomMonomial, CategoryTheory.Limits.MultispanIndex.toLinearOrder_fst, Ideal.isPrimary_finset_inf, MeasureTheory.Measure.pi_prod_map_IocProdIoc, Set.Ioi_subset_Ioc_union_Ioi, Rat.cast_min, CauSeq.lt_lim, lineMap_lt_right_iff_lt_one, iSupIndep.supIndep, tendsto_fract_right', Subalgebra.op_inf, Set.vadd_Icc, ValuationClass.map_add_le_max, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivCounitIso_inv_app_hom, Matrix.IsIrreducible.nonneg, sign_pos, isPiSystem_Ico_mem, smul_min_of_nonneg, Set.Ioo_min_max, IsCompact.exists_isLUB, ProbabilityTheory.condExpKernel_ae_eq_condExp', ValuationSubring.valuation_le_one, CategoryTheory.Limits.MultispanIndex.toLinearOrder_snd, PNat.natPred_monotone, SuccOrder.nhds_eq_pure, PowerSeries.le_order_map, Affine.Simplex.wSameSide_affineSpan_faceOpposite_point_left_iff, CategoryTheory.Limits.instHasIterationOfShapeElemIic, lineMap_le_lineMap_iff_of_lt', BoundedLatticeHom.coe_comp_lattice_hom', inf_iSup₂_eq, symmDiff_symmDiff_right, Set.pairwise_disjoint_Ioc_mul_zpow, inv_le_self_iff, monovaryOn_iff_forall_smul_nonneg, Finset.dens_le_one, ArchimedeanClass.FiniteElement.mk_intCast, Int.ceil_eq_zero_iff, max_add_min, Finset.le_prod_max_one, RingCon.coe_inf, Set.pairwise_disjoint_Ico_mul_zpow, CategoryTheory.TransfiniteCompositionOfShape.iic_isColimit, HahnEmbedding.IsPartial.strictMono, Finset.powerset_infs_powerset_self, MonomialOrder.lex_lt_iff_of_unique, emultiplicity_le_emultiplicity_iff, Finset.le_max_of_eq, max_min_distrib_left, isLocallyClosed_Ico, frontier_lt_subset_eq, add_min, BicartSq.le₂₄, Nat.floor_natCast, iUnion_Icc_intCast, Set.coe_projIci, MvPowerSeries.min_weightedOrder_le_add, SignType.neg_one_lt_one, Set.eq_empty_or_encard_eq_top_or_encard_diff_singleton_lt, max_div_min_eq_mabs', Nat.one_le_floor_iff, PNat.ofNat_lt_ofNat, RootPairing.zero_le_rootForm, Filter.bliminf_or_eq_inf, ZNum.isOrderedAddMonoid, Int.card_fintype_Ioo_of_lt, Dense.exists_le', MonomialOrder.degLex_le_iff, fn_max_add_fn_min, Filter.tendsto_zpow_atTop_atTop, Set.Ico_inter_Ico, instMulArchimedeanNNRat, tendsto_PNat_val_atTop_atTop, Tuple.graphEquiv₂_apply, le_oneLePart, AffineSubspace.inf_coe, WithTop.orderIsoSumLexPUnit_symm_inl, denselyOrdered_units_iff, Nat.measurable_ceil, HahnSeries.cardSuppLTSubfield_carrier, AffineSubspace.wOppSide_iff_exists_left, OrderIso.withZeroUnits_symm_apply, ENat.eq_top_iff_forall_gt, Int.card_box, LaurentSeries.derivative_iterate_coeff, Finset.coe_orderIsoOfFin_apply, NNRat.coe_lt_coe, Valuation.nonempty_rankOne_iff_mulArchimedean, QuadraticMap.toBilin_apply, Order.Ideal.IsMaximal.isPrime, MulArchimedeanClass.min_le_mk_mul, continuous_inf_dom_right, inf_le_iff, atBot_atTop_le_cocompact, tendsto_floor_atTop, MonomialOrder.bot_eq_zero, Function.support_min, Finset.uIcc_product_uIcc, Set.ordConnected_iff_disjoint_Ioo_empty, Function.locallyFinsuppWithin.instIsOrderedAddMonoid, AffineSubspace.map_inf_eq, ValuativeRel.IsDiscrete.has_maximal_element, Int.floor_mono, ArchimedeanClass.mk_add_lt_mk_right_iff, LinearMap.finrank_genEigenspace_le, FunctionField.InftyValuation.map_add_le_max', mabs_mul_le, Set.offDiag_mono, MulArchimedeanClass.mem_closedBallSubgroup_iff, FiniteMulArchimedeanClass.mem_ballSubgroup_iff, Finsupp.lt_of_forall_lt_of_lt, WithTop.isOpenEmbedding_coe, bihimp_le_iff_right, inv_mabs_le, MonomialOrder.toSyn_lt_iff_ne_zero, WeierstrassCurve.IsMinimal.val_Δ_maximal, Mathlib.Tactic.Order.ToInt.toInt_inf_toInt_eq_toInt, tendsto_inv_nhdsGT_zero, abs_sub_lt_iff, HasFDerivAt.abs, supPrime_iff_not_isMin, ArchimedeanClass.stdPart_eq_sInf, AffineSubspace.setOf_wOppSide_eq_image2, iUnion_Ioc_add_intCast, LinearOrderedField.cutMap_coe, Nat.floor_int, AbsoluteValue.abs_apply, Finset.sup'_lt_iff, Sublocale.coe_inf, Hyperreal.stdPart_coe, HasFDerivWithinAt.abs, NatOrdinal.toOrdinal_max, Odd.pow_neg_iff, AffineSubspace.coe_inf, OrderEmbedding.birkhoffSet_inf, Nonneg.instNontrivialSubtypeLeOfNatOfAddLeftMono, Module.End.iSup_genEigenspace_eq, projIcc_eq_one, HasSSubset.SSubset.lt, Hyperreal.infinitePos_iff_infinite_and_pos, Finset.lt_fold_min, strictConvex_Ioo, ArchimedeanClass.ballAddSubgroup_top, LaurentSeries.exists_ratFunc_val_lt, sameRay_smul_left_iff, BooleanSubalgebra.mk_inf_mk, Finpartition.parts_eq_empty_iff, AffineSubspace.wSameSide_and_wOppSide_iff, Int.Ioo_eq_finset_map, min_top_left, List.exists_map_eq_of_sorted_nonempty_iff_sbtw, Int.lt_floor_add_one, Multiset.Ico_filter_lt, SimpleGraph.disjoint_edgeSet, JordanHolderLattice.second_iso, LinOrd.id_apply, AlgebraicGeometry.IsOpenImmersion.map_ΓIso_inv_assoc, Module.End.genEigenspace_inf_le_add, interior_Icc, FiniteArchimedeanClass.liftOrderHom_mk, Finset.addConst_le_subConst_sq, Field.Emb.Cardinal.instIsSeparableSubtypeMemIntermediateFieldAdjoinImageToTypeOrdRankCompCoeBasisWellOrderedBasisLeastExtIioSingletonSet, Finset.prod_Ico_int_div, HahnSeries.embDomainOrderEmbedding_apply, OrderEmbedding.infIrredUpperSet_apply, ArchimedeanClass.mk_map_nonneg_of_archimedean, LinearOrderedCommMonoidWithZero.toIsOrderedMonoid, inf_add_sup, ENat.coe_toNat_le_self, Set.IicExtend_apply, Module.End.eigenspace_le_genEigenspace, bihimp_bihimp_self, UV.le_of_mem_compression_of_notMem, LocallyFiniteOrder.orderAddMonoidHom_strictMono, Order.isGLB_Ioi_iff_isPredPrelimit, inf_eq_div_oneLePart_div, Multiset.toFinsupp_inter, FiniteMulArchimedeanClass.mem_closedBallSubgroup_iff, Valued.hasBasis_nhds_zero, Lat.Iso.mk_inv, Finset.supIndep_iff_pairwiseDisjoint, MonomialOrder.degree_le_iff, Algebra.map_inf, ArchimedeanClass.FiniteResidueField.ofArchimedean_inj, Affine.Simplex.wOppSide_affineSpan_faceOpposite_iff, Set.indicator_nonpos_le_indicator, IsRetrocompact.finsetInf', Hyperreal.epsilon_lt_pos, abs_lt_iff_mul_self_lt, NonemptyFinLinOrd.hom_comp, Hyperreal.coe_nonneg, Finset.isGreatest_max', GenContFract.zero_le_of_den, Heyting.Regular.coe_le_coe, OrderIso.sumLexIioIci_symm_apply_Iio, Int.card_Ico_of_le, HahnEmbedding.ArchimedeanStrata.disjoint_ball_stratum, lowerSemicontinuous_iff_frequently, Finset.inclusion_exclusion_sum_inf_compl, IntermediateField.inf_relfinrank_right, Sublattice.mk_inf_mk, infIccOrderIsoIccSup_apply_coe, HahnEmbedding.ArchimedeanStrata.archimedeanClassMk_of_mem_stratum, Finset.uIcc_subset_uIcc_iff_le', PUnit.isOrderedCancelAddMonoid, sup_eq_sdiff_sup_sdiff_sup_inf, WithTop.continuous_coe, smul_min_of_nonpos, Nat.one_div_cast_pos, Set.Ioc_subset_Ioc_union_Ioc, Finset.Ico_inter_Ico, Padic.mulValuation_toFun, Finset.uIcc_subset_uIcc_iff_le, zpow_two_pos_of_ne_zero, SimpleGraph.FarFromTriangleFree.nonpos, Finset.inf'_pow, IsDedekindDomain.HeightOneSpectrum.valuation_div_le_one_iff, CategoryTheory.SmallObject.SuccStruct.Iteration.mkOfLimit.inductiveSystem_map, Cardinal.one_le_ofENat, Int.sub_one_lt_floor, Set.projIci_surjective, Ideal.height_le_spanRank_toENat_of_mem_minimal_primes, ArchimedeanClass.stdPart_map_real, Finset.prod_one_add_ordered, Tropical.add_eq_left_iff, instModuleFinite, Hyperreal.infinitePos_iff_infinitesimal_inv_pos, IsValuativeTopology.mem_nhds_iff', Finset.inf_eq_inter, HahnEmbedding.IsPartial.truncLT_mem_range, PrimitiveSpectrum.gc_closureOperator, IsDedekindDomain.HeightOneSpectrum.valuation_lt_one_iff_dvd, Complementeds.coe_top, NNRat.cast_nonneg, SignType.not_one_lt, ContinuousOn.strictMonoOn_of_injOn_Ioo, LinOrd.ofHom_id, WithZero.withZeroUnitsEquiv_symm_strictMono, iUnion_Ico_add_intCast, mapClusterPt_rightLim, CategoryTheory.Pairwise.cocone_pt, Affine.Simplex.mongePlane_def, Coheyting.boundary_sup_le, Affine.Simplex.wSameSide_affineSpan_faceOpposite_point_right_iff, AffineMap.lineMap_mono, iSup_inf_le_sSup_inf, isLUB_Iio, Submodule.IsMinimalPrimaryDecomposition.inf_eq, AddCon.inf_iff_and, ConvexCone.mem_inf, Set.Icc_succ_pred_eq_Ioo, IsDedekindDomain.HeightOneSpectrum.intValuation.map_add_le_max', BoundedLatticeHom.coe_comp_sup_hom, exists_isLocalExtr_Ioo_of_tendsto, Opens.pretopology_ofGrothendieck, Set.right_mem_uIoc, ENat.epow_right_mono, LaurentSeries.derivative_apply, Finsupp.Colex.wellFoundedLT_of_finite, Rat.cast_lt_natCast, LinearOrderedAddCommGroupWithTop.neg_pos, min_one, WithBot.coe_min, IsModularLattice.inf_sup_inf_assoc, Valuation.isEquiv_iff_val_le_one, Padic.comap_mulValuation_eq_padicValuation, CategoryTheory.SmallObject.SuccStruct.Iteration.obj_bot, sup_eq_and_inf_eq_iff, Set.exists_min_image, disjointed_add_one, Nucleus.comp_eq_right_iff_le, Polynomial.abs_tendsto_atBot_iff, oneLePart_inf_leOnePart_eq_one, AlgebraicGeometry.Proj.basicOpen_mul, DivisibleHull.instIsStrictOrderedModuleNNRat, Finset.SupIndep.disjoint_sup_sup, Filter.tendsto_const_mul_pow_atTop_iff, PowerSeries.le_order_mul, Finset.disjoint_sup_left, wellQuasiOrderedLE_iff_wellFoundedLT, Mathlib.Meta.NormNum.IsNat.natCeil, Set.sups_infs_subset_left, NumberField.FinitePlace.norm_lt_one_iff_mem, disjoint_compl_left, posSMulStrictMono_iff_PosSMulReflectLE, IntermediateField.extendScalars_inf, Set.pairwise_disjoint_Ico_add_intCast, lowerSemicontinuous_iff_isClosed_epigraph, Filter.liminf_sup_filter, hasBasis_nhdsSet_Iic_Iic, PNat.find_le_iff, CategoryTheory.instIsCardinalFilteredToTypeOrd, Valuation.Integers.not_denselyOrdered_of_isPrincipalIdealRing, isCompact_Ioo_iff, TopCat.Sheaf.objSupIsoProdEqLocus_hom_fst, Module.Basis.orientation_eq_or_eq_neg, VertexOperator.ncoeff_apply, tendsto_ceil_right_pure_floor_add_one, Rat.preimage_cast_Ico, Set.Ioc_subset_uIoc, quasiconvexOn_iff_le_max, HahnSeries.order_abs, Set.encard_lt_top_iff, Valuation.HasExtension.val_map_le_one_iff, AddCircle.equivIccQuot_comp_mk_eq_toIocMod, TopologicalSpace.Opens.functor_obj_map_obj, sup_inf_right, le_iff_forall_pos_lt_add', isComplemented_bot, Valuation.map_sub, FixedDetMatrices.reps_entries_le_m', Hyperreal.coe_pos, Rat.valuation_le_one_iff_den, BoundedLatticeHom.coe_toSupBotHom, infIooOrderIsoIooSup_symm_apply_coe, supIrred_iff_not_isMin, PosSMulReflectLT.toPosSMulMono, inf_lt_inf_of_lt_of_sup_le_sup, inf_sSup_eq, EReal.sign_mul, Hyperreal.archimedeanClassMk_neg_of_tendsto_atTop, MulArchimedeanClass.mk_mul_lt_mk_left_iff, min_mul_distrib', Tropical.trop_min, Nat.floor_div_eq_div, Valuation.mem_valuationSubring_iff, Complementeds.codisjoint_coe, LinearOrderedAddCommGroupWithTop.sub_left_strictMono_of_ne_top, Pi.card_uIcc, List.argmax_cons, Set.IicExtend_coe, tendsto_ceil_left, inv_le_leOnePart, continuousWithinAt_iff_continuous_left'_right', ArchimedeanClass.mk_natCast_nonneg, LaurentSeries.powerSeriesPart_coeff, isGreatest_himp, Finset.orderEmbOfFin_zero, himp_himp, Set.Icc_inter_Icc, WithZero.le_max_iff, Set.encard_le_card, SimpleGraph.hasse_preconnected_of_succ, segment_eq_Icc', Order.PartialIso.exists_across, ProbabilityTheory.Kernel.partialTraj_le_def, Frm.Iso.mk_inv, NNRat.nonpos_iff_eq_zero, disjoint_compl_compl_right_iff, leOnePart_eq_ite_lt, Ioc_subset_closure_interior, Set.subset_diff, Valuation.Integers.isIntegral_iff_v_le_one, disjointed_le_id, EReal.min_neg_neg, partialSups_succ, Set.monotoneOn_or_antitoneOn_iff_uIcc, sbtw_iff_right_ne_and_left_mem_image_Ioi, ArchimedeanClass.mk_right_le_mk_sub_iff, CategoryTheory.Sieve.functorPullback_inter, Set.uIcc_subset_uIcc_iff_le', upperSemicontinuous_iff_frequently, tendsto_pow_div_pow_atTop_zero, Multiset.max_sum_le, IsCauSeq.bounded, Set.not_disjoint_iff_nonempty_inter, Booleanisation.lift_le_lift, Valuation.Integers.isPrincipalIdealRing_iff_not_denselyOrdered, isOpen_Iio, PNat.factorMultiset_gcd, WeierstrassCurve.isGoodReduction_iff, Rat.toNNRat_lt_toNNRat_iff_of_nonneg, nhds_basis_Ioo_pos, nullMeasurableSet_le, min_div_div_left', NNRat.preimage_cast_Iic, Int.isCompl_even_odd, ArchimedeanClass.FiniteResidueField.ofArchimedean_injective, lineMap_le_left_iff_nonpos, Sublattice.infClosed, Finset.exists_max_image, Set.Iic.complementedLattice_iff, hnot_top, lt_tsub_comm, inf_le_sup, inf_left_le_sup_right, Set.Finite.encard_lt_encard, EReal.sign_coe, AddCircle.continuous_equivIoc_symm, Ordinal.toNatOrdinal_one, Affine.Simplex.sign_excenterWeights_singleton_neg, NonemptyFinLinOrd.Iso.mk_inv, BoundedLatticeHomClass.toBoundedOrderHomClass, SSet.stdSimplex.nonDegenerateEquiv_apply_apply, Rat.cast_lt_intCast, Valuation.RankOne.strictMono, tendsto_inv_atBot_nhdsLT_zero, Nat.floor_lt', Valuation.Integers.le_iff_dvd, SimpleGraph.IsUniform.pos, himp_le, CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.instIsIsoAppIncl, UpperSet.infIrred_Ici, mabs_div_sup_mul_mabs_div_inf, pullbackTopology_def, posPart_nonpos, four_mul_le_sq_add, le_sup_sdiff, Set.Icc_diff_pi_univ_Ioc_subset, LaurentSeries.exists_Polynomial_intValuation_lt, LinearOrderedAddCommGroupWithTop.top_pos, Hyperreal.infiniteNeg_iff_infinite_and_neg, MonomialOrder.degree_sum_le, tendsto_ceil_atBot, inf_Prop_eq, sdiff_eq, himp_eq_top_iff, Ioc_diff_botSet, round_le, LinearOrderedCommGroup.wellFoundedOn_setOf_ge_gt_iff_nonempty_discrete, LinearOrderedField.inducedOrderRingHom_toFun, ValuationSubring.valuation_le_one_iff, abs_sub_round_eq_min, Field.Emb.Cardinal.strictMono_leastExt, NNRat.natCast_le_cast, ArchimedeanClass.mk_zero, Finset.Ioc_inter_Ioc, CategoryTheory.TransfiniteCompositionOfShape.map_isoBot, Int.injOn_natAbs_Iic, Set.Ioc_diff_Iic, mem_segment_iff_sameRay, Set.exists_max_image, Set.disjoint_insert_left, ComplementedLattice.exists_isCompl, tsub_eq_tsub_min, IsDedekindDomain.HeightOneSpectrum.valuedAdicCompletion_eq_valuation', mem_extremePoints_iff_forall_segment, Padic.AddValuation.map_add, AlgebraicGeometry.Scheme.pretopology_le_inf, Nat.preimage_ceil_of_ne_zero, sdiff_sdiff_right, compl_lt_compl_iff_lt, Orientation.map_eq_det_inv_smul, PNat.map_subtype_embedding_Icc, MeasureTheory.integrable_iff_integrableAtFilter_atBot_atTop, HahnSeries.orderTop_le_of_coeff_ne_zero, Finset.Ioi_sub_one_eq_Ici, Order.exists_orderEmbedding_insert, sdiff_sdiff_sdiff_le_sdiff, cbiInf_eq_of_not_forall, NNRat.coe_ceil, Hyperreal.lt_of_tendsto_atTop, NNRat.preimage_cast_Ioi, Rat.natCast_le_cast, isCompact_Ioc_iff, Finset.nonneg_addConst, LatticeHom.map_inf', Set.exists_lower_bound_image, lowerSemicontinuousOn_iff_isClosed_epigraph, OrderType.type_eq_type, CircleDeg1Lift.iterate_monotone, toIcoDiv_zero_one, CategoryTheory.ObjectProperty.instSmallMin, concaveOn_iff_div, lt_add_iff_lt_left_or_exists_lt, Finsupp.card_uIcc, Dense.exists_ge', Nucleus.coe_toSublocale, grade_le_grade_iff, Tropical.add_eq_iff, AEMeasurable.min, Nat.iInf_le_succ, ValuationSubring.instIsScalarTowerSubtypeMemValuationSubringWithZeroMultiplicativeInt, Seminorm.closedBall_finset_sup, continuous_min, Order.Ideal.isPrime_iff_mem_or_compl_mem, Set.Iic_diff_Ioc, Int.orderedSMul, Valuation.map_add_le_max', IsModularLattice.sup_inf_sup_assoc, sdiff_inf_right_comm, inf_sdiff_self_right, minimal_iff_isLeast, add_abs_nonneg, inv_nhdsGT_zero, Sublattice.prodEquiv_toEquiv, Rat.cast_lt, Finset.Ioc_sub_one_right_eq_Ioo, Finset.Icc_succ_pred_eq_Ioo, Hyperreal.archimedeanClassMk_pos_of_tendsto, Finsupp.DegLex.single_antitone, WithTop.pred_eq_top, Finsupp.Lex.single_lt_iff, Nimber.add_nat, Complementeds.coe_inf, RootPairing.posRootForm_posForm_pos_of_ne_zero, tendsto_abs_nhdsNE_zero, monovary_iff_forall_smul_nonneg, exists_isExtrOn_uIoo_of_tendsto, closure_openSegment, Affine.Simplex.ExcenterExists.sign_signedInfDist_lineMap_excenter_touchpoint, min_add_add_right, Int.Ioc_filter_modEq_card, SimpleGraph.nonuniformWitnesses_spec, Polynomial.isBigO_atBot_of_degree_le, CategoryTheory.TransfiniteCompositionOfShape.fac, Finset.prod_add_ordered, lt_abs, Set.not_monotoneOn_not_antitoneOn_iff_exists_le_le, Finset.dens_strictMono, MeasureTheory.MemLp.inf, eventually_nhdsWithin_sign_eq_of_deriv_neg, OrderRingIso.subsingleton_left, inf_eq_and_sup_eq_iff, exists_abs_lt, LinearOrderedAddCommGroupWithTop.strictMono_add_left_of_ne_top, MeasureTheory.OuterMeasure.le_add_caratheodory, borel_eq_generateFrom_Ioc, Valued.isClosed_ball, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivFunctor_obj_pt, covBy_iff_le_iff_lt_left, WithZero.exists_ne_zero_and_le_and_le, Tuple.self_comp_sort, max_div_div_left', BoundedLatticeHom.map_top', disjoint_disjointed_of_lt, StieltjesFunction.measurableSet_Ioi, Topology.IsLocallyConstructible.finsetInf, Set.bdd_below_bdd_above_iff_subset_uIcc, TopCat.Presheaf.SheafConditionEqualizerProducts.piInters.hom_ext_iff, Finset.Ioo_succ_right_eq_Ioc, List.sortedLE_insertionSort, Submodule.comap_finsetInf, IsCompact.bddAbove, Set.bounded_ge_inter_ge, Even.pow_pos, JordanHolderLattice.isMaximal_inf_left_of_isMaximal_sup, sup_sdiff_inf, le_abs, sameRay_smul_left_iff_of_ne, Finset.diffs_compls_eq_infs, Heyting.Regular.coe_inf, Finset.Colex.ofColex_top, IicProdIoc_def, PNat.ofNat_le_ofNat, Finset.orderEmbOfFin_last, strictConvex_Iio, HahnSeries.order_mul_of_nonzero, Set.lt_eq_ssubset, List.exists_map_eq_of_sorted_nonempty_iff_wbtw, FiniteMulArchimedeanClass.withTopOrderIso_symm_apply, Finset.sum_Icc_eq_sum_Ico_add, FiniteArchimedeanClass.mem_closedBallAddSubgroup_iff, not_bddAbove_iff_isCofinal, Int.card_Ico, Set.Icc_diff_pi_univ_Ioo_subset, PseudoMetric.IsUltra.isTransitiveRel_ball, Set.nsmul_right_monotone, HahnModule.coeff_smul_order_add_order, Module.Basis.orientation_ne_iff_eq_neg, Valuation.srel_iff_lt, abs_mul_sign, MeasureTheory.Measure.pi_prod_map_IicProdIoc, Int.card_Ioc_of_le, Set.iUnion_Ico_eq_Iio_self_iff, LinearOrderedAddCommGroup.discrete_iff_not_denselyOrdered, IntermediateField.lift_inf, inf_sdiff_sup_left, Finset.Ioc_succ_succ, Finset.inf_eq_inter', ENat.natCast_lt_succ, upperSemicontinuousOn_iff_preimage_Iio, FiniteArchimedeanClass.mem_ball_iff, not_isCofinal_iff_bddAbove, Int.image_Ico_emod, PNat.equivNonZeroDivisorsNat_symm_apply_coe, grade_eq_grade_iff, WithZero.exists_ne_zero_and_lt_and_lt, CategoryTheory.TransfiniteCompositionOfShape.map_isColimit, TopCat.Sheaf.interUnionPullbackConeLift_right, ComplementedLattice.isStronglyCoatomic', PowerSeries.one_le_order_iff_constCoeff_eq_zero, inf_sup_self, continuousAt_iff_continuous_left'_right', OrderIso.subsingleton_of_wellFoundedGT', Profinite.NobelingProof.Products.eval_πs_image', Submodule.coe_finsetInf, MulArchimedeanClass.mk_le_mk_iff_lt, himp_inf_himp_inf_le, Filter.tendsto_mabs_atBot_atTop, OrderIso.sumLexIicIoi_symm_apply_Iic, Nat.succPNat_lt_succPNat, le_mabs_self, HahnSeries.SummableFamily.powerSeriesFamily_hsum_zero, HahnSeries.archimedeanClassMk_eq_archimedeanClassMk_iff, JordanHolderLattice.lt_of_isMaximal, LinearOrderedAddCommGroupWithTop.add_lt_top, Affine.Simplex.face_points, min_max_distrib_right, Filter.tendsto_abs_atBot_atTop, Finset.range_orderEmbOfFin, tendsto_nat_floor_div_atTop, Units.mem_posSubgroup, FiniteMulArchimedeanClass.liftOrderHom_mk, fn_min_mul_fn_max, tendsto_inv_atTop_nhdsGT_zero, Filter.comap_abs_atTop, compl_sup_le_himp, MulArchimedeanOrder.lt_def, ValuativeRel.ValueGroupWithZero.mk_lt_mk, ENat.toENNRealOrderEmbedding_apply, NNRat.natCast_lt_cast, Order.coheight_int, symmDiff_eq, monovaryOn_iff_exists_monotoneOn, strictConvex_iff_convex, intermediate_value_Ioo, Set.Ioc_pred_right_eq_Ioo, DivisibleHull.mk_le_mk, max_le_iff, FiniteGaloisIntermediateField.instIsSeparableSubtypeMemIntermediateFieldMin_1, one_lt_div_iff, TopologicalSpace.Closeds.coe_finset_inf, Continuous.bddBelow_range_of_hasCompactSupport, HurwitzZeta.hasSum_int_completedHurwitzZetaOdd, CategoryTheory.SimplicialThickening.functor_map, BoundedLatticeHom.dual_symm_apply_toFun, symmDiff_eq_sup_sdiff_inf, MonomialOrder.degree_mul_lt_iff_left_lt_of_ne_zero, Sublattice.prodEquiv_apply, IntermediateField.coe_inf, Field.Emb.Cardinal.equivSucc_coherence, NNRat.cast_le_one, Finpartition.default_eq_empty, Finset.Iio_add_one_eq_Iic, MeasurableSet.bihimp, Finset.sup_eq_top_iff, hnot_bot, LinearOrderedCommGroupWithZero.inl_eq_coe_inlₗ, WithTop.orderIsoSumLexPUnit_top, Nat.emultiplicity_two_factorial_lt, convexJoin_assoc, CategoryTheory.ObjectProperty.instIsStableUnderShiftByMin, MonomialOrder.degree_smul_le, Rat.comap_cast_atBot, max_eq_left_iff, Finset.Colex.lt_iff_exists_filter_lt, Polynomial.cyclotomic_pos_and_nonneg, Nucleus.toSublocale_le_toSublocale, WithZeroMulInt.toNNReal_le_one_iff, le_compl_self, max_lt_iff, Set.Ioc_sub_one_right_eq_Ioo, le_emultiplicity_of_pow_dvd, Finset.orderEmbOfFin_singleton, OrderIso.compl_symm_apply, Tuple.antitone_pair_of_not_sorted, tendsto_inv_atBot_zero, ContinuousOn.upperSemicontinuousOn, nhdsLT_sup_nhdsGE, Multiset.trop_inf, IsNonarchimedean.nmul_le, Finset.inf_eq_bot_iff, le_sdiff, Int.card_fintype_Icc_of_le, right_mem_openSegment_iff, Finset.Icc_sub_one_right_eq_Ico, sup_inf_left, Order.isSuccLimitRecOn_succ, antivaryOn_iff_exists_monotoneOn_antitoneOn, HahnSeries.leadingCoeff_pos_iff, abs_max_sub_max_le_max, MeasureTheory.stoppedValue_stoppedProcess_apply, countable_image_lt_image_Iio_within, CategoryTheory.Limits.MultispanShape.ofLinearOrder_L, MvPowerSeries.le_weightedOrder_smul, CovBy.inf_of_sup_of_sup_left, ofBoolRing_le_ofBoolRing_iff, Finset.sup_inf_distrib_right, iSup_inf_eq, Polynomial.isBigO_of_degree_le, lt_subset_interior_le, Finset.pluennecke_ruzsa_inequality_pow_div_pow_mul, IntermediateField.mem_inf, ofBoolAlg_mul_ofBoolAlg_eq_left_iff, HahnSeries.instNoZeroDivisors, HasCountableSeparatingOn.range_Ioi, CategoryTheory.Subfunctor.iSup_min, IsDedekindDomain.HeightOneSpectrum.valuation_of_mk', HasCountableSeparatingOn.range_Iio, toDual_min, HahnSeries.leadingCoeff_mul_of_ne_zero, Set.Ioo_subset_uIoo, isLocallyClosed_Ioc, Finset.Ioc_sub_one_sub_one_eq_Ico, not_linearIndependent_iffₒₛ, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquiv_inverse, Multiset.exists_max_image, sup_inf_self, ArchimedeanClass.min_le_mk_add, HahnSeries.order_le_of_coeff_ne_zero, Polynomial.le_trailingDegree_mul, Finset.addConst_le_card, div_nonpos_iff, sameRay_of_mem_orbit, Units.inv_pos, Set.Ioi_sub_one_eq_Ici, ArchimedeanClass.mk_le_mk_iff_lt, tendsto_floor_right, WithVal.lt_def, Order.isNormal_iff_strictMono_and_continuous, PNat.factorMultiset_le_iff', antivary_iff_exists_monotone_antitone, Set.bounded_gt_inter_gt, HahnSeries.order_ofForallLtEqZero, LaurentSeries.of_powerSeries_localization, CategoryTheory.MorphismProperty.instIsStableUnderRetractsMin, Set.powersetCard.ofFinEmbEquiv_symm_apply, one_min, IsValuativeTopology.mem_nhds_zero_iff, Finset.one_le_divConst, HahnSeries.coeff_mul_order_add_order, HahnEmbedding.Partial.eval_smul, fn_max_mul_fn_min, himp_le_left, nsmul_le_nsmul_iff_right, Cardinal.powerlt_min, min_idem, Order.Ico_succ_right, Int.le_ceil_iff, Finset.Iic_pred_eq_Iio, MulArchimedeanClass.mk_antitoneOn, iSupIndep_iff_supIndep_of_injOn, MulArchimedeanClass.mk_monotoneOn, Nat.ceil_le_floor_add_one, Tropical.untrop_add, MonomialOrder.degree_mul_le, Valuation.apply_posSubmonoid_pos, hasStrictDerivAt_abs, one_le_sq_iff_one_le_abs, Set.disjoint_prod, AffineIndependent.inf_affineSpan_eq_affineSpan_inter, Valuation.one_srel_iff, Pi.Colex.isStrictOrder, midpoint_le_left, RatFunc.valuation_eq_LaurentSeries_valuation, CategoryTheory.SmallObject.ιFunctorObj_eq, BicartSq.inf_eq, monovary_iff_smul_rearrangement, leOnePart_eq_one, List.minimum_cons, sum_Ioo_inv_sq_le, le_himp_iff', negPart_eq_ite, Nat.succPNat_strictMono, Set.compl_Ioi, Ordinal.le_enum_succ, monovary_comm, FiniteArchimedeanClass.subsemigroup_eq_addSubgroup, HahnSeries.orderTop_mul_of_ne_zero, AlgebraicGeometry.Scheme.Hom.appLE_appIso_inv, Stream'.Seq.at_least_as_long_as_coind, Finite.exists_max, NNRat.preimage_cast_Icc, bihimp_triangle, exists_Ioo_extr_on_Icc, continuousOn_iff_lower_upperSemicontinuousOn, toZ_iterate_pred_ge, AlgebraicGeometry.Scheme.PartialMap.equiv_iff_of_isSeparated, MeasureTheory.partialTraj_const, Finset.inf_sdiff_right, monovary_iff_exists_antitone, Set.left_mem_uIoc, Filter.Tendsto.min_right, Module.End.disjoint_genEigenspace, MvPolynomial.supDegree_esymm, Set.mem_Icc_iff_abs_le, Coheyting.boundary_inf, bihimp_eq, FloorRing.archimedean, Int.gc_coe_floor, ProbabilityTheory.gaussianReal_mul_const, PosSMulStrictMono.toPosSMulReflectLE, ENat.one_le_iff_ne_zero_withTop, add_le_add_iff_left_of_ne_top, WithZeroTopology.isClosed_iff, List.minimum_of_length_pos_le_getElem, strictConvex_Ici, neg_sup, TopologicalSpace.IsTopologicalBasis.inf, le_compl_iff_le_compl, TopologicalSpace.Opens.coe_finset_inf, Hyperreal.archimedeanClassMk_nonneg_of_tendsto, gc_sdiff_sup, mul_pos_iff, Order.not_isMin_succ, Continuous.if_le, Mathlib.Meta.NormNum.IsRat.natFloor, Function.isMinimalFor_argminOn, Set.indicator_eq_zero', Nat.choose_lt_pow_div, ArchimedeanClass.mem_addSubgroup_iff, Function.isMinimalFor_argmin, WithZeroTopology.hasBasis_nhds_zero, ArchimedeanClass.addSubgroup_eq_bot, Hyperreal.epsilon_lt_of_neg, Finset.sup'_inf_sup', Valuation.mem_leAddSubgroup_iff, Submodule.inf_iSup_genEigenspace, tendsto_nat_ceil_atTop, Nat.floor_ofNat, FirstOrder.Language.ClosedUnder.inf, Polynomial.trailingDegree_le_of_ne_zero, MeasureTheory.integrable_iff_integrableAtFilter_atTop, exists_nonneg_right_iff_sameRay, MonomialOrder.le_add_right, FiniteMultiplicity.emultiplicity_le_of_multiplicity_le, AddCircle.coe_image_Icc_eq, CharP.intCast_injOn_Ico, Finset.max_le_iff, Polynomial.isEquivalent_atTop_div, R1Space.inf, isLocallyClosed_Iio, RelHomClass.map_inf, bihimp_right_inj, Archimedean.embedReal_injective, IsPreconnected.ordConnected, bihimp_right_comm, min_abs_abs_le_abs_max, abs_sub_abs_le_abs_sub, exteriorPower.ιMultiDual_apply_ιMulti, nonemptyFinLinOrd_dual_comp_forget_to_linOrd, Topology.IsLower.tendsto_nhds_iff_lt, List.getD_min?_eq_untopD_minimum, LinearOrderedField.coe_mem_cutMap_iff, Valuation.vle_iff_le, Module.End.genEigenspace_eq_genEigenspace_maxUnifEigenspaceIndex_of_le, Order.Ioi_pred_eq_insert, SimpleGraph.not_isUniform_iff, LatticeCon.inf, Set.disjoint_image_iff, OrderIso.sumLexIicIoi_symm_apply_Ioi, MonomialOrder.degree_pow_le, cmp_mul_right', mapClusterPt_atTop_zpow_iff_pow, mul_self_pos, AlgebraicGeometry.Scheme.grothendieckTopology_eq_inf, ValuationSubring.monotone_mapOfLE, List.exists_map_eq_of_sorted_iff_sbtw, measurableSet_Ioi, PNat.add_one_le_iff, Int.preimage_Iic, Finset.nsmul_inf', MeasureTheory.Measure.inf_apply, Valued.toNormedField.norm_le_iff, Valuation.map_add', Set.disjoint_pi, map_pos_of_ne_zero, Orientation.oangle_sign_smul_left, exists_isLocalExtr_uIoo_of_tendsto, iUnion_Icc_add_intCast, Cardinal.ofENat_le_ofENat, le_iSup_inf_iSup, Int.Icc_eq_finset_map, BddDistLat.dual_map, ProbabilityTheory.Kernel.partialTraj_succ_self, ENat.toENNReal_lt, MulArchimedeanClass.ballSubgroup_antitone, CategoryTheory.Subfunctor.min_obj, Finset.uIcc_prod_def, Pi.uIcc_eq, IsDedekindDomain.HeightOneSpectrum.valuation_lt_one_iff_mem, countable_image_gt_image_Iio_within, Mathlib.Meta.Positivity.nonneg_of_isRat, bot_eq_one', Polynomial.le_trailingDegree_C_mul_X_pow, DivisibleHull.instIsOrderedCancelAddMonoid, IntermediateField.restrictScalars_inf, Valuation.ltSubmodule_monotone, Pi.lt_toColex_update_self_iff, Cardinal.ofNat_lt_ofENat, MeasureTheory.stoppedValue_stoppedProcess, Cardinal.card_typein_toType_lt, LaurentSeries.coe_X_compare, Set.indicator_eq_zero, Finset.dens_biUnion_le, HahnSeries.finiteArchimedeanClassOrderIsoLex_apply_snd, instArchimedeanNNRat, symmDiff_sup_inf, Int.card_fintype_Ioc_of_le, Module.Basis.orientation_comp_linearEquiv_eq_iff_det_pos, Nucleus.range_subset_range, LaurentSeries.hasseDeriv_comp_coeff, PNat.card_Ico, LinearGrowth.linearGrowthInf_inf, sameRay_neg_smul_left_iff_of_ne, sub_one_lt, le_symmDiff_iff_right, Set.empty_covBy_singleton, continuousAt_iff_continuous_left_right, symmDiff_triangle, Relation.cutExpand_le_invImage_lex, HahnSeries.cardSupp_div_le, CategoryTheory.SmallObject.instIsIsoRightAppArrowMapToTypeOrdFunctorIterationFunctor, CategoryTheory.Pairwise.cocone_ι_app, NumberField.RingOfIntegers.HeightOneSpectrum.adicAbv_def, Fin.castLEOrderEmb_toEmbedding, Orientation.oangle_sign_smul_add_smul_smul_add_smul, ValuativeRel.RankLeOneStruct.strictMono, Birkhoff_inequalities, GroupCone.oneLE.hasMemOrInvMem, Finset.Ici_succ_eq_Ioi, MonomialOrder.toSyn_monotone, Valued.integer.mulArchimedean_mrange_of_isCompact_integer, eventually_nhdsWithin_sign_eq_of_deriv_pos, Valuation.Integers.dvdNotUnit_iff_lt, InfiniteGalois.restrict_fixedField, nhds_eq_iInf_mabs_div, exists_le_mul_self, Padic.valuation_p_lt_one, Finset.dens_le_dens_sdiff_add_dens, disjoint_of_sSup_disjoint_of_le_of_le, LaurentSeries.intValuation_le_iff_coeff_lt_eq_zero, bihimp_iff_iff, Tropical.addLeftMono, OpenAddSubgroup.toOpens_inf, min_neg_neg, sdiff_le_inf_hnot, infsInfHom_apply, TopCat.Presheaf.IsSheaf.isSheafPreservesLimitPairwiseIntersections, PointedCone.tmul_subset_maxTensorProduct, BooleanAlgebra.le_iff_atom_le_imp, Finset.uIcc_map_sectL, Fin.attachFin_uIcc, MvPowerSeries.weightedOrder_mul_ge, Valuation.IsEquiv.lt_iff_lt, convexJoin_convexJoin_convexJoin_comm, MvPowerSeries.le_order, Nat.ceil_intCast, Finset.dens_lt_dens, Function.argminOn_le, RootPairing.zero_le_posForm, StieltjesFunction.mono, Finset.Iio_succ_eq_Iic, Set.one_le_encard_insert, min_max_distrib_left, RatFunc.algebraMap_apply_div, Int.Ico_filter_dvd_card, PNat.map_subtype_embedding_Ioo, Set.Nonempty.encard_pos, Set.compl_ordConnectedSection_ordSeparatingSet_mem_nhdsLE, convexHull_sum, PowerSeries.le_order_pow_of_constantCoeff_eq_zero, LinearOrderedSemiring.toOrderedSMul, Set.monotone_or_antitone_iff_uIcc, MonomialOrder.degLex_single_le_iff, ArchimedeanClass.mk_mul, strictConcaveOn_iff_slope_strict_anti_adjacent, Finset.inf_set_eq_iInter, HahnSeries.addVal_apply_of_ne, tendsto_ratCast_atBot_iff, isLeast_pair, Finset.inclusion_exclusion_card_biUnion, MeasureTheory.aecover_Icc_of_Icc, Set.pow_right_monotone, LinearOrderedCommGroup.wellFoundedOn_setOf_le_lt_iff_nonempty_discrete, posPart_pos_iff, Order.Iio_succ, Nimber.instWellFoundedLT, MvPolynomial.leadingCoeff_toLex_C, AddCircle.coe_image_Ioc_eq, Finset.Ico_succ_succ, leOnePart_max, Filter.tendsto_mul_const_atTop_iff, Finset.SupIndep.le_sup_iff, interior_Ioc, ArchimedeanClass.map_mk_eq, max_sub_min_eq_abs, Set.Ioi_pred_eq_Ici, inf_himp, MvPowerSeries.order_le, MeasureTheory.StronglyMeasurable.integral_condExpKernel', Multiset.Ico_inter_Ico, Finset.Colex.toColex_lt_toColex_iff_exists_forall_lt, Rat.preimage_cast_Iic, Finset.max'_eq_sorted_last, ENat.toENNReal_min, Finset.min'_subset, LinearLocallyFiniteOrder.instIsPredArchimedeanOfLocallyFiniteOrder, inf_iSup_eq, PredOrder.nhds_eq_pure, Ideal.finset_inf_span_singleton, CategoryTheory.MorphismProperty.RespectsLeft.inf, add_lt_add_iff_left_of_ne_top, hasBasis_nhdsSet_Iic_Iio, NatOrdinal.toOrdinal_natCast, Set.Ioc_pred_left_eq_Icc, PowerSeries.coe_zero, Module.End.mem_genEigenspace_top, Valued.closure_coe_completion_v_lt, List.minimum_eq_coe_iff, BooleanSubalgebra.infClosed, Coheyting.inf_hnot_self, Module.Basis.orientation_adjustToOrientation, MulArchimedeanClass.mk_div_lt_mk_left_iff, sdiff_sdiff_sup_sdiff, Pi.Lex.wellFoundedLT, sign_mul, grade_lt_grade_iff, BoundedLatticeHom.symm_dual_id, countable_setOf_covBy_left, posPart_eq_ite, Polynomial.isEquivalent_atBot_lead, Module.End.injOn_genEigenspace, Finset.mem_convexHull, LinearOrder.infClosed, OrderEmbedding.preimage_uIcc, ZNum.cast_le, ProbabilityTheory.condExp_ae_eq_integral_condExpKernel', IsDiscreteValuationRing.addVal_add, SetTheory.PGame.equiv_nim_grundyValue, Mathlib.Meta.NormNum.isRat_lt_false, Nonneg.coe_nnqsmul, Module.Basis.orientation_comp_linearEquiv_eq_neg_iff_det_neg, mul_neg_iff, Finset.nonneg_addConst_self, Finset.Icc_pred_right_eq_Ico, AbsoluteValue.map_units_int_smul, Module.End.genEigenspace_one, Profinite.NobelingProof.Products.lt_iff_lex_lt, Int.padicValuation_self, mabs_div, Valued.closure_coe_completion_v_mul_v_lt, inf_symmDiff_distrib_left, compl_le_self, Set.encard_iUnion_le_of_finite, mul_self_lt_one_iff, Nat.ceil_one, RootPairing.RootPositiveForm.rootLength_pos, measurable_IicProdIoc, Algebra.inf_toSubmodule, Int.Ioc_eq_finset_map, Hyperreal.infinitesimal_neg_iff_infiniteNeg_inv, CategoryTheory.ObjectProperty.instIsTriangulatedClosed₂MinOfIsClosedUnderIsomorphisms, Set.uIcc_eq_union, Set.disjoint_compl_right_iff_subset, Set.pairwise_disjoint_Ioo_zpow, HahnSeries.isUnit_iff, Int.instIsPredArchimedean, inf_lt_sup, Hyperreal.infiniteNeg_def, MulArchimedeanClass.mk_right_le_mk_mul_iff, Set.Finite.inf_of_left, IsMulIndecomposable.baseOf_subset_one_lt, isAtomic_of_isCoatomic_of_complementedLattice_of_isModular, gc_Ici_sInf, smul_nonpos_iff_neg_imp_nonneg, CategoryTheory.MorphismProperty.bijective_eq_sup, Set.Ico_diff_Iio, Set.unbounded_ge_iff_unbounded_inter_ge, inf_sup_right, isPiSystem_Ico, Valued.cauchy_iff, AffineSubspace.wSameSide_iff_exists_left, Nat.ceil_ofNat, MvPolynomial.schwartz_zippel_sup_sum, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.map_f', Asymptotics.IsEquivalent.tendsto_atBot_iff, Set.disjoint_image_image, Valuation.one_apply_le_one, Cardinal.toENatAux_gc, AddCircle.card_torsion_le_of_isSMulRegular_int, EReal.sign_bot, LinearOrderedAddCommGroup.Subgroup.negGen_neg, HahnSeries.min_order_le_order_add, LaurentSeries.exists_powerSeries_of_memIntegers, sbtw_pointReflection_of_ne, PointedCone.minTensorProduct_le_maxTensorProduct, transfiniteIterate_bot, CategoryTheory.TransfiniteCompositionOfShape.ici_isoBot, Set.compl_Iic, Set.Iic.coe_iInf, Nat.ceil_sub_natCast, nhds_inf, Filter.comap_mabs_atTop, nhdsWithin_Iio_isMeasurablyGenerated, comap_coe_nhdsLT_eq_atTop_iff, Cardinal.toNat_toENat, PNat.Ioc_eq_finset_subtype, ArchimedeanClass.mk_left_le_mk_add_iff, Finset.sort_sorted_lt, Booleanisation.lift_sdiff_comp, Finset.le_card_falling_div_choose, MulArchimedeanClass.mk_one, NonemptyInterval.snd_sup, eq_compl_iff_isCompl, lt_sup_iff, Finset.Ioc_pred_right_eq_Ioo, exists_pos_left_iff_sameRay, Function.disjoint_mulSupport_iff, MvPolynomial.monic_esymm, Finset.prod_min_le, Set.Ico_succ_left_eq_Ioo, Int.floor_eq_iff, FrameHom.coe_toInfTopHom, subsingleton_floorSemiring, ArchimedeanClass.FiniteResidueField.mk_eq_mk, ArchimedeanClass.stdPart_monotoneOn, SimpleGraph.compl_neighborSet_disjoint, abs_nonpos_iff, Ordinal.toNimber_one, Convex.min_le_combo, Polynomial.cardPowDegree_apply, monovaryOn_iff_smul_rearrangement, Odd.strictMono_pow, NNRat.instCanonicallyOrderedAdd, BooleanSubalgebra.val_inf, IsDedekindDomain.HeightOneSpectrum.adicValued_apply, Finset.prod_prod_Ioi_mul_eq_prod_prod_off_diag, InnerProductSpace.gramSchmidt_def', closure_Iio, bihimp_eq_sup_himp_inf, Set.not_disjoint_iff, inf_sq_eq_mul_div_mabs_div, Int.card_Icc_of_le, RootPairing.pairingIn_le_zero_iff, CategoryTheory.SmallObject.SuccStruct.extendToSucc.obj_eq, NumberField.FinitePlace.norm_def_int, WithTop.tendsto_untopA, Nat.Ico_filter_modEq_cast, CategoryTheory.TransfiniteCompositionOfShape.iic_F, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.w, Set.disjoint_iff_inter_eq_empty, hnot_inf_distrib, Finset.expect_mul_sq_le_sq_mul_sq, NNRat.coe_le_coe, CategoryTheory.SmallObject.SuccStruct.restrictionLTOfCoconeIso_hom_app, tendsto_ceil_left_pure, self_mul_sign, ContinuousWithinAt.lowerSemicontinuousWithinAt, separableClosure_inf_perfectClosure, Set.uIcc_subset_uIcc_iff_le, convexHullAddMonoidHom_apply, cocompact_eq_atBot, iInf_bool_eq, RingSeminormClass.toNonnegHomClass, vectorSpan_segment, HahnSeries.binomial_power, ENat.toENNReal_mono, OrderTopology.to_orderClosedTopology, Subalgebra.unop_inf, Ordinal.cof_eq_cof_toType, RootPairing.pairingIn_lt_zero_iff, LinearLocallyFiniteOrder.succFn_spec, List.argmax_eq_some_iff, inf_compl_self, Finset.card_truncatedInf_union_add_card_truncatedInf_sups, Heyting.Regular.coe_top, MonoidWithZeroHom.inr_mono, Coheyting.boundary_inf_le, IsValuativeTopology.hasBasis_nhds_zero', ExpGrowth.expGrowthInf_inf, inf_le_bihimp, Set.Icc.isCompl_iff, PowerSeries.coe_C, codisjoint_hnot_left, Finset.convexHull_eq, Mathlib.Meta.NormNum.isRat_le_false, Set.Infinite.exists_lt_map_eq_of_mapsTo, Set.Iic_sub_one_eq_Iio, div_sup, sdiff_eq_bot_iff, Polynomial.div_tendsto_leadingCoeff_div_of_degree_eq, PNat.find_lt_iff, Filter.not_tendsto_pow_atTop_atBot, Set.Ioc_union_Ioc_symm, le_neg_self_iff, upperSemicontinuousOn_iff_frequently, sdiff_le, AlgebraicGeometry.HasRingHomProperty.inf, min_right_comm, Finset.orderEmbOfCardLe_mem, exists_isLocalExtr_uIoo, pow_dvd_iff_le_emultiplicity, ENat.epow_left_mono, Nat.cast_min, Dense.borel_eq_generateFrom_Ico_mem, Mathlib.Meta.NormNum.isNNRat_le_true, tendsto_intCast_atTop_iff, PointedCone.tmul_subset_minTensorProduct, Nonneg.coe_inv, Polynomial.eventually_atTop_not_isRoot, Finset.fold_max_le, Order.lt_succ_iff, LinearOrderedField.inducedMap_mono, Polynomial.natTrailingDegree_le_trailingDegree, DFinsupp.toMultiset_inf, ValuativeRel.isRankLeOne_iff_mulArchimedean, Valuation.Integers.maximalIdeal_eq_setOf_le_v_algebraMap, Subalgebra.LinearDisjoint.rank_inf_eq_one_of_flat_of_inj, nhdsSet_Iic, Finset.sup_inf, exteriorPower.pairingDual_apply_apply_eq_one, OrderIso.sumLexIicIoi_apply_inr, ArchimedeanClass.mk_ratCast, iInf_split, Order.isLUB_Iio_iff_isSuccPrelimit, PowerSeries.coe_neg, BoundedLatticeHom.map_bot', LinearOrderedAddCommGroup.wellFoundedOn_setOf_ge_gt_iff_nonempty_discrete, pred_max, Set.exists_upper_bound_image, tendsto_floor_left', Set.Iic.coe_biInf, RootPairing.coxeterWeightIn_le_four, Finset.pluennecke_ruzsa_inequality_pow_div, Set.antitone_bforall, Order.succ_injective, MulArchimedeanClass.map_mk_eq, ProbabilityTheory.gaussianReal_map_mul_const, MeasureTheory.stoppedProcess_eq'', Nat.orderedSMul, Set.Iic_union_Ioi, MeasureTheory.integrableOn_Ioi_iff_integrableAtFilter_atTop_nhdsWithin, PowerSeries.min_order_le_order_add, CategoryTheory.OrthogonalReflection.iteration_map_succ_assoc, cmp_sub_zero, zsmul_left_strictMono, ValuationSubring.isIntegral_of_mem_ringOfIntegers', TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivUnitIso_inv_app_hom, LaurentSeries.hasseDeriv_coeff, Set.zero_mem_neg_add_iff, inf_compl_eq_bot', max_min_distrib_right, Rat.preimage_cast_Ici, Set.disjoint_insert_right, Set.pairwise_disjoint_Ioc_intCast, ArchimedeanClass.ballAddSubgroup_antitone, AddCircle.openPartialHomeomorphCoe_source, sign_apply, HahnSeries.embDomainOrderAddMonoidHom_injective, PosNum.cast_le, sq_lt_one_iff_abs_lt_one, Set.subset_compl_iff_disjoint_left, Polynomial.exists_approx_polynomial, Finite.exists_min, Profinite.NobelingProof.Products.lt_nil_empty, sq_sum_le_card_mul_sum_sq, tendsto_nat_floor_atTop, ValuativeRel.instIsOrderedMonoidValueGroupWithZero, Nimber.toOrdinal_eq_one, Tuple.comp_sort_eq_comp_iff_monotone, Set.Ici_diff_Ioi, Finset.Ico_add_one_right_eq_Icc, Directed.iSup_inf_eq, Sym2.sortEquiv_symm_apply, Ico_mem_nhds_iff, FrameHom.map_sSup', Types.monoOverEquivalenceSet_functor_map, PrimeMultiset.prod_inf, Finset.supIndep_pair, intermediate_value_Ioc', toENat_rank_span_set, TopCat.Sheaf.objSupIsoProdEqLocus_inv_snd, le_sup_inf, Finset.min'_lt_max', oneLePart_le_one, Int.comap_cast_atBot, ProbabilityTheory.condExpKernel_def, GenContFract.of_den_mono, SuccOrder.isOpen_iff, inf_iInf, iSup_inf_le_inf_sSup, DivisibleHull.qsmul_def, MvPolynomial.supDegree_toLex_C, Finset.mulConst_le_inv_dens, Finset.Ioc_pred_pred_eq_Ico, ArchimedeanClass.out_top, sign_one, ValuativeRel.uniformizer_inv_le_iff, Valuation.one_vlt_iff, DFinsupp.card_uIcc, neg_lt_self_iff, IsValuativeTopology.isClopen_ball, IsValuativeTopology.hasBasis_nhds, Set.Iic_pred_eq_Iio, Set.encard_mono, bihimp_comm, Order.Frame.MinimalAxioms.inf_iSup₂_eq, AbsoluteValue.IsAdmissible.exists_approx, abs_cases, Polynomial.tendsto_nhds_iff, Affine.Simplex.sSameSide_affineSpan_faceOpposite_iff, dvd_iff_emultiplicity_pos, AddCircle.measurePreserving_equivIoc, Rat.castOrderEmbedding_apply, ENat.add_lt_add_iff_left, BoolAlg.dual_map, biInf_ge_eq_inf, ArchimedeanClass.subsemigroup_strictAnti, Set.encard_singleton_inter, Matrix.IsIrreducible.exists_pos, Int.instStarOrderedRing, QuotientAddGroup.btw_coe_iff, Finset.sum_card_slice_div_choose_le_one, IsDedekindDomain.HeightOneSpectrum.intValuation_lt_one_iff_dvd, Filter.Eventually.exists_Ioo_subset, wbtw_iff_right_eq_or_left_mem_image_Ici, Mathlib.Meta.NormNum.isRat_le_true, CauSeq.const_le, FiniteMulArchimedeanClass.mk_le_mk, archimedean_iff_nat_lt, le_analyticOrderAt_sub, disjoint_compl_left_iff, Rat.toNNRat_pos, tendsto_pow_neg_atTop, Finset.sups_infs_subset_right, Asymptotics.IsEquivalent.tendsto_atTop_iff, WithZero.denselyOrdered_set_iff_subsingleton, le_analyticOrderAt_add, Set.Iic_subset_Iic_union_Icc, ProjectiveSpectrum.basicOpen_mul, IsConnected.Icc_subset, abs_pos, Set.subsingleton_Icc_iff, sdiff_inf_self_right, Set.bounded_lt_inter_lt, aemeasurable_uIoc_iff, infIrred_iff_not_isMax, Set.pairwise_disjoint_Ioo_zsmul, IsDiscreteValuationRing.map_algebraMap_eq_valuationSubring, LinearLocallyFiniteOrder.instIsSuccArchimedeanOfLocallyFiniteOrder, OrderIso.subsingleton_of_wellFoundedLT', Valuation.one_vle_iff, ENat.one_le_epow, lowerSemicontinuousOn_iff_frequently, Filter.tendsto_const_mul_pow_atBot_iff, IntermediateField.relfinrank_inf_mul_relfinrank, wbtw_iff_left_eq_or_right_mem_image_Ici, Ioo_subset_openSegment, Set.unbounded_lt_iff, abs_sub_map_le_div, convexHull_pi, ArchimedeanClass.ball_top, Cardinal.toENat_strictMonoOn, InnerProductSpace.span_gramSchmidt_Iic, Function.mulSupport_min, HahnSeries.pow_add, Fin.castAddOrderEmb_toEmbedding, CategoryTheory.Limits.Types.isPushout_of_bicartSq, Set.Nontrivial.exists_lt, SimpleGraph.FarFromTriangleFree.lt_half, Finset.Nonempty.inf_eq_bot_iff, round_eq_zero_iff, Pi.support_single_disjoint, Order.Frame.MinimalAxioms.inf_iSup_eq, NNRat.preimage_cast_Ici, abs_sup_sub_sup_le_abs, Finset.min_eq_bot, TopologicalSpace.Closeds.coe_inf, Language.IsRegular.inf, IntermediateField.LinearDisjoint.inf_eq_bot, AlgebraicGeometry.isOpenImmersion_eq_inf, HasSubset.Subset.disjoint_compl_left, div_inf, Submodule.IsMinimalPrimaryDecomposition.minimal, FiniteArchimedeanClass.mk_le_mk, Coheyting.boundary_hnot_le, CategoryTheory.SmallObject.iterationFunctorMapSuccAppArrowIso_hom_right_right_comp_assoc, HahnSeries.orderTop_mul, Ordinal.ToType.mk_symm_apply_coe, MonomialOrder.wf, ArchimedeanClass.FiniteElement.isUnit_iff_mk_eq_zero, Finset.fold_min_le, Hyperreal.instIsStrictOrderedRing, frontier_Ici_subset, Set.projIic_self, Valued.toNormedField.one_lt_norm_iff, LinOrd.forget_map, Field.Emb.Cardinal.filtration_apply, PrimeMultiset.prod_dvd_iff, Set.Ioc_pred_pred_eq_Ico, Coheyting.boundary_le_boundary_sup_sup_boundary_inf_left, Nat.iInf_lt_succ, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.sq, Finset.Ioo_pred_left_eq_Ioc, Affine.Simplex.ExcenterExists.sign_touchpointWeights, SimpleGraph.fromEdgeSet_disjoint, Rat.cast_mono, NNRat.ceil_coe, Nat.image_cast_int_Ioi, IsDedekindDomain.HeightOneSpectrum.intValuation_zero_lt, sq_lt_sq, CategoryTheory.Sieve.pullback_inter, Int.lt_zpow_succ_log_self, Set.infs_sups_subset_left, Finset.compls_sups, add_sq_le, Finset.le_dens_sdiff, strictConvex_Ioc, Finset.min'_lt_max'_of_card, toZ_iterate_succ, IsValuativeTopology.hasBasis_nhds_zero, AffineMap.lineMap_anti, LaurentSeries.LaurentSeriesRingEquiv_mem_valuationSubring, nhdsWithinLT_sup_nhdsWithinGT, IsDedekindDomain.HeightOneSpectrum.valuedAdicCompletion_eq_valuation, posSMulMono_iff_posSMulReflectLT, AddSubmonoid.mem_closure_image_pos_iff, Valuation.IsNontrivial_iff_exists_one_lt, Tropical.trop_add_def, Matroid.ExchangeProperty.encard_diff_le_aux, LinOrd.ext_iff, isOpen_Ioi, Affine.Simplex.sign_touchpointWeights_singleton_pos, NonemptyFinLinOrd.hom_hom_id, Padic.toEquiv_withValUniformEquiv_eq_toEquiv_withValRingEquiv, nhdsSet_Ici, instCommutativeMin, isCompact_Ico_iff, AddCircle.eq_coe_Ico, SetRel.image_mono, Set.Iio_subset_Iio_iff, Finset.iInf_union, CategoryTheory.MorphismProperty.instHasOfPrecompPropertyMin, Orientation.oangle_sign_smul_right, TopCat.Sheaf.interUnionPullbackConeLift_left, Ideal.quotientInfEquivQuotientProd_snd, disjointed_le, Finset.min_pair, Odd.zpow_nonneg_iff, Finset.Ioi_pred_eq_Ici, Function.Injective.image_strictMono, Asymptotics.isEquivalent_nat_floor, Module.End.genEigenspace_eq_iSup_genEigenspace_nat, AlgebraicGeometry.IsClosedImmersion.eq_inf, continuousSMul_inf, Finset.min'_lt_of_mem_erase_min', AlgebraicGeometry.Scheme.Hom.appLE_appIso_inv_assoc, Valuation.mem_ltAddSubgroup_iff, le_iff_forall_pos_lt_add, mabs_mabs_div_mabs_le_mabs_div, Cardinal.ofNat_le_ofENat, CategoryTheory.TransfiniteCompositionOfShape.ici_isColimit, IntermediateField.map_comap_eq, IsCompact.bddAbove_image, PNat.succ_eq_add_one, isStronglyAtomic, Ordinal.enum_succ_eq_top, Nimber.toOrdinal_one, iSupIndep.sup_indep_univ, doublyStochastic_eq_convexHull_permMatrix, mul_smul_one_lt_iff, PNat.factorMultiset_mono, LaurentSeries.valuation_LaurentSeries_equal_extension, cocompact_eq_atBot_atTop, inf_sdiff_assoc, IsDedekindDomain.inf_prime_pow_eq_prod, floorDiv_le_ceilDiv, Set.disjoint_univ, NonUnitalStarSubalgebra.prod_inf_prod, LaurentSeries.hasseDeriv_single_add, ENat.addLECancellable_coe, le_himp_iff, Interval.disjoint_coe, Set.disjoint_image_right, SetLike.coe_strictMono, Types.monoOverEquivalenceSet_functor_obj, Order.Frame.MinimalAxioms.inf_sSup_eq, nhdsLT_basis, scottContinuous_inf_left, CategoryTheory.MorphismProperty.pretopology_inf, Submodule.spanRank_toENat_eq_iInf_finset_card, Finset.min'_insert, himp_bihimp_right, AlgebraicGeometry.targetAffineLocally_affineAnd_eq_affineLocally, Order.succ_le_succ_iff, CompositionSeries.strictMono, LucasLehmer.two_lt_q, HahnSeries.orderTop_nsmul_le_orderTop_pow, variationOnFromTo.sub_self_monotoneOn, min_add_max, WeierstrassCurve.isMinimal_iff, Finset.pluennecke_ruzsa_inequality_nsmul_sub_nsmul_sub, CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.instIsIsoMapF, Set.Iio_ssubset_Iio_iff, trichotomy_of_mul_eq_mul, Dense.borel_eq_generateFrom_Ico_mem_aux, RatFunc.v_def, DFinsupp.Lex.wellFoundedLT_of_finite, Function.mulSupport_disjoint_iff, Function.locallyFinsuppWithin.negPart_add, ArchimedeanClass.FiniteResidueField.mk_ne_zero, Nat.one_sub_one_div_cast_nonneg, map_pos_of_ne_one, mul_min, zsmul_left_strictAnti, Set.Icc_add_one_left_eq_Ioc, Rat.padicValuation_eq_zero_iff, Set.OrdConnected.IciExtend, NNRat.cast_min, CategoryTheory.MorphismProperty.inf, Int.floor_toNat, NonemptyFinLinOrd.dual_map, LaurentSeries.LaurentSeries_coe, strictConvex_Ico, MeasureTheory.integrableOn_Iio_iff_integrableAtFilter_atBot_nhdsWithin, PNat.addLeftReflectLE, ENat.pow_lt_top_iff, CategoryTheory.SimplicialThickening.Path.left_le, CategoryTheory.SmallObject.SuccStruct.ofCocone_obj_eq_pt, Finsupp.DegLex.single_le_iff, Finset.centroid_mem_convexHull, ComplementedLattice.isStronglyCoatomic, compl_le_himp, Nucleus.sInf_apply, Int.existsUnique_mem_box, IsDedekindDomain.HeightOneSpectrum.intValuation_eq_one_iff, Set.Iio_add_one_eq_Iic, min_top_right, HahnSeries.archimedeanClassOrderIsoWithTop_apply, max_eq_bot, Set.OrdConnected.restrict, FiniteMulArchimedeanClass.mem_subgroup_iff, CategoryTheory.TransfiniteCompositionOfShape.ofOrderIso_isoBot, Set.Ico_add_one_left_eq_Ioo, Hyperreal.coe_min, CategoryTheory.MorphismProperty.RespectsRight.inf, Valuation.Integers.wfDvdMonoid_iff_wellFounded_gt_on_v, Set.encard_le_coe_iff_finite_ncard_le, Rat.preimage_cast_Iio, Finset.Ico_filter_le, Set.unbounded_gt_iff, Rat.cast_nonneg, AbsoluteValue.IsAdmissible.exists_partition, MvPowerSeries.le_order_smul, NNRat.toNNRat_mono, Heyting.Regular.coe_toRegular, AlgebraicGeometry.Scheme.basicOpen_appLE, WithTop.isEmbedding_coe, Set.monotone_setOf, oneTangentSpaceIcc_def, CategoryTheory.ObjectProperty.InheritedFromSource.instMin, LaurentSeries.powerSeries_ext_subring, Set.unit_valuation_eq_one, Set.Ioc_inter_Ioc, MeasurableSpace.inf_le_invariants_comp, himp_le_himp_himp_himp, compl_compl_inf_distrib, Finset.min'_eq_sorted_zero, VertexOperator.ext_iff, PowerSeries.le_order_pow, Polynomial.isBoundedUnder_abs_atBot_iff, OrderEmbedding.addRight_apply, negPart_lt, IsNonarchimedean.finset_image_add_of_nonempty, DivisibleHull.coeOrderAddMonoidHom_apply, PosSMulStrictMono.nnrat_of_rat, emultiplicity_prime_le_emultiplicity_image_by_factor_orderIso, BoundedLatticeHom.dual_apply_toFun, stdSimplex.barycenter_apply, mul_nonpos_iff, Nat.floor_le_ceil, Finset.min'_le_max', Int.one_le_ceil_iff, compl_sup_distrib, Hyperreal.lt_neg_of_pos_of_infinitesimal, Set.Iio_union_Ioi, Ordinal.iSup_typein_limit, nhdsSet_Iio, IsNonarchimedean.nsmul_le, Set.pairwise_disjoint_Ioc_add_intCast, AbsoluteValue.hasBasis_uniformity, squarefree_iff_emultiplicity_le_one, ArchimedeanClass.mk_le_mk_iff_ratCast, InnerProductSpace.gramSchmidtOrthonormalBasis_inv_blockTriangular, RegularSpace.inf, NNRat.one_lt_cast, geom_sum_neg_iff, OrderIso.infIrredUpperSet_apply, Set.Ico_disjoint_Ico, Finset.iInf_insert_update, bihimp_inf_sup, sdiff_sdiff_le, ValuativeRel.IsNontrivial.exists_lt_one, Set.unbounded_le_iff, bihimp_right_involutive, Order.lt_add_one_iff, Rat.toNNRat_add_le, Tuple.eq_sort_iff, MeasureTheory.stoppedProcess_eq_of_mem_finset, sign_neg, CategoryTheory.Triangulated.TStructure.ge_antitone, Cardinal.continuum_toENat, inv_nhdsLT_zero, Units.topology_eq_inf, Nat.range_cast_int, OrderIso.sumLexIicIoi_apply_inl, IsPreconnected.intermediate_value_Ioc, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivFunctor_obj_π_app, CompositionSeries.head_le_of_mem, SuccOrder.nhdsGT, ValuativeRel.le_uniformizer_iff, LinearOrderedCommGroupWithZero.inr_eq_coe_inrₗ, Ioc_mem_nhds_iff, inf_covBy_of_covBy_sup_left, Finset.Icc_succ_left_eq_Ioc, Field.Emb.Cardinal.deg_lt_aleph0, CategoryTheory.Functor.IsWellOrderContinuous.restriction_setIci, tendsto_const_mul_pow_nhds_iff, isPiSystem_image_Iio, DFinsupp.Lex.isStrictOrder, signedDist_smul, max_sub_max_le_max, iUnion_Ico_intCast, GenContFract.le_of_succ_succ_get?_contsAux_b, Finset.max_eq_top, Setoid.inf_def, ProbabilityTheory.gaussianPDFReal_inv_mul, nhdsGE_basis_Icc, Valuation.integer.v_irreducible_pos, Set.Ioo_subset_Ioc_union_Ioo, ClosedSubmodule.coe_inf, StieltjesFunction.measure_Icc, Finsupp.Lex.addRightStrictMono, Set.Ioi_subset_Ioi_iff, LieModule.genWeightSpaceChain_def, ConvexCone.isGenerating_iff_isReproducing, AlgebraicGeometry.isPreimmersion_eq_inf, isGreatest_compl, Sublattice.comap_equiv_eq_map_symm, Valuation.leIdeal_mono, Set.Ioc_diff_Ioi, FunctionField.inftyValuation.X_zpow, PNat.card_fintype_Ioo, LaurentSeries.hasseDeriv_comp, infIooOrderIsoIooSup_apply_coe, EReal.max_neg_neg, CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.ofComposableArrows_F, FiniteMulArchimedeanClass.congrOrderIso_symm, Int.ceil_le, Finset.Icc_subset_uIcc, Set.strictMonoOn_projIci, Booleanisation.lift_lt_lift, Tuple.antitone_pair_of_not_sorted', sdiff_inf, Polynomial.trailingDegree_lt_wf, le_iff_forall_one_lt_lt_mul, Set.finite_diff_iUnion_Ioo', le_inf_sup, antivaryOn_iff_smul_rearrangement, bihimp_eq_inf, DFA.acceptsFrom_inter, CauSeq.lim_lt, mabs_div_pos, OrderEmbedding.birkhoffSet_sup, SetRel.preimage_mono, Set.Iic_subset_Iic_union_Ioc, Finset.subConst_le_card, LaurentSeries.powerSeriesRingEquiv_coe_apply, PredOrder.nhdsLT, iInf_union, Set.ordConnected_of_uIcc_subset_left, Subalgebra.LinearDisjoint.rank_inf_eq_one_of_flat_left_of_inj, PNat.Prime.one_lt, AbsoluteValue.IsAdmissible.exists_partition', AlgebraicGeometry.IsOpenImmersion.ΓIso_inv, Finset.disjoint_sup_right, Topology.RelCWComplex.iUnion_openCell_eq_skeletonLT, SignType.neg_lt_neg_iff, sq_nonpos_iff, Set.Ioo_pred_left_eq_Ioc, Int.fract_add_le, Finset.trop_inf, HahnSeries.orderTop_add_le_mul, Set.range_projIic, leOnePart_min, LinOrd.Iso.mk_inv, CategoryTheory.TransfiniteCompositionOfShape.ofArrowIso_incl, Module.End.genEigenspace_le_genEigenspace_maxUnifEigenspaceIndex, FrameHomClass.toInfTopHomClass, HurwitzZeta.hasSum_nat_hurwitzZetaOdd, Finset.compls_infs, inf_sup_left, MeasureTheory.ae_restrict_uIoc_iff, LinearOrderedCommGroupWithZero.fst_comp_inl, upperClosure_eq_bot_iff, AlgebraicGeometry.isProper_eq, bihimp_self, ENat.le_coe_iff, IsCompact.exists_isMinOn, Sublocale.inf_mem, abs_pow_sub_pow_le, Int.ceil_lt_add_one, HahnEmbedding.ArchimedeanStrata.isInternal_stratum', Dense.borel_eq_generateFrom_Ioc_mem_aux, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivFunctor_map_hom, le_symmDiff_sup_left, Int.image_fract, Multiset.exists_min_image, OrderRingIso.apply_eq_self, Nimber.instZeroLEOneClass, Set.Iic_union_Ici, Fin.succAboveOrderEmb_toEmbedding, inf_sSup_eq_iSup_inf_sup_finset, PrincipalSeg.isNormal, AffineSubspace.map_inf_le, inv_mabs_le_inv, Positive.coe_inv, Rat.cast_nonpos, Finset.sortedLT_sort, Set.mulIndicator_eq_one', Hyperreal.lt_of_pos_of_infinitesimal, Finset.supIndep_iff_disjoint_erase, archimedean_iff_rat_le, one_lt_sq_iff_one_lt_abs, ArchimedeanClass.FiniteResidueField.mk_le_mk, OrderIso.subsingleton_of_wellFoundedLT, Filter.tendsto_pow_atTop_iff, Set.encard_le_encard_iff_encard_diff_le_encard_diff, mem_nhdsGE_iff_exists_Ico_subset, Affine.Simplex.sign_touchpointWeights_singleton_neg, LaurentSeries.powerSeriesEquivSubring_apply, iInf_dite, Set.Ico_add_one_add_one_eq_Ioc, MvPowerSeries.map_iterateFrobenius_expand, Function.support_disjoint_iff, Order.succ_eq_succ_iff, Finset.sum_sum_Ioi_add_eq_sum_sum_off_diag, Valuation.IsNontrivial.exists_one_lt, IsDedekindDomain.HeightOneSpectrum.intValuation_def, CategoryTheory.Limits.WalkingMultispan.inclusionOfLinearOrder_obj, OrderIso.pnatIsoNat_apply, LocallyFiniteOrder.orderAddMonoidHom_apply, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivInverse_obj_pt, not_lt_zero', Set.isCompl_range_inl_range_inr, SimpleGraph.le_card_nonuniformWitness, CategoryTheory.SmallObject.SuccStruct.transfiniteCompositionOfShapeιIteration_incl, Coheyting.boundary_le, inf_add, FunctionField.inftyValuation.X, InnerProductSpace.gramSchmidt_def'', RingCone.nonneg.hasMemOrNegMem, Set.unbounded_ge_inter_gt, StieltjesFunction.length_eq, CompleteLattice.ωScottContinuous.inf, Nat.cast_finsetInf', mem_nhdsLT_iff_exists_Ioo_subset, FiniteMulArchimedeanClass.min_le_mk_mul, MonomialOrder.degree_prod_le, min_mul_distrib, LinearOrderedSemifield.toPosSMulStrictMono_rat, Module.End.genEigenspace_zero_nat, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivUnitIso_hom_app_hom, antivary_iff_mul_rearrangement, MeasureTheory.Filtration.rightCont_eq, Set.infinite_iff_exists_gt, FiniteMultiplicity.emultiplicity_lt_of_multiplicity_lt, HahnSeries.leadingCoeff_nonneg_iff, WithZeroTopology.isOpen_iff, Measurable.nat_floor, toZ_iterate_pred, CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.ofComposableArrows_isoBot_inv, ENat.lt_add_one_iff, ENat.addLECancellable_of_ne_top, tendsto_intCast_atBot_iff, List.prod_min_le, Nimber.instNoMaxOrder, CategoryTheory.GrothendieckTopology.intersection_covering, ArchimedeanClass.archimedean_of_mk_eq_mk, Finset.max'_eq_iff, tendsto_nat_ceil_div_atTop, Finsupp.DegLex.isStrictOrder, Cardinal.ofENat_lt_ofENat, Finset.dens_mono, ArchimedeanClass.mk_eq_mk, NNRat.instOrderedSub, EReal.sign_top, Matrix.IsPrimitive.exists_pos_pow, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivUnitIsoApp_hom_hom, DFinsupp.support_sup_union_support_inf, inv_inf, Valuation.srel_one_iff, max_mul_mul_le_max_mul_max', Set.one_notMem_inv_mul_iff, LinearOrder.isSuccArchimedean_of_isPredArchimedean, Continuous.strictMono_of_inj, MonomialOrder.div_set, List.mem_argmax_iff, negPart_min, MulArchimedeanClass.mk_mul_lt_mk_right_iff, right_le_lineMap_iff_one_le, MonoidWithZeroHom.snd_mono, neg_le_negPart, nullMeasurableSet_lt', compl_bihimp_self, Module.End.genEigenspace_top, Ordinal.toNatOrdinal_zero, Set.preimage_eq_empty_iff, BoundedLatticeHomClass.map_top, gc_inf_himp, symmDiff_le_sup, Int.Icc_eq_pair, CategoryTheory.SmallObject.iterationFunctorMapSuccAppArrowIso_hom_left, HahnEmbedding.Partial.orderTop_eq_finiteArchimedeanClassMk, Valuation.IsUniformizer.val_pos, Set.Ioi_subset_Ici_iff, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivFunctorObj_pt, Finset.orderEmbOfFin_apply, bot_himp, AlgebraicGeometry.IsOpenImmersion.app_ΓIso_hom_assoc, IntermediateField.relfinrank_mul_relfinrank_eq_inf_relfinrank, MeasureTheory.aecover_Ioo_of_Ioo, intermediate_value_Ico', List.exists_map_eq_of_sorted_iff_wbtw, Odd.pow_pos_iff, PointedCone.minTensorProduct_comm, fderiv_norm_smul, Set.disjoint_iff_forall_ne, abs_add', LinOrd.ofHom_comp, HasFDerivAt.hasFDerivAt_norm_smul, NNRat.cast_pos, borel_eq_generateFrom_Ico, Set.coe_projIic, NatOrdinal.toOrdinal_eq_zero, tendsto_floor_atBot, OpenSubgroup.toOpens_inf, QuotientAddGroup.btw_coe_iff', Multiset.Ico_filter_le, CategoryTheory.IsGrothendieckAbelian.generatingMonomorphisms.functorToMonoOver_map, List.le_maximum_of_mem', negPart_nonpos', TopologicalSpace.Opens.functor_map_eq_inf, MeasureTheory.aecover_Ioc_of_Ioc, Finset.mem_inf, PNat.instWellFoundedLT, CategoryTheory.Subfunctor.Subpresheaf.iSup_min, Order.isNormal_iff', Cardinal.ofENat_strictMono, Pi.lt_toLex_update_self_iff, Int.preimage_Ioo, OrderType.type_le_type_iff, FunctionField.inftyValuedFqt.def, one_lt_oneLePart_iff, CategoryTheory.SmallObject.πFunctorObj_eq, isPiSystem_Iio, Finset.powerset_inter, isLeast_hnot, Set.abs_sub_le_of_uIcc_subset_uIcc, Mathlib.Tactic.Qify.nnratCast_lt, NonemptyFinLinOrd.id_apply, LTSeries.head_add_length_le_int, tendsto_ceil_left', hahnEmbedding_isOrderedModule_rat, AddValuation.map_sub, AlgebraicGeometry.universallyClosed_eq_universallySpecializing, Affine.Simplex.sign_signedInfDist_touchpoint_empty, Finsupp.Lex.addLeftStrictMono, FiniteArchimedeanClass.congrOrderIso_symm, Valuation.RankOne.strictMono', mabs_mul_eq_mul_mabs_iff, mabs_div_mabs_le_mabs_mul, PNat.lt_add_left, WithBot.orderIsoPUnitSumLex_toLex, SimpContFract.of_isContFract, tendsto_const_mul_zpow_atTop_zero, AffineIndependent.convexHull_inter', Finset.min'_pair, ofBoolRing_mul, ComplementedLattice.isStronglyAtomic', Int.addSubmonoid_closure_range_pow, Set.Ioi_inter_Ioo, AffineSubspace.sOppSide_pointReflection, max_eq_right_iff, Set.Ici_subset_Icc_union_Ioi, Finset.le_max', PredOrder.hasBasis_nhds_Ioc, sdiff_sdiff_right', Filter.tendsto_Ioc_uIcc_uIcc, GenContFract.of_one_le_get?_partDen, Valuation.vle_one_iff, sign_nonpos_iff, Set.Finite.exists_lt_map_eq_of_forall_mem, disjoint_partialSups_left, smul_nonneg_iff, Cardinal.toENat_le_iff_of_le_aleph0, PNat.sub_le, Finset.intervalGapsWithin_snd_of_lt, one_le_leOnePart, symmDiff_symmDiff_left, Valuation.IsEquiv.val_sub_one_lt_one_iff, LatticeHom.coe_toInfHom, Nat.one_div_cast_nonneg, Set.Icc_sub_one_right_eq_Ico, Finset.supIndep_univ_bool, ENat.coe_lt_coe, sign_pow, Set.powersetCard.mem_ofFinEmbEquiv_iff_mem_range, PowerSeries.order_le, iSup_inf_le_iSup_inf, measurableSet_Ioo, Valuation.Integers.coe_span_singleton_eq_setOf_le_v_algebraMap, LinearOrderedAddCommGroup.discrete_or_denselyOrdered, compl_sup, MonomialOrder.degLex_lt_iff, IsDedekindDomain.HeightOneSpectrum.adicValued.uniformContinuousConstSMul, IsValuativeTopology.hasBasis_nhds', LinearOrder.infConvergenceClass, ContinuousOn.surjOn_Icc, emultiplicity_lt_top, Finset.Ioo_add_one_right_eq_Ioc, CategoryTheory.Pretopology.mem_inf, Multiset.max_prod_le, sup_bihimp_bihimp, completelyRegularSpace_inf, AlgebraicGeometry.IsOpenImmersion.map_ΓIso_inv, isAtomic_iff_isCoatomic, HahnModule.orderTop_vAdd_le_orderTop_smul, strictConvex_iff_ordConnected, Int.card_Icc, Set.disjoint_image_inl_image_inr, NNRat.ofNat_le_cast, Cardinal.toENat_eq_top, sameRay_smul_right_iff_of_ne, extremePoints_doublyStochastic, Valuation.Integers.valuation_pos_iff_ne_zero, AlgebraicGeometry.RingedSpace.basicOpen_mul, hasDerivAt_abs, Valued.isOpen_closedBall, Finset.lt_inf'_iff, lineMap_le_right_iff_le_one, Int.floor_le_neg_one_iff, invOf_nonpos, exists_square_le, negPart_nonneg, AlgebraicGeometry.Flat.surjective_descendsAlong_surjective_inf_flat_inf_quasicompact, Affine.Simplex.sign_excenterWeights_empty, IsPreconnected.mapsTo_Ioi_or_Iio, Finset.intervalGapsWithin_succ_fst_of_lt, Field.Emb.Cardinal.strictMono_filtration, convexHull_eq_union_convexHull_finite_subsets, tendsto_fract_left, compl_antitone, Finset.sort_sorted_gt, PNat.card_Ioo, GenContFract.fib_le_of_contsAux_b, Multiset.inf_eq_inter, Set.disjoint_sdiff_left, compl_strictAnti, Complementeds.mk_top, leOnePart_eq_inv, Finset.le_min_iff, ENat.coe_le_coe, Int.cast_mono, gc_sSup_Iic, upperSemicontinuous_iff_isClosed_preimage, Hyperreal.lt_of_tendsto_atBot, max_bot_right, Nat.one_sub_one_div_cast_le_one, MvPowerSeries.weightedOrder_le, Mathlib.Meta.NormNum.IsRat.natCeil, IntermediateField.relfinrank_inf_mul_relfinrank_of_le, AlgebraicGeometry.IsProper.eq_valuativeCriterion, Finset.Ioc_pred_left_eq_Icc, Valuation.IsEquiv.one_le_iff_one_le, Set.Ioo_succ_right_eq_Ioc, Nucleus.mem_range, Int.ceil_toNat, min_mul_max, SignType.not_lt_neg_one, sdiff_compl, HahnEmbedding.Seed.truncLT_mem_range_baseEmbedding, NNRat.ceil_cast, Set.pairwise_disjoint_Ico_zpow, Filter.inf_liminf, inf_sdiff_sup_right, Nat.cast_div_le, Set.Iio_diff_Iic, Positive.isOrderedCancelMonoid, Finset.untrop_sum', AlgebraicGeometry.IsClosedImmersion.eq_isFinite_inf_mono, AlgebraicGeometry.Scheme.basicOpen_mul, Int.floor_pos, sup_eq_inf, Valued.mem_nhds_zero, Odd.zpow_pos_iff, abs_eq_neg_self, sign_eq_zero_iff, sameRay_neg_smul_right_iff_of_ne, HahnSeries.orderTop_le_orderTop_smul, compl_inf_self, Finset.le_card_infs_mul_card_sups, PNat.equivNonZeroDivisorsNat_apply_coe, Int.preimage_Ici, PseudoMetric.IsUltra.isTrans_ball, Finset.Colex.lt_iff_max'_mem, Valued.isOpen_ball, ENat.add_one_pos, sup_lt_iff, HahnSeries.orderTop_lt_iff_exists, AddCircle.liftIoc_eq_lift_Icc, Nimber.lt_wf, abs_sub_nonpos, Booleanisation.comp_sup_comp, ArchimedeanClass.mk_map_of_archimedean, CategoryTheory.IsGrothendieckAbelian.generatingMonomorphisms.instIsWellOrderContinuousFunctor, Dense.exists_le, CauSeq.lim_le, SuccOrder.isOpen_singleton_iff, ValuationSubring.mem_principalUnitGroup_iff, LocallyBoundedVariationOn.exists_monotoneOn_sub_monotoneOn, monovary_iff_forall_mul_nonneg, pow_lt_one_iff, ArchimedeanClass.FiniteResidueField.instArchimedean, Valued.mem_nhds, Mathlib.Meta.Positivity.abs_pos_of_ne_zero, Ordinal.lsub_typein, OrderMonoidWithZeroHom.coe_mul, abs_sub_map_le_sub, Set.Ico_inter_Iio, punctured_nhds_eq_nhdsWithin_sup_nhdsWithin, Nat.one_div_pos_of_nat, FiniteArchimedeanClass.withTopOrderIso_symm_apply, IntermediateField.relrank_inf_mul_relrank_of_le, Set.disjoint_preimage_iff, Archimedean.exists_orderAddMonoidHom_real_injective, norm_inf_sub_inf_le_norm, AddMonoidAlgebra.supDegree_sub_lt_of_leadingCoeff_eq, Finset.abs_expect_le, Order.embedding_from_countable_to_dense, HahnEmbedding.Partial.mem_domain, Ordinal.toNatOrdinal_eq_zero, Cardinal.one_lt_ofENat, Even.add_pow_le, intermediate_value_univ, CategoryTheory.MorphismProperty.IsStableUnderComposition.inf, himp_inf_self, Filter.tendsto_Icc_uIcc_uIcc, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivInverse_map_hom, Topology.CWComplex.iUnion_openCell_eq_skeleton, Finset.Ioo_filter_lt, sq_pos_iff, AlgebraicGeometry.UniversallyClosed.eq_valuativeCriterion, Hyperreal.infinite_iff_abs_lt_abs, Finset.infs_compls_eq_diffs, EReal.le_iff_sign, BoundedLatticeHom.coe_toBoundedOrderHom, Language.mem_inf, LaurentSeries.powerSeriesEquivSubring_coe_apply, AlgebraicGeometry.IsOpenImmersion.app_ΓIso_hom, FloorSemiring.eventually_mul_pow_lt_factorial_sub, WithTop.tendsto_untopD, Finset.nonneg_subConst_self, Pi.Colex.wellFoundedLT, max_cases, Ordinal.enum_zero_eq_bot, Polynomial.isBoundedUnder_abs_atTop_iff, IsDedekindDomain.HeightOneSpectrum.valuationOfNeZero_eq, Finset.min'_eq_iff, LinOrd.coe_id, Finset.sup_sdiff_left, Nat.ceil_sub_ofNat, Function.argmin_le, HahnSeries.embDomainOrderAddMonoidHom_apply, LatticeHom.coe_comp_inf_hom, Set.Ici_diff_Ici, MulArchimedeanClass.out_top, NNRat.coe_mono, sq_nonneg, MeasureTheory.stoppedProcess_stoppedProcess', convexOn_pow, Set.abs_sub_left_of_mem_uIcc, HahnEmbedding.Seed.mem_domain_baseEmbedding, one_le_pow_iff, MulArchimedeanClass.mk_left_le_mk_div_iff, Finset.isGLB_iff_isLeast, le_compl_iff_disjoint_left, le_symmDiff_iff_left, SimpleGraph.IsCompleteBetween.disjoint, Nat.ceil_sub_one, Finset.sum_Icc_of_even_eq_range, BoundedLatticeHomClass.toSupBotHomClass, Heyting.Regular.coe_lt_coe, Finsupp.Lex.single_antitone, Topology.RelCWComplex.skeleton_monotone, Set.disjoint_sdiff_right, sameRay_neg_smul_right_iff, RootPairing.RootPositiveForm.exists_pos_eq, disjointed_eq_inf_compl, Finset.inclusion_exclusion_sum_biUnion, symmDiff_le_iff, Set.finite_iff_bddBelow_bddAbove, PowerSeries.coe_X, Valued.integer.locallyFiniteOrder_units_mrange_of_isCompact_integer, sInf_insert, AffineSubspace.sSameSide_iff_exists_right, NNRat.preimage_cast_Ico, codisjoint_hnot_hnot_left_iff, SMulPosReflectLT.toSMulPosMono, FiniteDimensional.exists_relation_sum_zero_pos_coefficient_of_finrank_succ_lt_card, mem_convexHull_iff_exists_fintype, UV.disjoint_of_mem_compression_of_notMem, inf_eq_iff_sup_eq, inf_sup_symmDiff, Hyperreal.ofSeq_le_ofSeq, Ico_subset_closure_interior, MeasureTheory.Measure.measure_Ioo_eq_zero, Set.mem_uIoc, Complementeds.coe_bot, Set.Ioc_union_Ioc_union_Ioc_cycle, Booleanisation.lift_lt_comp, neg_le_abs, SuccOrder.isSuccLimit_of_mem_frontier, Set.univ_disjoint, liminf_finset_inf', le_iff_forall_lt_rat_imp_le, toZ_iterate_succ_le, Sublocale.toNucleus_le_toNucleus, Finset.sup'_inf_distrib_left, tsub_min, PNat.card_fintype_Ioc, LaurentSeries.instLaurentSeriesComplete, TopCat.Sheaf.objSupIsoProdEqLocus_hom_snd, round_le_add_half, Cardinal.ofENat_lt_nat, LinearOrderedCommGroup.to_noMinOrder, Odd.zpow_neg_iff, inf_lt_iff, AbsoluteValue.map_units_int, nullMeasurableSet_Iio, Set.encard_image_le, sdiff_le_comm, convexHull_toCone_isLeast, sameRay_or_sameRay_neg_iff_not_linearIndependent, IsDedekindDomain.HeightOneSpectrum.valuation_surjective, NNRat.cast_nonpos, Set.Ioc_sub_one_sub_one_eq_Ico, Int.le_floor, Hyperreal.omega_pos, Valuation.rel_one_iff, Rat.cast_lt_zero, MvPowerSeries.weightedOrder_add_of_weightedOrder_ne, Int.fract_eq_self, List.minimum_anti, Set.Ico_add_one_right_eq_Icc, lowerSemicontinuousAt_iff_frequently, CategoryTheory.TransfiniteCompositionOfShape.ofComposableArrows_isoBot, Set.projIci_self, Rat.cast_strictMono, convex_iff_div, HahnSeries.single_div_single, exists_pred_iterate_or, LinearOrderedCommGroupWithZero.wellFoundedOn_setOf_ge_gt_iff_nonempty_discrete_of_ne_zero, Padic.withValUniformEquiv_cast_apply, Module.End.generalized_eigenvec_disjoint_range_ker, AlgebraicGeometry.isomorphisms_eq_isOpenImmersion_inf_surjective, NonemptyFinLinOrd.comp_apply, ComplementedLattice.isStronglyAtomic, JordanHolderLattice.isMaximal_inf_right_of_isMaximal_sup, Cardinal.ofENat_le_one, SimpleGraph.right_nonuniformWitnesses_card, Hyperreal.infiniteNeg_iff_infinitesimal_inv_neg, ArchimedeanClass.mk_intCast_nonneg, countable_image_lt_image_Ioi, tendsto_inv_nhdsLT_zero, DFinsupp.Colex.wellFoundedLT_of_finite, convexIndependent_iff_finset, pow_div_pow_eventuallyEq_atTop, HahnSeries.archimedeanClassMk_le_archimedeanClassMk_iff, LaurentSeries.valuation_coe_ratFunc, Set.zero_notMem_sub_iff, DivisibleHull.archimedeanClassOrderIso_apply, Int.fract_lt_one, Hyperreal.archimedeanClassMk_omega_neg, frontier_le_subset_eq, Set.one_notMem_div_iff, posPart_lt, bihimp_left_inj, Valuation.Integers.isPrincipal_iff_exists_eq_setOf_valuation_le, zsmul_lt_zsmul_iff_right, PNat.card_fintype_Ico, posPart_inf_negPart_eq_zero, Hyperreal.archimedeanClassMk_coe_nonneg, Matrix.mem_glpos, PrimitiveSpectrum.kernel_hull, CategoryTheory.MorphismProperty.instHasOfPostcompPropertyMin, CategoryTheory.TransfiniteCompositionOfShape.iic_incl_app, IsValuativeTopology.isClosed_ball, min_add_min_le_min_add_add, bihimp_left_injective, CategoryTheory.ObjectProperty.instIsStableUnderShiftMin, AddCircle.continuous_equivIco_symm, nhdsWithinLE_sup_nhdsWithinGE, HahnSeries.inv_def, intermediate_value_Icc, Cardinal.ofENat_pos, Padic.coe_withValRingEquiv, Int.Ico_filter_modEq_card, Nucleus.iInf_apply, Valuation.Integer.not_isUnit_iff_valuation_lt_one, Int.pred_eq_pred, CategoryTheory.TransfiniteCompositionOfShape.ofOrderIso_F, Matrix.IsPrimitive.nonneg, Finset.Ioo_sub_one_left_eq_Ioc, Padic.comap_mulValuation_eq_int_padicValuation, Fintype.exists_disjointed_le, Nat.floor_sub_natCast, Finset.one_le_divConst_self, Nat.image_cast_int_Ioo, Int.Ioc_filter_dvd_eq, OrderIso.asBoolAlgAsBoolRing_apply, Int.preimage_Icc, MeasureTheory.ae_const_le_iff_forall_lt_measure_zero, AffineSubspace.wSameSide_iff_exists_right, continuousAt_sign_of_neg, Affine.Simplex.sSameSide_affineSpan_faceOpposite_point_right_iff, isPiSystem_Ioc_mem, div_pos_iff, measurableSet_lt, Finsupp.support_inf_union_support_sup, AddCircle.continuousAt_equivIoc, ENat.add_le_add_iff_right, OrderEmbedding.addLeft_apply, Iic_mem_nhdsSet_Iic_iff, Rat.cast_pos_of_pos, Nat.Prime.emultiplicity_factorial_le_div_pred, UniqueFactorizationMonoid.le_emultiplicity_iff_replicate_le_normalizedFactors, LinearOrderedCommGroupWithZero.fst_apply, variationOnFromTo.monotoneOn, Cardinal.toENat_le_natCast_iff, cauchy_davenport_minOrder_add, Set.toENat_cardinalMk, inf_right_le_sup_right, NumberField.FinitePlace.norm_eq_one_iff_notMem, MulArchimedeanClass.ballSubgroup_top, grade_injective, Finset.Ico_diff_Ico_right, ArchimedeanClass.mem_closedBall_iff, Polynomial.div_tendsto_atBot_zero_iff_degree_lt, disjoint_inf_sdiff, Set.bounded_le_inter_lt, countable_of_isolated_left', Dense.exists_seq_strictAnti_tendsto, Set.range_projIci, Set.Ici_subset_Ico_union_Ici, Valuation.vlt_one_iff, AlgebraicGeometry.Scheme.Hom.preimage_inf, Finset.le_min'_iff, abs_abs_sub_abs_le_abs_sub, extremePoints_convexHull_subset, ENat.mul_left_strictMono, Set.Finite.disjoint_toFinset, sup_inf_sdiff, Finset.intervalGapsWithin_fst_of_lt_lt, Module.End.mem_genEigenspace_one, mabs_mul', Finset.compls_infs_eq_diffs, bihimp_bihimp_cancel_left, LaurentSeries.valuation_compare, mem_segment_iff_div, Cardinal.enat_gc, Padic.isUniformInducing_cast_withVal, le_iff_oneLePart_leOnePart, IsModularLattice.isModularLattice_Ici, MeasureTheory.aecover_Ico_of_Ioo, ArchimedeanClass.mk_ratCast_nonneg, Subalgebra.LinearDisjoint.rank_inf_eq_one_of_flat_right_of_inj, NonUnitalAlgebra.inf_toSubmodule, Hyperreal.tendsto_atBot_iff, inf_sdiff, sdiff_inf_distrib, FiniteArchimedeanClass.addSubgroup_strictAnti, Nat.one_le_ceil_iff, PowerSeries.le_order, leOnePart_eq_ite, Orientation.someBasis_orientation, nucleusIsoSublocale.eq_toSublocale, Set.pairwiseDisjoint_range_singleton, min_div_div_right', Even.zpow_pos_iff, HahnEmbedding.ArchimedeanStrata.archimedean_stratum, exposedPoints_subset_extremePoints, SimpleGraph.nonuniformWitness_spec, LatticeHomClass.map_inf, Right.nsmul_neg_iff, StarSubalgebra.coe_inf, Set.isPWO_iff_isWF, le_symmDiff_sup_right, two_mul_le_add_pow_two, LieAlgebra.IsKilling.rootSpace_zsmul_add_ne_bot_iff_mem, PNat.find_min', Int.ceil_pos, Finset.inf_sup_inf, PointedCone.maxTensorProduct_comm, Finset.fold_max_lt, WithTop.tendsto_coe_atTop, AlgebraicGeometry.IsOpenImmersion.app_ΓIso_hom_apply, Set.disjoint_empty, Tuple.eq_sort_iff', abs_lt, Set.one_lt_encard_iff, Set.Icc_add_one_sub_one_eq_Ioo, negPart_eq_zero, min_zero, MvPowerSeries.order_mul_ge, FiniteMulArchimedeanClass.ballSubgroup_strictAnti, Finpartition.le, symmDiff_symmDiff_right', Finset.mem_inf', HahnSeries.lt_iff, HahnSeries.instIsOrderedAddMonoidLex, instIsCountablyGenerated_atTop, continuousVAdd_inf, Module.End.IsFinitelySemisimple.genEigenspace_eq_eigenspace, ArchimedeanClass.mk_le_mk_add_of_archimedean, DivisibleHull.mk_lt_mk, sup_inf_le, sInfHomClass.toInfTopHomClass, Submonoid.closure_image_isMulIndecomposable_baseOf, AlgebraicGeometry.geometrically_inf, ArchimedeanOrder.lt_def, Rat.toNNRat_le_toNNRat_iff, IsCompact.exists_isGLB, AbsoluteValue.IsAdmissible.toIsEuclidean, Rat.le_toNNRat_iff_coe_le, Cardinal.toENatAux_le_nat, Finsupp.Colex.addLeftMono, Hyperreal.lt_of_tendsto_zero_of_pos, Set.disjoint_diagonal_offDiag, SetRel.gc_leftDual_rightDual, Finset.Icc_add_one_sub_one_eq_Ioo, Cardinal.toENat_le_nat, Rat.toNNRat_le_iff_le_coe, Set.inf_eq_inter, Rat.cast_le_intCast, Complex.UnitDisc.tendsto_pow_atTop_nhds_zero, Set.encard_pos, mem_nhdsLE_iff_exists_Icc_subset, WithZeroMulInt.toNNReal_strictMono, NNRat.instOrderTopology, Int.preimage_floor_singleton, tsub_tsub_eq_min, RatFunc.single_one_eq_pow, Finset.Ioo_succ_succ, Finset.map_orderEmbOfFin_univ, sdiff_eq_self_iff_disjoint, closure_Ico, LaurentSeries.tendsto_valuation, abs_max_le_max_abs_abs, HahnSeries.SummableFamily.powers_toFun, Subalgebra.centralizer_coe_sup, Tropical.add_eq_right_iff, nhdsLT_eq_bot_iff, left_le_midpoint, csInf_union, Module.End.genEigenspace_div, Finset.exists_min_image, Set.unbounded_le_inter_lt, List.Perm.maximum_eq, Int.mem_box, Ordinal.typein_lt_self, DirectedOn.inf_sSup_eq, LocallyConvexSpace.convex_open_basis_zero, Valuation.IsEquiv.le_one_iff_le_one, Set.encard_le_coe_iff, himp_bihimp_eq_inf, countable_setOf_isolated_left_within, Set.Iic_diff_Iic, isPiSystem_Icc, Zsqrtd.instIsOrderedAddMonoidCastInt, PowerSeries.heval_unit, List.maximum_mono, Units.inv_neg, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivUnitIsoApp_inv_hom, Ioi_mem_nhdsSet_Ici_iff, MeasureTheory.Measure.measure_Ioo_pos, hasBasis_nhdsSet_Ici_Ici, not_bddAbove_iff, pos_invOf_of_invertible_cast, Polynomial.abs_tendsto_atBot, List.foldr_min_of_ne_nil, Set.infinite_iff_exists_lt, Valuation.integer.coe_span_singleton_eq_setOf_le_v_coe, Nat.choose_le_pow_div, DFinsupp.Colex.total_le, Valuation.Integers.wellFounded_gt_on_v_iff_discrete_mrange, oneLePart_lt, AlgebraicGeometry.Scheme.Hom.appLE_appIso_inv_apply, PUnit.canonicallyOrderedAdd, StieltjesFunction.measure_Ioc, LinearOrder.bot_topologicalSpace_eq_generateFrom, strictConvex_iff_div, zpow_right_mono, PNat.natPred_strictMono, pow_div_pow_eventuallyEq_atBot, ContinuousOn.lowerSemicontinuousOn, LaurentSeries.coe_range_dense, CategoryTheory.Limits.MultispanShape.ofLinearOrder_fst, InnerProductSpace.span_gramSchmidt_Iio, Odd.pow_lt_pow, Field.Emb.Cardinal.iSup_adjoin_eq_top, MeasureTheory.integrableOn_Ici_iff_integrableAtFilter_atTop, toWellOrderExtension_strictMono, Set.notMem_Iio, FiniteArchimedeanClass.coe_congrOrderIso_apply, disjoint_compl_right, MeasureTheory.integrableOn_Iic_iff_integrableAtFilter_atBot, Nat.nth_eq_orderEmbOfFin, compl_le_compl_iff_le, TopCat.Presheaf.IsSheaf.isSheafPairwiseIntersections, zero_le', MvPowerSeries.le_weightedOrder, Module.End.genEigenspace_eq_genEigenspace_finrank_of_le, NonemptyFinLinOrd.hom_hom_comp, nhdsLE_basis_Icc, OrderIso.compl_apply, AlgebraicGeometry.IsFinite.eq_isProper_inf_isAffineHom, tendsto_floor_left_pure_ceil_sub_one, Set.compl_Iio, SimpleGraph.FarFromTriangleFree.lt_one, Ordinal.toNatOrdinal_natCast, le_compl_comm, HahnSeries.orderTop_self_sub_one_pos_iff, min_cases, SimpleGraph.left_nonuniformWitnesses_card, AbsoluteValue.map_prod, Finset.lt_min'_iff, PowerSeries.intValuation_X, mabs_eq_inv_self, IsSumSq.nonneg, pow_two_pos_of_ne_zero, Set.Ioc_subset_Ioo_union_Icc, AddCircle.continuousAt_equivIco, isCofinal_setOf_imp_lt, TopCat.Presheaf.isGluing_iff_pairwise, SimplexCategory.toCat_obj, Finset.lt_sup_iff, Set.projIci_surjOn, Finpartition.mk_mem_sparsePairs, inf_sdiff_distrib_right, two_nsmul_inf_eq_add_sub_abs_sub, Set.mulIndicator_eq_one, continuousAt_sign_of_pos, ENNReal.monotone_zpow, Set.Icc_subset_uIcc', Int.floor_lt_self_iff, le_sup_iff, NatOrdinal.toOrdinal_symm_eq, CategoryTheory.SmallObject.SuccStruct.iterationCocone_pt, Polynomial.div_tendsto_atTop_zero_of_degree_lt, LocallyFiniteOrder.denselyOrdered_iff_subsingleton, toIcoMod_zero_one, Int.Ico_eq_finset_map, IsDedekindDomain.HeightOneSpectrum.adicValued_apply', instSMulPosStrictMonoIntOfIsOrderedAddMonoid, compl_le_hnot, NonUnitalStarAlgebra.coe_inf, Hyperreal.stdPart_of_tendsto, Polynomial.cardPowDegree_nonzero, OrderRingHom.subsingleton, mul_inf, MulArchimedeanClass.mem_ballSubgroup_iff, PredOrder.nhdsLE, Finset.min_le_of_eq, midpoint_mem_segment, CompositionSeries.toList_sorted, Set.encard_lt_encard_iff_encard_diff_lt_encard_diff, isLocallyClosed_Ioo, strictConcaveOn_iff_div, Int.gc_ceil_coe, LocallyFiniteOrder.orderAddMonoidHom_toAddMonoidHom, trichotomy_of_add_eq_add, ArchimedeanClass.mk_eq_top_iff, NatOrdinal.toOrdinal_one, ArchimedeanClass.mk_le_add_mk_of_archimedean, toDual_bihimp, Pi.instNoMaxOrderColexForallOfWellFoundedGTOfNonempty, Heyting.Regular.toRegular_coe, sup_inf_bihimp, Order.isNormal_iff, iInf_or, Finset.inf'_le_iff, sdiff_top, PowerSeries.IsWeierstrassFactorization.degree_eq_coe_lift_order_map, isGreatest_pair, supClosure_infClosure, OrderIso.subsingleton_of_wellFoundedGT, ArchimedeanClass.mk_right_le_mk_add_iff, Rat.cast_le_natCast, mabs_max_le_max_mabs_mabs, archimedean_iff_int_lt, Set.Ico_succ_right_eq_Icc, Directed.inf_iSup_eq, ArchimedeanClass.FiniteResidueField.mk_lt_mk, Finset.SupIndep.pairwiseDisjoint, Finset.min_insert, stdSimplex.barycenter_eq_centerMass, NNRat.Nonneg.coe_ofScientific, tendsto_const_mul_zpow_atTop_nhds_iff, HahnSeries.min_orderTop_le_orderTop_sub, Ordinal.toNimber_zero, CategoryTheory.SmallObject.iterationFunctorObjObjRightIso_ιIteration_app_right, Polynomial.div_tendsto_zero_of_degree_lt, cocompact_le_atBot_atTop, nhdsGT_eq_bot_iff, IsPreconnected.Icc_subset, nucleusIsoSublocale.symm_eq_toNucleus, Finsupp.DegLex.instIsOrderedCancelAddMonoidDegLexNat, cmp_mul_left', Mathlib.Meta.Positivity.pos_of_isRat, min_lt_max, NatOrdinal.toOrdinal_toNatOrdinal, ofDual_symmDiff, biInf_inf, FiniteMulArchimedeanClass.subgroup_eq_bot, interior_Ico, SMulPosStrictMono.toSMulPosReflectLE, csSup_inter_le, RootPairing.rootForm_pos_of_ne_zero, Set.ordConnected_iff_uIcc_subset_right, OrderIso.withZeroUnits_apply, LinOrd.hom_comp, AffineSpace.asymptoticNhds_eq_smul, smul_max_of_nonpos, exteriorPower.pairingDual_apply_apply_eq_one_zero, exists_seq_strictMono_tendsto, IsRealClosed.nonneg_iff_isSquare, UpperSet.infIrred_iff_of_finite, MulArchimedeanClass.subgroup_antitone, WithZeroTopology.Iio_mem_nhds_zero, AddCircle.openPartialHomeomorphCoe_symm_apply, le_compl_compl, ProbabilityTheory.condExpKernel_eq, lt_mabs, Types.monoOverEquivalenceSet_inverse_obj, GenContFract.IntFractPair.succ_nth_stream_b_le_nth_stream_fr_inv, SignType.pos_iff, SuccOrder.prelimitRecOn_succ, frontier_Iic, AbsoluteValue.IsAdmissible.exists_approx_aux, Finset.subConst_le_inv_dens, upperSemicontinuous_iff_IsClosed_hypograph, NatOrdinal.instWellFoundedLT, Nat.preimage_floor_zero, Module.End.genEigenspace_nat, Order.height_int, Affine.Simplex.ExcenterExists.signedInfDist_excenter, Icc_mem_nhds_iff, antivaryOn_iff_forall_mul_nonpos, IsSquare.nonneg, Padic.coe_withValRingEquiv_symm, AlgebraicGeometry.Scheme.basicOpen_res, MulArchimedeanClass.closedBallSubgroup_top, Booleanisation.lift_inf_lift, Dense.exists_lt, SuccOrder.nhdsGE, TopCat.Sheaf.objSupIsoProdEqLocus_inv_fst, HahnSeries.leadingCoeff_mul_of_nonzero, Mathlib.Tactic.Order.ToInt.toInt_nlt_toInt, Nucleus.restrict_toSublocale, Int.abs_sub_lt_one_of_floor_eq_floor, frontier_Iic_subset, map_bihimp, sdiff_eq_sdiff_iff_inf_eq_inf, archimedean_iff_rat_lt, mabs_min_le_max_mabs_mabs, Valuation.HasExtension.mk_smul_mk, Nat.floor_eq_zero, Finset.inf_eq_sInf_image, Subalgebra.map_comap_eq, BoundedLatticeHom.dual_comp, maximal_subtype, Finset.sup_himp_right, WithTop.denselyOrdered_set_iff_subsingleton, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.w_assoc, compl_eq_iff_isCompl, ValuationSubring.mem_nonunits_iff, min_mul_mul_right, Cardinal.toENat_comp_ofENat, inf_eq_half_smul_add_sub_abs_sub, one_lt_leOnePart_iff, symmDiff_eq_top, Real.Angle.sign_toReal, IsAbsoluteValue.abs_abv_sub_le_abv_sub, Valued.toNormedField.norm_lt_iff, Ideal.quotientInfEquivQuotientProd_fst, MeasureTheory.aecover_Ioc_of_Ico, PseudoMetric.coe_finsetSup, NNRat.preimage_cast_Ioo, Int.floor_le, Set.one_mem_div_iff, PowerSeries.IsWeierstrassFactorizationAt.degree_eq_coe_lift_order_map_of_ne_top, Set.sups_infs_subset_right, symmDiff_sdiff_inf, Valuation.rel_iff_le, sq_le_one_iff_abs_le_one, Polynomial.abs_isBoundedUnder_iff, Finset.inf_eq_iInf, HahnSeries.order_pow, MulArchimedeanClass.mk_le_mk, BoundedContinuousFunction.coe_inf, StieltjesFunction.iInf_Ioi_eq, Set.Ici_succ_eq_Ioi, Con.inf_iff_and, quasilinearOn_iff_mem_uIcc, lt_add_iff_lt_right_or_exists_lt, sign_eq_sign_or_eq_neg, Finset.prod_Icc_succ_eq_mul_endpoints, Hyperreal.lt_of_st_lt, MulArchimedeanClass.mk_eq_top_iff, OrderEmbedding.birkhoffSet_apply, Pi.instNoMaxOrderLexForallOfWellFoundedLTOfNonempty, LocallyFiniteOrder.orderMonoidHom_strictMono, CategoryTheory.ObjectProperty.instContainsZeroMinOfIsClosedUnderIsomorphisms, Rat.toNNRat_lt_iff_lt_coe, Set.Ico_subset_Icc_union_Ioo, countable_image_gt_image_Ioi, ENat.strictMono_map_iff, MonomialOrder.lex_lt_iff, Nat.lt_ceil, FloorRing.gc_coe_floor, CategoryTheory.TransfiniteCompositionOfShape.ofArrowIso_isColimit, MonomialOrder.eq_zero_iff, Filter.bliminf_not_inf, VertexOperator.ncoeff_of_coeff, CompositionSeries.total, PNat.natPred_lt_natPred, Filter.tendsto_div_const_atBot_iff, symmDiff_symmDiff_inf, CircleDeg1Lift.pow_monotone, ENat.one_lt_top, Valuation.Integers.valuation_irreducible_pos, Module.End.genEigenspace_le_maximal, nhdsLE_sup_nhdsGT, LaurentSeries.comparePkg_eq_extension, Set.pairwise_disjoint_Ico_intCast, NumberField.toNNReal_valued_eq_adicAbv, HahnSeries.finiteArchimedeanClassOrderIsoLex_apply_fst, Valuation.vlt_iff_lt, le_compl_iff_disjoint_right, Cardinal.toENat_le_iff_of_lt_aleph0, lowerSemicontinuousOn_iff_preimage_Iic, MonoidWithZeroHom.inr_strictMono, nullMeasurableSet_Ico, convexJoin_left_comm, FiniteArchimedeanClass.ballAddSubgroup_strictAnti, min_add_add_left, generateFrom_union_isOpen, one_lt_pow_iff, codisjoint_inf_left, compl_top, instArchimedeanInt, CategoryTheory.HasLiftingProperty.transfiniteComposition.sqFunctor_obj, Nat.sub_one_lt_floor, Order.iso_of_countable_dense, disjoint_disjointed, Rat.preimage_cast_Ioo, DivisibleHull.archimedeanClassOrderIso_symm_apply, Ordinal.ToType.mk_apply, Nonneg.coe_div, borel_eq_generateFrom_Ioc_le, iInter_Iic_eq_empty_iff, Valued.hasBasis_uniformity, LinearOrderedField.coe_lt_inducedMap_iff, IsSublattice.infClosed, Sym2.inf_le_sup, Set.Iic.isCompl_iff, ArchimedeanClass.addSubgroup_strictAntiOn, isCompl_compl, Nat.floor_mono, Seminorm.closedBall_finset_sup', ArchimedeanClass.FiniteResidueField.ordConnected_preimage_mk, LinearMap.rank_comp_le, Valuation.mem_ltSubmodule_iff, nhds_basis_Ioo, MeasureTheory.stoppedValue_stoppedProcess_ae_eq, one_lt_mul_self_iff, SimpleGraph.disjoint_fromEdgeSet, StieltjesFunction.outer_Ioc, Module.End.mem_genEigenspace_nat, IsPreconnected.intermediate_value, Set.Iio_inter_Iio, sdiff_eq_left, bot_bihimp, List.minimum_le_of_mem', Nat.le_ceil, inf_sdiff_left_comm, Finset.inf'_id_eq_csInf, RatFunc.single_zpow, PNat.instNoMaxOrder, isPiSystem_Ici, FiniteArchimedeanClass.submodule_strictAnti, MeasureTheory.aecover_Ioo_of_Ico, symmDiff_eq_sup, PNat.lt_add_one_iff, ArchimedeanClass.mk_one, HahnSeries.orderTop_abs, Set.compl_Ici, NNRat.cast_lt_one, Field.Emb.Cardinal.adjoin_image_leastExt, Complementeds.isCompl_coe, div_nonneg_iff, inf_eq_half_smul_add_sub_abs_sub', Set.pairwiseDisjoint_fiber, mul_nonneg_iff_neg_imp_nonpos, borel_eq_generateFrom_Ioi, LaurentSeries.valuation_def, OrderIso.sumLexIioIci_apply_inl, zero_lt_iff, Set.projIci_coe, Mathlib.Tactic.Order.ToInt.exists_translation, HahnSeries.le_order_iff_forall, Valuation.integer.v_irreducible_lt_one, Cardinal.ofENat_toENat_le, sum_Ioc_inv_sq_le_sub, EReal.sign_mul_inv_abs, WithTop.orderIsoSumLexPUnit_symm_inr, himp_bihimp, Int.natCast_strictMono, Left.pow_lt_one_iff, Nat.ceil_zero, Algebra.coe_inf, Ordinal.typein_one_toType, MeasureTheory.aecover_Iio_of_Iio, disjoint_sup_left, NNRat.floor_def, sdiff_sdiff_right_self, PNat.card_Ioc, ArchimedeanClass.mem_ballAddSubgroup_iff, HahnSeries.forallLTEqZero_supp_BddBelow, LaurentSeries.derivative_iterate, Convex.combo_le_max, convexHull_prod, instWellFoundedGTUnit, Set.bounded_le_inter_le, Filter.isBoundedUnder_le_abs, IsModularLattice.isModularLattice_Iic, PNat.natPred_le_natPred, LinearOrderedCommMonoidWithZero.toMulPosStrictMono, inf_strictMonoOn_Icc_sup, zero_min, Rat.cast_pos, MvPowerSeries.order_add_of_order_ne, Set.encard_insert_le, Nat.pow_le_choose, FunctionField.inftyValuation.C, EisensteinSeries.tendsto_tsum_one_div_linear_sub_succ_eq, BoundedLatticeHom.coe_toInfTopHom, Nat.map_cast_int_atTop, OrderTopology.of_discreteTopology, NNRat.preimage_cast_Ioc, LatticeHom.coe_comp_inf_hom', Valuation.IsNontrivial.exists_lt_one, SSet.stdSimplex.face_inter_face, Set.Ici.isCompl_iff, HahnSeries.instIsOrderedRingLexOfNoZeroDivisors, Even.zpow_nonneg, mem_nhds_iff_exists_Ioo_subset, FiniteGaloisIntermediateField.instIsGaloisSubtypeMemIntermediateFieldMin, Set.encard_le_one_iff, Ordinal.toNimber_toOrdinal, Cardinal.toENat_le_one, interior_Ioo, bihimp_bihimp_bihimp_comm, Field.Emb.Cardinal.instFiniteDimensionalSubtypeMemIntermediateFieldAdjoinImageToTypeOrdRankCompCoeBasisWellOrderedBasisLeastExtIioSingletonSet, neg_one_lt_zero, Affine.Simplex.sign_signedInfDist_incenter, Affine.Simplex.ExcenterExists.sign_signedInfDist_excenter, LinearOrderedAddCommGroup.to_noMaxOrder, Finsupp.Colex.single_le_iff, MeasureTheory.aecover_Icc_of_Ioo, Ordinal.cof_type_lt, Nat.ceil_natCast, LinearOrderedAddCommGroup.isAddCyclic_iff_not_denselyOrdered, round_eq_iff, PNat.lt_find_iff, FiniteMulArchimedeanClass.subsemigroup_eq_subgroup, Set.Iio_subset_Iio_union_Ico, isCompl_bot_top, Finset.pluennecke_ruzsa_inequality_pow_div_pow_div, Ordinal.toNimber_max, mem_segment_add_sub, OrderTopology.of_linearLocallyFinite, Filter.tendsto_div_const_atTop_iff, IntermediateField.lift_relrank_comap_comap_eq_lift_relrank_inf, isClosed_Ico_iff, MeasureTheory.countable_meas_le_ne_meas_lt, Finset.sup_inf_sup, Set.encard_le_encard_of_injOn, UniformSpace.toTopologicalSpace_inf, Complementeds.coe_lt_coe, min_eq_left_iff, sdiff_le_iff, Set.Iio_subset_Iic_union_Ico, frontier_Iio, le_sup_sdiff_sup_sdiff, Hyperreal.IsSt.lt, denselyOrdered_set_iff_subsingleton, Set.zero_notMem_neg_add_iff, NNRat.cast_lt, infClosure_supClosure, Set.encard_tsub_one_le_encard_diff_singleton, Set.disjoint_image_inl_range_inr, pow_pos_iff, ENat.mul_le_mul_right_iff, CompleteLatticeHom.toOrderIsoRangeOfInjective_apply, HomotopicalAlgebra.RelativeCellComplex.Cells.hj, convexHull_eq_union, subsingleton_setOf_mem_iff_pairwise_disjoint, EReal.sign_mul_abs, Order.Ioo_eq_empty_iff_pred_le, DistLat.Iso.mk_hom, Set.pairwiseDisjoint_image_right_iff, Cardinal.toENat_injOn, ArchimedeanClass.min_le_mk_sub, Ideal.eq_inf_of_isPrime_inf, PredOrder.isOpen_singleton_iff, LinearIndepOn.encard_le_toENat_rank, Finset.compl_truncatedInf, Ordinal.sup_typein_limit, Int.preimage_ceil_singleton, TopologicalSpace.Opens.infLELeft_apply, antivary_iff_forall_mul_nonpos, pow_le_one_iff, Sublocale.infClosed, Rat.HeightOneSpectrum.valuation_equiv_padicValuation, DivisibleHull.instIsStrictOrderedModuleRat, le_inv_self_iff, LaurentSeries.valuation_le_iff_coeff_lt_log_eq_zero, Interval.coe_inf, convexHull_eq, Types.monoOverEquivalenceSet_unitIso, GenContFract.le_of_succ_get?_den, RootPairing.RootPositiveForm.zero_lt_apply_root_root_iff, IntermediateField.inf_toSubfield, Cardinal.toENat_eq_nat, exists_seq_strictAnti_tendsto_nhdsWithin, Pi.instNoMinOrderColexForallOfWellFoundedGTOfNonempty, convexJoin_assoc_aux, isPiSystem_Ioo, Orientation.oangle_sign_smul_add_smul_right, MeasureTheory.aecover_Ico_of_Ioc, borel_eq_generateFrom_Iio, Rat.lt_toNNRat_iff_coe_lt, div_le_div_flip, codisjoint_himp_self_left, CategoryTheory.HasLiftingProperty.transfiniteComposition.sqFunctor_map, sup_himp_bihimp, HasSolidNorm.orderClosedTopology, Set.one_lt_encard_iff_nontrivial, LaurentSeries.uniformContinuous_coeff, CategoryTheory.MorphismProperty.IsCardinalForSmallObjectArgument.preservesColimit, CategoryTheory.MorphismProperty.instHasTwoOutOfThreePropertyMin, GenContFract.zero_le_of_contsAux_b, Mathlib.Meta.NormNum.IsInt.natCeil, Finsupp.DegLex.wellFoundedLT, LinearOrderedAddCommGroup.Subgroup.exists_neg_generator, AddSubgroup.isLeast_of_closure_iff_eq_abs, negPart_eq_neg, ArchimedeanClass.eq_zero_or_top_of_archimedean, tendsto_pow_div_pow_atTop_atTop, mabs_lt, NonemptyInterval.fst_sup, LinearLocallyFiniteOrder.le_succFn, Submodule.finset_inf_coe, HeytAlg.Iso.mk_hom, PowerSeries.coe_one, CategoryTheory.IsGrothendieckAbelian.generatingMonomorphisms.functorToMonoOver_obj, Submodule.mem_finsetInf, HasStrictFDerivAt.hasStrictFDerivAt_norm_smul, min_le_emultiplicity_add, Polynomial.signVariations_eq_eraseLead_add_ite, List.sortedGE_mergeSort, Ordinal.toNimber_eq_one, Filter.Germ.const_min, Multiset.toDFinsupp_inter, Valuation.mem_leIdeal_iff, AffineSubspace.mem_inf_iff, FinBoolAlg.hasForgetToFinPartOrd_forget₂_map, WithZeroTopology.tendsto_zero, Finset.inf'_eq_csInf_image, LinearOrderedAddCommGroupWithTop.sub_le_sub_iff_left_of_ne_top, Int.card_fintype_Ico_of_le, LaurentSeries.hasseDeriv_zero, IsNonarchimedean.multiset_image_add, BooleanSubalgebra.mem_map_equiv, Padic.norm_rat_le_one_iff_padicValuation_le_one, emultiplicity_pos_iff, liminf_finset_inf, Sublattice.map_symm_eq_iff_eq_map, LinearOrderedSemiring.toLocallyConvexSpace, Finset.exists_pos_of_sum_zero_of_exists_nonzero, Nonneg.Icc_subset_segment, Set.nontrivial_iff_exists_lt, Set.bounded_ge_inter_gt, posPart_mono, Set.notMem_Ici, Valued.isClosed_closedBall, SignType.lt_one_iff, ENat.succ_def, Finpartition.bot_notMem, PrimitiveSpectrum.hull_sSup, mem_nhdsGT_iff_exists_Ioo_subset, ComplementedLattice.instOrderDual, Cardinal.nat_le_ofENat, Set.smul_Icc, negPart_eq_neg_inf_zero, Lat.Iso.mk_hom, Finset.Ico_succ_left_eq_Ioo, Set.integer_valuation_le_one, grade_covBy_grade_iff, sdiff_symmDiff_left, CategoryTheory.SmallObject.SuccStruct.instIsWellOrderContinuousIterationFunctor, interior_Iic, Filter.Tendsto.min, Valuation.coe_ltAddSubgroup, Cardinal.ofENat_toENat_eq_self, AddCircle.coe_image_Ico_eq, Finset.sum_sym2_filter_not_isDiag, Finset.Iic_sub_one_eq_Iio, Order.le_succ_bot_iff, IsDedekindDomain.HeightOneSpectrum.coe_smul_adicCompletion, List.max_sum_le, Finsupp.DegLex.le_iff, NonUnitalStarAlgebra.map_inf, Rat.surjective_padicValuation, interior_Ioi, Real.smoothTransition.projIcc, Set.Finite.convexHull_eq_image, MonoidWithZeroHom.inl_mono, convexJoin_right_comm, nhdsWithinLT_sup_nhdsWithinGE, Finset.inf_sdiff_left, Affine.Simplex.sOppSide_affineSpan_faceOpposite_point_right_iff, antivaryOn_iff_exists_antitoneOn_monotoneOn, CategoryTheory.MorphismProperty.precoverage_inf, Matrix.isIrreducible_iff, MvPolynomial.schwartz_zippel_sum_degreeOf, Mathlib.Meta.NormNum.IsInt.natFloor, FiniteMulArchimedeanClass.val_mk, Set.range_injOn_strictMono, FiniteArchimedeanClass.ball_strictAnti, right_le_midpoint, FrameHom.toFun_eq_coe, compl_le_iff_compl_le, Int.ceil_mono, CategoryTheory.TransfiniteCompositionOfShape.ofComposableArrows_incl_app, not_denselyOrdered_withZero_int, Ideal.multiset_prod_le_inf, Continuous.exists_forall_le_of_hasCompactMulSupport, ArchimedeanClass.orderHom_top, ENat.exists_nat_gt, Topology.IsLower.isTopologicalBasis_insert_univ_subbasis, mem_openSegment_iff_div, HahnEmbedding.Partial.eval_zero, CategoryTheory.Sieve.inter_apply, nhdsGE_basis, CategoryTheory.MorphismProperty.IsStableUnderCobaseChange.inf, measurable_IocProdIoc, Cardinal.ofENat_toENat, Ordinal.typein_le_typein', StieltjesFunction.measure_Ico, Left.nsmul_neg_iff, IsNonarchimedean.apply_intCast_le_one_of_isNonarchimedean, Set.ordConnected_iff_uIcc_subset, Finset.exists_inf_eq_iInf, le_himp, NNRat.cast_le_natCast, antivaryOn_iff_forall_smul_nonpos, List.minimum_concat, tendsto_floor_left, CategoryTheory.Limits.MultispanIndex.toLinearOrder_left, Multiset.sum_min_le, abs_add_le, OrderEmbedding.isEmbedding_of_ordConnected, LinearOrderedCommGroup.to_noMaxOrder, convexHull_rangle_single_eq_stdSimplex, Opens.toPretopology_grothendieckTopology, Hyperreal.InfinitePos.pos, Function.Injective.encard_range, Set.biUnion_Ioc_eq_Ioi_self_iff, instAssociativeMin, Set.encard_le_one_iff_eq, sameRay_smul_right_iff, HahnSeries.finiteArchimedeanClassOrderIso_apply, LaurentSeries.ratfuncAdicComplRingEquiv_apply, LinearOrderedAddCommGroupWithTop.strictMono_add_right_of_ne_top, instIsLocalizationIntPosRat, BoundedLatticeHomClass.map_bot, WithTop.tendsto_nhds_top_iff, Polynomial.isLittleO_atBot_of_degree_lt, m_Birkhoff_inequalities, min_mabs_mabs_le_mabs_max, AffineSpace.asymptoticNhds_eq_smul_vadd, MonomialOrder.div, Int.strictMonoOn_natAbs, Finset.pluennecke_ruzsa_inequality_pow_mul, Nimber.toOrdinal_symm_eq, convexHull_union, StarSubalgebra.mem_inf, sq_pos_of_ne_zero, convexHull_sub, Hyperreal.infinitePos_def, Topology.RelCWComplex.skeletonLT_I, CategoryTheory.ObjectProperty.instIsTriangulatedMinOfIsClosedUnderIsomorphisms, Cardinal.aleph_toENat, maximal_iff_isGreatest, cmp_div_one', WithZeroTopology.orderClosedTopology, Int.cast_le_neg_one_or_one_le_cast_of_ne_zero, Irreducible.maximalIdeal_pow_eq_setOf_le_v_coe_pow, FiniteGaloisIntermediateField.instIsSeparableSubtypeMemIntermediateFieldMin, Finset.lt_fold_max, tendsto_ceil_right, PowerSeries.coeff_heval_zero, Finset.inf_univ_eq_iInf, MeasureTheory.Measure.measure_Ioi_pos, smul_nonneg_iff_pos_imp_nonneg, MonomialOrder.lex_le_iff, oneLePart_eq_self, exists_pos_left_iff_sameRay_and_ne_zero, HahnSeries.instIsDomainOfIsCancelAdd, abs_add_three, sameRay_neg_smul_left_iff, Nat.floor_zero, CategoryTheory.SmallObject.prop_iterationFunctor_map_succ, Rat.cast_le, Order.not_isMax_pred, BicartSq.min_eq, Set.functorToTypes_map, zsmul_le_zsmul_iff_right, antivary_iff_forall_smul_nonpos, Finset.Ico_filter_lt, le_posPart, FiniteArchimedeanClass.min_le_mk_add, Finset.min_mono, Set.lt_iff_ssubset, IsDedekindDomain.HeightOneSpectrum.intValuation_exists_uniformizer, Continuous.bddBelow_range_of_hasCompactMulSupport, AlgebraicGeometry.isomorphisms_eq_stalkwise, antivaryOn_iff_mul_rearrangement, Set.Ioo_sub_one_left_eq_Ioc, Nat.inv_pos_of_nat, HahnSeries.min_le_min_add, DFA.accepts_inter, convexHull_list_sum, Set.not_monotoneOn_not_antitoneOn_iff_exists_lt_lt, iSupIndep_iff_supIndep, Nat.floor_one, Set.definable_finset_inf, Nat.floor_sub_ofNat, exists_Icc_mem_subset_of_mem_nhds, measurableSet_Ioc, Filter.Eventually.intCast_atBot, MonomialOrder.degree_sPolynomial_le, OrderEmbedding.range_inj, AffineSubspace.wOppSide_iff_exists_right, EReal.sign_neg, LinearOrderedField.cutMap_self, add_self_nonpos_iff, Sublocale.range_toNucleus, GroupCone.oneLE.isMaxMulCone, WithVal.le_def, HasCountableSeparatingOn.range_Ici, Finset.pluennecke_ruzsa_inequality_nsmul_sub, Hyperreal.stdPart_omega, Set.Ioc_inter_Ioi, Nat.floor_eq_iff', List.argmin_eq_some_iff, AlgebraicGeometry.IsFinite.eq_inf, IsDiscreteValuationRing.addVal_le_iff_dvd, Mathlib.Meta.NormNum.isNNRat_le_false, isPiSystem_Icc_mem, ArchimedeanClass.liftOrderHom_mk, Nat.isCompl_even_odd, sup_sub_inf_eq_abs_sub, Valuation.HasExtension.val_map_lt_one_iff, Filter.cardinalInterFilter_inf, LinearOrderedAddCommGroupWithTop.sub_self_nonneg, Finset.inf'_sup_distrib_left, LinearOrderedField.cutMap_bddAbove, CategoryTheory.TransfiniteCompositionOfShape.map_incl, ArchimedeanClass.orderHom_mk, inf_div, WithBot.denselyOrdered_set_iff_subsingleton, Set.Ici.subtype_functor_final, Metric.isBounded_of_abs_le, Set.Iic_subset_Iio_union_Icc, one_le_mabs, IicProdIoc_comp_restrict₂, CategoryTheory.SimplicialThickening.Path.le_right, StieltjesFunction.length_Ioc, Order.lt_succ_bot_iff, Continuous.lowerSemicontinuous, MvPolynomial.IsSymmetric.antitone_supDegree, Set.encard_le_encard, AlgebraicGeometry.IsOpenImmersion.map_ΓIso_hom, ENat.toENNReal_le, Valuation.one_le_val_iff, Cardinal.toENat_eq_iff_of_le_aleph0, FiniteMulArchimedeanClass.mk_lt_mk, Set.zero_mem_sub_iff, Submonoid.closure_image_one_lt_and_isMulIndecomposable, WithTop.coe_min, Set.Ioo_disjoint_Ioo, MulArchimedeanClass.mk_right_le_mk_div_iff, IsCompact.bddBelow_image, BoundedLatticeHom.coe_comp_inf_hom', Finset.prod_Icc_of_even_eq_range, four_mul_le_pow_two_add, AlgebraicGeometry.GeometricallyIntegral.eq_geometricallyReduced_inf_geometricallyIrreducible, leOnePart_eq_inv', Valuation.Compatible.vle_iff_le, Mathlib.Tactic.PNatToNat.coe_le_coe, SetTheory.PGame.nim_grundyValue, Iotop_subset_Ioc, PNat.le_one_iff, atTop_le_cocompact, WithZeroTopology.isOpen_Iio, iSupIndep_iff_supIndep_univ, NNRat.floor_natCast_div_natCast, PrimitiveSpectrum.hull_iSup, Finsupp.Lex.addRightMono, isModularLattice_iff_inf_sup_inf_assoc, IntermediateField.map_inf, Int.fract_nonneg, MonomialOrder.degree_sub_leadingTerm_lt_degree, TopologicalSpace.Opens.coe_inf, Int.Ico_filter_modEq_eq, NonemptyInterval.coe_sup_interval, projIcc_eq_zero, Finsupp.support_sup_union_support_inf, iSup_inf_of_monotone, nhds_bot_basis_Iic, Set.integer_eq, mabs_div_lt_iff, measurableSet_lt', Ici_mem_nhdsSet_Ici_iff, Positive.coe_zpow, Int.injOn_natAbs_Ici, WithTop.continuousOn_untopA, compl_bihimp_compl, Set.pairwiseDisjoint_image_left_iff, nhds_top_basis, Hyperreal.abs_lt_real_iff_infinitesimal, Int.preimage_fract, zpow_le_zpow_iff_left, inv_lt_self_iff, instLawfulOrderSup_mathlib, Set.monotone_image, Int.Ioc_filter_modEq_eq, CategoryTheory.ObjectProperty.prop_inf_iff, Int.addSubmonoid_closure_range_mul_self, AffineIndependent.not_wbtw_of_injective, Hyperreal.infinitesimal_pos_iff_infinitePos_inv, Multiset.abs_sum_le_sum_abs, iInf_insert, AddGroupCone.nonneg.isMaxCone, bihimp_fst, oneLePart_eq_ite, Topology.IsLocallyConstructible.finsetInf', CategoryTheory.ObjectProperty.instSmallMin_1, PowerSeries.order_add_of_order_ne, Module.End.hasGenEigenvector_iff, MulArchimedeanClass.orderHom_mk, Module.Basis.orientation_neg_single, IsCompact.exists_isGreatest, Ideal.fst_comp_quotientInfEquivQuotientProd, MvPolynomial.leadingCoeff_toLex, Measurable.min, LinearOrder.isPredArchimedean_of_isSuccArchimedean, Ico_subset_biUnion_Ico, Set.wcovBy_insert, hnot_anti, ArchimedeanClass.mk_div, IntermediateField.relfinrank_comap_comap_eq_relfinrank_inf, abs_le_one_iff_mul_self_le_one, nullMeasurableSet_lt, Set.range_IicExtend, CategoryTheory.TransfiniteCompositionOfShape.map_F, antivary_comm, HahnSeries.leadingCoeff_neg_iff, CategoryTheory.SimplicialThickening.Path.le, ENat.tendsto_nhds_top_iff_natCast_lt, inf_sdiff_right, bihimp_isCommutative, Filter.Germ.min_def, Order.IsNormal.strictMono, iUnion_Ioc_intCast, convexOn_iff_div, Booleanisation.lift_le_comp, Finset.infs_sups_subset_left, norm_inf_le_add, Nonneg.coe_zpow, left_mem_openSegment_iff, MonomialOrder.degree_monomial_le, CategoryTheory.SimplicialThickening.functor_id, HahnSeries.order_mul_of_ne_zero, Units.zero_lt, Set.range_injOn_strictAnti, OrderMonoidWithZeroHom.comp_mul, IntermediateField.inf_relfinrank_left, AffineSubspace.setOf_sOppSide_eq_image2, AddValuation.map_add, Module.End.mem_genEigenspace_zero, Finset.Ioc_disjoint_Ioc, Valuation.ltIdeal_mono, sSup_inter_le, Valuation.IsEquiv.lt_one_iff_lt_one, norm_inf_sub_inf_le_add_norm, Set.encard_iUnion_le_of_fintype, ProbabilityTheory.gaussianPDFReal_mul, continuous_inf_rng, Even.convexOn_pow, abs_sub_pos, Set.one_le_encard_iff_nonempty, Int.sign_eq_sign, Ideal.height_le_spanRank_toENat, Archimedean.embedReal_one, BoundedLatticeHom.coe_comp_inf_hom, borel_eq_generateFrom_Iic, MonomialOrder.degLex_single_lt_iff, CategoryTheory.OrthogonalReflection.iteration_map_succ_surjectivity, Set.unbounded_ge_iff, strictConvexOn_iff_div, nhdsLE_sup_nhdsGE, mabs_mabs_div_mabs_le, NNRat.bddAbove_coe, CategoryTheory.Limits.WalkingMultispan.inclusionOfLinearOrder_map, PointedCone.mem_maxTensorProduct, MeasureTheory.aecover_Ico_of_Icc, minimal_subtype, DFinsupp.support_inf_union_support_sup, List.getElem_le_maximum_of_length_pos, lineMap_lt_lineMap_iff_of_lt', Seminorm.ball_finset_sup, Int.padicValuation_le_one, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.w₁, CompleteLattice.MulticoequalizerDiagram.min_eq, Finsupp.support_inf, bihimp_eq', ArchimedeanClass.addValuation_apply, MeasureTheory.aecover_Ico_of_Ico, Valuation.isEquiv_iff_val_lt_one, Cardinal.natCast_eq_toENat_iff, le_max_iff, IsDedekindDomain.HeightOneSpectrum.embedding_mul_absNorm, cauchy_davenport_minOrder_mul, nsmul_pos_iff, IntermediateField.inf_relrank_left, Set.not_equitableOn, AffineSubspace.not_sOppSide_self, HahnSeries.inv_single, Valuation.IsUniformizer.val_lt_one, CompositionSeries.le_last_of_mem, ENat.eq_top_iff_forall_ge, MultilinearMap.map_sub_map_piecewise, Cardinal.ofENat_le_nat, Finsupp.Colex.single_lt_iff, ContinuousAt.lowerSemicontinuousAt, segment_subset_closure_openSegment, CategoryTheory.SmallObject.iterationFunctorMapSuccAppArrowIso_hom_right_right_comp, LatticeHomClass.toInfHomClass, IsNonarchimedean.finset_powerset_image_add, ringHom_monotone, SMulPosReflectLE.toSMulPosStrictMono, Mathlib.Tactic.PNatToNat.coe_lt_coe, monovaryOn_iff_exists_antitoneOn, MonomialOrder.degree_sub_LTerm_lt, HahnModule.instIsTorsionFree, wbtw_pointReflection, Set.instPreservesColimitsOfShapeFunctorToTypesOfIsFilteredOrEmpty, NNRat.cast_lt_natCast, linOrd_dual_comp_forget_to_Lat, instNonemptySeedRatReal, abs_min_sub_min_le_max, countable_setOf_isolated_left, Finset.pluennecke_ruzsa_inequality_nsmul_sub_nsmul_add, Hyperreal.coe_le_coe, MulArchimedeanClass.min_le_mk_div, CategoryTheory.TransfiniteCompositionOfShape.ofComposableArrows_isColimit, LocallyFiniteOrder.orderMonoidWithZeroHom_strictMono, sdiff_eq_self_iff_disjoint', Nimber.toOrdinal_zero, monovaryOn_iff_mul_rearrangement, ENat.mul_le_mul_left_iff, AffineSubspace.setOf_wSameSide_eq_image2, strictMono_inf_prod_sup, NatOrdinal.toOrdinal_zero, BoundedLatticeHomClass.toInfTopHomClass, mul_nonneg_of_three, Module.End.genEigenspace_le_genEigenspace_finrank, MonomialOrder.sPolynomial_lt_of_degree_ne_zero_of_degree_eq, mabs_div_mabs_le_mabs_div, hnot_le_comm, NumberField.FinitePlace.norm_le_one, min_mabs_mabs_le_mabs_min, infIccOrderIsoIccSup_symm_apply_coe, PUnit.inf_eq, CategoryTheory.Limits.MultispanShape.ofLinearOrder_snd, Order.Iic_succ, isCompl_top_bot, PseudoMetric.finsetSup_apply, add_self_neg_iff, Coheyting.boundary_sup_sup_boundary_inf, Dense.exists_seq_strictMono_tendsto, Module.End.mem_genEigenspace, Collinear.wbtw_or_wbtw_or_wbtw, Heyting.IsRegular.disjoint_compl_left_iff, Valuation.mem_integer_iff, Set.covBy_iff_exists_insert, Set.disjoint_range_inl_image_inr, AlgebraicGeometry.isPullback_opens_inf_le, FinBddDistLat.dual_map, Nat.cast_mul_floor_div_cancel, Units.mulArchimedean_iff, PowerSeries.coe_pow, infPrime_iff_infIrred, Nat.mul_cast_floor_div_cancel, IntermediateField.relrank_inf_mul_relrank, Set.powersetCard.mem_range_ofFinEmbEquiv_symm_iff_mem, nsmul_nonpos_iff, Ideal.radical_finset_inf, Finsupp.DegLex.monotone_degree, Finset.card_uIcc_prod, le_emultiplicity_iff_replicate_subperm_primeFactorsList, ArchimedeanClass.mk_antitoneOn, partialSups_add_one_eq_sup_disjointed, isOrderBornology_iff_eq_orderBornology, Int.succ_eq_succ, Rat.toNNRat_lt_toNNRat_iff, Algebra.mem_inf, isPiSystem_Iic, Affine.Simplex.face_points', Finset.codisjoint_inf_left, sup_himp_distrib, nhdsGT_sup_nhdsWithin_singleton, MeasureTheory.Filtration.coeFn_inf, HahnSeries.addVal_apply, tendsto_fract_right, Cardinal.toENat_nat, tendsto_floor_left_pure_sub_one, Hyperreal.coe_lt_coe, LinearOrderedCommGroup.Subgroup.exists_generator_lt_one, Tropical.trop_inf, HahnEmbedding.Partial.exists_domain_eq_top, LaurentSeries.mem_integers_of_powerSeries, cmp_add_right, Topology.RelCWComplex.skeletonLT_monotone, div_lt_one_iff, FiniteMulArchimedeanClass.subgroup_strictAnti, PowerSeries.nat_le_order, WeierstrassCurve.IsGoodReduction.goodReduction, LinearOrderedCommGroupWithZero.discrete_iff_not_denselyOrdered, FinBoolAlg.hasForgetToFinPartOrd_forget₂_obj_str, abs_abs_sub_abs_le, NNRat.coe_min, LaurentSeries.instIsFractionRingPowerSeries, CategoryTheory.Subfunctor.Subpresheaf.max_min, LinearOrderedCommGroup.discrete_or_denselyOrdered, Finset.dens_union_le, Polynomial.roots_countP_pos_le_signVariations, Valued.isClopen_closedBall, ArchimedeanClass.mk_eq_zero_of_archimedean, Set.pairwise_disjoint_Ico_add_zsmul, PNat.map_subtype_embedding_Ioc, SimplexCategory.toCat_map, Dense.Ioi_eq_biUnion, upperSemicontinuousOn_iff_isClosed_hypograph, MeasureTheory.Integrable.inf, Nimber.toOrdinal_toNimber, HahnSeries.cardSupp_hsum_powers_le, AlgebraicGeometry.Scheme.IdealSheafData.support_sup, MeasureTheory.Lp.coeFn_inf, min_inv_inv', Sublocale.toNucleus_apply, posPart_eq_zero, abs_eq_self, tendsto_intCast_atTop_atTop, bihimp_isAssociative, NonemptyFinLinOrd.mono_iff_injective, lt_neg_self_iff, nhdsLT_sup_nhdsGT, Ideal.snd_comp_quotientInfEquivQuotientProd, Rat.preimage_cast_Ioc, iUnion_Iio_eq_univ_iff, LinearOrderedCommGroupWithZero.inl_apply, Set.bounded_lt_inter_le, nhdsLT_neBot, ArchimedeanClass.mk_sub_lt_mk_left_iff, WithTop.continuous_untop, CategoryTheory.SmallObject.preservesColimit, Filter.tendsto_abs_atTop_atTop, Orientation.eq_or_eq_neg_of_isEmpty, Valuation.leAddSubgroup_monotone, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquiv_functor, LinearOrderedCommGroupWithZero.inr_apply, Finsupp.Lex.single_le_iff, isPiSystem_Ioo_mem, Orientation.oangle_sign_smul_add_smul_left, bihimp_hnot_self, Dense.exists_gt, convexOn_zpow, RootPairing.posRootForm_rootFormIn_posDef, Finpartition.parts_extendOfLE_of_eq, Module.End.genEigenspace_zero, not_linearIndepOn_finset_iffₒₛ, Polynomial.le_trailingDegree_X_pow, continuousWithinAt_iff_continuous_left_right, Matroid.toENat_cRank_eq, mabs_sup_div_sup_le_mabs, neg_inf, List.minimum_le_coe_iff, measurableSet_bddBelow_range, ValuationSubring.algebraMap_injective, Hyperreal.st_eq_sSup, Nonneg.toNonneg_lt, PosSMulMono.toPosSMulReflectLT, abs_min_le_max_abs_abs, Finset.orderEmbOfFin_mem, Ordinal.toNatOrdinal_toOrdinal, inf_symmDiff_symmDiff, Set.Finite.encard_biUnion_le, Finset.max_prod_le, ContinuousWithinAt.upperSemicontinuousWithinAt, MvPowerSeries.le_order_pow, MeasureTheory.aecover_Icc_of_Ico, Nat.factorization_gcd, OrderHom.map_inf_fixedPoints_le, Set.projIic_eq_self, continuousAt_sign_of_ne_zero, AffineSubspace.wOppSide_pointReflection, inf_sdiff_distrib_left, tendsto_floor_right', compl_bihimp, TopCat.Sheaf.interUnionPullbackCone_pt, IsValuativeTopology.mem_nhds_iff, abs_nonneg, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquiv_unitIso, RatFunc.single_inv, PowerSeries.heval_mul, Int.lt_floor_iff, lowerSemicontinuousWithinAt_iff_frequently, Filter.liminf_piecewise, MulArchimedeanClass.subgroup_eq_bot, nhds_basis_mabs_div_lt, Valuation.pos_iff, LinearOrderedCommGroup.discrete_iff_not_denselyOrdered, Valued.norm_pos_iff_valuation_pos, wbtw_midpoint, codisjoint_himp_self_right, Nat.ceil_eq_iff, exists_zero_lt, List.maximum_eq_coe_iff, sSup_inf_eq, Rat.natCast_lt_cast, HahnSeries.SummableFamily.support_powerSeriesFamily_subset, bihimp_top, disjoint_sdiff_self_left, Ordinal.enum_zero_le', HahnSeries.zero_ofSuppBddBelow, smulPosMono_iff_smulPosReflectLT, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivInverseObj_pt, MeasureTheory.IsSetSemiring.Ioc, List.sortedGE_insertionSort, Types.monoOverEquivalenceSet_counitIso, LocallyFiniteOrder.orderAddMonoidEquiv_apply, Right.sign_neg, List.le_maximum_of_length_pos_iff, Set.compl_Ioc, AffineIndependent.convexHull_inter, IsModularLattice.complementedLattice_Iic, List.coe_minimum_of_length_pos, exists_le_add_iff_le_right, LinOrd.comp_apply, NatOrdinal.toOrdinal_eq_one, Finset.Ici_add_one_eq_Ioi, isPiSystem_image_Ici, ArchimedeanClass.FiniteElement.mk_natCast, Odd.geom_sum_pos, abs_le', LinOrd.coe_comp, IsDedekindDomain.HeightOneSpectrum.valuation_le_one, ENat.one_lt_card, ENat.self_le_mul_right, AlgebraicGeometry.IsIntegralHom.eq_universallyClosed_inf_isAffineHom, LaurentPolynomial.degree_T_le, ENat.add_le_add_iff_left, PosSMulMono.toPosSMulReflectLE, Order.Ideal.IsPrime.isMaximal, tendsto_pow_atTop_nhds_zero_iff, Set.Ioi_inter_Ioi, Dense.borel_eq_generateFrom_Ioc_mem, ENat.mul_right_strictMono, sdiff_sdiff_left', CategoryTheory.SmallObject.iterationFunctorObjObjRightIso_ιIteration_app_right_assoc, instIsPrincipalIdealRingSubtypeMemSubringIntegerWithZeroMultiplicativeIntValuation, CompositionSeries.head_le, Finset.max'_lt_iff, comap_coe_nhdsGT_eq_atBot_iff, Finset.listMap_orderEmbOfFin_finRange, FinBoolAlg.dual_map, strictConvex_Ioi, Ordinal.familyOfBFamily_enum, Polynomial.div_tendsto_atTop_zero_iff_degree_lt, Valued.toNormedField.norm_lt_one_iff, le_min_iff, bihimp_snd, IsSimpleOrder.instIsAtomic, CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.ofComposableArrows_isoBot_hom, IntermediateField.relrank_mul_relrank_eq_inf_relrank, OrderIso.asBoolAlgAsBoolRing_symm_apply, IsRetrocompact.finsetInf, add_inf, UpperSet.total_le, instLawfulOrderInf_mathlib, Nat.add_one_le_ceil_iff, HahnSeries.mem_orderTopSubOnePos_iff, Continuous.exists_forall_ge_of_hasCompactMulSupport, denselyOrdered_iff_denselyOrdered_units_and_nontrivial_units, Measurable.nat_ceil, Continuous.min, SuccOrder.nhdsLT_eq_nhdsNE, CategoryTheory.TransfiniteCompositionOfShape.ici_incl, Heyting.IsRegular.inf, IsDedekindDomain.HeightOneSpectrum.valuationOfNeZeroToFun_eq, Order.sub_one_lt_iff, ZSpan.mem_fundamentalDomain, exists_succ_iterate_or, MeasureTheory.aecover_Ioo_of_Icc, Set.Iio_subset_Iic_union_Ioo, Set.Ici_eq_singleton_iff_isTop, Real.log_of_ne_zero, Set.disjoint_range_iff, ArchimedeanClass.mk_map_of_archimedean', Module.End.genEigenspace_le_smul, CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.mem_map, Order.lt_one_iff_nonpos, iInf_inf_eq, inf_himp_le, Subgroup.isLeast_of_closure_iff_eq_mabs, MvPowerSeries.min_order_le_add, AlgebraicGeometry.Scheme.pretopology_eq_inf, Nonneg.orderedSub, AddCircle.liftIco_eq_lift_Icc, PNat.card_fintype_Icc, MeasureTheory.ae_restrict_uIoc_eq, Finset.Nonempty.dens_pos, succ_max, LaurentSeries.coeff_coe_powerSeries, FiniteArchimedeanClass.addSubgroup_eq_bot, WithZero.min_le_iff, mabs_div_le_iff, WithZeroTopology.nhds_eq_update, ValuativeRel.uniformizer_lt_one, nhdsGT_neBot, archimedean_iff_int_le, MeasurableSpace.measurableSet_inf, min_eq_top, countable_setOf_covBy_right, PowerSeries.le_order_prod, ValuativeRel.uniformizer_pos, HahnEmbedding.Partial.exists_isMax, sup_sdiff_injOn, Archimedean.mkRat_mem_ratLt, CauSeq.bounded, Seminorm.ball_finset_sup', NNRat.cast_le_ofNat, exists_uIoo_isExtrOn_uIcc, Ordinal.type_toType, le_add_iff_lt_right_or_exists_le, Pi.mulSupport_mulSingle_disjoint, LinearOrderedAddCommGroup.isAddCyclic_iff_nonempty_equiv_int, biSup_inter_of_pairwise_disjoint, TwoSidedIdeal.inf_ringCon, HahnSeries.orderTop_embDomain, Valuation.IsRankOneDiscrete.exists_generator_lt_one, Set.prod_subset_compl_diagonal_iff_disjoint, SignType.neg_iff, Ordinal.nmul_eq_mul, PowerSeries.order_add_of_order_eq, Set.Finite.convexHull_eq, BoundedGENhdsClass.of_closedIicTopology, Archimedean.embedRealFun_strictMono, hnot_le_iff_codisjoint_right, HahnSeries.cardSupp_inv_le, MeasureTheory.Measure.measure_Iio_pos, Hyperreal.stdPart_epsilon, min_add, Set.IsPWO.of_linearOrder, Profinite.NobelingProof.Products.instWellFoundedLT, mabs_div_le_one, Sublattice.prodEquiv_symm_apply, ZNum.isStrictOrderedRing, MulArchimedeanClass.mk_div_lt_mk_right_iff, Matrix.eRank_submatrix_le, Associates.FactorSet.sup_add_inf_eq_add, Finset.dens_le_dens, BooleanAlgebra.eq_iff_atom_le_iff, DFinsupp.Lex.total_le, Complex.sum_div_factorial_le, Set.empty_disjoint, Hyperreal.ofSeq_lt_ofSeq, Module.End.genEigenspace_restrict, ContinuousAt.upperSemicontinuousAt, orderTopology_of_ordConnected, PolynormableSpace.inf, finSumEquivOfFinset_inl, exists_one_lt', inf_sdiff_left, CategoryTheory.TransfiniteCompositionOfShape.ofOrderIso_isColimit, BddLat.dual_map, exists_rat_lt, CategoryTheory.SimplicialThickening.functor_obj_as, Set.Ioo_subset_uIoo', Set.Ioc_sub_one_left_eq_Icc, Archimedean.of_locallyFiniteOrder, VertexOperator.coeff_eq_ncoeff, FunctionField.inftyValuation_apply, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.w₂, IsCompact.exists_isMaxOn, inf_mul_sup, MulArchimedeanClass.mulArchimedean_of_mk_eq_mk, Order.Ioc_pred_left, isClosed_Ioo_iff, MulArchimedeanOrder.le_def, Fintype.not_linearIndependent_iffₒₛ, min_add_distrib, nonneg_add_self_iff, zpow_lt_zpow_iff_left, sub_le_sub_flip, Odd.pow_nonpos_iff, Polynomial.cyclotomic_pos, le_bihimp_iff, Algebra.inf_toSubsemiring, bihimp_eq_top, Dense.borel_eq_generateFrom_Icc_mem, Finset.Iic_diff_Ioc, Set.disjoint_union_left, ValuativeRel.instMulArchimedeanValueGroupWithZeroOfIsRankLeOne, iSup_inf_of_antitone, ArchimedeanClass.ball_antitone, Set.Ioo_inter_Ioo, Finset.Ico_succ_succ_eq_Ioc, Int.Ico_filter_dvd_eq, starConvex_iff_div, nhdsSet_Ioi, NonUnitalAlgebra.inf_toNonUnitalSubsemiring, Mathlib.Meta.NormNum.IsNat.natFloor, isStronglyCoatomic, Left.sign_neg, Affine.Simplex.sOppSide_affineSpan_faceOpposite_iff, CategoryTheory.MorphismProperty.IsLocalAtTarget.inf, measurableSet_bddAbove_range, Finset.le_max, HahnSeries.min_orderTop_le_orderTop_add, instWellFoundedGTWithZeroMultiplicativeIntLeOne, Profinite.NobelingProof.Products.eval_πs_image, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.w₁_assoc, PNat.one_le_find, LaurentSeries.powerSeriesPart_zero, bihimp_bot, Finset.sum_Icc_succ_eq_add_endpoints, Valuation.val_le_one_iff, Finset.sum_le_sum_Ioc, isCoatomic_of_isAtomic_of_complementedLattice_of_isModular, Filter.tendsto_mul_const_atBot_iff, HahnSeries.leadingCoeff_nonpos_iff, StieltjesFunction.right_continuous, sdiff_inf_sdiff, Odd.pow_le_pow, liminf_min, Set.instOrdConnectedOrdConnectedComponent, PrimitiveSpectrum.gc, LaurentSeries.exists_ratFunc_eq_v, HahnSeries.SummableFamily.powerSeriesFamily_smul, Finpartition.exists_le_of_le, Cardinal.natCast_le_toENat_iff, Polynomial.trailingDegree_one_le, Set.Ioi_subset_Ioc_union_Ici, min_bot_right, Int.card_Ioo_of_lt, Valued.toNormedField.one_le_norm_iff, Pi.Lex.isStrictOrder, Sublattice.mem_map_equiv, EReal.sign_mul_inv_abs', countable_image_gt_image_Iio, Stream'.Seq.lt_length'_iff, Set.Finite.encard_strictMonoOn, le_iff_forall_one_lt_le_mul, BicartSq.le₃₄, csInf_pair, ENat.add_lt_add_iff_right, wellFoundedLT_toType, one_lt_ltOnePart_iff, IsModularLattice.complementedLattice_Icc, openSegment_subset_union, Nat.cast_inv_le_one, Finset.divConst_le_inv_dens, multiplicity_le_emultiplicity, iInf_pair, ZMod.valMinAbs_spec, Hyperreal.gt_of_neg_of_infinitesimal, LinearOrderedCommGroupWithZero.wellFoundedOn_setOf_le_lt_iff_nonempty_discrete_of_ne_zero, bihimp_himp_right, Int.add_one_le_ceil_iff, Nat.lt_floor_add_one, Finsupp.Lex.wellFoundedLT_of_finite, OrderIso.sumLexIioIci_apply_inr, Rat.comap_cast_atTop, MonomialOrder.degree_sPolynomial_lt_sup_degree, Padic.isDenseInducing_cast_withVal, left_lt_lineMap_iff_pos, add_lt_add_iff_right_of_ne_top, Set.encard_le_one_iff_subsingleton, HahnEmbedding.Seed.domain_baseEmbedding, NNRat.cast_lt_ofNat, Nat.one_div_lt_one_div, Booleanisation.comp_le_comp, inf_compl_eq_bot, bihimp_assoc, Finsupp.toMultiset_inf, Set.monotone_powerset, AddUnits.topology_eq_inf, abs_le_iff_mul_self_le, PNat.mod_le, Continuous.bddAbove_range_of_hasCompactSupport, ArchimedeanClass.mem_closedBallAddSubgroup_iff, Finset.disjiUnion_Iic_disjointed, sign_eq_neg_one_iff, FiniteArchimedeanClass.withTopOrderIso_apply_coe, CategoryTheory.SimplicialThickening.functor_comp, LinearOrderedField.mem_cutMap_iff, Module.End.pos_finrank_genEigenspace_of_hasEigenvalue, Submodule.isPrimary_finsetInf, Set.Iio_injective, Finset.orderEmbOfFin_compl_singleton_apply, Complementeds.mk_inf_mk, ENat.lt_coe_add_one_iff, Dense.borel_eq_generateFrom_Icc_mem_aux, Dense.topology_eq_generateFrom, Asymptotics.isLittleO_pow_pow_atTop_of_lt, DFinsupp.Colex.isStrictOrder, CircleDeg1Lift.translationNumber_mono, Metric.isBounded_of_abs_lt, Finset.mulConst_le_divConst_sq, le_sdiff_sup, ENat.card_le_one, negPart_eq_ite_lt, Polynomial.le_trailingDegree_X, Module.length_eq_rank, zsmul_left_mono, Coheyting.boundary_bot, WithTop.nhds_coe, min_left_commutative, AlgebraicGeometry.ValuativeCriterion.eq, FiniteMulArchimedeanClass.coe_congrOrderIso_apply, Nat.image_cast_int_Ico, SetTheory.PGame.nim_add_nim_equiv, intermediate_value_Ioc, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.w₂_assoc, NNRat.preimage_cast_Iio, CauSeq.const_pos, iInf_split_single, PseudoMetric.nonneg, Ioo_subset_Iotop, intermediate_value_Ico, MonomialOrder.degree_sub_leadingTerm_lt_iff, NNRat.ofNat_lt_cast, abs_inf_sub_inf_le_abs, Set.pairwise_disjoint_Ioo_intCast, sign_eq_one_iff, exists_le_add_iff_le_left, Set.Ioi_injective, Set.unbounded_lt_inter_lt, Subfield.toIsStrictOrderedRing, ArchimedeanClass.FiniteResidueField.instIsOrderedRing, Cardinal.toENat_lt_top, MonomialOrder.degree_sub_leadingTerm_le, Coheyting.boundary_le_boundary_sup_sup_boundary_inf_right, Valuation.exists_div_eq_of_surjective, le_abs', Valuation.Integers.maximalIdeal_pow_eq_setOf_le_v_algebraMap_pow, sdiff_symmDiff_right, Submonoid.mem_closure_image_one_lt_iff, compl_bot, IsDedekindDomain.HeightOneSpectrum.intValuation_apply, Finset.min'_eq_inf', nhdsLE_basis, isAtom_compl, Cardinal.lift_min, Int.preimage_Ico, le_add_iff_lt_left_or_exists_le, HahnSeries.le_orderTop_iff_forall, SetLike.coe_mono, MvPowerSeries.le_order_pow_of_constantCoeff_eq_zero, posPart_min, ArchimedeanClass.mk_inv, continuous_inf_dom_left, Valuation.Integers.isPrincipalIdealRing_iff_not_denselyOrdered_mrange, Complementeds.disjoint_coe, Finsupp.DegLex.single_strictAnti, List.trop_minimum, Set.Icc_subset_Icc_union_Icc, Finset.lt_max'_of_mem_erase_max', Ordinal.toNatOrdinal_max, NonUnitalAlgebra.map_inf, upperSemicontinuousWithinAt_iff_frequently, Set.IciExtend_apply, Set.uIoc_eq_union, Set.IicExtend_self, convexHull_range_eq_exists_affineCombination, mabs_le_one, Matrix.isPrimitive_iff, Real.arcsin_projIcc, wbtw_iff_sameRay_vsub, NonemptyFinLinOrd.Iso.mk_hom, toBoolAlg_mul, LaurentSeries.valuation_X_pow, LaurentPolynomial.degree_C_le, Set.ordConnected_uIoc, Order.le_succ_iff_eq_or_le, Nimber.toOrdinal_eq_zero, countable_setOf_isolated_right_within, tendsto_mabs_nhdsNE_one, Tropical.inf_eq_add, lt_max_iff, HahnSeries.le_order_smul, Finset.sum_mul_sq_le_sq_mul_sq, Finset.exists_mem_eq_inf', IsDedekindDomain.HeightOneSpectrum.intValuation_lt_one_iff_mem, DistribLattice.mem_ideal_sup_principal, Set.monotone_projIci, Int.padicValuation_eq_zero_iff, LaurentSeries.hasseDeriv_single, Finset.compl_truncatedSup, Valuation.Integers.dvd_iff_le, List.maximum_concat, Cardinal.toENat_congr, CategoryTheory.Limits.instIsWellOrderContinuousCompOfPreservesWellOrderContinuousOfShape, OrderMonoidWithZeroHom.mul_apply, ENat.range_natCast, Finset.sum_min_le, Polynomial.eventually_no_roots, NumberField.FinitePlace.norm_def, NonUnitalStarAlgebra.mem_inf, CauSeq.coe_inf, lt_min_iff, FiniteArchimedeanClass.mem_closedBall_iff, antivary_iff_exists_antitone_monotone, Even.pow_pos_iff, analyticOrderAt_add_of_ne, Int.Ioc_filter_dvd_card, discreteTopology_iff_orderTopology_of_pred_succ, toZ_le_iff, AddUnits.min_val, Valuation.one_rel_iff, MulArchimedeanClass.orderHom_top, Valuation.le_one_of_subsingleton, NonnegSpectrumClass.iff_spectrum_nonneg, Finset.codisjoint_inf_right, mabs_cases, Nat.preimage_Ico, GenContFract.abs_sub_convs_le, CategoryTheory.Functor.WellOrderInductionData.Extension.zero_val, OrderEmbedding.birkhoffFinset_sup, NNRat.castOrderEmbedding_apply, continuousAt_iff_lower_upperSemicontinuousAt, Filter.Eventually.intCast_atTop, ArchimedeanClass.closedBall_top, Finset.card_truncatedSup_union_add_card_truncatedSup_infs, PosSMulStrictMono.toPosSMulReflectLT, ENat.one_le_iff_ne_zero, IsComplemented.inf, Finsupp.Colex.single_strictMono, NonarchimedeanHomClass.map_add_le_max, AlgebraicGeometry.descendsAlong_universallyOpen_surjective_inf_flat_inf_quasicompact, PNat.addLeftStrictMono, countable_image_lt_image_Iio, mem_segment_sub_add, monovary_iff_exists_monotone, Pi.toColex_update_lt_self_iff, Order.Ideal.IsPrime.mem_or_compl_mem, WithZero.withZeroUnitsEquiv_strictMono, LinearOrderedAddCommGroupWithTop.sub_lt_sub_iff_left_of_ne_top, hahnEmbedding_isOrderedAddMonoid, List.maximum_append, ENat.lt_one_iff_eq_zero, Matroid.toENat_cRk_eq, HasCountableSeparatingOn.range_Iic, LinearOrderedCommGroupWithZero.discrete_or_denselyOrdered, IsSimpleOrder.instIsCoatomic, GenContFract.IntFractPair.nth_stream_fr_nonneg, Function.disjoint_support_iff, Finset.isLeast_min', bihimp_eq_bot, isComplemented_top, List.argmin_cons, Tuple.monotone_sort, Set.Ioi_ssubset_Ioi_iff, Set.encard_le_encard_diff_add_encard, ProbabilityTheory.Kernel.partialTraj_eq_prod, Finpartition.parts_inf, Icc_subset_segment, Finset.mem_uIcc, LinearOrderedAddCommGroup.to_noMinOrder, Filter.tendsto_const_mul_atTop_iff, Affine.Simplex.altitude_def, PNat.le_find_iff, contMDiffOn_projIcc, Mathlib.Meta.NormNum.isNNRat_lt_true, Cardinal.toENat_eq_one, Order.isSuccPrelimitRecOn_succ, Ordinal.toNatOrdinal_symm_eq, NonemptyFinLinOrd.hom_id, OrderIso.isCompl_iff, MonomialOrder.iocam, posPart_eq_ite_lt, Finset.max_abv_sum_one_le, LinearMap.lift_rank_comp_le, mem_nhdsLE_iff_exists_Ioc_subset, ENat.not_lt_zero, MonomialOrder.degree_sub_LTerm_le, sup_sdiff_symmDiff, Rat.padicValuation_le_one_iff, Finset.Ico_succ_right_eq_Icc, codisjoint_hnot_hnot_right_iff, HahnSeries.leadingCoeff_abs, left_le_lineMap_iff_nonneg, exists_lt_add_iff_lt_right, MonomialOrder.lex_le_iff_of_unique, lineMap_lt_left_iff_neg, LinearOrderedCommGroup.isCyclic_iff_nonempty_equiv_int, Measurable.lt, tendsto_ratCast_atTop_iff, Set.disjoint_iff, ArchimedeanClass.stdPart_eq_sSup, OrderEmbedding.mulLeft_apply, max_eq_iff, IsDedekindDomain.HeightOneSpectrum.notMem_adicCompletionIntegers, Set.one_mem_inv_mul_iff, bot_eq_zero', tendsto_smul_comp_nat_floor_of_tendsto_nsmul, Hyperreal.gt_of_tendsto_zero_of_neg, Cardinal.mk_Iio_ord_toType, Hyperreal.epsilon_pos, PosSMulReflectLE.toPosSMulStrictMono, LaurentPolynomial.degree_C_mul_T_le, Multiset.prod_min_le, Set.IciExtend_coe, LinearOrderedCommGroup.isCyclic_iff_not_denselyOrdered, instDenselyOrderedUnits, AffineSubspace.comap_inf, upperSemicontinuousOn_iff_preimage_Ici, Hyperreal.archimedeanClassMk_epsilon_pos, Finset.dens_pos, Set.mem_uIcc, iSup_inf_iSup, Profinite.NobelingProof.Products.head_lt_ord_of_isGood, disjoint_sdiff_sdiff, Finpartition.avoid_parts_val, Finset.nonneg_subConst, NNRat.cast_lt_zero, CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.mem_incl_app, Set.Nonempty.not_disjoint, WithBot.orderIsoPUnitSumLex_bot, Ordinal.sup_typein_succ, AddCon.coe_inf, exists_pos_right_iff_sameRay_and_ne_zero, Hyperreal.tendsto_atTop_iff, IsAddIndecomposable.baseOf_subset_pos, Set.powersetCard.ofFinEmbEquiv_apply, LinearOrderedCommMonoidWithZero.toZeroLeOneClass, AlgebraicGeometry.IsOpenImmersion.map_ΓIso_inv_apply, Set.notMem_uIoc, Topology.IsUpper.tendsto_nhds_iff_lt, AlgebraicGeometry.descendsAlong_universallyInjective_surjective_inf_flat_inf_quasicompact, Mathlib.Tactic.Order.ToInt.toInt_lt_toInt, LaurentSeries.powerSeriesPart_eq_zero, LinearOrderedField.toPosSMulStrictMono_rat, ENat.coe_lt_top, NonUnitalStarAlgebra.inf_toNonUnitalSubalgebra, MonomialOrder.degree_sPolynomial, Polynomial.isBigO_atTop_of_degree_le, one_le_oneLePart, Nat.preimage_ceil_zero, ProbabilityTheory.condExpKernel_apply_eq_condDistrib, nhdsGE_basis_Ico, Ordinal.nadd_eq_add, HahnSeries.BddBelow_zero, Continuous.bddAbove_range_of_hasCompactMulSupport, Cardinal.nat_lt_ofENat, polynomialFunctions.comap_compRightAlgHom_iccHomeoI, Polynomial.valuation_X_eq_neg_one, hahnEmbedding_isOrderedModule, Ordinal.one_toType_eq, List.Perm.minimum_eq, LinearOrderedAddCommGroup.tendsto_nhds, Nat.ceil_add_le, AbsoluteValue.eq_trivial_of_isEquiv_trivial, closure_Ioc, Finset.Ico_add_one_add_one_eq_Ioc, inf_ind, TopologicalSpace.Opens.mk_inf_mk, Set.Iio_inter_Ioo, restrict₂_comp_IicProdIoc, Finset.isLUB_iff_isGreatest, ProbabilityTheory.Kernel.traj_eq_prod, MonomialOrder.degree_X_le_single, NatOrdinal.lt_wf, PNat.lt_succ_self, WithBot.add_one_le_iff, tendsto_zero_geometric_tsum_pnat, IsNonarchimedean.add_pow_le, MeasureTheory.stoppedProcess_eq_stoppedValue, Int.fract_eq_iff, closure_Ioi, Set.disjoint_univ_pi, convexOn_iff_slope_mono_adjacent, ArchimedeanClass.mk_zpow, lt_tsub_iff_left, BicartSq.le₁₃, Nat.image_cast_int_Iio, Set.ordConnected_uIcc, mem_nhdsGE_iff_exists_Icc_subset, Affine.Simplex.sOppSide_affineSpan_faceOpposite_point_left_iff, mabs_eq_self, MeasureTheory.AEStronglyMeasurable.aestronglyMeasurable_uIoc_iff, bihimp_right_injective, Int.instIsOrderedAddMonoid, add_le_add_iff_right_of_ne_top, closure_Ioo, MvPowerSeries.le_order_map, atBot_le_cocompact, MulArchimedean.of_locallyFiniteOrder, Set.pairwiseDisjoint_singleton_iff_injOn, Hyperreal.coeRingHom_toFun, Even.zpow_pos, Nat.floor_pos, himp_eq_sSup, StieltjesFunction.right_continuous', sdiff_triangle, leOnePart_anti, HahnEmbedding.Partial.toOrderAddMonoidHom_injective, monovaryOn_iff_forall_mul_nonneg
toSemilatticeSup 📖	CompOp	3052 math math: max_choice, max_sub_min_eq_abs', NonUnitalSubalgebra.coe_starClosure, AlgebraicGeometry.Scheme.toSpecΓ_apply, IsLocalMaxOn.max, LatticeHom.toFun_eq_coe, AlgebraicGeometry.Scheme.Opens.ι_image_basicOpen, AlgebraicGeometry.Γ_map_morphismRestrict, MeasureTheory.Measure.MeasureDense.approx, iSup_insert, Submodule.finrank_sup_add_finrank_inf_eq, AlgebraicGeometry.Scheme.Hom.smoothLocus_eq_top_iff, IsCyclotomicExtension.adjoin_primitive_root_eq_top, sub_sup, Algebra.range_ofId, NonUnitalSubalgebra.center_eq_top, sInf_univ, CategoryTheory.sheafBotEquivalence_functor, Subalgebra.LinearDisjoint.inf_eq_bot, IsWeakUpperModularLattice.covBy_sup_of_inf_covBy_covBy, AlgebraicGeometry.Scheme.ΓSpecIso_inv_naturality_assoc, csSup_pair, map_symmDiff', Finset.sup_add_sup, Filter.Tendsto.max_left, LinearMap.quotientInfEquivSupQuotient_symm_apply_eq_zero_iff, Submodule.rTensorOne_symm_apply, WithTop.coe_max, AlgebraicGeometry.Scheme.Hom.toPartialMap_hom, AlgebraicGeometry.Scheme.map_PrimeSpectrum_basicOpen_of_affine, coinduced_bot, AlgebraicGeometry.Scheme.bot_mem_grothendieckTopology, IntermediateField.finInsepDegree_top, MonomialOrder.sPolynomial_leadingTerm_mul', iSup_pair, Pi.symmDiff_def, LatticeHom.withTopWithBot_apply, sdiff_sup_cancel, SSet.Subcomplex.preimage_eq_top_iff, AffineSubspace.direction_sup_eq_sup_direction, OrderEmbedding.supIrredLowerSet_apply, DFinsupp.toMultiset_sup, measurable_from_top, Module.End.isSemisimple_restrict_iff, AlgebraicGeometry.IsAffineOpen.isoSpec_inv_appTop, Set.inter_symmDiff_distrib_left, AlgebraicGeometry.Scheme.germ_stalkClosedPointTo, continuous_sup_rng_right, sup_div_inf_eq_mabs_div, Nat.iSup_lt_succ', Algebra.lift_cardinalMk_adjoin_le, IntermediateField.adjoin_eq_top_iff_of_isAlgebraic, MvPolynomial.isWeightedHomogeneous_zero_iff_weightedTotalDegree_eq_zero, Measurable.max, SymmetricAlgebra.rank_eq, Finset.max_union, Subgroup.sup_eq_closure_mul, compl_symmDiff_self, Mathlib.Tactic.Order.ToInt.toInt_sup_toInt_eq_toInt, Finset.sup_singleton_eq_self, TopCat.Sheaf.interUnionPullbackCone_snd, iSupIndep.injOn_iInf, Finset.comp_sup_eq_sup_comp_of_is_total, Set.smul_set_symmDiff, IntermediateField.LinearDisjoint.iff_inf_eq_bot, Cardinal.powerlt_max, Subgroup.exists_mem_sup, max_div_div_right, Sublattice.sup_mem, min_sub_sub_left, LinearMap.map_le_map_iff, AlgebraicGeometry.ΓSpec.locallyRingedSpaceAdjunction_counit_app, MeasurableSpace.comap_const, LatticeCon.r_inf_sup_iff, AlgebraicGeometry.Scheme.IsQuasiAffine.toIsImmersion, AlgebraicGeometry.StructureSheaf.globalSectionsIso_inv, biSup_le_eq_sup, OrderEmbedding.birkhoffFinset_inf, TopologicalSpace.Opens.mem_top, AlgebraicGeometry.iSup_affineOpens_eq_top, AlgebraicGeometry.isAffineOpen_top, AddQuantale.add_sup_distrib, Finset.truncatedSup_infs, sup_himp_self_right, MeasureTheory.Integrable.sup, AlgebraicGeometry.AffineSpace.isoOfIsAffine_inv, ofBoolRing_sub, MonomialOrder.degree_add_of_ne, MeasureTheory.Measure.sub_top, AlgebraicGeometry.Scheme.support_nilradical, covBy_iff_le_iff_lt_right, Finset.sup'_add', posPart_max, BiheytingHom.map_sdiff', Finpartition.combine_parts, Ordinal.max_zero_left, AddSubgroup.map_eq_map_iff, Multiset.Ico_sub_Ico_left, Submodule.comm_trans_lTensorOne, IntermediateField.extendScalars_sup, Cardinal.mk_list_eq_max_mk_aleph0, IntermediateField.coe_algebraMap_over_bot, RingCon.toCon_eq_bot, add_max, Finset.le_fold_max, AddSubgroup.exists_mem_sup, NonUnitalStarAlgebra.mem_bot, IsDedekindDomain.HeightOneSpectrum.iInf_localization_eq_bot, AddSubmonoid.sup_eq_closure, Cardinal.mk_list_le_max, Equiv.Perm.support_prod_of_pairwise_disjoint, inf_right_le_sup_left, lt_compl_self, Algebra.adjoin_singleton_intCast, Finset.disjSups_right_comm, CategoryTheory.ObjectProperty.HasCardinalLT.sup, Subalgebra.LinearDisjoint.sup_free_of_free, Subalgebra.pi_top, AlgebraicGeometry.Scheme.Opens.toSpecΓ_SpecMap_presheaf_map_top, NonUnitalStarAlgebra.mem_sup_right, continuous_sup_dom, AlgebraicGeometry.LocallyRingedSpace.notMem_prime_iff_unit_in_stalk, sSup_univ, Monoid.Coprod.range_inl_sup_range_inr, AlgebraicGeometry.Scheme.restrictFunctorΓ_inv_app, List.getD_max?_eq_unbotD_maximum, Multiset.sup_eq_union, StarSubalgebra.mem_sup_left, AlgebraicGeometry.instIsDomainCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTopOfIsIntegral, MeasurableSpace.comap_bot, MeasureTheory.OuterMeasure.mkMetric_top, MeasureTheory.measureReal_symmDiff_le, symmDiff_eq', GradedAlgebra.exists_finset_adjoin_eq_top_and_homogeneous_ne_zero, Finset.inf'_sup_inf', CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.D₁_W, Cardinal.mk_multiset_of_nonempty, AffineBasis.tot, Finset.bind_def, Algebra.mem_top, AlgebraicGeometry.AffineSpace.toSpecMvPolyIntEquiv_symm_apply, Submodule.mem_sup', Filter.liminf_const_top, iSup_bool_eq, MeasureTheory.NullMeasurableSet.exists_isOpen_symmDiff_lt, List.maximum_cons, AlgebraicGeometry.Scheme.fromSpecStalk_toSpecΓ_assoc, MeasureTheory.exists_measure_symmDiff_lt_of_generateFrom_isSetRing, Set.Ioc_union_Ioc', Finset.le_sup'_iff, AlgebraicGeometry.AffineSpace.SpecIso_hom_appTop, sup_inf_inf_compl, List.foldr_max_of_ne_nil, MeasureTheory.hittingAfter_bot_le_iff, OrderHom.le_map_sup_fixedPoints, AlgebraicGeometry.LocallyRingedSpace.basicOpen_eq_bot_iff_forall_evaluation_eq_zero, mabs_le_max_mabs_mabs, instCommutativeMax, MeasureTheory.MemLp.sup, iSup_split, sdiff_le_iff', IsOpen.exists_subset_affineIndependent_span_eq_top, IsModularLattice.sup_inf_le_assoc_of_le, Sublattice.map_equiv_eq_comap_symm, SSet.iSup_subcomplexOfSimplex_prod_eq_top, AlgebraicGeometry.Scheme.Hom.preimage_bot, TopologicalSpace.Opens.mem_sup, LinearPMap.domain_supSpanSingleton, IntermediateField.coe_bot, inf_symmDiff_distrib_right, Submodule.mulMap_one_right_eq, OrdinalApprox.gfp_mem_range_gfpApprox, CompleteLattice.isCompactElement_finsetSup, CompleteBooleanAlgebra.himp_eq, sup_compl_le_himp, Ideal.sum_eq_sup, Subgroup.map_sup, Subalgebra.comap_map_eq, Function.support_max, Subalgebra.finrank_sup_eq_finrank_right_mul_finrank_of_free, Set.infs_sups_subset_right, AlgebraicGeometry.Scheme.zeroLocus_eq_univ_iff_subset_nilradical, List.max_prod_le, AlgebraicGeometry.Scheme.Opens.topIso_inv, Finset.Icc_min_max, abs_le_max_abs_abs, Set.image_symmDiff, Set.Ioc_union_Ioc_right, CategoryTheory.Sieve.mem_iff_pullback_eq_top, bot_sdiff, IntermediateField.lift_insepDegree_bot', ciSup_partialSups_eq', sdiff_symmDiff, CategoryTheory.Subfunctor.Subpresheaf.max_obj, AddCon.sup_def, Submodule.isOrtho_sup_right, NonUnitalAlgebra.coe_bot, Subsemiring.map_sup, Submonoid.comap_sup_map_of_injective, iInf_of_empty, sSup_eq_bot, inseparable_top, ClosedSubmodule.toSubmodule_sup, Submodule.fst_sup_snd, two_nsmul_sup_eq_add_add_abs_sub, TensorAlgebra.adjoin_range_ι, NonUnitalStarAlgebra.coe_bot, NonUnitalAlgebra.mem_sup_left, NonUnitalStarAlgebra.mem_top, FirstOrder.Language.Substructure.map_sup, codisjoint_bihimp_sup, Pi.symmDiff_apply, AlgHom.equalizer_eq_top, DualNumber.range_lift, IsCompl.bihimp_eq_bot, iSup_false, algebraicClosure.algebraicClosure_eq_bot, bihimp_bihimp_sup, iInf_sup_iInf, AffineSubspace.comap_bot, PUnit.bot_eq, Subgroup.map_eq_map_iff, max_neg_neg, BoundedLatticeHom.coe_comp_sup_hom', iInf_false, Cardinal.mul_le_max_of_aleph0_le_right, compl_inf, AlgebraicGeometry.Scheme.Hom.id_appTop, sup_sdiff_right_self, CategoryTheory.Presheaf.imageSieve_app, Set.Icc_min_max, Finset.sup_eq_union', max_le_max_left, AddSubgroup.mem_sup_left, symmDiff_compl_self, bot_lt_iSup, iInf_eq_top, IsGaloisGroup.fixingSubgroup_top, IsUpperModularLattice.covBy_sup_of_inf_covBy, Cardinal.sum_pow_le_max_aleph0, CategoryTheory.Presieve.isSheaf_bot, Con.sup_eq_conGen, FiniteGaloisIntermediateField.instIsGaloisSubtypeMemIntermediateFieldMax, MonotoneOn.max, LatticeHom.coe_withTopWithBot, AddSubmonoid.op_sup, MonoidAlgebra.cardinalMk_of_infinite, MeasurableSpace.generateFrom_empty, IsGaloisGroup.fixedPoints_top, RingCon.comap_bot, MeasureTheory.condLExp_bot', AlgebraicGeometry.Scheme.ideal_ker_le_ker_ΓSpecIso_inv_comp, Algebra.toSubsemiring_eq_top, IntermediateField.botEquiv_symm, inf_himp_bihimp, Subalgebra.op_bot, IsModularLattice.exists_disjoint_and_sup_eq, Set.Iio_union_Ioo, AddSubgroup.comap_map_eq, Finset.symmDiff_eq_union_iff, AddMonoidAlgebra.Monic.supDegree_mul, sdiff_sdiff_sup_sdiff', max_add_add_le_max_add_max, MeasureTheory.OuterMeasure.trim_top, Measurable.sup_of_right, IsLocalRing.closedPoint_mem_iff, AlgebraicGeometry.Scheme.isoSpec_inv_toSpecΓ, Filter.bliminf_sup_le_and, QuotientAddGroup.leftRel_eq_top, AddSubgroup.normal_add, Subsemiring.op_sup, MeasureTheory.measure_symmDiff_eq_top, Cardinal.mul_eq_max_of_aleph0_le_right, AEMeasurable.max, Finset.Nonempty.sup_eq_top_iff, MonomialOrder.degree_sub_le, IsNonarchimedean.apply_sum_le_sup_of_isNonarchimedean, Algebra.adjoin_singleton_algebraMap, RingCon.matrix_top, SSet.Subcomplex.range_eq_top, AlgHom.fieldRange_eq_map, IntermediateField.relfinrank_bot_right, Field.exists_primitive_element, cbiSup_eq_of_not_forall, isGalois_iff_isGalois_top, AlgebraicGeometry.isIso_ΓSpec_adjunction_unit_app_basicOpen, AlgebraicGeometry.isNoetherian_iff_of_finite_affine_openCover, Coheyting.boundary_top, AlgebraicGeometry.Scheme.ι_toIso_inv, symmDiff_symmDiff_self', Finset.Colex.toColex_lt_toColex_iff_max'_mem, Finset.compl_inf, Order.pred_injective, CategoryTheory.Subfunctor.range_toRange, UnitAddTorus.mFourierSubalgebra_closure_eq_top, InfiniteGalois.mem_bot_iff_fixed, Finset.lt_sup'_iff, Frm.Iso.mk_hom, instAssociativeMax, AddMonoidAlgebra.Monic.supDegree_mul_of_ne_zero_right, Algebra.toSubring_eq_top, lt_max_of_lt_left, Set.toFinset_symmDiff, AddCon.toSetoid_top, Finset.mem_sup, sup_iSup, ProbabilityTheory.condIndep_bot_left, LieSubalgebra.span_union, symmDiff_top, NumberField.adjoin_eq_top_of_infinitePlace_lt, Set.coe_projIcc, Subalgebra.rank_sup_eq_rank_left_mul_rank_of_free, Finset.isWF_sup, sup_inf_inf_sdiff, Cardinal.mk_finsupp_lift_of_infinite, Polynomial.IsSplittingField.splits_iff, sup_biInf_le_biInf_sup, AlgebraicGeometry.Scheme.IdealSheafData.equivOfIsAffine_apply, Partition.bot_notMem, isLeast_sdiff, SSet.Subcomplex.topIso_inv_app_coe, max_lt_max_left_iff, Submodule.coe_sup, himp_bot, bot_lt_affineSpan, ExpGrowth.expGrowthSup_add, ConditionallyCompleteLinearOrderedField.toZeroLEOneClass, TensorProduct.quotientTensorQuotientEquiv_symm_apply_mk_tmul, Subfield.map_sup, biUnion_range_succ_disjointed, LatticeHom.withTopWithBot_id, polynomialFunctions.starClosure_topologicalClosure, AddSubgroup.add_normal, Coheyting.hnot_boundary, AlgebraicGeometry.Scheme.IdealSheafData.equivOfIsAffine_symm_apply, Disjoint.sup_sdiff_cancel_left, CategoryTheory.GrothendieckTopology.trivial_covering, AddSubgroup.mem_sup_of_normal_left, hnot_symmDiff_self, AffineEquiv.span_eq_top_iff, AlgebraicGeometry.Scheme.SpecΓIdentity_hom_app, Set.indicator_symmDiff, Subgroup.mul_normal, AffineSubspace.direction_eq_top_iff_of_nonempty, BooleanAlgebra.sdiff_eq, Set.Ioo_inter_Ioi, StarSubalgebra.bot_toSubalgebra, min_le_max_of_mul_le_mul, IsCompl.symmDiff_eq_top, Finset.Colex.le_iff_max'_mem, AlgebraicGeometry.Scheme.IdealSheafData.support_mul, symmDiff_right_comm, IsCompl.le_sup_right_iff_inf_left_le, Mathlib.Tactic.Bound.lt_max_of_lt_left_or_lt_right, Subfield.splits_bot, ConditionallyCompleteLinearOrder.compare_eq_compareOfLessAndEq, List.le_max_of_le', induced_const, IsGreatest.insert, Algebra.toSubring_bot, MvPolynomial.degreeOf_sum_le, inf_eq_sup, max_inv_one, affineSpan_singleton_union_vadd_eq_top_of_span_eq_top, Finset.inf_sup_distrib_right, MvPolynomial.supDegree_esymmAlgHomMonomial, integralClosure_eq_top_iff, sup_le_inf, ofDual_min, interior_convexHull_nonempty_iff_affineSpan_eq_top, Finset.max_sum_le, Subfield.cardinalMk_closure_le_max, isGLB_Ioi, Finset.compl_sup, CompleteSublattice.top_mem, Subgroup.coe_mul_of_left_le_normalizer_right, AlgebraicGeometry.Scheme.isoSpec_inv_preimage_zeroLocus, Subalgebra.LinearDisjoint.inf_eq_bot_of_commute, Cardinal.mul_eq_left_iff, NumberField.isTotallyReal_sup, Coheyting.hnot_eq_top_iff_exists_boundary, Algebra.map_sup, TopologicalSpace.eq_top_iff_forall_inseparable, sSup_empty, AlgebraicGeometry.ProjectiveSpectrum.Proj.toOpen_toSpec_val_c_app_assoc, AlgebraicGeometry.PresheafedSpace.Γ_obj_op, Sym2.sortEquiv_apply_coe, IntermediateField.adjoin_zero, AddSubmonoid.sup_mul, Submonoid.map_sup_comap_of_surjective, sInf_sup_le_iInf_sup, TopCat.Sheaf.interUnionPullbackCone_fst, IntermediateField.adjoin_univ, Set.symmDiff_def, Disjoint.le_symmDiff_sup_symmDiff_right, AlgebraicGeometry.Scheme.Modules.toOpen_fromTildeΓ_app, TopCat.GlueData.MkCore.V_id, AffineSubspace.linear_topEquiv, Subalgebra.algebra_isAlgebraic_bot_right, Submonoid.mem_sup, UniformSpace.toTopologicalSpace_top, MvPolynomial.totalDegree_eq, iSup_partialSups_eq, isOpen_sup, Sylow.normalizer_sup_eq_top', NonUnitalAlgebra.mem_sup_right, CategoryTheory.Subfunctor.Subpresheaf.preimage_eq_top_iff, Subalgebra.unop_sup, Subalgebra.comm_trans_rTensorBot, AffineSubspace.not_wSameSide_bot, inf_left_le_sup_left, AlgebraicGeometry.Scheme.bot_mem_precoverage, symmDiff_top', CategoryTheory.Sieve.top_apply, Subalgebra.algebra_isAlgebraic_bot_left_iff, LinearMap.range_domRestrict_eq_range_iff, Algebra.EssFiniteType.adjoin_mem_finset, lt_inf_iff, AlgebraicGeometry.Scheme.Hom.preimage_top, sSup_insert, TopologicalSpace.Closeds.instContinuousSup, Polynomial.IsSplittingField.adjoin_rootSet, AddCon.toSetoid_bot, Submodule.comap_map_sup_of_comap_le, HeytAlg.Iso.mk_inv, AlgebraicGeometry.Scheme.isoSpec_hom, AlgebraicGeometry.Scheme.ι_toIso_inv_assoc, NNRat.coe_max, LinearMap.span_singleton_sup_orthogonal_eq_top, Projectivization.Subspace.span_sup, Multiset.support_sum_subset, MvPolynomial.degrees_def, MeasureTheory.measureReal_symmDiff_eq, Left.min_le_max_of_add_le_add, symmDiff_of_ge, max_inv_inv', TopologicalSpace.Closeds.coe_eq_empty, Algebraic.cardinalMk_le_max, FirstOrder.Language.Substructure.map_sup_comap_of_surjective, AlgebraicGeometry.Proj.basicOpenToSpec_app_top, NonUnitalSubalgebra.prod_top, max_bot_left, TopologicalSpace.NoetherianSpace.exists_finset_irreducible, UniformContinuous.sup_closeds, AlgebraicGeometry.Scheme.Hom.image_top_eq_opensRange, ConditionallyCompleteLinearOrderedField.toPosMulStrictMono, bihimp_himp_left, symmDiff_left_inj, NonUnitalSubsemiring.closure_union, negPart_max, disjoint_symmDiff_inf, inf_sup_le, oneLePart_max, Submonoid.mrange_inl_sup_mrange_inr, Finset.Ico_diff_Ico_left, MeasurableSpace.map_const, sSup_union, AddSubsemigroup.map_sup, DistribLattice.le_sup_inf, top_symmDiff, Submonoid.prod_bot_sup_bot_prod, NonUnitalStarAlgebra.coe_top, symmDiff_assoc, AlgebraicGeometry.Scheme.toSpecΓ_naturality_assoc, Finset.support_sum_subset, max_mul_min, AddSubmonoid.smul_sup, sSupHom.coe_bot, Ideal.smul_sup, Nimber.toOrdinal_max, Sublocale.top_mem, AlgebraicGeometry.SurjectiveOnStalks.iff_of_isAffine, IsModularLattice.exists_inf_eq_and_sup_eq, AlgebraicGeometry.SpecMap_ΓSpecIso_hom, abs_eq_max_neg, Subalgebra.center_eq_top, Algebra.IsAlgebraic.cardinalMk_le_max, CompleteBooleanAlgebra.sdiff_eq, NumberField.mixedEmbedding.exists_primitive_element_lt_of_isComplex, IsIntegrallyClosedIn.integralClosure_eq_bot, hasCardinalLT_subtype_max, SSet.iSup_skeleton, FirstOrder.Language.Substructure.comap_sup_map_of_injective, integralClosure_idem, Subgroup.normal_subgroupOf_sup_of_le_normalizer, Tropical.untrop_max, PrimeSpectrum.iSup_basicOpen_eq_top_iff, IsNormalClosure.adjoin_rootSet, sdiff_sup, AddMonoidAlgebra.supDegree_mem_range, instIsAbelianGaloisSubtypeMemIntermediateFieldBot, AffineBasis.tot', Submodule.neg_sup, Finset.sup_set_eq_biUnion, LatticeHom.withTopWithBot_comp, Submodule.sup_eq_range, Subring.op_sup, CategoryTheory.Sieve.functorPullback_bot, himp_top, sub_inf, TopologicalSpace.Opens.isOpenEmbedding_obj_top, Submodule.sub_mem_sup, sup_eq_mul_oneLePart_div, AlgebraicGeometry.LocallyRingedSpace.Γ_obj_op, Algebra.mem_bot, AlgebraicGeometry.AffineSpace.isoOfIsAffine_inv_appTop_coord, Fin.top_eq_last, Subsemigroup.mul_mem_sup, Algebra.adjoin_union, sdiff_symmDiff', AddMonoid.Coprod.mrange_lift, AlgebraicGeometry.AffineSpace.isoOfIsAffine_inv_over_assoc, biSup_symmDiff_biSup_le, himp_eq, CategoryTheory.Sieve.generate_bot, Ideal.mem_sup_left, max_mul_of_nonneg, Valuation.map_add_of_distinct_val, SSet.Subcomplex.eq_top_iff_of_hasDimensionLT, AlgebraicGeometry.Scheme.isoSpec_hom_naturality, RingCon.sup_def, CategoryTheory.Subfunctor.max_obj, iInf₂_eq_top, induced_topology_pure, lipschitzWith_sup_right, AlgebraicGeometry.Scheme.toSpecΓ_isoSpec_inv_assoc, FirstOrder.Language.Substructure.small_bot, Set.Ioc_disjoint_Ioc, CompletelyDistribLattice.sdiff_le_iff, le_hnot_inf_hnot, Valuation.map_add, WellFoundedGT.finite_ne_bot_of_iSupIndep, isBoundedUnder_le_finset_sup', essInf_measure_zero, AddSubgroup.relIndex_map_map, Finset.Colex.toColex_le_toColex_iff_max'_mem, lt_max_of_sq_lt_mul, Polynomial.SplittingFieldAux.adjoin_rootSet, Finset.powerset_sups_powerset_self, Finset.Ico_union_Ico', openSegment_eq_Ioo', AffineSubspace.direction_affineSpan_insert, RingCon.subsingleton_quotient, MonomialOrder.degree_add_le, Finset.sup_univ_eq_ciSup, Multiset.sup_powerset_len, AffineSubspace.vectorSpan_union_of_mem_of_mem, Finset.smul_finset_symmDiff, Set.mem_symmDiff, beattySeq'_symmDiff_beattySeq_pos, CategoryTheory.Sieve.generate_top, IsAddFoelner.tendsto_meas_vadd_symmDiff_vadd, min_le_max, StarSubalgebra.mem_bot, AddMonoidAlgebra.supDegree_mul, SSet.Subcomplex.topIso_inv_ι, AlgebraicGeometry.Scheme.toSpecΓ_naturality, AlgebraicGeometry.Scheme.Hom.quasiFiniteLocus_eq_top, Monoid.Coprod.mrange_eq, IntermediateField.fixingSubgroup_top, CauSeq.coe_sup, AffineSubspace.coe_eq_univ_iff, BooleanSubalgebra.sup_mem, CategoryTheory.Sieve.equalizer_self, max_div_min_eq_mabs, IntermediateField.bot_toSubalgebra, TopologicalSpace.Opens.mk_univ, MonoidHom.noncommCoprod_range, MeasureTheory.abs_measureReal_sub_le_measureReal_symmDiff', top_bihimp, Algebra.toSubmodule_bot, Sym2.inf_eq_inf_and_sup_eq_sup, compl_symmDiff, AlgebraicGeometry.LocallyRingedSpace.Γ_Spec_left_triangle, fn_min_add_fn_max, Algebra.map_bot, Order.Coframe.MinimalAxioms.iInf_sup_eq, Ordinal.card_omega0_opow, Subfield.mem_bot_iff_pow_eq_self, LatticeHom.withTopWithBot'_toFun, List.max_le_of_forall_le, AlgebraicGeometry.RingedSpace.mem_top_basicOpen, Subfield.isTotallyReal_bot, Submodule.smul_sup', HahnEmbedding.ArchimedeanStrata.ball_sup_stratum_eq, compl_sup_compl_le, min_lt_max_of_add_lt_add, PMF.toOuterMeasure_caratheodory, sup_strictMonoOn_Icc_inf, disjoint_sup_right, ofBoolRing_add, Fin.rev_top, IntermediateField.sup_toSubalgebra_of_isAlgebraic_left, IntermediateField.relfinrank_top_right, abs_sub_sup_add_abs_sub_inf, Subrepresentation.toSubmodule_sup, JordanHolderLattice.sup_eq_of_isMaximal, IndiscreteTopology.eq_top, IntermediateField.restrictScalars_sup, sup_Ioc_disjointed_of_monotone, Submodule.finiteDimensional_finset_sup, Finset.seq_def, Fintype.sup_disjointed, Algebra.adjoin_singleton_zero, Finset.max_pair, liminf_eq_top, UV.compress_of_disjoint_of_le', Submodule.submoduleOf_sup_of_le, Finset.inf_sup, IsFoelner.tendsto_meas_smul_symmDiff, AlgebraicGeometry.Scheme.Hom.toPartialMap_domain, OrderEmbedding.coe_birkhoffFinset, CategoryTheory.Subfunctor.max_min, Algebra.coe_bot, CompleteLinearOrder.top_sdiff, Setoid.injective_iff_ker_bot, BicartSq.max_eq, Submodule.toConvexCone_top, MeasureTheory.condLExp_bot, Dynamics.coverEntropyEntourage_union, sSupHom.bot_apply, Order.pred_le_iff_eq_or_le, AlgebraicGeometry.IsAffineOpen.isoSpec_inv, Finset.inf_sup_distrib_left, MeasurableSpace.generateFrom_sup_generateFrom, inv_sup, AlgebraicGeometry.Scheme.Γ_obj, CategoryTheory.Presieve.isSheafFor_top_sieve, IsCompl.sup_inf, symmDiff_fst, Finset.sups_infs_subset_left, OrderIso.supIrredLowerSet_symm_apply, AlgebraicGeometry.isLocallyNoetherian_iff_of_affine_openCover, Submonoid.sup_eq_closure_mul, Finset.sup'_inf_distrib_right, Monotone.map_sup, SSet.hasDimensionLT_subcomplex_top_iff, IntermediateField.restrictScalars_top, SSet.Subcomplex.instSubsingletonHomToSSetBot, abs_max_sub_max_le_abs, EuclideanGeometry.Sphere.orthRadius_center, sup_lt_of_lt_sdiff_left, DistLat.Iso.mk_inv, TopologicalSpace.isOpen_top_iff, MeasureTheory.OuterMeasure.trim_sup, Monotone.max, AlgebraicGeometry.IsLocallyArtinian.isArtinianRing_of_isAffine, AlgebraicGeometry.StructureSheaf.toPushforwardStalkAlgHom_apply, AlgebraicGeometry.Scheme.preimage_basicOpen_top, Fin.top_eq_zero, Submonoid.mem_sup_left, MvPolynomial.adjoin_range_X, Set.definable_finset_sup, AddSubgroup.relIndex_sup_left, max_lt_max_right_iff, AlgebraicGeometry.Scheme.ΓSpecIso_inv, MeasureTheory.IsSetSemiring.isSetRing_supClosure, NonUnitalAlgebra.range_id, IntermediateField.mem_top, ENat.lift_one, bot_symmDiff, Submodule.finiteDimensional_sup, AlgebraicGeometry.Scheme.isoSpec_hom_naturality_assoc, FreeAlgebra.cardinalMk_le_max, AlgebraicGeometry.Scheme.isoSpec_inv_image_zeroLocus, LinearMap.map_coprod_prod, Cardinal.aleph_add_aleph, Field.primitive_element_iff_algHom_eq_of_eval', sdiff_self, CategoryTheory.GrothendieckTopology.top_mem, IsDedekindDomain.integer_empty, AlgebraicGeometry.ΓSpec.locallyRingedSpaceAdjunction_counit_app', AffineSubspace.not_sSameSide_bot, Subgroup.FG.finset_sup, Order.Ideal.coe_sup_eq, adjoin_eq_top_of_conductor_eq_top, MeasureTheory.Measure.MeasureDense.fin_meas_approx, Finset.infs_sups_subset_right, Finset.inf'_sup_distrib_right, MeasureTheory.edist_indicatorConstLp_eq_enorm, MonoidAlgebra.cardinalMk_lift_of_infinite, symmDiff_comm, disjoint_partialSups_right, Multiset.finset_sum_eq_sup_iff_disjoint, UV.sup_sdiff_mem_of_mem_compression_of_notMem, sup_lt_sup_of_lt_of_inf_le_inf, Finset.inf_himp_right, Subalgebra.eq_bot_of_finrank_one, AlgebraicGeometry.Scheme.Opens.ι_image_basicOpen_topIso_inv, Set.Iio_union_Ico, IntermediateField.relrank_top_right, AddSubgroup.add_mem_sup, AlgebraicGeometry.SpecMap_ΓSpecIso_inv_toSpecΓ, Subalgebra.LinearDisjoint.rank_sup_of_free, MeasureTheory.AddContent.supClosure_apply_finpartition, AffineBasis.affineSpan_eq_top_of_toMatrix_left_inv, Ordinal.iSup_sum, Ideal.mul_left_self_sup, StarSubalgebra.mul_mem_sup, symmDiff_sdiff_right, MeasureTheory.hittingBtwn_bot_le_iff, AlgebraicGeometry.Scheme.toSpecΓ_preimage_zeroLocus, max_add_add_left, continuous_bot, AddSubmonoid.closure_union, Subring.comap_map_eq, sup_eq_iff_inf_eq, Algebra.coe_top, IntermediateField.LinearDisjoint.bot_left, TopologicalSpace.Opens.inclusion'_top_functor, FirstOrder.Language.Substructure.cg_bot, IntermediateField.isTotallyReal_bot, MeasureTheory.Measure.mkMetric_top, Multiset.toFinsupp_union, sup_eq_iSup, WType.cardinalMk_le_max_aleph0_of_finite', SSet.Subcomplex.eq_top_iff_contains_nonDegenerate, Finset.sup_inf_distrib_left, max_top_right, AlgebraicGeometry.Scheme.fromSpecStalk_appTop, MeasureTheory.IsSetSemiring.mem_supClosure_iff, ConditionallyCompleteLinearOrderedField.toIsOrderedCancelAddMonoid, Algebra.TensorProduct.map_ker, Finset.max_eq_sup_coe, Subalgebra.unop_top, Submodule.map_sup, compl_inf_eq_bot, le_iff_eq_sup_sdiff, AlgebraicGeometry.PresheafedSpace.Γ_map_op, Subalgebra.lTensorBot_one_tmul, ConvexOn.le_max_of_mem_Icc, Filter.Tendsto.max, Projectivization.Subspace.span_empty, Order.pred_top_le_iff, Multiset.mem_sup_map_support_iff, Finset.max'_pair, max_one_div_max_inv_one_eq_self, max_sub_sub_left, symmDiff_left_involutive, Dynamics.coverEntropy_union, limsup_eq_bot, AlgebraicGeometry.Scheme.id_appTop, NonUnitalAlgebra.mul_mem_sup, sSup_compact_eq_top, Subalgebra.mulMap_bot_left_eq, symmDiff_sdiff_left, Order.Coframe.MinimalAxioms.sup_iInf_eq, AlgebraicGeometry.Scheme.Opens.toSpecΓ_appTop_assoc, sup_add, FirstOrder.Language.card_functions_sum_skolem₁_le, Finset.vadd_finset_symmDiff, sup_biSup, PSet.rank_insert, fixedPoints_submonoid_sup, ValuationClass.map_add_le_max, LinearMap.comap_leq_ker_subToSupQuotient, Set.Ioo_min_max, sup_sdiff_cancel_right, toDual_max, BoundedLatticeHom.coe_comp_lattice_hom', AffineSubspace.bot_coe, symmDiff_symmDiff_right, Convex.interior_nonempty_iff_affineSpan_eq_top, Submodule.map_mkQ_eq_top, Subring.closure_union, IntermediateField.instFiniteSubtypeMemBot, IntermediateField.isCyclotomicExtension_lcm_sup, max_add_min, Finset.le_prod_max_one, Polynomial.adjoin_rootSet_eq_range, Submodule.eq_top_of_disjoint, AffineSubspace.parallel_bot_iff_eq_bot, Subsemigroup.map_sup, CategoryTheory.Presheaf.equalizerSieve_self_eq_top, BoolAlg.hasForgetToHeytAlg_forget₂_map, IntermediateField.sup_toSubalgebra_of_isAlgebraic, SimpleGraph.chromaticNumber_sum, max_min_distrib_left, essSup_const_bot, not_bddBelow_iff, iInf_sup_of_monotone, AlgebraicGeometry.Scheme.fromSpecStalk_toSpecΓ, AddSubmonoid.neg_sup, AlgebraicGeometry.Scheme.ker_toSpecΓ, TopCat.Presheaf.map_germ_eq_Γgerm, Algebra.top_toSubmodule, Set.coe_projIci, IsLocalMinOn.max, max_div_min_eq_mabs', MeasureTheory.measure_symmDiff_le, fn_max_add_fn_min, SSet.Subcomplex.preimage_range, AddSubsemigroup.comap_sup_map_of_injective, AlgebraicGeometry.Scheme.ker_of_isAffine, Set.Ico_inter_Ico, Subalgebra.fg_of_submodule_fg, Subsemiring.unop_sup, AddSubsemigroup.mem_sup_left, AlgebraicGeometry.IsAffineOpen.algebraMap_Spec_obj, AlgebraicGeometry.isBasis_basicOpen, max_zero_add_max_neg_zero_eq_abs_self, Finset.sup'_pow, Filter.limsup_sup_filter, Sublattice.supClosed, inf_le_iff, CompleteSublattice.bot_mem, AlgebraicGeometry.Scheme.Γevaluation_naturality_apply, Coheyting.hnot_hnot_sup_boundary, FunctionField.InftyValuation.map_add_le_max', AddMonoidAlgebra.cardinalMk_of_infinite', CliffordAlgebra.adjoin_range_ι, Polynomial.natDegree_sum_eq_of_disjoint, Submonoid.smul_sup, AlgebraicGeometry.Flat.flat_and_surjective_iff_faithfullyFlat_of_isAffine, CompleteLattice.isCompactElement_iff_exists_le_iSup_of_le_iSup, MeasureTheory.dense_of_generateFrom_isSetSemiring, AffineSubspace.span_union, supPrime_iff_not_isMin, Cardinal.mul_eq_max, List.le_max_of_le, Finset.sup'_lt_iff, LinearMap.quotientInfEquivSupQuotient_apply_mk, AlgebraicGeometry.LocallyRingedSpace.coe_toΓSpecSheafedSpace_hom_base_hom_apply_asIdeal, NatOrdinal.toOrdinal_max, OrderEmbedding.birkhoffSet_inf, Filter.Tendsto.max_right, smul_max_of_nonneg, AddSubgroup.mem_sup', Polynomial.Splits.adjoin_rootSet_eq_range, Cardinal.mk_freeMonoid, Set.sup_eq_union, Cardinal.mk_bounded_set_le, MeasureTheory.preVariation.Finset.sup_measurableSetSubtype_eq_biUnion, IntermediateField.finrank_eq_one_iff, Setoid.top_def, AlgebraicGeometry.isIntegral_appTop_of_universallyClosed, IntermediateField.lift_top, min_top_left, iSup_eq_top, Finset.subset_range_sup_succ, AlgebraicGeometry.ΓSpec.adjunction_counit_app, IntermediateField.eq_bot_of_isAlgClosed_of_isAlgebraic, inf_add_sup, Finset.disjSups_left_comm, MeasureTheory.measure_neg_vadd_symmDiff, AlgebraicGeometry.tilde.isoTop_hom, CategoryTheory.Subfunctor.range_eq_top, borel_eq_top_of_discrete, IntermediateField.insepDegree_bot', AddSubsemigroup.unop_sup, Lat.Iso.mk_inv, Subgroup.comap_sup_eq, biSup_ge_eq_sup, Nat.cast_finsetSup', CoheytingHomClass.map_top, symmDiff_right_inj, Finset.fold_max_add, IntermediateField.fg_sup, Set.Iic_union_Ioc, Submonoid.FG.finset_sup, AlgebraicGeometry.Scheme.Opens.toSpecΓ_appTop, MeasurableSpace.cardinal_generateMeasurableRec_le, Filter.tendsto_nhds_max_left, infIccOrderIsoIccSup_apply_coe, Finset.uIcc_subset_uIcc_iff_le', CategoryTheory.Subfunctor.Subpresheaf.image_top, sup_eq_sdiff_sup_sdiff_sup_inf, smul_min_of_nonpos, toBoolAlg_add, Finset.Ico_inter_Ico, Finset.uIcc_subset_uIcc_iff_le, Algebra.sup_toSubsemiring, Order.pred_le_pred_iff, PrimeSpectrum.basicOpen_zero, AlgebraicGeometry.ProjectiveSpectrum.Proj.toStalk_stalkMap_toSpec_assoc, LowerSet.supIrred_iff_of_finite, GradedAlgebra.exists_finset_adjoin_eq_top_and_homogeneous, AddSubgroup.coe_add_of_left_le_normalizer_right, AlgebraicGeometry.Γ_restrict_isLocalization, IntermediateField.restrictScalars_eq_top_iff, Set.Iio_union_Ioo', CategoryTheory.GrothendieckTopology.bot_covers, beattySeq_symmDiff_beattySeq'_pos, AffineSubspace.smul_bot, Irrational.beattySeq_symmDiff_beattySeq_pos, isDenseEmbedding_pure, Set.Ioc_inter_Ioo_of_right_le, TopologicalSpace.Opens.coe_eq_empty, CategoryTheory.top_apply, AlgebraicGeometry.ProjectiveSpectrum.Proj.toStalk_stalkMap_toSpec, Subalgebra.mem_starClosure, Coheyting.boundary_sup_le, AddSubgroup.map_le_map_iff, NonUnitalAlgebra.toSubmodule_bot, Nat.cast_max, Complementeds.mk_sup_mk, Set.union_symmDiff_subset, IsDedekindDomain.HeightOneSpectrum.intValuation.map_add_le_max', BoundedLatticeHom.coe_comp_sup_hom, iSup_split_single, Subalgebra.finrank_right_dvd_finrank_sup_of_free, AlgebraicGeometry.ΓSpecIso_obj_hom, IsModularLattice.inf_sup_inf_assoc, NumberField.Units.dirichletUnitTheorem.map_logEmbedding_sup_torsion, CategoryTheory.GrothendieckTopology.Cover.preOneHypercover_sieve₁, sup_eq_and_inf_eq_iff, sup_hnot_self, disjointed_add_one, WType.cardinalMk_le_max_aleph0_of_finite, Finset.SupIndep.disjoint_sup_sup, ConvexOn.le_on_segment, AlgebraicGeometry.Spec.germ_stalkMapIso_hom_assoc, Order.pred_lt_iff_eq_or_lt, PrimeSpectrum.iInf_localization_eq_bot, AlgebraicGeometry.Scheme.Hom.preimage_basicOpen_top, Subalgebra.mul_toSubmodule, Finset.symmDiff_nonempty, IntermediateField.bot_eq_top_of_finrank_adjoin_eq_one, Finset.disjoint_sup_left, ofBoolAlg_sup, Set.sups_infs_subset_left, Setoid.mk_eq_top, MeasureTheory.OuterMeasure.comap_top, Ideal.mul_sup, TopCat.Sheaf.objSupIsoProdEqLocus_hom_fst, CategoryTheory.Sieve.overEquiv_top, ProbabilityTheory.iIndep_comap_mem_iff, IntermediateField.botContinuousSMul, quasiconvexOn_iff_le_max, Field.exists_primitive_element_of_finite_bot, Polynomial.sup_aeval_range_eq_top_of_isCoprime, CategoryTheory.GrothendieckTopology.close_eq_top_iff_mem, TopologicalSpace.Opens.functor_obj_map_obj, sup_inf_right, Subalgebra.unop_bot, Valuation.map_sub, Finset.sup'_eq_csSup_image, AffineSubspace.parallel_iff_direction_eq_and_eq_bot_iff_eq_bot, BoundedLatticeHom.coe_toSupBotHom, CategoryTheory.Sieve.arrows_eq_top_iff, infIooOrderIsoIooSup_symm_apply_coe, supIrred_iff_not_isMin, sup_eq_half_smul_add_add_abs_sub', AddSubgroup.index_map, Rat.cast_max, symmDiff_snd, Disjoint.symmDiff_eq_sup, AlgebraicGeometry.exists_appTop_π_eq_of_isAffine_of_isLimit, Cardinal.mk_list_eq_max, IsSemisimpleModule.sup, Setoid.sup_eq_eqvGen, Set.Icc_inter_Icc, WithZero.le_max_iff, segment_eq_Icc', NonUnitalSubring.map_sup, CategoryTheory.Sieve.arrows_top, Frm.Iso.mk_inv, QuotientAddGroup.rightRel_eq_top, Finsupp.supported_union, EReal.min_neg_neg, AlgebraicGeometry.Scheme.OpenCover.iSup_opensRange, AntitoneOn.map_min, Subgroup.relIndex_map_map, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.image_preimage_is_empty, AddMonoid.Coprod.range_eq, Set.uIcc_subset_uIcc_iff_le', Set.Ioo_inter_Ioc_of_left_le, Polynomial.sup_ker_aeval_eq_ker_aeval_mul_of_coprime, AffineSubspace.mem_top, Multiset.max_sum_le, max_idem, Algebra.bijective_algebraMap_iff, min_div_div_left', TopologicalSpace.Closeds.lipschitz_sup, Subalgebra.topEquiv_apply, BooleanAlgebra.inf_compl_le_bot, Cardinal.mk_freeAddGroup, CategoryTheory.topologyOfClosureOperator_sieves, Set.Iic.complementedLattice_iff, hnot_top, inf_le_sup, inf_left_le_sup_right, AddSubmonoid.sup_eq_range, Field.exists_primitive_element_of_finite_top, sup_eq_half_smul_add_add_abs_sub, IntermediateField.adjoin_simple_eq_top_iff_of_isAlgebraic, continuous_top, AlgebraicGeometry.Scheme.Γevaluation_naturality_assoc, mabs_div_sup_mul_mabs_div_inf, LatticeHom.withBot_toFun, essInf_const_top, Submodule.mul_sup, Disjoint.sup_left, le_sup_sdiff, AddSubgroup.op_sup, AlgebraicGeometry.Scheme.IdealSheafData.coe_support_ofIdealTop, Order.Coframe.MinimalAxioms.sup_iInf₂_eq, MonomialOrder.degree_sum_le, SSet.instHasDimensionLTToSSetBotSubcomplex, Max.left_comm, himp_eq_top_iff, CategoryTheory.MorphismProperty.bot_mem_precoverage, LowerSemicontinuousAt.sup, IntermediateField.rank_adjoin_eq_one_iff, CategoryTheory.ObjectProperty.instEssentiallySmallMax, Finset.Ioc_inter_Ioc, Finset.max'_eq_sup', Submonoid.map_sup, Set.Ioc_diff_Iic, WeierstrassCurve.Affine.CoordinateRing.degree_norm_smul_basis, LatticeHom.withTop'_toFun, mabs_div_le_max_div, partialSups_disjointed, sdiff_sdiff_right, AlgebraicGeometry.ΓSpec.toOpen_comp_locallyRingedSpaceAdjunction_homEquiv_app, AddGroupTopology.toTopologicalSpace_top, sSup_diff_singleton_bot, LinearMap.sup_range_inl_inr, AlgebraicGeometry.Scheme.Opens.toSpecΓ_top, LatticeHom.map_inf', Cardinal.mk_finsupp_nat, TopologicalSpace.Closeds.coe_bot, IntermediateField.adjoin_one, IntermediateField.rank_top, StrictConvexOn.lt_on_openSegment, CompleteDistribLattice.top_sdiff, CategoryTheory.sheafBotEquivalence_inverse_map_val, LinearMap.span_singleton_sup_ker_eq_top, OrdinalApprox.lfpApprox_ord_eq_lfp, Finset.smul_finset_symmDiff₀, CategoryTheory.Sieve.generate_of_singleton_isSplitEpi, AlgebraicGeometry.AffineSpace.SpecIso_inv_appTop_coord, CategoryTheory.Sieve.functorPullback_top, max_eq_top, Topology.IsGeneratedBy.sup, Valuation.map_add_le_max', AlgebraicGeometry.germ_stalkClosedPointIso_hom_assoc, IsModularLattice.sup_inf_sup_assoc, Filter.blimsup_sup_not, AlgebraicGeometry.Scheme.IdealSheafData.support_eq_top_iff, TopologicalSpace.Opens.coe_finset_sup, NonUnitalAlgebra.top_toNonUnitalSubsemiring, Monotone.map_max, MeasureTheory.IsSetSemiring.diff_mem_supClosure, Quotient.subsingleton_iff, toBoolAlg_add_add_mul, Setoid.bot_def, inf_eq_and_sup_eq_iff, CategoryTheory.Subfunctor.Subpresheaf.bot_obj, Subfield.bot_eq_of_zMod_algebra, Set.Finite.toFinset_symmDiff, PowerBasis.adjoin_gen_eq_top, max_div_div_left', BoundedLatticeHom.map_top', StarSubalgebra.eq_top_iff, AddMonoidAlgebra.cardinalMk_lift_of_infinite, Ideal.sup_mul_right_self, sup_sdiff_inf, IsLocalMin.max, le_sInf_inter, IntermediateField.adjoin_root_eq_top, AffineSubspace.smul_top, ConvexCone.toPointedCone_top, Subgroup.mem_sup_of_normal_right, Submodule.comap_sup_map_of_injective, Int.cast_max, MeasurableSpace.measurableSet_bot_iff, Subfield.map_bot, iInf_ne_top_subtype, CategoryTheory.GrothendieckTopology.discrete_eq_top, inf_sdiff_sup_left, TopCat.Presheaf.map_germ_eq_Γgerm_assoc, Subalgebra.mulMap'_surjective, Submodule.comm_trans_rTensorOne, NonUnitalStarAlgebra.top_toNonUnitalSubalgebra, AddSubgroup.comap_sup_eq_of_le_range, partialSups_eq_sUnion_image, CoheytingHom.map_top', MeasureTheory.OuterMeasure.zero_caratheodory, AddSubgroup.closure_add_le, TopCat.Sheaf.interUnionPullbackConeLift_right, BicartSq.sup_eq, ConvexCone.mem_top, inf_sup_self, AddSubsemigroup.op_sup, sup_sdiff_right, symmDiff_eq_right, Subgroup.relIndex_sup_right, min_max_distrib_right, CategoryTheory.sheafBotEquivalence_unitIso, fn_min_mul_fn_max, compl_sup_le_himp, Tropical.trop_sup_def, symmDiff_eq, MeasureTheory.Content.innerContent_bot, MeasurableSpace.comap_prodMk, IntermediateField.extendScalars_self, IsMinOn.max, MeasureTheory.le_measure_symmDiff, max_le_iff, MeasureTheory.OuterMeasure.top_caratheodory, AlgebraicGeometry.StructureSheaf.globalSectionsIso_hom, Polynomial.degree_sum_le, symmDiff_eq_sup_sdiff_inf, IntermediateField.finrank_top, Finset.mem_sup_support_iff, Set.mulIndicator_symmDiff, Finset.sup_eq_top_iff, hnot_bot, max_eq_left_iff, IntermediateField.restrictScalars_adjoin_eq_sup, le_compl_self, CategoryTheory.ObjectProperty.instIsClosedUnderIsomorphismsMax, max_lt_iff, AlgebraicGeometry.Scheme.basicOpen_add_le, iSup_dite, NonUnitalStarAlgebra.range_eq_top, IsDedekindDomain.HeightOneSpectrum.intValuation.le_max_iff_min_le, nilpotencyClass_pi, csSup_empty, IsPGroup.to_sup_of_normal_left', MvPolynomial.weightedTotalDegree_eq_zero_iff, separableClosure.eq_top_iff, MeasureTheory.measure_symmDiff_inv_smul, ProbabilityTheory.iIndepSet.iIndep_comap_mem, Algebra.mem_sup_left, LinearMap.quotientInfEquivSupQuotient_injective, Algebra.top_toSubring, sup_inf_left, Subgroup.mem_sup_left, abs_max_sub_max_le_max, posPart_def, AlgebraicGeometry.ΓSpec.left_triangle, CategoryTheory.Subfunctor.eq_top_iff_isIso, Finset.sup_inf_distrib_right, AlgebraicGeometry.Scheme.Modules.toOpen_fromTildeΓ_app_assoc, CategoryTheory.sheafBotEquivalence_inverse_obj_val, AlgebraicGeometry.AffineSpace.comp_homOfVector, IntermediateField.top_toSubalgebra, Subfield.roots_X_pow_char_sub_X_bot, IntermediateField.cardinalMk_adjoin_le, Submodule.dualAnnihilator_sup_eq, Submonoid.inv_sup, Subsemigroup.closure_union, untrop_sum, MeasureTheory.Lp.coeFn_sup, MeasureTheory.OuterMeasure.sup_apply, CompleteBooleanAlgebra.le_sup_inf, Subsemigroup.unop_sup, Subgroup.toSubmonoid_zpowers, IntermediateField.relrank_top_left, Subalgebra.finrank_left_dvd_finrank_sup_of_free, sup_inf_self, Cardinal.mk_freeAddMonoid, Submodule.lTensorOne'_tmul, Subsemigroup.comap_sup_map_of_injective, NumberField.Units.regOfFamily_div_regulator, AlgebraicGeometry.Scheme.instIsOpenImmersionToSpecΓOfIsQuasiAffine, CategoryTheory.ObjectProperty.prop_sup_iff, AlgebraicGeometry.Scheme.homOfLE_appTop, Order.Frame.le_himp_iff, Submodule.rTensorOne'_tmul_one, AddSubmonoid.mul_sup, CategoryTheory.MorphismProperty.HasCardinalLT.sup, WithTop.ge_of_forall_gt_iff_ge, IsGaloisGroup.fixedPoints_bot, Finset.symmDiff_subset_sdiff, AlgebraicGeometry.Scheme.isoSpec_inv_naturality_assoc, Submodule.dualCoannihilator_sup_eq, QuotientAddGroup.comap_map_mk', Antitone.map_max, AlgebraicGeometry.IsAffineOpen.fromSpec_app_self, OrderIso.supIrredLowerSet_apply, nhds_top, Con.toSetoid_eq_bot, BooleanSubalgebra.mk_sup_mk, MeasureTheory.condExp_bot, Submodule.rTensorOne'_tmul, Finset.union_mem_sups, TopologicalSpace.Opens.mem_bot, max_add_add_right, AlgebraicGeometry.PresheafedSpace.restrictTopIso_hom, LowerSemicontinuousWithinAt.sup, Cardinal.mul_le_max_of_aleph0_le_left, fn_max_mul_fn_min, exists_root_adjoin_eq_top_of_isCyclic, Cardinal.power_nat_le_max, AlgebraicGeometry.AffineSpace.hom_ext_iff, iSupIndep.injOn, mul_max_of_nonneg, AlgebraicGeometry.ΓSpec.unop_locallyRingedSpaceAdjunction_counit_app', MvPolynomial.weightedTotalDegree_one, Heyting.Regular.coe_bot, Subalgebra.mul_toSubmodule_le, MeasurableSpace.generateFrom_singleton_univ, AffineSubspace.direction_sup, Quantale.mul_bot, max_mul_mul_right, CovBy.sup_of_inf_of_inf_left, Algebra.IsAlgebraic.lift_cardinalMk_le_max, MvPolynomial.supDegree_esymm, sup_le_of_le_sdiff_left, Coheyting.boundary_inf, bihimp_eq, AlgebraicGeometry.Scheme.isoSpec_Spec_hom, ENat.lift_zero, SSet.skeleton_succ, sSup_atoms_eq_top, IntermediateField.finrank_eq_one_iff_eq_top, BoundedContinuousFunction.coe_sup, SSet.Subcomplex.iSup_ofSimplex_nonDegenerate_eq_top, neg_sup, Units.max_val, Finset.symmDiff_subset_union, gc_sdiff_sup, MonomialOrder.sPolynomial_def, Finset.sup_lt_iff, AlgebraicGeometry.tilde.isIso_toOpen_top, CompleteLinearOrder.himp_bot, AddSubmonoid.exists_mem_sup, AddSubgroup.coe_add_of_right_le_normalizer_left, Finset.sup'_inf_sup', Nat.factorization_lcm, fixedPoints_addSubmonoid_sup, FirstOrder.Language.isExtensionPair_iff_exists_embedding_closure_singleton_sup, iSupIndep_ne_bot, Set.Ico_union_Ico', Subfield.extendScalars_top, AlgebraicGeometry.HasRingHomProperty.appTop, NumberField.IsCMField.closure_realFundSystem_sup_torsion, AlgebraicGeometry.LocallyRingedSpace.basicOpen_zero, Module.Basis.flag_succ, min_abs_abs_le_abs_max, AddSubgroup.unop_sup, IntermediateField.LinearDisjoint.finrank_sup, AffineSubspace.mk'_top, iInf_sup_iInf_le, MonoidAlgebra.cardinalMk_of_infinite', Algebra.zariskisMainProperty_iff_exists_saturation_eq_top, iSup_sup_eq, NumberField.is_primitive_element_of_infinitePlace_lt, LinearGrowth.linearGrowthSup_sup, StarSubalgebra.coe_bot, Finset.max_eq_sup_withBot, Subring.prod_bot_sup_bot_prod, UniformSpace.toTopologicalSpace_bot, CompHausLike.LocallyConstant.locallyConstantIsoContinuousMap_hom, CategoryTheory.Presheaf.isLocallySurjective_iff_range_sheafify_eq_top, Finset.max'_insert, MonoidAlgebra.exists_finset_adjoin_eq_top, AlgebraicGeometry.Scheme.isNilpotent_iff_basicOpen_eq_bot, IntermediateField.finrank_adjoin_eq_one_iff, Equiv.Perm.support_mul_le, WithTop.untop₀_max, UV.sup_sdiff_mem_of_mem_compression, Module.End.isFinitelySemisimple_iff, symmDiff_eq_iff_sdiff_eq, Subgroup.FG.sup, IntermediateField.bot_eq_top_of_rank_adjoin_eq_one, ENNReal.iSup_ennreal, sSup_eq_bot', SeparationQuotient.inseparableSetoid_eq_top_iff, AlgebraicGeometry.Scheme.isPullback_toSpecΓ_toSpecΓ, CompleteLinearOrder.le_himp_iff, AlgebraicGeometry.Scheme.instSubsingletonCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensBot, partialSups_eq_biSup, dist_mulIndicator, AlgebraicGeometry.Scheme.ΓSpecIso_naturality, Submodule.fg_finset_sup, supsSupHom_apply, Algebra.TensorProduct.productMap_range, AlgebraicGeometry.Scheme.restrictFunctorΓ_hom_app, Subsemigroup.mem_sup_left, Partition.bot_notMem', symmDiff_sup_inf, AlgebraicGeometry.Scheme.IdealSheafData.vanishingIdeal_sup, AddSubgroup.codisjoint_addSubgroupOf_sup, TopologicalSpace.Clopens.exists_finset_eq_sup_prod, IntermediateField.finrank_bot, Subgroup.subgroupOf_sup, symmDiff_self, le_symmDiff_iff_right, symmDiff_triangle, HahnSeries.cardSupp_div_le, NonUnitalAlgebra.map_sup, sdiff_sdiff_self, IsNonarchimedean.add_eq_max_of_ne, norm_sup_le_add, Birkhoff_inequalities, PowerBasis.adjoin_eq_top_of_gen_mem_adjoin, LatticeCon.sup, SimpleGraph.extremalNumber_of_fintypeCard_eq, iSup_ite, RelHomClass.map_sup, NonUnitalAlgebra.eq_top_iff, AddSubgroup.ofAddUnits_inf, AlgebraicGeometry.SheafedSpace.Γ_map, IsIntegrallyClosed.integralClosure_eq_bot, Ideal.Filtration.sup_N, Right.min_le_max_of_mul_le_mul, isFoelner_iff, min_neg_neg, IsIntegrallyClosed.integralClosure_eq_bot_iff, ofBoolAlg_symmDiff, Subgroup.comap_sup_comap_le, Fin.attachFin_uIcc, EReal.coe_toENNReal_eq_max, Polynomial.IsSplittingField.adjoin_rootSet', Multiset.nodup_sup_iff, IntermediateField.sepDegree_bot, AlgebraicGeometry.germ_stalkClosedPointIso_hom, Submodule.sup_smul, ProbabilityTheory.Kernel.iIndep_comap_mem_iff, AddQuantale.add_bot, AlgebraicGeometry.Scheme.toSpecΓ_isoSpec_inv, Submodule.rTensorOne_tmul, min_max_distrib_left, Ordinal.max_eq_zero, AlgebraicGeometry.IsFinite.instHasAffinePropertyAndIsAffineFiniteCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTopHomAppTop, symmDiff_left_surjective, Subgroup.ofUnits_inf, LowerSemicontinuous.sup, BiheytingHom.toFun_eq_coe, isLeast_pair, AlgebraicGeometry.IsAffineOpen.instIsAffineToSchemeBasicOpen, IntermediateField.finInsepDegree_bot', leOnePart_max, Finset.SupIndep.le_sup_iff, iSup_option_elim, Finset.fold_sup_bot_singleton, max_sub_min_eq_abs, OrdinalApprox.gfpApprox_ord_eq_gfp, BooleanSubalgebra.mem_closure_iff_sup_sdiff, CategoryTheory.Coverage.eq_top_pullback, NumberField.Units.closure_fundSystem_sup_torsion_eq_top, Finset.sup_eq_biUnion, Filter.sup_limsup, IsFoelner.tendsto_meas_smul_symmDiff_smul, lt_max_of_lt_right, Multiset.Ico_inter_Ico, FirstOrder.Language.Substructure.closure_insert, Cardinal.mk_freeRing, Monoid.Coprod.mrange_lift, Subsemigroup.op_sup, Set.apply_indicator_symmDiff, Ideal.mem_span_singleton_sup, LieSubmodule.sup_toSubmodule, le_max_of_two_nsmul_le_add, KaehlerDifferential.kerTotal_map, IntermediateField.restrictScalars_bot_eq_self, mul_max, Disjoint.le_symmDiff_sup_symmDiff_left, sdiff_sdiff_sup_sdiff, Module.End.invtSubmodule.sup_mem, sInf_sup_eq, max_zero_sub_max_neg_zero_eq_self, AlgebraicGeometry.Scheme.toIso_inv_ι_assoc, AlgebraicGeometry.SheafedSpace.restrictTopIso_inv, Cardinal.add_eq_max', IsRetrocompact.finsetSup, AlgebraicGeometry.Scheme.toSpecΓ_appTop, inf_symmDiff_distrib_left, Ordinal.card_opow_le_of_omega0_le_right, Order.Coframe.top_sdiff, IntermediateField.fg_bot, Filter.limsInf_top, IntermediateField.sup_def, ciSup_or', AlgebraicGeometry.Scheme.IdealSheafData.support_eq_bot_iff, IsPGroup.to_sup_of_normal_right, MeasurableSpace.CountablyGenerated.sup, CategoryTheory.Presheaf.isLocallySurjective_iff_range_sheafify_eq_top', symmDiff_isAssociative, AddSubmonoid.add_mem_sup, TensorProduct.quotientTensorQuotientEquiv_apply_tmul_mk_tmul_mk, inf_lt_sup, Cardinal.mul_mk_eq_max, GroupTopology.toTopologicalSpace_bot, MvPolynomial.degrees_sum_le, AlgHom.range_eq_top, Algebra.adjoin_singleton_one, Set.Ico_diff_Iio, CategoryTheory.Subfunctor.Subpresheaf.epi_iff_range_eq_top, inf_sup_right, NonUnitalAlgebra.mem_top, Set.subset_symmDiff_union_symmDiff_right, MvPolynomial.schwartz_zippel_sup_sum, NonUnitalStarAlgebra.toNonUnitalSubalgebra_eq_top, SSet.Subcomplex.image_top, LSeries.abscissaOfAbsConv_binop_le, Finset.supIndep_product_iff, Set.symmDiff_subset_union, MeasureTheory.tendsto_measure_symmDiff_preimage_nhds_zero, IntermediateField.finrank_sup_le, AddMonoidAlgebra.exists_supDegree_mem_support, CompleteSublattice.coe_bot, Ideal.map_sup_comap_of_surjective, Submonoid.op_sup, AffineSubspace.affineSpan_eq_top_iff_vectorSpan_eq_top_of_nonempty, IntermediateField.adjoin_empty, Cardinal.aleph_max, NonemptyInterval.snd_sup, lt_sup_iff, LSeries.abscissaOfAbsConv_add_le, AffineSubspace.topEquiv_symm_apply_coe, Subgroup.map_le_map_iff, FrameHom.coe_toInfTopHom, ciSup_of_empty, Fin.bot_eq_zero, Finset.le_sup_iff, LatticeHom.coe_toSupHom, Field.Emb.Cardinal.eq_bot_of_not_nonempty, AlgebraicGeometry.StructureSheaf.algebraMap_obj_top_bijective, Finset.sup_sdiff_right, TopologicalSpace.Opens.inclusion'_map_eq_top, sup_mul, bihimp_eq_sup_himp_inf, IntermediateField.rank_bot, Subalgebra.centralizer_eq_top_iff_subset, covBy_sup_of_inf_covBy_left, OreLocalization.cardinalMk_le_max, hnot_inf_distrib, AlgebraicGeometry.IsAffineOpen.fromSpec_preimage_self, iSup_eq_dif, OrderEmbedding.supIrredLowerSet_surjective, separableClosure_inf_perfectClosure, Set.uIcc_subset_uIcc_iff_le, HeytingHom.map_himp', Subgroup.normal_mul, CoheytingHom.map_sdiff', inf_compl_self, Finset.card_truncatedInf_union_add_card_truncatedInf_sups, MeasureTheory.Measure.add_top, Coheyting.boundary_inf_le, biUnion_Iic_disjointed, max_le_mul_of_one_le, AlgebraicGeometry.LocallyRingedSpace.Γevaluation_naturality_apply, Set.Icc.isCompl_iff, Ordinal.card_opow_omega0, Algebra.top_toSubsemiring, Subalgebra.rTensorBot_tmul_one, Quantale.sup_mul_distrib, Subgroup.comap_map_eq, div_sup, Cardinal.add_eq_max, sdiff_eq_bot_iff, max_mul_mul_left, negPart_def, Set.Ioc_union_Ioc_symm, TopologicalSpace.Compacts.coe_finset_sup, Tropical.trop_max_def, AlgebraicGeometry.Spec_zeroLocus_eq_zeroLocus, sdiff_eq_sInf, NonUnitalStarAlgebra.mul_mem_sup, AlgebraicGeometry.Scheme.Opens.ι_appTop, Finset.fold_max_le, Ideal.map_sup, MeasureTheory.hitting_bot_le_iff, Subgroup.mem_sup, Finset.sup_inf, FirstOrder.Language.Substructure.CG.sup, AffineSubspace.nonempty_sup_left, Finset.exists_mem_eq_sup, LatticeHom.withTopWithBot_toFun, LinearMap.range_coprod, Subalgebra.finrank_sup_eq_finrank_left_mul_finrank_of_free, BoundedLatticeHom.map_bot', Subfield.bot_eq_of_charZero, pred_max, Cardinal.preAleph_max, AddSubmonoid.mrange_inl_sup_mrange_inr, Monoid.Coprod.range_lift, IsIntegrallyClosedIn.integralClosure_eq_bot_iff, CompletelyDistribLattice.le_himp_iff, AffineMap.map_top_of_surjective, Subalgebra.finrank_sup_le_of_free, Ideal.comap_map_quotientMk, AlgebraicGeometry.Scheme.map_basicOpen, CategoryTheory.Subfunctor.Subpresheaf.top_obj, MeasureTheory.IsSetRing.partialSups_mem, Subalgebra.starClosure_toSubalgebra, max_min_distrib_right, sdiff_sup_self, List.zipWith_swap_prod_support', NonUnitalAlgebra.adjoin_univ, AlgebraicGeometry.isRetrocompact_basicOpen, GeneralizedBooleanAlgebra.inf_inf_sdiff, Order.pred_top_lt_iff, Submodule.comap_map_mkQ, List.support_sum_eq, AlgebraicGeometry.Scheme.isoSpec_inv_naturality, OpenAddSubgroup.toAddSubgroup_sup, Con.sup_def, IntermediateField.bot_eq_top_iff_finrank_eq_one, FrameHom.map_sSup', IsComplemented.sup, TopCat.Sheaf.objSupIsoProdEqLocus_inv_snd, le_sup_inf, Polynomial.degree_add_le_of_le, symmDiff_isCommutative, IntermediateField.adjoin_eq_bot_iff, MvPolynomial.supDegree_toLex_C, MeasureTheory.SimpleFunc.simpleFunc_bot', Submodule.rTensorOne_tmul_one, sup_iInf_le_iInf_sup, AlgebraicGeometry.Scheme.Hom.quasiFiniteLocus_eq_top_iff, sdiff_sdiff, AlgebraicGeometry.instQuasiSeparatedToSpecΓOfQuasiSeparatedSpaceCarrierCarrierCommRingCat, Finset.truncatedInf_sups_of_notMem, Multiset.map_finset_sup, CategoryTheory.Sieve.pullback_eq_top_of_mem, List.mem_foldr_sup_support_iff, nndist_mulIndicator, CategoryTheory.GrothendieckTopology.trivial_eq_bot, MeasureTheory.eLpNorm_indicator_sub_indicator, AlgebraicGeometry.Scheme.comp_appTop_assoc, IsMaxFilter.max, FirstOrder.Language.Substructure.closure_empty, Finset.add_sup, NonUnitalStarAlgebra.mem_sup_left, AlgebraicGeometry.Proj.basicOpen_one, Subgroup.map_le_map_iff', Filter.limsup_bot, ciSup_partialSups_eq, IntermediateField.lift_sepDegree_bot', Finset.sups_infs_subset_right, Finset.disjSups_disjSups_disjSups_comm, AntitoneOn.map_max, AlexandrovDiscrete.sup, ExpGrowth.le_expGrowthInf_add, Submodule.inf_orthogonal, CompletelyDistribLattice.top_sdiff, Mathlib.Tactic.Bound.le_max_of_le_left_or_le_right, BoundedLatticeHom.toFun_eq_coe, GeneralizedHeytingAlgebra.le_himp_iff, Subalgebra.op_top, AlgebraicGeometry.Scheme.isoSpec_Spec, LSeries.abscissaOfAbsConv_convolution_le, CategoryTheory.Subfunctor.Subpresheaf.range_id, AffineSubspace.coe_eq_bot_iff, iSup₂_eq_bot, essSup_measure_zero, Algebra.adjoin_singleton_natCast, abs_sup_sub_sup_le_abs, Polynomial.cardinalMk_eq_max, sup_iSup_nat_succ, IntermediateField.LinearDisjoint.inf_eq_bot, ClosedSubmodule.mem_sup, Order.isPredLimitRecOn_pred, div_inf, AlgebraicGeometry.Scheme.Hom.preimage_sup, Subgroup.sup_subgroupOf_eq, Field.exists_primitive_element_iff_finite_intermediateField, compl_symmDiff_compl, AntitoneOn.max, MeasurableSet.symmDiff, Finset.max'_union, Filter.EventuallyEq.symmDiff, AlgebraicGeometry.IsClosedImmersion.hasAffineProperty, Field.Emb.Cardinal.filtration_apply, Coheyting.boundary_le_boundary_sup_sup_boundary_inf_left, FirstOrder.Language.Substructure.map_bot, AlgebraicGeometry.Scheme.preimage_opensRange_toSpecΓ, Subalgebra.finite_sup, Set.infs_sups_subset_left, Finset.compls_sups, indiscreteTopology_iff, AlgebraicGeometry.Scheme.Spec.algebraMap_residueFieldIso_inv, CauSeq.rat_sup_continuous_lemma, Subalgebra.bot_eq_top_iff_finrank_eq_one, IsAlgClosed.cardinal_le_max_transcendence_basis', Ideal.comap_map_of_surjective, Subalgebra.mulMap_bot_right_eq, mul_sup, max_lt_max, AddSubmonoid.coe_sup, min_lt_max_of_mul_lt_mul, AlgebraicGeometry.Scheme.eq_zeroLocus_of_isClosed_of_isAffine, AddMonoidAlgebra.exists_finset_adjoin_eq_top, TopCat.Sheaf.interUnionPullbackConeLift_left, AlgebraicGeometry.Scheme.Opens.ι_preimage_self, CategoryTheory.Subfunctor.instIsIsoFunctorTypeιTop, AddSubgroup.sup_normal, trop_iInf, AddSubgroup.FG.finset_sup, CategoryTheory.Subfunctor.bot_obj, Finset.supIndep_sigma_iff', AlgebraicGeometry.Scheme.toSpecΓ_image_zeroLocus, AlgebraicGeometry.PresheafedSpace.ofRestrict_top_c, Submodule.restrictScalars_sup, Finset.sup_eq_iSup, max_max_max_comm, max_one_mul_max_inv_one_eq_mabs_self, AlgebraicGeometry.toSpecΓ_SpecMap_ΓSpecIso_inv_assoc, AlgebraicGeometry.SheafedSpace.Γ_obj_op, TopologicalSpace.Closeds.coe_sup, BooleanSubalgebra.val_sup, csSup_insert, Subalgebra.rank_sup_eq_rank_right_mul_rank_of_free, AlgebraicGeometry.Scheme.IdealSheafData.mul_inf, Algebra.isAlgebraic_iff, TopologicalSpace.Closeds.coe_top, AddSubgroup.mem_sup_right, AddSubgroup.sup_eq_closure, min_add_max, SetTheory.PGame.birthday_def, Subalgebra.lTensorBot_symm_apply, Finset.isPWO_sup, AlgebraicGeometry.IsAffineOpen.fromSpec_app_self_apply, NonUnitalStarAlgebra.comap_top, sup_inf_assoc_of_le, Finset.partiallyWellOrderedOn_sup, exists_sSupIndep_disjoint_sSup_atoms, FirstOrder.Language.Term.card_sigma, CategoryTheory.Precoverage.sup_mem_coverings, Submonoid.unop_sup, FreeAlgebra.adjoin_range_ι, LinearMap.eqOn_sup, ContinuousMap.subalgebra_topologicalClosure_eq_top_of_separatesPoints, Finset.nsmul_sup', max_top_left, Submodule.add_mem_sup, Con.toSetoid_bot, min_top_right, MvPolynomial.degreeOf_eq_sup, Finset.untrop_sum, max_eq_bot, MeasureTheory.sigmaFinite_bot_iff, SSet.Subcomplex.topIso_inv_ι_assoc, AlgebraicGeometry.Scheme.inv_appTop, Submodule.sup_orthogonal_inf_of_hasOrthogonalProjection, Algebra.TensorProduct.map_range, IntermediateField.finrank_top', Order.Coframe.sdiff_le_iff, AlgebraicGeometry.isLocalization_away_of_isAffine, Finset.Ico_filter_le, Cardinal.mk_bounded_subset_le, AlgebraicGeometry.IsAffineOpen.ι_basicOpen_preimage, iSup_neg, AffineSubspace.direction_top, Set.Ioc_inter_Ioc, Affine.Simplex.span_eq_top, CompleteLattice.ωScottContinuous.sup, MonomialOrder.sPolynomial_monomial_mul, infClosed_preimage_ofDual, IntermediateField.lift_bot, NumberField.mixedEmbedding.exists_primitive_element_lt_of_isReal, Finset.iSup_insert, IsGalois.fixedField_top, DeltaGeneratedSpace.sup, WithBot.sInf_empty, AddSubsemigroup.mem_sup_right, Submodule.sup_dualAnnihilator_le_inf, Finset.disjSups_assoc, compl_sup_distrib, TopologicalSpace.Opens.eq_bot_or_top, AlgebraicGeometry.morphismRestrict_appTop, IsLocalRing.closed_point_mem_iff, CompleteLinearOrder.compare_eq_compareOfLessAndEq, AlgebraicGeometry.Scheme.IdealSheafData.ofIdealTop_ideal, UpperSemicontinuous.sup, sup_compl_eq_top, CategoryTheory.Precoverage.IsStableUnderSup.sup_mem_coverings, Set.Ico_disjoint_Ico, Submonoid.closure_mul_le, bihimp_inf_sup, Algebra.IsAlgebraic.isNormalClosure_iff, iInf_top, AddCon.sup_eq_addConGen, MeasureTheory.hittingAfter_eq_sInf, MeasureTheory.condLExp_bot_ae_eq, IntermediateField.sup_toSubalgebra_of_left, Finset.centerMass_le_sup, NonUnitalSubring.closure_union, AlgebraicGeometry.Scheme.Hom.preimage_opensRange, StarSubalgebra.toSubalgebra_eq_top, Submonoid.mul_mem_sup, AlgebraicGeometry.ΓSpecIso_hom_stalkClosedPointIso_inv, Multiset.mem_sup, IsLocalMax.max, StarSubalgebra.mem_top, AlgebraicGeometry.AffineSpace.toSpecMvPolyIntEquiv_apply, Set.Finite.symmDiff_congr, CategoryTheory.GrothendieckTopology.bot_covering, Submodule.mulMap_one_left_eq, Projectivization.Subspace.sup_span, AffineSubspace.isEmpty_bot, max_sub_max_le_max, AlgebraicGeometry.LocallyRingedSpace.Γ_map, Set.inter_symmDiff_distrib_right, Finset.sup_singleton_apply, Submodule.smul_sup, IntermediateField.adjoin_simple_eq_bot_iff, IntermediateField.relfinrank_bot_left, AlgebraicGeometry.isCompactOpen_iff_eq_basicOpen_union, Cardinal.add_mk_eq_max, exists_subset_affineIndependent_affineSpan_eq_top, IsSublattice.supClosed, Sublattice.comap_equiv_eq_map_symm, AlgebraicGeometry.Spec.algebraMap_stalkIso_inv, infIooOrderIsoIooSup_apply_coe, EReal.max_neg_neg, AddMonoidAlgebra.cardinalMk_lift_of_infinite', LinearPMap.domain_sup, sdiff_inf, le_inf_sup, RingCon.matrix_bot, CompleteLinearOrder.le_total, OrderEmbedding.birkhoffSet_sup, IntermediateField.LinearDisjoint.rank_sup, Algebra.adjoin_adjoin_coe_preimage, NNRat.cast_max, TopologicalSpace.Closeds.coe_finset_sup, Finset.disjoint_sup_right, HeytingHomClass.map_bot, MeasureTheory.measure_inv_smul_symmDiff, AlgebraicGeometry.eq_top_of_sigmaSpec_subset_of_isCompact, HomogeneousIdeal.toIdeal_sup, IntermediateField.rank_sup_le_of_isAlgebraic, leOnePart_min, Algebra.adjoin_top, Subgroup.mul_mem_sup, TopologicalSpace.Opens.mk_empty, FrameHomClass.toInfTopHomClass, Finset.compls_infs, inf_sup_left, bihimp_self, iSup_ne_bot_subtype, abs_pow_sub_pow_le, Finset.coe_symmDiff, Finset.mem_sup', AlgebraicGeometry.PresheafedSpace.Γ_obj, Subalgebra.FG.sup, AffineSubspace.perpBisector_eq_top, le_symmDiff_sup_left, IntermediateField.adjoin_intCast, Submodule.isQuotientEquivQuotientPrime_iff, Algebra.adjoin_root_eq_top_of_isSplittingField, inf_sSup_eq_iSup_inf_sup_finset, Subalgebra.LinearDisjoint.finrank_sup_of_free, Finset.supIndep_iff_disjoint_erase, ZFSet.rank_insert, AlgebraicGeometry.PresheafedSpace.toRestrictTop_c, Algebra.surjective_algebraMap_iff, MvPolynomial.degrees_add_le, Subgroup.smul_sup, IntermediateField.sepDegree_bot', Polynomial.supDegree_eq_degree, CategoryTheory.Presheaf.isSheaf_bot, AlgebraicGeometry.Scheme.isoSpec_inv_toSpecΓ_assoc, FirstOrder.Language.Substructure.closure_union, IntermediateField.LinearDisjoint.bot_right, Filter.limsSup_bot, Submodule.span_union, IsRetrocompact.finsetSup', Finset.add_sup', AffineSubspace.pointwise_vadd_bot, Field.primitive_element_iff_minpoly_degree_eq, Submonoid.coe_sup, Algebra.toSubmodule_eq_top, AddSubmonoid.closure_add_le, AlgHom.fieldRange_eq_top, Order.pred_lt_pred_iff, Set.Ioo_inter_Ioc_of_right_lt, iSup_emptyset, AffineSubspace.finiteDimensional_sup, AddSubgroup.mem_sup_of_normal_right, StarSubalgebra.map_sup, Submodule.rank_add_le_rank_add_rank, Submodule.sup_mul, discreteTopology_bot, sup_sdiff_left_self, sup_sdiff_self_left, DFinsupp.support_sup_union_support_inf, inv_inf, max_mul_mul_le_max_mul_max', DualNumber.range_inlAlgHom_sup_adjoin_eps, AlgebraicGeometry.Scheme.toOpen_eq, negPart_min, max_le_max, Submodule.spanRank_sup_le_sum_spanRank, isPurelyInseparable_iff_perfectClosure_eq_top, Fin.cast_top, sup_inf_le_assoc_of_le, symmDiff_sdiff, Cardinal.mk_freeGroup, isBoundedUnder_le_finset_sup, compl_bihimp_self, RingCon.coe_bot, FirstOrder.Language.Substructure.FG.sup, IntermediateField.rank_eq_one_iff, symmDiff_sdiff_eq_sup, symmDiff_le_sup, supPrime_iff_supIrred, bot_himp, Subalgebra.fg_bot, Algebra.adjoin_univ, Multiset.Ico_filter_le, AlgHom.equalizer_same, Subgroup.comap_sup_eq_of_le_range, AddMonoid.Coprod.range_lift, Polynomial.degree_sub_le, IntermediateField.eq_bot_of_isPurelyInseparable_of_isSeparable, Ordinal.card_opow_eq_of_omega0_le_right, CategoryTheory.Subfunctor.image_top, PUnit.top_eq, TopologicalSpace.Closeds.coe_eq_univ, Equiv.Perm.support_prod_le, TopologicalSpace.Clopens.surjective_finset_sup_prod, iInf₂_sup_eq, AffineIndependent.affineSpan_eq_top_iff_card_eq_finrank_add_one, ProjectiveSpectrum.basicOpen_zero, MeasurableSpace.cardinal_measurableSet_le, IntermediateField.adjoin_root_eq_top_of_isSplittingField, CompleteDistribLattice.sdiff_le_iff, AlgebraicGeometry.ΓSpecIso_inv_ΓSpec_adjunction_homEquiv, Set.Ioi_inter_Ioo, max_eq_right_iff, algebraicClosure.eq_top_iff, AffineSubspace.not_sOppSide_bot, CategoryTheory.Sieve.functorPushforward_union, sdiff_sdiff_right', Subgroup.relIndex_sup_left, Finset.sup_mem_of_nonempty, MeasurableSpace.cardinal_generateMeasurable_le, disjoint_partialSups_left, LatticeHom.withBot'_toFun, symmDiff_symmDiff_left, Quantale.mul_sup_distrib, symmDiff_symmDiff_cancel_left, CompleteDistribLattice.MinimalAxioms.iInf_sup_le_sup_sInf, IsOpen.exists_between_affineIndependent_span_eq_top, Finset.max_insert, Setoid.eq_top_iff, compl_sup, AffineSubspace.top_coe, IsAlgClosed.cardinal_le_max_transcendence_basis, Multiset.max_prod_le, sup_bihimp_bihimp, Setoid.sup_def, AlgebraicGeometry.toSpecΓ_SpecMap_ΓSpecIso_inv, AddMonoidAlgebra.Monic.supDegree_mul_of_ne_zero_left, Field.primitive_element_iff_minpoly_natDegree_eq, Polynomial.sup_ker_aeval_le_ker_aeval_mul, sInfHom.coe_top, AlgebraicGeometry.instIsIsoModulesSpecOfCarrierFromTildeΓUnitOpensCarrierCarrierCommRingCatRingCatSheaf, Subalgebra.fg_top, Multiset.count_finset_sup, NonUnitalAlgebra.toSubmodule_eq_top, isDenseInducing_pure, symmDiff_eq_bot, AlgebraicGeometry.Scheme.Hom.inv_appTop, SSet.iSup_skeletonOfMono, BooleanAlgebra.himp_eq, affineSpan_coe_preimage_eq_top, MeasureTheory.Filtration.coeFn_sup, Continuous.max, Set.Iic_union_Icc', AffineSubspace.pointwise_vadd_top, IntermediateField.isScalarTower_over_bot, ProbabilityTheory.condVar_bot', AddSubgroup.mem_sup, TwoSidedIdeal.top_ringCon, AffineSubspace.nonempty_sup_right, AddMonoidAlgebra.Monic.supDegree_pow, max_bot_right, Ideal.ofList_append, AffineSubspace.perpBisector_self, max_div_div_right_of_nonpos, min_mul_max, UpperSemicontinuousOn.sup, Finset.sup'_add, inf_sdiff_sup_right, CovBy.sup_of_inf_of_inf_right, sup_sq_eq_mul_mul_mabs_div, Topology.IsUpper.toContinuousInf, AlgebraicGeometry.Spec_zeroLocus, sup_eq_inf, IntermediateField.bot_toSubfield, AlgebraicGeometry.Scheme.ΓSpecIso_inv_naturality, Algebra.EssFiniteType.aux, Subgroup.closure_mul_le, compl_inf_self, Finset.le_card_infs_mul_card_sups, MonotoneOn.map_sup, Finset.Colex.lt_iff_max'_mem, IntermediateField.topEquiv_symm_apply_coe, AffineSubspace.span_empty, sup_lt_iff, AddSubmonoid.sup_eq_closure_add, BiheytingHom.map_himp', biInf_sup_le_biInf_sup, NonUnitalStarAlgebra.map_bot, AffineSubspace.map_bot, MeasurableSpace.comap_sup, affineSpan_eq_top_of_nonempty_interior, Subalgebra.lTensorBot_tmul, le_max_of_le_right, Booleanisation.comp_sdiff_lift, Submodule.sup_orthogonal_of_hasOrthogonalProjection, NonUnitalAlgebra.adjoin_empty, SSet.iSup_range_eq_top_of_isColimit, Subring.unop_sup, Measurable.sup_of_left, IntermediateField.rank_top', Subalgebra.topEquiv_symm_apply_coe, TopCat.Presheaf.isSheaf_on_punit_iff_isTerminal, AlgebraicGeometry.Scheme.SpecΓIdentity_inv_app, partialSups_eq_ciSup_Iic, Set.apply_mulIndicator_symmDiff, MeasureTheory.MeasuredSets.dist_def, MeasureTheory.OuterMeasure.boundedBy_top, AlgebraicGeometry.Scheme.Pullback.diagonalCoverDiagonalRange_eq_top_of_injective, Subalgebra.rank_sup_le_of_free, UV.compress_of_disjoint_of_le, iInf_eq_dif, TopologicalSpace.Clopens.coe_finset_sup, AddMonoid.Coprod.mrange_inl_sup_mrange_inr, max_cases, CompleteSublattice.coe_top, CategoryTheory.ObjectProperty.isoClosure_sup, CategoryTheory.Sieve.functorPushforward_bot, Finset.sup_sdiff_left, iSup_sup, ConditionallyCompleteLinearOrder.le_total, IntermediateField.topEquiv_apply, limsup_max, Algebra.isIntegral_sup, ProbabilityTheory.condIndep_bot_right, Order.Frame.himp_bot, QuotientGroup.comap_map_mk', mem_bot_iff_intCast, Finset.symmDiff_subset_sdiff', le_symmDiff_iff_left, AlgebraicGeometry.basicOpen_eq_of_affine', Multiset.support_sum_eq, IntermediateField.adjoin_natCast, BoundedLatticeHomClass.toSupBotHomClass, AlgebraicGeometry.AffineSpace.isoOfIsAffine_hom_appTop, Left.min_le_max_of_mul_le_mul, symmDiff_le_iff, TopologicalSpace.Opens.coe_bot, List.support_sum_subset, le_max_of_le_left, Nat.sup_divisors_id, LatticeHom.coe_comp_sup_hom, inf_eq_iff_sup_eq, inf_sup_symmDiff, AffineSubspace.topEquiv_apply, symmDiff_eq_Xor', Cardinal.aleph_mul_aleph, AlgebraicGeometry.instIsDominantToSpecΓOfCompactSpaceCarrierCarrierCommRingCat, dist_indicator, LinearMap.comap_eq_sup_ker_of_disjoint, Set.Ioc_union_Ioc_union_Ioc_cycle, AlgebraicGeometry.Scheme.preimage_eq_top_of_closedPoint_mem, Finset.powersetCard_sup, inf_le_left, iInf_extend_top, Finset.sup'_inf_distrib_left, TopologicalSpace.Closeds.isClopen_singleton_bot, IsCyclotomicExtension.singleton_one, MeasureTheory.hittingBtwn_eq_sInf, TopCat.Sheaf.objSupIsoProdEqLocus_hom_snd, SSet.finite_subcomplex_top_iff, Subalgebra.op_sup, inf_lt_iff, AlgebraicGeometry.Scheme.isoSpec_Spec_inv, oneLePart_def, SSet.Subcomplex.preimage_max, Nat.cast_finsetSup, Algebra.adjoin_restrictScalars, Submodule.finite_finset_sup, TwoSidedIdeal.sup_ringCon, Set.partialSups_eq_accumulate, IsPGroup.to_sup_of_normal_right', fixedPoints_subgroup_sup, Set.Iic_union_Icc, Submodule.finrank_add_le_finrank_add_finrank, NonUnitalAlgebra.coe_top, Ordinal.card_opow_le_of_omega0_le_left, Ideal.mem_quotient_iff_mem_sup, symmDiff_right_surjective, QuotientGroup.rightRel_eq_top, NonUnitalAlgebra.map_top, Subalgebra.LinearDisjoint.val_mulMap_tmul, IntermediateField.isPurelyInseparable_bot, AddQuantale.bot_add, AlgebraicGeometry.Scheme.germ_stalkClosedPointTo_assoc, AlgebraicGeometry.Scheme.topIso_hom, Finset.mul_sup', Disjoint.sup_right, MeasurableSpace.generateFrom_singleton, sup_sInf_le_iInf_sup, AlgebraicGeometry.finite_appTop_of_universallyClosed, ConvexOn.le_on_segment', Subgroup.sup_normal, AffineSubspace.span_univ, IntermediateField.top_toSubfield, Finset.iSup_insert_update, TopologicalSpace.IsOpenCover.iSup_eq_top, Subalgebra.mulMap_range, Submodule.lt_sup_iff_notMem, sup_sub, CategoryTheory.Sieve.pushforward_union, Max.right_comm, Fintype.exists_disjointed_le, CircleDeg1Lift.sup_apply, AffineSubspace.map_eq_bot_iff, sdiff_sdiff_left, Submonoid.mem_sup_right, Subfield.extendScalars_sup, NonUnitalAlgebra.to_subring_eq_top, RingOfIntegers.exponent_eq_one_iff, disjointed_succ, Subsemigroup.mem_sup_right, FirstOrder.Language.Term.card_le, Finsupp.support_inf_union_support_sup, AddSubsemigroup.map_sup_comap_of_surjective, ConvexOn.sup, sSup_eq_top, Set.Ioc_inter_Ioo_of_left_lt, AlgebraicGeometry.specTargetImageFactorization_app_injective, Ideal.IsMaximal.coprime_of_ne, inf_right_le_sup_right, MeromorphicOn.negPart_divisor_add_le_max, Subalgebra.rTensorBot_symm_apply, Algebra.comap_top, covBy_sup_of_inf_covBy_of_inf_covBy_right, Ideal.add_eq_sup, AlgebraicGeometry.PresheafedSpace.Γ_map, NonUnitalAlgebra.toNonUnitalSubring_eq_top, ProbabilityTheory.indep_bot_right, StrictConvexOn.sup, Ordinal.card_opow_eq_of_omega0_le_left, sup_inf_sdiff, sdiff_sup_sdiff_cancel, sdiff_inf_distrib, AlgebraicGeometry.StructureSheaf.toOpenₗ_top_bijective, ProbabilityTheory.condVar_bot_ae_eq, supClosed_preimage_toDual, AffineSubspace.direction_bot, IntermediateField.isSeparable_sup, biInf_sup_biInf, Submonoid.FG.sup, le_symmDiff_sup_right, iInf_sup_eq, CategoryTheory.Sieve.functorInclusion_top_isIso, Finset.support_sum_eq, Filter.Germ.const_max, MeasureTheory.upperCrossingTime_zero', Submodule.IsLattice.sup, Finset.inf_sup_inf, MaximalSpectrum.iInf_localization_eq_bot, Finset.fold_max_lt, CompleteBooleanAlgebra.top_le_sup_compl, AffineBasis.isUnit_toMatrix_iff, Algebra.IsCentral.center_eq_bot, IsGaloisGroup.fixingSubgroup_bot, AlgebraicGeometry.Scheme.IdealSheafData.ideal_sup, Set.Iic_union_Ioc', AffineSubspace.sup_direction_le, Set.exists_seq_iSup_eq_top_iff_countable, symmDiff_symmDiff_right', Polynomial.degree_sum_eq_of_disjoint, max_mul, Fin.rev_zero_eq_top, AlgebraicGeometry.AffineSpace.isoOfIsAffine_hom, sup_himp_self_left, sup_inf_le, sInfHomClass.toInfTopHomClass, leOnePart_def, AffineSubspace.instNonemptySubtypeMemTop, Set.Finite.symmDiff, Finset.sup_eq_sSup_image, Submodule.map₂_sup_left, ProbabilityTheory.indep_bot_left, Subsemiring.closure_union, Submodule.sup_eq_top_iff, LinearMap.ker_sup_ker_le_ker_comp_of_commute, coinduced_sup, LinearMap.range_ofIsCompl, AlgebraicGeometry.affineAnd_apply, Polynomial.degree_add_le, ConvexOn.le_sup_of_mem_convexHull, abs_max_le_max_abs_abs, UpperSemicontinuousWithinAt.sup, ENat.toENNReal_max, Subalgebra.centralizer_coe_sup, max_mul_mul_le_max_mul_max, Hyperreal.coe_max, MeasureTheory.abs_measureReal_sub_le_measureReal_symmDiff, Cardinal.add_mk_eq_max', IntermediateField.fg_top, instDiscreteMeasurableSpace, AddSubmonoid.mem_sup, Submodule.lTensorOne_symm_apply, Finset.comp_sup_eq_sup_comp_of_nonempty, CategoryTheory.PreZeroHypercover.presieve₀_sum, Order.isPredPrelimitRecOn_pred, MeasureTheory.OuterMeasure.top_apply', AlgebraicGeometry.AffineSpace.reindex_appTop_coord, AlgebraicGeometry.Spec.algebraMap_stalkIso_inv_assoc, IntermediateField.finInsepDegree_bot, MvPolynomial.cardinalMk_le_max_lift, MvPolynomial.supported_empty, disjointed_apply, IsCyclotomicExtension.iff_adjoin_eq_top, Subalgebra.coe_starClosure, AddSubmonoid.map_sup_comap_of_surjective, Order.pred_eq_pred_iff, MeasureTheory.measure_symmDiff_eq, AlgEquiv.fieldRange_eq_top, Finset.exists_mem_eq_sup', MeasureTheory.AEEqFun.coeFn_posPart, LinearOrder.bot_topologicalSpace_eq_generateFrom, MonomialOrder.sPolynomial_monomial_mul', Booleanisation.comp_inf_comp, Ideal.ofList_cons_smul, MeasureTheory.SimpleFunc.simpleFunc_bot, Field.Emb.Cardinal.iSup_adjoin_eq_top, Filter.tendsto_nhds_max_right, AlgebraicGeometry.ΓSpec.toSpecΓ_of, affineSpan_eq_bot, Sylow.normalizer_sup_eq_top, ProbabilityTheory.condVar_bot, fixedPoints.lfp_eq_sSup_iterate, Set.symmDiff_eq_empty, Finset.sup'_id_eq_csSup, sup_sdiff, Filter.limsup_const_bot, CoheytingHom.toFun_eq_coe, symmDiff_hnot_self, sInf_diff_singleton_top, Subring.smul_sup, abs_sub_le_max_sub, JacobsonNoether.exists_separable_and_not_isCentral', BooleanAlgebra.top_le_sup_compl, AlgebraicGeometry.exists_appTop_π_eq_of_isLimit, Monotone.disjointed_succ_sup, Finset.lt_sup_iff, AlgebraicGeometry.IsAffine.affine, max_aleph0_card_le_rank_fun_nat, StarSubalgebra.coe_top, AlgebraicGeometry.AffineTargetMorphismProperty.IsLocal.to_basicOpen, FreeAlgebra.cardinalMk_le_max_lift, le_sup_iff, AlgebraicGeometry.SheafedSpace.Γ_obj, Fin.rev_last_eq_bot, Submodule.lTensorOne'_one_tmul, Subsemiring.prod_bot_sup_bot_prod, AlgebraicGeometry.Scheme.IdealSheafData.vanishingIdeal_top, IntermediateField.lift_cardinalMk_adjoin_le, symmDiff_left_injective, MeasureTheory.SignedMeasure.of_symmDiff_compl_positive_negative, LinearMap.coe_quotientInfToSupQuotient, AlgebraicGeometry.Proj.basicOpen_zero, LatticeHom.birkhoffFinset_injective, Sublattice.supClosed', Subfield.closure_union, NonUnitalStarAlgebra.map_sup, sup_inf_bihimp, IntermediateField.finrank_bot', AlgebraicGeometry.Scheme.mem_basicOpen_top, sdiff_top, isGreatest_pair, supClosure_infClosure, ConvexCone.isGenerating_top, mabs_max_le_max_mabs_mabs, Function.mulSupport_max, Quantale.bot_mul, CategoryTheory.Pretopology.toGrothendieck_bot, Partition.bot_lt_of_mem, AlgebraicGeometry.Scheme.Opens.ι_image_basicOpen', min_lt_max, AlgebraicGeometry.LocallyRingedSpace.Γevaluation_naturality_assoc, Algebra.eq_top_iff, Filter.liminf_bot, Finset.sup_eq_zero, AffineSubspace.map_sup, Setoid.mk_eq_bot, smul_max_of_nonpos, AffineSubspace.comap_top, Submodule.map_sup_comap_of_surjective, Finset.symmDiff_eq_empty, fourierSubalgebra_closure_eq_top, le_csInf_inter, symmDiff_eq_left, himp_self, Filter.limsInf_bot, Set.mabs_mulIndicator_symmDiff, AlgebraicGeometry.AffineSpace.homOverEquiv_apply, NonUnitalStarAlgebra.range_id, Subalgebra.rank_eq_one_iff, sdiff_bot, DiscreteTopology.eq_bot, LSeries.abscissaOfAbsConv_sub_le, sSup_pair, Subalgebra.prod_top, Finset.max_abv_sum_one_le_of_isNonarchimedean, CategoryTheory.Sieve.overEquiv_symm_top, TopCat.Sheaf.objSupIsoProdEqLocus_inv_fst, MonotoneOn.map_max, NonUnitalAlgebra.comap_top, MeasureTheory.Measure.toOuterMeasure_top, hnot_sup_self, NonUnitalStarAlgebra.map_top, LinearOrder.supClosed, symmDiff_right_injective, AddSubgroup.ofAddUnits_sup_addUnits, AlgebraicGeometry.Scheme.comp_appTop, mabs_min_le_max_mabs_mabs, Submodule.span_sup, Finset.sup_himp_right, Cardinal.powerlt_aleph0_le, StrictConvexOn.lt_on_open_segment', IntermediateField.botEquiv_def, inf_sup_le_assoc_of_le, le_max_of_sq_le_mul, iInf_sup_le_iInf_sup, symmDiff_eq_top, AlgebraicGeometry.IsClosedImmersion.isAffine_surjective_of_isAffine, EMetric.Closeds.lipschitz_sup, CategoryTheory.sieve₁'_toPreOneHypercover_eq_top, PseudoMetric.coe_finsetSup, subalgebra_top_finrank_eq_submodule_top_finrank, Finset.truncatedInf_sups, IntermediateField.adjoin_eq_top_iff, Set.sups_infs_subset_right, symmDiff_sdiff_inf, MonoidAlgebra.cardinalMk_lift_of_infinite', AddSubsemigroup.closure_union, Valuation.Integers.integralClosure, MeasureTheory.AddContent.supClosure_apply_of_mem, Fin.range_natAdd_eq_Ioi, IntermediateField.finSepDegree_bot', InfClosed.supClosure, IsCyclotomicExtension.Rat.adjoin_singleton_eq_top, AlgebraicGeometry.Scheme.fromSpecStalk_app, MvPolynomial.totalDegree_finset_sum, Subgroup.op_sup, Algebra.mem_sup_right, OrderEmbedding.birkhoffSet_apply, TopologicalSpace.Opens.coe_sup, HeytingHom.map_bot', Projectivization.Subspace.span_union, IntermediateField.rank_sup_le, AddSubgroup.toAddSubmonoid_zmultiples, AlgebraicGeometry.AffineSpace.toSpecMvPolyIntEquiv_comp, Algebra.IsUnramifiedAt.exists_notMem_forall_ne_mem_and_adjoin_eq_top, sup_sdiff_cancel', AlgebraicGeometry.isField_of_universallyClosed, max_le_add_of_nonneg, polynomialFunctions.topologicalClosure, symmDiff_symmDiff_inf, MeasureTheory.ae_eq_set_symmDiff, sInf_empty, RingCon.range_mkₐ, MeasureTheory.measure_symmDiff_neg_vadd, AlgebraicGeometry.LocallyRingedSpace.Γevaluation_eq_zero_iff_notMem_basicOpen, stronglyMeasurable_bot_iff, symmDiff_of_le, AlgebraicGeometry.Scheme.Spec.algebraMap_residueFieldIso_inv_assoc, LinearMap.coprod_map_prod, compl_top, IntermediateField.eq_bot_of_isSepClosed_of_isSeparable, WellFoundedLT.finite_ne_bot_of_iSupIndep, MeasurableSpace.map_top, iSup_eq_if, Multiset.max_le_of_forall_le, Cardinal.add_eq_left_iff, Sym2.inf_le_sup, Set.Iic.isCompl_iff, ConditionallyCompleteLinearOrderBot.csSup_empty, FirstOrder.Language.Substructure.elementarySkolem₁Reduct.instSmall, sdiff_symmDiff_eq_sup, sup_sdiff_distrib, Algebra.map_top, CategoryTheory.Subfunctor.top_obj, bot_bihimp, collapse_modular, PUnit.sup_eq, TopologicalSpace.Closeds.uniformContinuous_sup, Subalgebra.eq_bot_of_rank_le_one, AlgebraicGeometry.Scheme.Hom.smoothLocus_eq_top, Cardinal.mk_finsupp_of_infinite, symmDiff_eq_sup, CategoryTheory.Sieve.functorPushforward_top, norm_sup_sub_sup_le_add_norm, MeasureTheory.IsStoppingTime.max, Polynomial.degree_update_le, AddMonoid.Coprod.mrange_eq, NonUnitalStarSubalgebra.center_eq_top, AlgebraicGeometry.IsAffineOpen.fromSpec_top, IntermediateField.bot_eq_top_of_finrank_adjoin_le_one, isArtinian_sup, Booleanisation.lift_sup_lift, CategoryTheory.Presieve.isSeparatedFor_top, Submodule.lTensorOne_tmul, AddQuantale.sup_add_distrib, AddCon.toSetoid_eq_bot, IntermediateField.relrank_bot_right, Subsemiring.smul_sup, Heyting.Regular.coe_sup, nndist_indicator, Finset.mem_symmDiff, Submonoid.closure_union, disjoint_sup_left, AlgebraicGeometry.Scheme.IdealSheafData.support_top, mabs_eq_max_inv, Subalgebra.comm_trans_lTensorBot, limsup_finset_sup, Convex.combo_le_max, InfiniteGalois.fixedField_bot, Subgroup.codisjoint_subgroupOf_sup, CompletelyDistribLattice.himp_bot, NonUnitalAlgebra.map_bot, sup_sInf_eq, AlgebraicGeometry.Scheme.map_basicOpen_map, Subgroup.coe_mul_of_right_le_normalizer_left, CompleteLattice.ωScottContinuous.top, CompleteLattice.sInf_le, inf_strictMonoOn_Icc_sup, Filter.limsup_piecewise, AddSubgroup.comap_sup_eq, StarAlgHom.range_eq_map_top, IsSepClosed.separableClosure_eq_bot_iff, MeasureTheory.OuterMeasure.isCaratheodory_partialSups, Subfield.closure_empty, AlgebraicGeometry.Scheme.Hom.comp_appTop, HeytingAlgebra.himp_bot, NonUnitalStarAlgebra.eq_top_iff, GeneralizedBooleanAlgebra.sup_inf_sdiff, LatticeHom.coe_comp_sup_hom', Subalgebra.bot_eq_top_of_finrank_eq_one, AlgebraicGeometry.IsIntegralHom.hasAffineProperty, Cardinal.mul_eq_max_of_aleph0_le_left, HeytingHom.toFun_eq_coe, RingCon.toCon_eq_top, AlgebraicGeometry.Scheme.germ_stalkClosedPointTo_Spec, MeasureTheory.OuterMeasure.map_top_of_surjective, Ordinal.toNimber_max, AlgebraicGeometry.Scheme.basicOpen_zero, isCoboundedUnder_le_finset_sup', Finset.sup_inf_sup, IsAddFoelner.tendsto_meas_vadd_symmDiff, Finset.wellFoundedOn_sup, sdiff_le_iff, LatticeHomClass.toSupHomClass, le_sup_sdiff_sup_sdiff, iInf_eq_bot, AlgebraicGeometry.instHasAffinePropertyIsomorphismsSchemeAndIsAffineIsIsoCommRingCatAppTop, infClosure_supClosure, TensorProduct.map_ker, eq_bot_of_singletons_open, DistLat.Iso.mk_hom, NonUnitalSubsemiring.map_sup, Finset.sup_div₀, untrop_sum_eq_sInf_image, Finset.compl_truncatedInf, MvPolynomial.supported_univ, IntermediateField.adjoin_union, conductor_eq_top_iff_adjoin_eq_top, UpperSemicontinuousAt.sup, fixedPoints.gfp_eq_sInf_iterate, Ordinal.omega_max, Subalgebra.isAlgebraic_bot_iff, Subgroup.mem_sup_of_normal_left, sup_himp_bihimp, TwoSidedIdeal.bot_ringCon, WithBot.coe_max, CategoryTheory.Sieve.union_apply, AdjoinRoot.adjoinRoot_eq_top, AlgebraicGeometry.isAffineOpen_bot, AlgebraicGeometry.Scheme.IsLocallyDirected.V_self, borel_eq_top_of_countable, Polynomial.cardinalMk_le_max, sup_div, HeytAlg.Iso.mk_hom, Submodule.sup_toAddSubmonoid, StarSubalgebra.mem_sup_right, CategoryTheory.GrothendieckTopology.top_mem', TopCat.Presheaf.Γgerm_res_apply, IntermediateField.extendScalars_top, iInf₂_eq_bot, ciSup_false, ConditionallyCompleteLinearOrderedField.toIsStrictOrderedRing, perfectClosure.eq_bot_of_isSeparable, BooleanSubalgebra.map_sup, AddSubsemigroup.add_mem_sup, Sublattice.coe_sup, LinearMap.map_eq_top_iff, Sublattice.map_symm_eq_iff_eq_map, ConvexCone.coe_top, MeasurableSpace.measurableSet_top, CategoryTheory.Presheaf.equalizerSieve_eq_top_iff, ProbabilityTheory.Kernel.indep_bot_left, isNoetherian_sup, Lat.Iso.mk_hom, IntermediateField.fixedField_bot, Submodule.mem_sup, sdiff_symmDiff_left, Order.Frame.MinimalAxioms.inf_sSup_le_iSup_inf, Sublattice.mk_sup_mk, List.max_sum_le, NonUnitalAlgebra.range_eq_top, WithTop.le_of_forall_lt_iff_le, sup_sdiff_self_right, IntermediateField.lift_sup, Set.vadd_set_symmDiff, BooleanAlgebra.le_top, Finset.inf_sdiff_left, AlgebraicGeometry.LocallyRingedSpace.Γevaluation_ne_zero_iff_mem_basicOpen, AlgebraicGeometry.basicOpen_eq_of_affine, AlgebraicGeometry.LocallyRingedSpace.Γ_map_op, Algebra.cardinalMk_adjoin_le, OrdinalApprox.lfp_mem_range_lfpApprox, Set.symmDiff_nonempty, FrameHom.toFun_eq_coe, Filter.blimsup_sup_le_or, add_sup, Algebra.mul_mem_sup, AlgebraicGeometry.Scheme.ΓSpecIso_naturality_assoc, top_himp, AlgebraicGeometry.IsAffineOpen.fromSpec_toSpecΓ_assoc, MeasureTheory.AEEqFun.posPart_mk, Complex.adjoin_I, Finset.sup_add, max_neg_zero, SSet.Subcomplex.range_eq_top_iff, Con.toSetoid_top, AlgebraicGeometry.Scheme.IdealSheafData.inf_mul, Partition.coe_removeBot, AlgebraicGeometry.PresheafedSpace.toRestrictTop_base, AlgebraicGeometry.LocallyRingedSpace.isUnit_res_toΓSpecMapBasicOpen, Ideal.le_comap_sup, Monoid.Coprod.range_eq, Heyting.isRegular_bot, AlgebraicGeometry.ΓSpec_adjunction_homEquiv_eq, Nat.iSup_lt_succ, ContinuousMap.elemental_id_eq_top, MeasureTheory.exists_measure_symmDiff_lt_of_generateFrom_isSetSemiring, Subgroup.closure_union, CompleteLattice.isCompactElement_iff_exists_le_sSup_of_le_sSup, NumberField.Units.finiteIndex_iff_sup_torsion_finiteIndex, MeasureTheory.OuterMeasure.map_top, Filter.blimsup_not_sup, m_Birkhoff_inequalities, min_mabs_mabs_le_mabs_max, Set.preimage_symmDiff, symmDiff_left_comm, Ideal.ofList_cons, Algebra.FiniteType.out, iSup_option, Antitone.map_min, Sublattice.le_comap_sup, polynomialFunctions_closure_eq_top', Finsupp.support_sup, Finset.lt_fold_max, AddSubgroup.sup_eq_closure_add, Submodule.exists_mem_sup, Subalgebra.val_mulMap'_tmul, AffineSubspace.affineSpan_eq_top_iff_vectorSpan_eq_top_of_nontrivial, Projectivization.Subspace.span_univ, AlgebraicGeometry.Scheme.toIso_inv_ι, Multiset.toDFinsupp_union, MvPolynomial.weightedTotalDegree_rename_of_injective, IntermediateField.sup_toSubalgebra_of_right, Submodule.span_insert, FirstOrder.Language.Substructure.instIsEmptySubtypeMemBotOfConstants, Ideal.comap_map_of_surjective', IntermediateField.insepDegree_bot, Cardinal.sum_pow_eq_max_aleph0, IsAlgClosed.algebraicClosure_eq_bot_iff, AlgHom.eqOn_sup, sup_sdiff_eq_sup, IntermediateField.rank_bot', OpenSubgroup.toOpens_top, Submodule.FG.sup, iInf_eq_if, IntermediateField.le_sup_toSubalgebra, TopologicalSpace.Opens.map_top, isCoboundedUnder_le_max, MonomialOrder.degree_sPolynomial_le, CategoryTheory.Functor.imageSieve_map, AddSubmonoid.map_sup, partialSups_eq_biUnion_range, Set.Ioc_inter_Ioi, Set.Finite.sup, ofDual_bihimp, Set.subset_image_symmDiff, AlgebraicGeometry.LocallyRingedSpace.toΓSpec_preimage_zeroLocus_eq, sup_sub_inf_eq_abs_sub, Finset.inf'_sup_distrib_left, AlgebraicGeometry.LocallyRingedSpace.SpecΓIdentity_hom_app, covBy_iff_lt_iff_le_right, CategoryTheory.Sieve.pullback_top, IntermediateField.insepDegree_top, covBy_sup_of_inf_covBy_of_inf_covBy_left, Order.pred_lt_iff, MvPolynomial.IsSymmetric.antitone_supDegree, ZFSet.rank_pair, BooleanSubalgebra.le_comap_sup, ProjectiveSpectrum.basicOpen_one, Filter.blimsup_false, min_le_max_of_add_le_add, Set.Ioo_disjoint_Ioo, IsPGroup.to_sup_of_normal_left, Finset.powerset_union, Finset.sym_succ, AlgebraicGeometry.Scheme.Γevaluation_naturality, ExpGrowth.expGrowthSup_sup, MeasureTheory.condExp_bot', iSup_symmDiff_iSup_le, sup_iInf₂_eq, IsGalois.tfae, Filter.blimsup_or_eq_sup, Subfield.card_bot, AlgebraicGeometry.basicOpen_eq_bot_iff, RingCon.coe_top, isModularLattice_iff_inf_sup_inf_assoc, Finset.sup_toFinset, max_zero_sub_eq_self, OpenAddSubgroup.toOpens_top, MeasureTheory.Submartingale.sup, AlgebraicGeometry.Scheme.IdealSheafData.ker_glueDataObjι_appTop, CategoryTheory.Sieve.uliftFunctorInclusion_top_isIso, toDual_symmDiff, AlgebraicGeometry.Spec.germ_stalkMapIso_hom, MonomialOrder.coeff_sPolynomial_sup_eq_zero, Finsupp.support_sup_union_support_inf, CategoryTheory.ObjectProperty.instSmallMax, Finset.sup_univ_eq_iSup, IntermediateField.LinearDisjoint.eq_bot_of_self, instLawfulOrderSup_mathlib, Subgroup.index_map, NonUnitalStarSubalgebra.prod_top, ProbabilityTheory.Kernel.indep_bot_right, CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.D₃_W, separableClosure.separableClosure_eq_bot, AlgebraicGeometry.Spec.fromSpecStalk_eq, NonUnitalAlgebra.top_toSubring, Cardinal.mul_eq_max', AddMonoid.Coprod.range_inl_sup_range_inr, ContinuousMapZero.elemental_eq_top, AlgebraicGeometry.AffineSpace.isoOfIsAffine_inv_over, IntermediateField.fg_top_iff, MvPolynomial.leadingCoeff_toLex, IntermediateField.sup_toSubfield, Set.IccExtend_apply, Ideal.span_union, AddSubmonoid.addSubmonoid_smul_sup, CategoryTheory.MorphismProperty.toSet_max, AlgebraicGeometry.LocallyRingedSpace.basicOpen_eq_bot_of_isNilpotent, IntermediateField.sup_toSubalgebra_of_isAlgebraic_right, symmDiff_right_involutive, fixedPoints_addSubgroup_sup, CategoryTheory.GrothendieckTopology.top_covers, CategoryTheory.Presieve.factorsThru_top, NonUnitalAlgebra.mem_bot, AlgebraicGeometry.LocallyRingedSpace.Γevaluation_naturality, Finset.infs_sups_subset_left, AlgebraicGeometry.Proj.iSup_basicOpen_eq_top, AlgebraicGeometry.IsAffineOpen.fromSpec_preimage_basicOpen', CompleteLattice.le_sSup, continuous_sup_rng_left, induced_top, AlgebraicGeometry.Scheme.IdealSheafData.support_bot, map_symmDiff, AlgebraicGeometry.Scheme.Hom.opensRange_of_isIso, AlgebraicGeometry.LocallyRingedSpace.toΓSpecMapBasicOpen_eq, Submodule.lTensorOne_one_tmul, symmDiff_symmDiff_symmDiff_comm, Finsupp.toMultiset_sup, Finset.Ioc_disjoint_Ioc, Disjoint.symmDiff_right, IntermediateField.relfinrank_top_left, Ideal.IsHomogeneous.sup, CompleteLinearOrder.sdiff_le_iff, iSup_of_empty, AlgebraicGeometry.Scheme.Opens.instIsIsoCommRingCatAppLEιTopToScheme, Ordinal.max_zero_right, IntermediateField.map_sup, AlgebraicGeometry.IsAffineOpen.sup_of_disjoint, sInf_eq_top, iInf_neg, IsTranscendenceBasis.lift_cardinalMk_eq_max_lift, IsTranscendenceBasis.lift_rank_eq_max_lift, AlgebraicGeometry.IsAffineOpen.ΓSpecIso_hom_fromSpec_app, List.zipWith_swap_prod_support, CategoryTheory.sheafBotEquivalence_counitIso, Submodule.rank_sup_add_rank_inf_eq, Finset.truncatedSup_infs_of_notMem, GroupTopology.toTopologicalSpace_top, biSup_sup, Fin.val_top, Finset.sup_eq_union, MvRatFunc.rank_eq_max_lift, iInf_lt_top, Con.toSetoid_eq_top, DFinsupp.support_inf_union_support_sup, MeasureTheory.OuterMeasure.dirac_caratheodory, max_left_commutative, bihimp_eq', IntermediateField.finSepDegree_top, SSet.N.iSup_subcomplex_eq_top, covBy_sup_of_inf_covBy_right, IsOpen.affineSpan_eq_top, le_max_iff, CategoryTheory.Sieve.id_mem_iff_eq_top, BooleanAlgebra.bot_le, Submodule.finite_sup, Antitone.max, AffineSubspace.not_wOppSide_bot, AlgebraicGeometry.instQuasiCompactToSpecΓOfCompactSpaceCarrierCarrierCommRingCat, IsAdjoinRoot.primitive_element_root, AlgebraicGeometry.AffineSpace.comp_homOfVector_assoc, MvPolynomial.cardinalMk_le_max, abs_min_sub_min_le_max, Subgroup.mem_sup_right, Submodule.mem_sup_left, strictMono_inf_prod_sup, AlgebraicGeometry.Scheme.Opens.ι_image_top, Cardinal.mk_freeCommRing, infIccOrderIsoIccSup_symm_apply_coe, sup_sdiff_self, AddSubgroup.comap_sup_comap_le, LowerSemicontinuousOn.sup, Subfield.extendScalars_self, PseudoMetric.finsetSup_apply, Coheyting.boundary_sup_sup_boundary_inf, Field.Emb.Cardinal.adjoin_basis_eq_top, NonUnitalAlgebra.top_toSubmodule, Cardinal.mk_freeAbelianGroup, Subgroup.mem_sup', iSup_eq_bot, limsup_finset_sup', Algebra.TensorProduct.adjoin_tmul_eq_top, iInf_sup_of_antitone, MeasurableSet.exists_isOpen_symmDiff_lt, AlgebraicGeometry.Scheme.Γ_obj_op, sup_ind, ContinuousMap.starSubalgebra_topologicalClosure_eq_top_of_separatesPoints, BiheytingAlgebra.top_sdiff, partialSups_add_one_eq_sup_disjointed, Submonoid.sup_eq_range, MvPolynomial.support_symmDiff_support_subset_support_add, IntermediateField.relrank_bot_left, sup_himp_distrib, SSet.Subcomplex.topIso_hom, MeasureTheory.MeasurePreserving.measure_symmDiff_preimage_iterate_le, CompleteBooleanAlgebra.inf_compl_le_bot, Subalgebra.LinearDisjoint.eq_bot_of_commute_of_self, CategoryTheory.Sieve.pullback_ofObjects_eq_top, Submodule.mem_sup_right, AlgebraicGeometry.Scheme.basicOpen_eq_bot_iff_forall_evaluation_eq_zero, AlgebraicGeometry.HasRingHomProperty.iff_of_source_openCover, Submodule.sup_set_smul, AddSubmonoid.FG.finset_sup, min_div_div_right_of_nonpos, Subalgebra.finrank_bot, CategoryTheory.Subfunctor.Subpresheaf.max_min, Order.pred_lt_iff_eq_or_gt, MeasureTheory.IsSetRing.finsetSup_mem, HasSolidNorm.continuousSup, Submodule.sup_span, AlgebraicGeometry.Scheme.Opens.topIso_hom, NonUnitalSubalgebra.starClosure_toNonUnitalSubalgebra, MeasureTheory.OuterMeasure.top_apply, sup_sdiff_left, LinearPMap.supSpanSingleton_apply_mk, HahnSeries.cardSupp_hsum_powers_le, sup_lt_of_lt_sdiff_right, Ideal.mem_sup_right, min_inv_inv', Ideal.sup_mul, CategoryTheory.presheafIsGeneratedBy_of_isFinite, Set.abs_indicator_symmDiff, EuclideanGeometry.orthogonalProjection_sup_of_orthogonalProjection_eq, ZMod.fieldRange_castHom_eq_bot, Cardinal.add_le_max, Finset.sup'_mul, Algebra.sup_def, Subalgebra.restrictScalars_top, QuotientGroup.leftRel_eq_top, Subsemigroup.map_sup_comap_of_surjective, PrimeSpectrum.basicOpen_one, bihimp_hnot_self, AlgebraicGeometry.Scheme.Hom.comp_appTop_assoc, Finpartition.sup_parts, AlgebraicGeometry.IsAffineOpen.fromSpec_app_of_le, Nat.iSup_le_succ', AffineSubspace.eq_bot_or_nonempty, Polynomial.degree_sub_le_of_le, MeasureTheory.Measure.top_add, AlgebraicGeometry.AffineSpace.map_appTop_coord, top_symmDiff', AntitoneOn.map_sup, mabs_sup_div_sup_le_mabs, Polynomial.supDegree_eq_natDegree, neg_inf, AlgebraicGeometry.Scheme.toSpecΓ_preimage_basicOpen, Polynomial.degree_add_eq_of_leadingCoeff_add_ne_zero, PrimeSpectrum.iSup_basicOpen_eq_top_iff', Filter.bliminf_false, Nonneg.toNonneg_lt, abs_min_le_max_abs_abs, ConditionallyCompleteLinearOrderedField.toMulPosStrictMono, inf_symmDiff_symmDiff, Finset.max_prod_le, MeasureTheory.hitting_eq_sInf, LieSubalgebra.add_eq_sup, AlgebraicGeometry.isIso_fromTildeΓ_iff, top_sdiff', BooleanSubalgebra.supClosed, sup_iInf_eq, Submodule.map_add_le, IntermediateField.mem_bot, CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.D₄_W, compl_bihimp, TopCat.Sheaf.interUnionPullbackCone_pt, AlgebraicGeometry.PresheafedSpace.restrictTopIso_inv, Submodule.covBy_span_singleton_sup, Algebra.IsCentral.out, polynomialFunctions_closure_eq_top, AlgebraicGeometry.Scheme.openCoverBasicOpenTop_f, hnot_hnot_sup_distrib, IsCompl.inf_sup, IsDedekindDomain.integer_univ, bihimp_top, Ordinal.card_opow_le, MeasureTheory.MeasuredSets.edist_def, ClosedSubmodule.coe_sup, AddSubmonoid.prod_bot_sup_bot_prod, PredOrder.prelimitRecOn_pred, AlgebraicGeometry.LocallyRingedSpace.toΓSpecSheafedSpace_hom_c_app, tsub_add_eq_max, IsAdjoinRoot.adjoin_root_eq_top, NonUnitalAlgebra.toNonUnitalSubring_top, Set.Icc_union_Icc', iInf_emptyset, Ideal.sup_mul_left_self, MeasureTheory.measure_symmDiff_eq_zero_iff, Subgroup.IsComplement'.sup_eq_top, AlgebraicGeometry.isField_of_isIntegral_of_subsingleton, Cardinal.mk_finsupp_lift_of_infinite', Submodule.wcovBy_span_singleton_sup, Finset.sup'_univ_eq_ciSup, TopologicalSpace.Opens.not_nonempty_iff_eq_bot, Set.Ioi_inter_Ioi, AlgebraicGeometry.ProjectiveSpectrum.Proj.toOpen_toSpec_val_c_app, AddSubgroup.FG.sup, Finset.sup_id_eq_sSup, symmDiff_symmDiff_cancel_right, Subgroup.unop_sup, Cardinal.power_le_max_power_one, CategoryTheory.PreOneHypercover.sieve₀_trivial, Finset.sup_himp_left, CategoryTheory.Subfunctor.preimage_eq_top_iff, AddSubgroup.closure_union, IntermediateField.fixingSubgroup_bot, compl_sup_eq_top, NonUnitalAlgebra.adjoin_union, CategoryTheory.Subfunctor.Subpresheaf.eq_top_iff_isIso, sdiff_sdiff_eq_sdiff_sup, iSup₂_eq_top, ContinuousLinearMap.range_coprod, generateFrom_inter, Finpartition.sum_combine, Ideal.mul_right_self_sup, symmDiff_bot, MeasureTheory.AddContent.supClosure_apply, Finset.exists_sup_eq_iSup, CategoryTheory.Presieve.isSheafFor_top, Submodule.prod_sup_prod, Nonneg.orderedSub, AlgebraicGeometry.IsAffineOpen.fromSpec_toSpecΓ, Subalgebra.bot_eq_top_iff_rank_eq_one, succ_max, IntermediateField.coe_top, AlgebraicGeometry.AffineSpace.homOfVector_appTop_coord, continuous_max, BiheytingAlgebra.sdiff_le_iff, min_eq_top, Finset.add_sup'', isGalois_bot, Monoid.Coprod.mrange_inl_sup_mrange_inr, AddSubmonoid.FG.sup, iSup_union, AlgebraicGeometry.Scheme.IsQuasiAffine.isBasis_basicOpen, Subalgebra.rTensorBot_tmul, AddSubmonoid.unop_sup, sup_sdiff_injOn, Cardinal.mul_le_max, Fin.zero_eq_top, LowerSet.supIrred_Iic, AlgebraicGeometry.Scheme.isoSpec_image_zeroLocus, disjointed_partialSups, MeasurableSpace.measurableSet_sup, Finset.symmDiff_eq_union, iSup_extend_bot, Order.Coframe.MinimalAxioms.sup_sInf_eq, AddOreLocalization.cardinalMk_le_max, Algebra.range_id, HahnSeries.cardSupp_inv_le, sSupHomClass.toSupBotHomClass, Polynomial.SplittingField.adjoin_rootSet, Filter.sup_liminf, AlgebraicGeometry.isCompact_and_isOpen_iff_finite_and_eq_biUnion_basicOpen, isSplittingField_iff_intermediateField, RingCon.sup_eq_ringConGen, Associates.FactorSet.sup_add_inf_eq_add, Submodule.add_eq_sup, iSup_bot, AlgebraicGeometry.PresheafedSpace.restrict_top_presheaf, isGalois_iff_isGalois_bot, max_le_max_right, Fin.rev_bot, Subring.map_sup, CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.D₂_W, Subspace.dualAnnihilator_inf_eq, TrivSqZeroExt.range_inlAlgHom_sup_adjoin_range_inr, inf_mul_sup, Polynomial.adjoin_X, KaehlerDifferential.kerTotal_map', AddSubgroup.addSubgroupOf_sup, IntermediateField.normal_sup, AffineSubspace.bot_parallel_iff_eq_bot, bihimp_eq_top, edist_indicator, AddMonoidAlgebra.cardinalMk_of_infinite, AddSubmonoid.mem_sup_left, FirstOrder.Language.Substructure.fg_bot, Set.Ioo_inter_Ioo, AddSubgroup.relIndex_sup_right, Submodule.sup_toAddSubgroup, CompleteDistribLattice.MinimalAxioms.inf_sSup_le_iSup_inf, AddSubgroup.map_sup, Finset.sup'_eq_zero, CategoryTheory.PreZeroHypercover.presieve₀_add, Ordinal.lsub_sum, Finset.sup_id_set_eq_sUnion, MeasureTheory.OuterMeasure.map_sup, MeasureTheory.NullMeasurableSet.symmDiff, bihimp_bot, norm_sup_sub_sup_le_norm, TopologicalSpace.Opens.coe_top, max_sub_sub_right, isAddFoelner_iff, sup_Prop_eq, Filter.Germ.max_def, toBoolRing_symmDiff, Disjoint.symmDiff_left, CategoryTheory.Subfunctor.epi_iff_range_eq_top, IntermediateField.finrank_adjoin_simple_eq_one_iff, iSup_sum, LinearMap.quotientInfEquivSupQuotient_surjective, Sublattice.mem_map_equiv, CompleteLattice.ωScottContinuous.bot, CategoryTheory.PreOneHypercover.sieve₁_trivial, StarSubalgebra.top_toSubalgebra, Order.Coframe.MinimalAxioms.iInf_sup_le_sup_sInf, IsCyclotomicExtension.lcm_sup, SequentialSpace.sup, AffineSubspace.sup_direction_lt_of_nonempty_of_inter_empty, Set.Ioo_union_Ioo', Ideal.span_insert, Finset.instAssociativeDisjSups, CategoryTheory.Subfunctor.Subpresheaf.range_eq_top, AlgebraicGeometry.LocallyRingedSpace.toΓSpec_preimage_basicOpen_eq, instIndiscreteTopology, bihimp_himp_right, sup_eq_add_posPart_sub, Subalgebra.LinearDisjoint.eq_bot_of_self, FreeAlgebra.cardinalMk_eq_max, MonomialOrder.degree_sPolynomial_lt_sup_degree, Submodule.map₂_sup_right, ZFSet.rank_union, AhlswedeZhang.infSum_union_add_infSum_sups, NonUnitalAlgebra.toNonUnitalSubsemiring_eq_top, Submonoid.sup_eq_closure, TopologicalSpace.Opens.coe_eq_univ, sInf_eq_bot, Set.smul_set_symmDiff₀, Field.primitive_element_iff_algHom_eq_of_eval, inf_compl_eq_bot, csSup_union, IntermediateField.finiteDimensional_sup, AlgebraicGeometry.IsAffineOpen.isoSpec_hom_appTop, separableClosure.eq_bot_iff, Right.min_le_max_of_add_le_add, CovBy.sup_of_inf_left, Subalgebra.LinearDisjoint.bot_left, Submodule.isOrtho_sup_left, Finset.disjiUnion_Iic_disjointed, Subalgebra.rank_bot, AlgebraicGeometry.instIsIsoModulesSpecOfCarrierFromTildeΓFreeOpensCarrierCarrierCommRingCat, lt_max_of_two_nsmul_lt_add, CategoryTheory.Subfunctor.range_id, CovBy.sup_of_inf_right, Ordinal.preOmega_max, partialSups_disjoint_of_disjoint, NonUnitalSubalgebra.mem_starClosure, le_sdiff_sup, IntermediateField.fixingSubgroup_sup, Set.symmDiff_union_subset, trop_sInf_image, Subalgebra.LinearDisjoint.bot_right, Submonoid.exists_mem_sup, MeasureTheory.dist_indicatorConstLp_eq_norm, IntermediateField.rank_adjoin_simple_eq_one_iff, Cardinal.add_eq_right_iff, separableClosure.adjoin_eq_of_isAlgebraic_of_isSeparable, AddCon.toSetoid_eq_top, Tropical.untrop_sup, OpenSubgroup.toSubgroup_sup, Subgroup.ofUnits_sup_units, notMem_iff_exists_ne_and_isConjRoot, AlgebraicGeometry.instIsAffineHomιBasicOpen, Coheyting.boundary_le_boundary_sup_sup_boundary_inf_right, sdiff_symmDiff_right, Cardinal.mk_finsupp_of_infinite', BoundedLatticeHom.coe_comp_lattice_hom, compl_bot, Finset.mul_sup₀, MvPolynomial.cardinalMk_eq_max_lift, Algebra.adjoin_empty, Subalgebra.fg_bot_toSubmodule, Algebra.botEquiv_symm_apply, MeasurableSpace.generateFrom_singleton_empty, NonUnitalStarAlgebra.toNonUnitalSubalgebra_bot, AffineSubspace.notMem_bot, iSup_or, Ordinal.toNatOrdinal_max, Set.IciExtend_apply, exists_glb_Ioi, lowerBounds_Ioi, IsMaxOn.max, lt_max_iff, Submodule.comap_sup_of_injective, LinearMap.range_add_le, DistribLattice.mem_ideal_sup_principal, Finset.compl_truncatedSup, FirstOrder.Language.Substructure.lift_card_closure_le, TopologicalLattice.toContinuousSup, GeneralizedCoheytingAlgebra.sdiff_le_iff, Order.Coframe.MinimalAxioms.sInf_sup_eq, Sublattice.map_sup, List.maximum_concat, IntermediateField.isPurelyInseparable_sup, MeasureTheory.condExp_bot_ae_eq, AddSubgroup.map_le_map_iff', Submodule.small_sup, PSet.rank_pair, AddSubmonoid.comap_sup_map_of_injective, CategoryTheory.Sieve.generate_of_contains_isSplitEpi, Subalgebra.rank_top, Finset.sup_mul₀, Complementeds.coe_sup, AlgebraicGeometry.HasRingHomProperty.iff_of_isAffine, Finset.four_functions_theorem, Subalgebra.bot_eq_top_of_rank_eq_one, RingCon.toCon_bot, CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.Diagram.sup_W, OrderEmbedding.birkhoffFinset_sup, sInfHom.top_apply, AddMonoidAlgebra.supDegree_mem_support, Finset.card_truncatedSup_union_add_card_truncatedSup_infs, Disjoint.sup_sdiff_cancel_right, CategoryTheory.Subfunctor.Subpresheaf.range_toRange, AlgebraicGeometry.SheafedSpace.restrictTopIso_hom, IsGalois.mem_bot_iff_fixed, FreeAlgebra.cardinalMk_eq_max_lift, NonarchimedeanHomClass.map_add_le_max, Finset.image_symmDiff, Subalgebra.finrank_eq_one_iff, AlgebraicGeometry.ΓSpec.toSpecΓ_unop, Cardinal.lift_max, MeasureTheory.OuterMeasure.toMeasure_top, Set.Iio_union_Ico', AddSubmonoid.mem_sup_right, DFinsupp.support_sup, List.maximum_append, IsMinFilter.max, IntermediateField.map_bot, LinearMap.prod_eq_sup_map, subalgebra_top_rank_eq_submodule_top_rank, ConvexOn.le_max_of_mem_segment, AddSubgroup.normal_addSubgroupOf_sup_of_le_normalizer, CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.Diagram.sup_P, PrimeSpectrum.basicOpen_eq_bot_iff, AlgebraicGeometry.Scheme.IdealSheafData.vanishingIdeal_bot, AlgebraicGeometry.SheafedSpace.Γ_map_op, AlgebraicGeometry.Scheme.isNilpotent_iff_basicOpen_eq_bot_of_isCompact, Nat.iSup_le_succ, Finset.mem_uIcc, MeasureTheory.IsStoppingTime.max_const, TrivSqZeroExt.range_liftAux, SSet.skeletonOfMono_succ, Monotone.disjointed_add_one_sup, Set.union_symmDiff_union_subset, Finset.max_abv_sum_one_le, sup_sdiff_symmDiff, RingCon.toCon_top, max_add, MonomialOrder.sPolynomial_mul_monomial, max_div_div_right', PredOrder.colimitRecOn_pred, LinearMap.surjective_domRestrict_iff, max_eq_iff, Finset.iSup_union, Antitone.map_sup, MvPolynomial.cardinalMk_eq_max, isCyclic_tfae, MonomialOrder.sPolynomial_leadingTerm_mul, separableClosure.eq_bot_of_isPurelyInseparable, Subalgebra.eq_bot_of_isPurelyInseparable_of_isSeparable, Subalgebra.finite_bot, IntermediateField.finSepDegree_bot, affineSpan_eq_top_iff_nonempty_of_subsingleton, CategoryTheory.Sieve.functorPullback_union, edist_mulIndicator, AlgebraicGeometry.SpecMap_ΓSpecIso_inv_toSpecΓ_assoc, Set.subset_symmDiff_union_symmDiff_left, Algebra.Subalgebra.restrictScalars_adjoin, Algebraic.cardinalMk_lift_le_max, FirstOrder.Language.BoundedFormula.card_le, MonomialOrder.degree_sPolynomial, CategoryTheory.GrothendieckTopology.top_covering, inf_le_right, AddMonoidAlgebra.apply_supDegree_add_supDegree, Filter.limsSup_top, Fin.succ_top, AlgebraicGeometry.LocallyRingedSpace.Γ_obj, Algebra.rank_adjoin_le, LinearMap.ker_comp_eq_of_commute_of_disjoint_ker, CoheytingAlgebra.top_sdiff, AddGroupTopology.toTopologicalSpace_bot, AlgebraicGeometry.Scheme.Spec_fromSpecStalk, IntermediateField.sepDegree_top, IsGaloisGroup.fixedPoints_eq_bot, Subgroup.sup_eq_closure, AddUnits.max_val, sInf_sup_sInf, add_tsub_eq_max, LinearMap.BilinForm.span_singleton_sup_orthogonal_eq_top, sup_le_of_le_sdiff_right, SSet.skeleton_zero, setOf_isOpen_sup, Submodule.comap_map_eq, sdiff_triangle, AlgebraicGeometry.Scheme.toSpecΓ_base

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
ext 📖	—	Preorder.toLE PartialOrder.toPreorder SemilatticeInf.toPartialOrder toSemilatticeInf	—	—	SemilatticeSup.ext SemilatticeInf.ext inf_le_left inf_le_right le_inf
inf_le_left 📖	mathematical	—	Preorder.toLE PartialOrder.toPreorder SemilatticeSup.toPartialOrder toSemilatticeSup inf	—	—
inf_le_right 📖	mathematical	—	Preorder.toLE PartialOrder.toPreorder SemilatticeSup.toPartialOrder toSemilatticeSup inf	—	—
le_inf 📖	mathematical	Preorder.toLE PartialOrder.toPreorder SemilatticeSup.toPartialOrder toSemilatticeSup	inf	—	—

LinearOrder

Definitions

Name	Category	Theorems
toLattice 📖	CompOp	10 math math: lt_inf_iff, min_min_min_comm, inf_le_iff, lt_sup_iff, max_max_max_comm, sup_lt_iff, inf_lt_iff, le_sup_iff, sup_ind, inf_ind

Monotone

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
inf 📖	mathematical	Monotone PartialOrder.toPreorder SemilatticeInf.toPartialOrder	Pi.instMinForall_mathlib SemilatticeInf.toMin	—	inf_le_inf
le_map_sup 📖	mathematical	Monotone PartialOrder.toPreorder SemilatticeSup.toPartialOrder	Preorder.toLE SemilatticeSup.toMax	—	sup_le le_sup_left le_sup_right
map_inf 📖	mathematical	Monotone PartialOrder.toPreorder SemilatticeInf.toPartialOrder Lattice.toSemilatticeInf DistribLattice.toLattice instDistribLatticeOfLinearOrder	SemilatticeInf.toMin	—	map_sup dual
map_inf_le 📖	mathematical	Monotone PartialOrder.toPreorder SemilatticeInf.toPartialOrder	Preorder.toLE SemilatticeInf.toMin	—	le_inf inf_le_left inf_le_right
map_sup 📖	mathematical	Monotone PartialOrder.toPreorder SemilatticeInf.toPartialOrder Lattice.toSemilatticeInf DistribLattice.toLattice instDistribLatticeOfLinearOrder SemilatticeSup.toPartialOrder	SemilatticeSup.toMax Lattice.toSemilatticeSup	—	LE.total sup_of_le_right sup_of_le_left
max 📖	mathematical	Monotone PartialOrder.toPreorder SemilatticeInf.toPartialOrder Lattice.toSemilatticeInf DistribLattice.toLattice instDistribLatticeOfLinearOrder	SemilatticeSup.toMax Lattice.toSemilatticeSup	—	sup
min 📖	mathematical	Monotone PartialOrder.toPreorder SemilatticeInf.toPartialOrder Lattice.toSemilatticeInf DistribLattice.toLattice instDistribLatticeOfLinearOrder	SemilatticeInf.toMin	—	inf
of_le_map_sup 📖	mathematical	Preorder.toLE PartialOrder.toPreorder SemilatticeSup.toPartialOrder SemilatticeSup.toMax	Monotone	—	monotone_dual_iff of_map_inf_le
of_left_le_map_sup 📖	mathematical	Preorder.toLE SemilatticeSup.toMax	Monotone PartialOrder.toPreorder SemilatticeSup.toPartialOrder	—	monotone_dual_iff of_map_inf_le_left
of_map_inf 📖	mathematical	SemilatticeInf.toMin	Monotone PartialOrder.toPreorder SemilatticeInf.toPartialOrder	—	of_map_inf_le Eq.le
of_map_inf_le 📖	mathematical	Preorder.toLE PartialOrder.toPreorder SemilatticeInf.toPartialOrder SemilatticeInf.toMin	Monotone	—	of_map_inf_le_left LE.le.trans inf_le_left
of_map_inf_le_left 📖	mathematical	Preorder.toLE SemilatticeInf.toMin	Monotone PartialOrder.toPreorder SemilatticeInf.toPartialOrder	—	inf_eq_right
of_map_sup 📖	mathematical	SemilatticeSup.toMax	Monotone PartialOrder.toPreorder SemilatticeSup.toPartialOrder	—	dual of_map_inf
sup 📖	mathematical	Monotone PartialOrder.toPreorder SemilatticeSup.toPartialOrder	Pi.instMaxForall_mathlib SemilatticeSup.toMax	—	sup_le_sup

MonotoneOn

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
inf 📖	mathematical	MonotoneOn PartialOrder.toPreorder SemilatticeInf.toPartialOrder	Pi.instMinForall_mathlib SemilatticeInf.toMin	—	dual sup
map_inf 📖	mathematical	MonotoneOn PartialOrder.toPreorder SemilatticeInf.toPartialOrder Lattice.toSemilatticeInf DistribLattice.toLattice instDistribLatticeOfLinearOrder Set Set.instMembership	SemilatticeInf.toMin	—	map_sup dual
map_sup 📖	mathematical	MonotoneOn PartialOrder.toPreorder SemilatticeInf.toPartialOrder Lattice.toSemilatticeInf DistribLattice.toLattice instDistribLatticeOfLinearOrder SemilatticeSup.toPartialOrder Set Set.instMembership	SemilatticeSup.toMax Lattice.toSemilatticeSup	—	le_total sup_of_le_right sup_of_le_left
max 📖	mathematical	MonotoneOn PartialOrder.toPreorder SemilatticeInf.toPartialOrder Lattice.toSemilatticeInf DistribLattice.toLattice instDistribLatticeOfLinearOrder	SemilatticeSup.toMax Lattice.toSemilatticeSup	—	sup
min 📖	mathematical	MonotoneOn PartialOrder.toPreorder SemilatticeInf.toPartialOrder Lattice.toSemilatticeInf DistribLattice.toLattice instDistribLatticeOfLinearOrder	SemilatticeInf.toMin	—	inf
of_map_inf 📖	mathematical	SemilatticeInf.toMin	MonotoneOn PartialOrder.toPreorder SemilatticeInf.toPartialOrder	—	inf_eq_left
of_map_sup 📖	mathematical	SemilatticeSup.toMax	MonotoneOn PartialOrder.toPreorder SemilatticeSup.toPartialOrder	—	dual of_map_inf
sup 📖	mathematical	MonotoneOn PartialOrder.toPreorder SemilatticeSup.toPartialOrder	Pi.instMaxForall_mathlib SemilatticeSup.toMax	—	sup_le_sup

Ne

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
inf_lt_or_inf_lt 📖	mathematical	—	Preorder.toLT PartialOrder.toPreorder SemilatticeInf.toPartialOrder SemilatticeInf.toMin	—	inf_lt_left inf_lt_right not_ge_or_not_le
lt_sup_or_lt_sup 📖	mathematical	—	Preorder.toLT PartialOrder.toPreorder SemilatticeSup.toPartialOrder SemilatticeSup.toMax	—	left_lt_sup right_lt_sup not_le_or_not_ge

OrderDual

Definitions

Name	Category	Theorems
instDistribLattice 📖	CompOp	3 math math: DistLat.dual_map, BddDistLat.dual_map, FinBddDistLat.dual_map
instLattice 📖	CompOp	34 math math: isSublattice_preimage_ofDual, instIsWeakLowerModularLatticeOrderDual, Finset.uIcc_toDual, instIsModularLatticeOrderDual, instIsUpperModularLatticeOrderDual, BoundedLatticeHom.dual_id, Lat.dual_map, DistLat.dual_map, BoundedLatticeHom.symm_dual_comp, LatticeHom.dual_symm_apply_toFun, ofDual_preimage_latticeClosure, instHasSolidNorm, LatticeHom.dual_apply_toFun, LatticeHom.symm_dual_id, instIsWeakUpperModularLatticeOrderDual, BoundedLatticeHom.dual_symm_apply_toFun, Set.uIcc_ofDual, LatticeHom.dual_id, BddDistLat.dual_map, Set.uIcc_toDual, BoundedLatticeHom.symm_dual_id, topologicalLattice, BoolAlg.dual_map, LatticeHom.symm_dual_comp, BoundedLatticeHom.dual_apply_toFun, LatticeHom.dual_comp, instIsLowerModularLatticeOrderDual, BoundedLatticeHom.dual_comp, ComplementedLattice.instOrderDual, IsSublattice.dual, isSublattice_preimage_toDual, FinBddDistLat.dual_map, FinBoolAlg.dual_map, BddLat.dual_map
instSemilatticeInf 📖	CompOp	15 math math: supIrred_ofDual, Finset.ofDual_inf, SemilatticeInf.dual_dual, SupClosed.dual, SemilatticeSup.dual_dual, infClosed_preimage_ofDual, SupPrime.dual, infPrime_toDual, Finset.toDual_sup, infIrred_toDual, supClosed_preimage_toDual, Finset.ofDual_inf', SupIrred.dual, supPrime_ofDual, Finset.toDual_sup'
instSemilatticeSup 📖	CompOp	16 math math: supClosed_preimage_ofDual, supPrime_toDual, infClosed_preimage_toDual, infPrime_ofDual, InfPrime.dual, SemilatticeInf.dual_dual, supIrred_toDual, Finset.toDual_inf', Finset.ofDual_sup', InfIrred.dual, SemilatticeSup.dual_dual, Finset.toDual_inf, infIrred_ofDual, InfClosed.dual, SemilatInfCat.dual_obj_isSemilatticeSup, Finset.ofDual_sup

Pairwise

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
of_gt 📖	mathematical	Symmetric	Pairwise	—	pairwise_iff_gt
of_lt 📖	mathematical	Symmetric	Pairwise	—	pairwise_iff_lt

Pi

Definitions

Name	Category	Theorems
instDistribLattice 📖	CompOp	—
instLattice 📖	CompOp	49 math math: oneLePart_apply, Sublattice.pi_top, Set.image_single_uIcc_right, Sublattice.pi_univ_eq_bot_iff, Sublattice.coe_pi, abs_def, negPart_apply, abs_apply, Set.image_mulSingle_uIcc_left, BoundedContinuousFunction.coe_posPart, ConvexOn.isBoundedUnder_abs, coe_evalLatticeHom, Set.image_mulSingle_uIcc, Sublattice.pi_univ_bot, card_uIcc, leOnePart_apply, MeasureTheory.Submartingale.pos, RCLike.abs_wInner_le, Sublattice.le_pi, MeasureTheory.lpNorm_abs, uIcc_eq, leOnePart_def, Set.image_mulSingle_uIcc_right, isSublattice_pi, BoundedContinuousFunction.coe_abs, Real.abs_circleAverage_le_circleAverage_abs, ConcaveOn.isBoundedUnder_abs, Set.pi_univ_uIcc, negPart_def, Sublattice.pi_bot, Set.image_single_uIcc_left, Set.image_update_uIcc_left, Set.image_single_uIcc, posPart_def, ContinuousMap.coe_mabs, Set.image_update_uIcc, Set.image_update_uIcc_right, posPart_apply, Sublattice.mem_pi, BoundedContinuousFunction.coe_negPart, oneLePart_def, CircleIntegrable.abs, Sublattice.pi_univ_eq_bot, Sublattice.pi_empty, evalLatticeHom_apply, HasCompactSupport.abs, ContinuousMap.coe_abs, parallelepiped_single, MeasureTheory.MemLp.abs
instMaxForall_mathlib 📖	CompOp	76 math math: symmDiff_def, ContinuousWithinAt.sup', MeasureTheory.Integrable.sup, Monotone.sup, GroupSeminorm.coe_sup, CategoryTheory.ObjectProperty.HasCardinalLT.sup, MeasureTheory.MemLp.sup, AddCon.sup_def, symmDiff_apply, MeasureTheory.SimpleFunc.coe_sup, Continuous.sup', NonarchAddGroupSeminorm.coe_sup, AddGroupNorm.coe_sup, hasCardinalLT_subtype_max, Filter.EventuallyLE.sup_le, RingCon.sup_def, MeasureTheory.StronglyMeasurable.sup, CauSeq.coe_sup, DFinsupp.coe_sup, QuasiconvexOn.sup, GroupNorm.coe_sup, Seminorm.coe_sup, Filter.EventuallyEq.sup, CategoryTheory.ObjectProperty.instEssentiallySmallMax, single_sup, Filter.EventuallyLE.le_sup_of_le_right, MeasureTheory.AEFinStronglyMeasurable.sup, CategoryTheory.ObjectProperty.instIsClosedUnderIsomorphismsMax, MeasureTheory.Lp.coeFn_sup, CategoryTheory.ObjectProperty.prop_sup_iff, BoundedContinuousFunction.coe_sup, SupBotHom.coe_sup, MonotoneOn.sup, LinearGrowth.linearGrowthSup_sup, Ideal.Filtration.sup_N, Con.sup_def, CompleteLattice.ωScottContinuous.sup, mulSingle_sup, CompactlySupportedContinuousMap.coe_sup, AEMeasurable.sup', TopHom.coe_sup, AntitoneOn.sup, sup_apply, Filter.EventuallyLE.le_sup_of_le_left, Setoid.sup_def, MeasureTheory.Filtration.coeFn_sup, Finset.sup_sup, sup_def, SupHom.coe_sup, CategoryTheory.ObjectProperty.isoClosure_sup, PseudoMetric.coe_sup, MeasureTheory.FinStronglyMeasurable.sup, ContinuousAt.sup', Measurable.sup', ConvexOn.sup, StrictConvexOn.sup, AlgebraicGeometry.Scheme.IdealSheafData.ideal_sup, NonarchAddGroupNorm.coe_sup, MeasureTheory.ae_eq_set_symmDiff, BotHom.coe_sup, Filter.EventuallyLE.sup, ContinuousOn.sup', ExpGrowth.expGrowthSup_sup, MeasureTheory.Submartingale.sup, CategoryTheory.ObjectProperty.instSmallMax, MeasureTheory.AEStronglyMeasurable.sup, Filter.Tendsto.sup_nhds', dist_inf_sup_pi, HasCompactMulSupport.sup, HasCompactSupport.sup, Function.update_sup, OrderHom.coe_sup, Antitone.sup, AddGroupSeminorm.coe_sup, CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.Diagram.sup_P, ContinuousMap.coe_sup
instMinForall_mathlib 📖	CompOp	72 math math: CategoryTheory.ObjectProperty.InheritedFromTarget.instMin, MeasureTheory.stoppedProcess_stoppedProcess, CompactlySupportedContinuousMap.coe_inf, CategoryTheory.ObjectProperty.instIsClosedUnderIsomorphismsMin, Function.update_inf, Nucleus.coe_inf, StrictConcaveOn.inf, MonotoneOn.inf, Finset.inf_inf, ConcaveOn.inf, Measurable.inf', TopHom.coe_inf, Ideal.Filtration.inf_N, Con.coe_inf, bihimp_apply, bihimp_def, single_inf, ContinuousAt.inf', CategoryTheory.ObjectProperty.IsLocal.inf, MeasureTheory.FinStronglyMeasurable.inf, RingCon.coe_inf, CategoryTheory.ObjectProperty.instSmallMin, MeasureTheory.MemLp.inf, QuasiconcaveOn.inf, CategoryTheory.ObjectProperty.instIsStableUnderShiftByMin, HasCompactMulSupport.inf, MeasureTheory.StronglyMeasurable.inf, LinearGrowth.linearGrowthInf_inf, Relation.cutExpand_le_invImage_lex, CategoryTheory.ObjectProperty.instIsTriangulatedClosed₂MinOfIsClosedUnderIsomorphisms, inf_def, ExpGrowth.expGrowthInf_inf, ContinuousOn.inf', Antitone.inf, CategoryTheory.ObjectProperty.InheritedFromSource.instMin, Setoid.inf_def, AntitoneOn.inf, CompleteLattice.ωScottContinuous.inf, ContinuousMap.coe_inf, OrderHom.coe_inf, DFinsupp.coe_inf, MeasureTheory.AEFinStronglyMeasurable.inf, CategoryTheory.ObjectProperty.instIsStableUnderShiftMin, AlgebraicGeometry.geometrically_inf, MeasureTheory.SimpleFunc.coe_inf, ContinuousWithinAt.inf', maximal_subtype, Monotone.inf, BoundedContinuousFunction.coe_inf, mulSingle_inf, CategoryTheory.ObjectProperty.instContainsZeroMinOfIsClosedUnderIsomorphisms, AlgebraicGeometry.Scheme.IdealSheafData.ideal_inf, CategoryTheory.ObjectProperty.instIsTriangulatedMinOfIsClosedUnderIsomorphisms, CategoryTheory.ObjectProperty.prop_inf_iff, CategoryTheory.ObjectProperty.instSmallMin_1, inf_apply, InfHom.coe_inf, minimal_subtype, Filter.Tendsto.inf_nhds', MeasureTheory.Filtration.coeFn_inf, MeasureTheory.Integrable.inf, MeasureTheory.Lp.coeFn_inf, dist_inf_sup_pi, MeasureTheory.AEStronglyMeasurable.inf, InfTopHom.coe_inf, BotHom.coe_inf, Continuous.inf', HasCompactSupport.inf, AEMeasurable.inf', CauSeq.coe_inf, AddCon.coe_inf, Filter.EventuallyEq.inf
instSemilatticeInf 📖	CompOp	15 math math: Continuous.finset_inf', ContinuousAt.finset_inf, ContinuousMap.coe_inf', ContinuousOn.finset_inf, Finset.inf_apply, infClosed_pi, ContinuousOn.finset_inf', ContinuousWithinAt.finset_inf, ContinuousAt.finset_inf', ContinuousWithinAt.finset_inf', Continuous.finset_inf, Filter.Tendsto.finset_inf'_nhds, CompactlySupportedContinuousMap.coe_finsetInf', Finset.inf'_apply, Filter.Tendsto.finset_inf_nhds
instSemilatticeSup 📖	CompOp	23 math math: ContinuousAt.finset_sup, Continuous.finset_sup, ContinuousAt.finset_sup', Finset.sup'_apply, supClosed_pi, Filter.Tendsto.finset_sup_nhds, ContinuousOn.finset_sup', Finset.measurable_range_sup', ContinuousWithinAt.finset_sup, ContinuousWithinAt.partialSups, ContinuousOn.partialSups, Filter.Tendsto.finset_sup'_nhds, ContinuousAt.partialSups, ContinuousOn.finset_sup, Continuous.finset_sup', ContinuousMap.coe_sup', Finset.sup_apply, Continuous.partialSups, Finset.measurable_sup', CompactlySupportedContinuousMap.coe_finsetSup', Filter.Tendsto.partialSups, ContinuousWithinAt.finset_sup', partialSups_apply

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
inf_apply 📖	mathematical	—	instMinForall_mathlib	—	—
inf_def 📖	mathematical	—	instMinForall_mathlib	—	—
sup_apply 📖	mathematical	—	instMaxForall_mathlib	—	—
sup_def 📖	mathematical	—	instMaxForall_mathlib	—	—

Prod

Definitions

Name	Category	Theorems
instDistribLattice 📖	CompOp	—
instLattice 📖	CompOp	31 math math: Sublattice.coe_prod, LatticeHom.fst_apply, Finset.uIcc_map_sectR, Sublattice.mem_prod, Sublattice.prod_mono_left, Set.uIcc_prod_uIcc, Sublattice.prod_mono, Finset.uIcc_product_uIcc, Sublattice.top_prod_top, latticeClosure_prod, Sublattice.prodEquiv_toEquiv, Sublattice.prodEquiv_apply, Sublattice.prod_eq_bot, Sublattice.prod_left_mono, Finset.uIcc_prod_def, Finset.uIcc_map_sectL, Sublattice.prod_bot, LatticeHom.coe_snd, Sublattice.prod_right_mono, LatticeHom.snd_apply, Sublattice.top_prod, Sublattice.bot_prod, Sublattice.le_prod_iff, Set.uIcc_prod_eq, Sublattice.prod_eq_top, LatticeHom.coe_fst, Finset.card_uIcc_prod, Sublattice.prodEquiv_symm_apply, Sublattice.prod_mono_right, Sublattice.prod_top, IsSublattice.prod
instMax_mathlib 📖	CompOp	7 math math: sup_def, snd_sup, symmDiff_fst, symmDiff_snd, swap_sup, mk_sup_mk, fst_sup
instMin_mathlib 📖	CompOp	7 math math: snd_inf, fst_inf, mk_inf_mk, bihimp_fst, inf_def, swap_inf, bihimp_snd
instSemilatticeInf 📖	CompOp	5 math math: Finset.inf_prodMap, Finset.inf'_prodMap, InfClosed.prod, Finset.prodMk_inf'_inf', infClosure_prod
instSemilatticeSup 📖	CompOp	5 math math: Finset.prodMk_sup'_sup', Finset.sup'_prodMap, Finset.sup_prodMap, SupClosed.prod, supClosure_prod

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
fst_inf 📖	mathematical	—	instMin_mathlib	—	—
fst_sup 📖	mathematical	—	instMax_mathlib	—	—
inf_def 📖	mathematical	—	instMin_mathlib	—	—
mk_inf_mk 📖	mathematical	—	instMin_mathlib	—	—
mk_sup_mk 📖	mathematical	—	instMax_mathlib	—	—
snd_inf 📖	mathematical	—	instMin_mathlib	—	—
snd_sup 📖	mathematical	—	instMax_mathlib	—	—
sup_def 📖	mathematical	—	instMax_mathlib	—	—
swap_inf 📖	mathematical	—	instMin_mathlib	—	—
swap_sup 📖	mathematical	—	instMax_mathlib	—	—

SemilatticeInf

Definitions

Name	Category	Theorems
inf 📖	CompOp	3 math math: inf_le_right, inf_le_left, le_inf
mk' 📖	CompOp	1 math math: semilatticeSup_mk'_partialOrder_eq_semilatticeInf_mk'_partialOrder
toMin 📖	CompOp	1366 math math: max_sub_min_eq_abs', MeasureTheory.IsStoppingTime.measurableSet_inter_le_iff, Multiset.Ico_sub_Ico_right, sub_sup, Subalgebra.LinearDisjoint.inf_eq_bot, Nat.iInf_le_succ', Finset.min'_union, Set.image_subset_infs_left, Order.Frame.MinimalAxioms.iSup_inf_eq, AlgebraicGeometry.descendsAlong_isOpenImmersion_surjective_inf_flat_inf_quasicompact', AffineSubspace.direction_inf, biSup_inf_le_inf_biSup, Set.Iic.coe_sInf, InfHom.top_apply, CategoryTheory.ObjectProperty.InheritedFromTarget.instMin, Finset.image_subset_infs_left, iInf_inf, Nucleus.coe_toInfHom, sup_div_inf_eq_mabs_div, min_eq_bot, Set.Finite.inf_of_right, continuousMul_inf, TopCat.Sheaf.interUnionPullbackCone_snd, Set.Icc_union_Ici', IntermediateField.LinearDisjoint.iff_inf_eq_bot, iInf_sum, AlgebraicGeometry.Scheme.Hom.image_preimage_eq_opensRange_inter, IntermediateField.normal_inf, AlgebraicGeometry.descendsAlong_universallyClosed_surjective_inf_flat_inf_quasicompact, Finset.le_fold_min, Set.Ioo_union_Ioi', min_sub_sub_left, Units.min_val, himp_inf_distrib, LatticeCon.r_inf_sup_iff, StarSubalgebra.map_inf, mul_inf₀, OrderEmbedding.birkhoffFinset_inf, Finset.truncatedSup_infs, AlgebraicGeometry.RingedSpace.basicOpen_res, OrderIsoClass.toInfHomClass, quasiconcaveOn_iff_min_le, Mathlib.Tactic.Bound.min_le_of_left_le_or_right_le, tsub_add_min, MeasureTheory.stoppedProcess_stoppedProcess, AddGroupTopology.toTopologicalSpace_inf, CovBy.inf_of_sup_of_sup_right, bihimp_left_involutive, Disjoint.le_bot, ofDual_max, CategoryTheory.MorphismProperty.universally_inf, Submodule.toConvexCone_inf, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivInverse_obj_π_app, InfTopHom.inf_apply, CategoryTheory.Dial.tensorObjImpl_rel, inf_right_le_sup_left, bihimp_bihimp_cancel_right, min_bot_left, CompactlySupportedContinuousMap.coe_inf, sInf_pair, IsCompl.inf_left_eq_bot_iff, WithBot.coe_inf, CategoryTheory.ObjectProperty.instIsClosedUnderIsomorphismsMin, HasSolidNorm.continuousInf, min_mul_mul_left, AffineSubspace.direction_inf_of_mem, Set.Ioc_union_Ioc_left, IntermediateField.relrank_comap_comap_eq_relrank_inf, Filter.bliminf_inf_not, Filter.blimsup_and_le_inf, bihimp_eq_left, symmDiff_eq', Finset.Iio_filter_lt, InfHom.bot_apply, min_lt_min_right_iff, TopologicalLattice.toContinuousInf, inf_inf_sdiff, CompleteLattice.MulticoequalizerDiagram.eq_inf, instIdempotentOpMin_mathlib, Set.Ioc_union_Ioc', AddMonoidAlgebra.le_infDegree_add, sup_inf_inf_compl, Finset.fold_min_lt, IsModularLattice.sup_inf_le_assoc_of_le, inf_symmDiff_distrib_right, sInf_union, biSup_inf_le_biSup_inf, Set.Ici.coe_inf, himp_triangle, Set.mem_infs, Finset.Icc_min_max, IsMinFilter.inf, sdiff_symmDiff, MeasureTheory.hittingBtwn_univ, AlgebraicGeometry.IsAffineOpen.isCompact_pullback_inf, inf_mem_infClosure, ArchimedeanClass.min_le_mk_of_le_of_le, inf_eq_sub_posPart_sub, IsLeast.insert, induced_inf, scottContinuous_inf_right, GroupTopology.toTopologicalSpace_inf, min_add_distrib', IsMinFilter.min, IsCompactlyGenerated.BooleanGenerators.sSup_inter, codisjoint_bihimp_sup, MeasureTheory.AEEqFun.coeFn_inf, IsCompl.bihimp_eq_bot, NonUnitalAlgebra.coe_inf, CategoryTheory.Subobject.inf_eq_of_isDetecting, CauSeq.rat_inf_continuous_lemma, emultiplicity_add_eq_min, min_le_of_mul_le_sq, bihimp_bihimp_sup, toBoolRing_inf, inf_covBy_of_covBy_sup_of_covBy_sup_right, inf_eq_iInf, max_neg_neg, compl_inf, LocallyConvexSpace.inf, Sublattice.inf_mem, Set.Icc_min_max, inf_mul, Mathlib.Tactic.Bound.min_lt_of_left_lt_or_right_lt, Set.Ioo_inter_Iio, Function.update_inf, Filter.cardinalInterFilter_sup, min_lt_min_left_iff, min_mul, StarSubalgebra.inf_toSubalgebra, meromorphicOrderAt_add_of_ne, ConvexCone.coe_inf, inf_covBy_of_covBy_sup_of_covBy_sup_left, csInf_insert, sSup_inf_sSup, Nucleus.coe_inf, CategoryTheory.MorphismProperty.ContainsIdentities.inf, NatOrdinal.toOrdinal_min, leOnePart_eq_inv_inf_one, inf_himp_bihimp, sdiff_sdiff_sup_sdiff', StrictConcaveOn.inf, Topology.IsLower.toContinuousInf, min_mul_min_le_min_mul_mul', MonotoneOn.inf, List.foldr_inf_eq_inf_toFinset, FiniteGaloisIntermediateField.instFiniteDimensionalSubtypeMemIntermediateFieldMin_1, Finset.inf_ite, continuous_inf_dom_left₂, AlgebraicGeometry.isPullback_opens_inf, Frm.Iso.mk_hom, codisjoint_inf_right, Finset.inf_inf, CovBy.inf_of_sup_left, disjoint_left_comm, MvPowerSeries.min_lexOrder_le, ENNReal.iInf_ennreal, Set.coe_projIcc, sup_inf_inf_sdiff, CovBy.inf_of_sup_right, himp_inf_le, min_abs_abs_le_abs_min, inf_inf_distrib_left, Finset.min_union, AlgebraicGeometry.isImmersion_eq_inf, min_choice, BooleanAlgebra.sdiff_eq, min_le_max_of_mul_le_mul, SemilatInfCat_dual_comp_forget_to_partOrd, Nat.iInf_lt_succ', IsCompl.le_sup_right_iff_inf_left_le, smul_inf_le, WithTop.untop₀_min, Codisjoint.bihimp_right, CategoryTheory.Regular.frobeniusStrongEpiMonoFactorisation_I, inf_eq_sup, sup_le_inf, bihimp_right_surjective, AlgebraicGeometry.descendsAlong_isomorphisms_surjective_inf_flat_inf_quasicompact, iSup₂_inf_eq, Tropical.min_eq_add, continuousAdd_inf, inf_biInf, ofBoolAlg_inf, CategoryTheory.GrothendieckTopology.arrow_intersect, CategoryTheory.GrothendieckTopology.intersection_covering_iff, continuous_inf_dom_right₂, TopCat.Sheaf.interUnionPullbackCone_fst, iInf_ite, AlgebraicGeometry.Scheme.IdealSheafData.radical_mul, NonUnitalSubalgebra.prod_inf_prod, AlgebraicGeometry.IsSeparated.eq_valuativeCriterion, generateFrom_union, Ordinal.toNimber_min, inf_left_le_sup_left, AlgebraicGeometry.IsClosedImmersion.eq_proper_inf_monomorphisms, lt_inf_iff, inf_le_inf, Subalgebra.prod_inf_prod, TopCat.pullback_topology, CategoryTheory.MorphismProperty.IsMultiplicative.inf, IntermediateField.inf_toSubalgebra, OrderIso.map_inf, Left.min_le_max_of_add_le_add, max_inv_inv', iInf_option, ConcaveOn.inf, inf_of_le_left, Set.Icc.disjoint_iff, BooleanSubalgebra.inf_mem, bihimp_himp_left, CategoryTheory.MorphismProperty.IsLocalAtSource.inf, inf_iInf_nat_succ, Monotone.min, negPart_max, disjoint_symmDiff_inf, CategoryTheory.Subobject.inf_comp_left, NonUnitalAlgebra.mem_inf, inf_sup_le, Set.IsWF.min_union, min_sub_sub_right, inf_sdiff_inf, Set.Iic.isCompl_inf_inf_of_isCompl_of_le, DistribLattice.le_sup_inf, Codisjoint.inf_right, MeasureTheory.IsStoppingTime.min, max_mul_min, SSet.Subcomplex.degenerate_eq_top_iff, IsModularLattice.exists_inf_eq_and_sup_eq, CompleteBooleanAlgebra.sdiff_eq, Int.cast_min, ConcaveOn.ge_on_segment', inf_mul₀, sdiff_sup, Valuation.leIdeal_map_algebraMap_eq_leSubmodule_min, topologicalGroup_inf, CategoryTheory.Subfunctor.Subpresheaf.min_obj, sub_inf, Filter.inf_limsup, oneLePart_min, sdiff_symmDiff', topologicalAddGroup_inf, AlgebraicGeometry.Scheme.Hom.image_preimage_eq_opensRange_inf, IsMinOn.min, mabs_inf_div_inf_le_mabs, min_le_add_of_nonneg_right, TopHom.coe_inf, bihimp_eq_right, SSet.Subcomplex.preimage_min, bihimp_himp_eq_inf, Nimber.toOrdinal_min, ScottContinuous.inf₂, Set.Ioc_disjoint_Ioc, Finset.iInf_insert, le_hnot_inf_hnot, biSup_inf_biSup, AlgebraicGeometry.Scheme.IdealSheafData.radical_inf, sdiff_inf_self_left, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivInverseObj_π_app, pred_min, CategoryTheory.Subobject.inf_arrow_factors_right, min_eq_right_iff, Finset.Ico_union_Ico', openSegment_eq_Ioo', CategoryTheory.Subobject.prod_eq_inf, IntermediateField.inf_relrank_right, iSup_inf_le_inf_iSup, min_le_max, min_min_min_comm, inf_sdiff_self_left, ContinuousMap.inf_apply, max_div_min_eq_mabs, PrimeSpectrum.basicOpen_mul, top_bihimp, compl_symmDiff, fn_min_add_fn_max, inf_top_eq, Finset.inf_union, compl_sup_compl_le, min_lt_max_of_add_lt_add, sup_strictMonoOn_Icc_inf, not_infIrred, RingCon.inf_iff_and, continuousNeg_inf, Order.Frame.MinimalAxioms.sSup_inf_eq, CategoryTheory.MorphismProperty.DescendsAlong.inf, abs_sub_sup_add_abs_sub_inf, TopCat.prod_topology, CategoryTheory.MorphismProperty.CodescendsAlong.inf, Heyting.Regular.coe_sdiff, CircleDeg1Lift.inf_apply, FiniteGaloisIntermediateField.instFiniteDimensionalSubtypeMemIntermediateFieldMin, CategoryTheory.Subfunctor.max_min, IsLowerModularLattice.inf_covBy_of_covBy_sup, CategoryTheory.MorphismProperty.IsStableUnderBaseChange.inf, Sublattice.coe_inf, Con.coe_inf, inv_sup, Codisjoint.sup_lt_right_of_left_ne_bot, IsCompl.sup_inf, Set.forall_infs_iff, AddValuation.map_add_of_distinct_val, Finset.sup'_inf_distrib_right, meromorphicOrderAt_add, Finset.truncatedInf_union, inf_sub, Filter.Tendsto.min_left, Finset.forall_infs_iff, Nucleus.idempotent', Filter.tendsto_nhds_min_right, List.sum_min_le, TopologicalSpace.Opens.mem_inf, AlgebraicGeometry.instDescendsAlongSchemeMinMorphismPropertySurjectiveFlatLocallyOfFinitePresentationOfQuasiCompactOfIsZariskiLocalAtTarget, TopologicalSpace.IsTopologicalBasis.inf_induced, MeasureTheory.IsStoppingTime.measurableSet_inter_le_const_iff, Pi.bihimp_apply, Pi.bihimp_def, himp_bihimp_left, AlgebraicGeometry.HasAffineProperty.affineAnd_eq_of_propertyIsLocal, Pi.single_inf, AlgebraicGeometry.Etale.instHasOfPostcompPropertySchemeMinMorphismPropertyLocallyOfFiniteTypeFormallyUnramified, Ordinal.toNatOrdinal_min, Finpartition.sum_restrict, bihimp_left_comm, AlgebraicGeometry.Scheme.IdealSheafData.map_inf, Antitone.le_map_inf, MeasureTheory.stoppedProcess_eq_stoppedValue_apply, min_le_iff, biInf_le_eq_inf, Subfield.extendScalars_inf, inf_sup_assoc_of_le, AlgebraicGeometry.IsFinite.eq_proper_inf_locallyQuasiFinite, List.minimum_append, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivFunctorObj_π_app, sup_eq_iff_inf_eq, IsLocalMinOn.inf, min_eq_iff, TwoSidedIdeal.mem_inf, Finset.sup_inf_distrib_left, CategoryTheory.ObjectProperty.IsLocal.inf, inf_covBy_of_covBy_sup_right, IsLocalMinOn.min, DirectedOn.sSup_inf_eq, inf_le_of_right_le, IsMaxOn.inf, MeasurableSpace.map_inf, compl_inf_eq_bot, le_iff_exists_inf, succ_min, MeasureTheory.IsStoppingTime.measurableSet_eq_stopping_time_min, max_sub_sub_left, bihimp_left_surjective, continuousInv_inf, min_lt_iff, bihimp_le_iff_left, iInf_option_elim, Filter.bliminf_or_le_inf, Rat.cast_min, PrimitiveSpectrum.hull_inf, AddMonoidAlgebra.le_inf_support_add, Subalgebra.op_inf, MeasureTheory.FinStronglyMeasurable.inf, smul_min_of_nonneg, Set.Ioo_min_max, ProbabilityTheory.condExpKernel_ae_eq_condExp', BoundedLatticeHom.coe_comp_lattice_hom', inf_iSup₂_eq, symmDiff_symmDiff_right, max_add_min, RingCon.coe_inf, IsMaxFilter.inf, max_min_distrib_left, inf_le_ite, add_min, MvPowerSeries.min_weightedOrder_le_add, max_div_min_eq_mabs', Filter.bliminf_or_eq_inf, fn_max_add_fn_min, Set.Ico_inter_Ico, AffineSubspace.inf_coe, MulArchimedeanClass.min_le_mk_mul, continuous_inf_dom_right, disjoint_iff, min_mul_of_nonneg, inf_le_iff, Function.support_min, AffineSubspace.map_inf_eq, IsLocalMin.inf, Set.infs_singleton, bihimp_le_iff_right, Mathlib.Tactic.Order.ToInt.toInt_inf_toInt_eq_toInt, Sublocale.coe_inf, AffineSubspace.coe_inf, OrderEmbedding.birkhoffSet_inf, Finset.lt_fold_min, BooleanSubalgebra.mk_inf_mk, Set.Ico.coe_inf, min_top_left, Multiset.Ico_filter_lt, JordanHolderLattice.second_iso, inf_le_right, AlgebraicGeometry.IsOpenImmersion.map_ΓIso_inv_assoc, List.min_le_of_le, InfHom.const_apply, inf_add_sup, Set.IicExtend_apply, Finset.singleton_infs, bihimp_bihimp_self, min_le_mul_of_one_le_right, inf_eq_div_oneLePart_div, Multiset.toFinsupp_inter, Algebra.map_inf, mul_min_of_nonneg, IntermediateField.inf_relfinrank_right, Sublattice.mk_inf_mk, infIccOrderIsoIccSup_apply_coe, Finset.uIcc_subset_uIcc_iff_le', sup_eq_sdiff_sup_sdiff_sup_inf, smul_min_of_nonpos, Finset.Ico_inter_Ico, Multiset.inf_add, Finset.uIcc_subset_uIcc_iff_le, Finset.inf_eq_inter, Affine.Simplex.mongePlane_def, inf_of_le_right, iSup_inf_le_sSup_inf, AddCon.inf_iff_and, ConvexCone.mem_inf, min_one, WithBot.coe_min, IsModularLattice.inf_sup_inf_assoc, inf_le_inf_left, sup_eq_and_inf_eq_iff, Set.Iic.coe_inf, oneLePart_inf_leOnePart_eq_one, AlgebraicGeometry.Proj.basicOpen_mul, Set.infs_subset_iff, BddLat.forget_semilatInf_partOrd_eq_forget_bddOrd_partOrd, IntermediateField.extendScalars_inf, Filter.liminf_sup_filter, TopCat.Sheaf.objSupIsoProdEqLocus_hom_fst, TopologicalSpace.Opens.functor_obj_map_obj, sup_inf_right, infIooOrderIsoIooSup_symm_apply_coe, inf_lt_inf_of_lt_of_sup_le_sup, inf_sSup_eq, min_mul_distrib', Tropical.trop_min, isGreatest_himp, himp_himp, Set.Icc_inter_Icc, segment_eq_Icc', inf_inf_inf_comm, Frm.Iso.mk_inv, Set.Ico_union_Ici', DFinsupp.support_inf, EReal.min_neg_neg, AntitoneOn.map_min, CategoryTheory.Sieve.functorPullback_inter, Set.uIcc_subset_uIcc_iff_le', PNat.factorMultiset_gcd, LowerSemicontinuous.inf, min_div_div_left', BooleanAlgebra.inf_compl_le_bot, Set.Iic.complementedLattice_iff, inf_le_sup, inf_left_le_sup_right, mabs_div_sup_mul_mabs_div_inf, pullbackTopology_def, min_le_min_right, inf_le_of_left_le, min_lt_of_right_lt, inf_Prop_eq, sdiff_eq, isGLB_pair, inf_left_idem, abs_sub_round_eq_min, Finset.Ioc_inter_Ioc, tsub_eq_tsub_min, ext_inf, Padic.AddValuation.map_add, AlgebraicGeometry.Scheme.pretopology_le_inf, sdiff_sdiff_right, top_inf_eq, cbiInf_eq_of_not_forall, LatticeHom.map_inf', CategoryTheory.ObjectProperty.instSmallMin, AEMeasurable.min, Nat.iInf_le_succ, continuous_min, Set.Iic_diff_Ioc, IsModularLattice.sup_inf_sup_assoc, sdiff_inf_right_comm, inf_sdiff_self_right, IsLocalMaxOn.inf, Complementeds.coe_inf, min_add_add_right, MeasureTheory.MemLp.inf, inf_eq_and_sup_eq_iff, MeasureTheory.OuterMeasure.le_add_caratheodory, BoxIntegral.Prepartition.iUnion_inf, Set.singleton_infs_singleton, max_div_div_left', InfHom.withBot_toFun, TopCat.Presheaf.SheafConditionEqualizerProducts.piInters.hom_ext_iff, JordanHolderLattice.isMaximal_inf_left_of_isMaximal_sup, sup_sdiff_inf, Heyting.Regular.coe_inf, QuasiconcaveOn.inf, himp_inf_himp_cancel, IntermediateField.lift_inf, inf_sdiff_sup_left, Finset.inf_eq_inter', TopCat.Sheaf.interUnionPullbackConeLift_right, inf_sup_self, himp_inf_himp_inf_le, Order.PFilter.inf_mem, AntitoneOn.min, min_max_distrib_right, Order.PFilter.inf_mem_iff, fn_min_mul_fn_max, symmDiff_eq, FiniteGaloisIntermediateField.instIsSeparableSubtypeMemIntermediateFieldMin_1, Multiset.inf_coe, symmDiff_eq_sup_sdiff_inf, IntermediateField.coe_inf, MeasurableSet.bihimp, CategoryTheory.ObjectProperty.instIsStableUnderShiftByMin, disjoint_right_comm, LowerSemicontinuousAt.inf, HasCompactMulSupport.inf, sup_inf_left, MeasureTheory.stoppedValue_stoppedProcess_apply, Finsupp.inf_apply, inf_lt_of_right_lt, CovBy.inf_of_sup_of_sup_left, Finset.sup_inf_distrib_right, iSup_inf_eq, IntermediateField.mem_inf, StrictConcaveOn.lt_on_openSegment, CategoryTheory.Subfunctor.iSup_min, toDual_min, BoxIntegral.Prepartition.inf_split, CompleteBooleanAlgebra.le_sup_inf, BoxIntegral.Prepartition.exists_splitMany_inf_eq_filter_of_finite, sup_inf_self, ArchimedeanClass.min_le_mk_add, Order.Frame.le_himp_iff, SemilatInfCat.coe_forget_to_partOrd, Antitone.map_max, CategoryTheory.MorphismProperty.instIsStableUnderRetractsMin, one_min, MeasureTheory.Martingale.stoppedValue_min_ae_eq_condExp, fn_max_mul_fn_min, Cardinal.powerlt_min, min_idem, Tropical.untrop_add, AffineIndependent.inf_affineSpan_eq_affineSpan_inter, Lattice.BicartSq.inf_eq, List.minimum_cons, le_himp_iff', inf_le_inf_right, inf_lt_left_or_right, AlgebraicGeometry.Scheme.Hom.appLE_appIso_inv, RightOrdContinuous.map_inf, bihimp_triangle, AlgebraicGeometry.Scheme.PartialMap.equiv_iff_of_isSeparated, Filter.Tendsto.min_right, Coheyting.boundary_inf, bihimp_eq, neg_sup, TopologicalSpace.IsTopologicalBasis.inf, TopHom.inf_apply, CategoryTheory.Subobject.inf_isPullback, Finset.sup'_inf_sup', Sum.Lex.inr_inf, StrictConcaveOn.lt_on_open_segment', FirstOrder.Language.ClosedUnder.inf, Disjoint.inf_right', Set.Ico_union_Ico', R1Space.inf, Set.Ici.disjoint_iff, MonotoneOn.map_inf, RelHomClass.map_inf, bihimp_right_inj, bihimp_right_comm, min_abs_abs_le_abs_max, LowerSemicontinuousWithinAt.inf, List.getD_min?_eq_untopD_minimum, LatticeCon.inf, disjoint_assoc, AlgebraicGeometry.Scheme.grothendieckTopology_eq_inf, MeasureTheory.Measure.inf_apply, le_iSup_inf_iSup, CategoryTheory.Subfunctor.min_obj, CompleteLinearOrder.le_himp_iff, IntermediateField.restrictScalars_inf, not_infPrime, MeasureTheory.stoppedValue_stoppedProcess, symmDiff_sup_inf, min_le_of_left_le, AlgebraicGeometry.Scheme.IdealSheafData.vanishingIdeal_sup, LinearGrowth.linearGrowthInf_inf, WithZero.coe_inf, Relation.cutExpand_le_invImage_lex, Birkhoff_inequalities, Finset.inf_insert, InfiniteGalois.restrict_fixedField, inf_comm, LowerSemicontinuousOn.inf, bihimp_iff_iff, OpenAddSubgroup.toOpens_inf, Right.min_le_max_of_mul_le_mul, min_neg_neg, sdiff_le_inf_hnot, infsInfHom_apply, Fin.attachFin_uIcc, bddLat_dual_comp_forget_to_semilatSupCat, min_max_distrib_left, le_inf, isLeast_pair, leOnePart_max, max_sub_min_eq_abs, inf_himp, MeasureTheory.StronglyMeasurable.integral_condExpKernel', Multiset.Ico_inter_Ico, InfHom.withTop_toFun, ENat.toENNReal_min, inf_iSup_eq, CategoryTheory.MorphismProperty.RespectsLeft.inf, Coheyting.inf_hnot_self, sdiff_sdiff_sup_sdiff, ProbabilityTheory.condExp_ae_eq_integral_condExpKernel', IsDiscreteValuationRing.addVal_add, IsMinOn.inf, inf_symmDiff_distrib_left, Algebra.inf_toSubmodule, CategoryTheory.ObjectProperty.instIsTriangulatedClosed₂MinOfIsClosedUnderIsomorphisms, inf_lt_sup, min_lt_of_add_lt_two_nsmul, Set.Finite.inf_of_left, MeasureTheory.IsStoppingTime.measurableSpace_min, CategoryTheory.MorphismProperty.bijective_eq_sup, inf_sup_right, MeasureTheory.IsStoppingTime.measurableSet_min_iff, HahnSeries.min_order_le_order_add, Set.Iic.coe_iInf, nhds_inf, Booleanisation.lift_sdiff_comp, Finset.prod_min_le, FrameHom.coe_toInfTopHom, Convex.min_le_combo, BooleanSubalgebra.val_inf, InfHom.withTop'_toFun, bihimp_eq_sup_himp_inf, bihimp_of_le, inf_sq_eq_mul_div_mabs_div, LowerSet.iicInfHom_apply, hnot_inf_distrib, le_inf_iff, separableClosure_inf_perfectClosure, Set.uIcc_subset_uIcc_iff_le, iInf_bool_eq, Subalgebra.unop_inf, inf_compl_self, IsLocalMax.min, Coheyting.boundary_inf_le, ExpGrowth.expGrowthInf_inf, inf_le_bihimp, Set.Icc.isCompl_iff, div_sup, inf_eq_inf_iff_right, Set.Ioc_union_Ioc_symm, AlgebraicGeometry.HasRingHomProperty.inf, min_right_comm, Antitone.map_sup_le, Nat.cast_min, IsLocalMaxOn.min, DFinsupp.toMultiset_inf, Antitone.inf, Subalgebra.LinearDisjoint.rank_inf_eq_one_of_flat_of_inj, iInf_split, Set.Iic.coe_biInf, CompletelyDistribLattice.le_himp_iff, PowerSeries.min_order_le_order_add, bddLat_dual_comp_forget_to_semilatInfCat, IsCompl.inf_eq_bot, inf_compl_eq_bot', max_min_distrib_right, Set.Ioo_union_Ioi, GeneralizedBooleanAlgebra.inf_inf_sdiff, Directed.iSup_inf_eq, FrameHom.map_sSup', PrimeMultiset.prod_inf, TopCat.Sheaf.objSupIsoProdEqLocus_inv_snd, le_sup_inf, InfHom.inf_apply, CategoryTheory.Regular.instIsRegularEpiFrobeniusMorphism, ProbabilityTheory.condExpKernel_def, inf_iInf, iSup_inf_le_inf_sSup, bihimp_comm, Order.Frame.MinimalAxioms.inf_iSup₂_eq, biInf_ge_eq_inf, Codisjoint.bihimp_left, le_analyticOrderAt_sub, le_analyticOrderAt_add, AntitoneOn.map_max, ProjectiveSpectrum.basicOpen_mul, sdiff_inf_self_right, IntermediateField.relfinrank_inf_mul_relfinrank, GeneralizedHeytingAlgebra.le_himp_iff, Set.Icc_union_Ici, inf_sdiff_eq_bot_iff, Function.mulSupport_min, Filter.tendsto_nhds_min_left, Order.Frame.MinimalAxioms.inf_iSup_eq, TopologicalSpace.Closeds.coe_inf, Language.IsRegular.inf, IntermediateField.LinearDisjoint.inf_eq_bot, AlgebraicGeometry.isOpenImmersion_eq_inf, div_inf, CategoryTheory.Regular.frobeniusStrongEpiMonoFactorisation_e, Multiset.inf_ndunion, Finset.singleton_infs_singleton, Finset.fold_min_le, BoxIntegral.Prepartition.IsPartition.inf, Coheyting.boundary_le_boundary_sup_sup_boundary_inf_left, Nat.iInf_lt_succ, CategoryTheory.Sieve.pullback_inter, CategoryTheory.Subobject.inf_factors, Tropical.trop_add_def, WCovBy.inf_eq, instCommutativeMin, min_lt_max_of_mul_lt_mul, Finset.iInf_union, CategoryTheory.MorphismProperty.instHasOfPrecompPropertyMin, Multiset.inf_cons, TopCat.Sheaf.interUnionPullbackConeLift_left, Ideal.quotientInfEquivQuotientProd_snd, Finset.min_pair, AlgebraicGeometry.IsClosedImmersion.eq_inf, continuousSMul_inf, AlgebraicGeometry.Scheme.Hom.appLE_appIso_inv_assoc, IntermediateField.map_comap_eq, Set.Iic_inter_Iic, Codisjoint.bihimp_inf_bihimp_le_right, Finset.inf'_cons, MeasureTheory.condExp_min_stopping_time_ae_eq_restrict_le_const, inf_sdiff_assoc, NonUnitalStarSubalgebra.prod_inf_prod, le_himp_iff, Order.Frame.MinimalAxioms.inf_sSup_eq, MeasureTheory.IsStoppingTime.measurableSpace_min_const, scottContinuous_inf_left, CategoryTheory.MorphismProperty.pretopology_inf, Finset.min'_insert, himp_bihimp_right, AlgebraicGeometry.targetAffineLocally_affineAnd_eq_affineLocally, min_add_max, CompactlySupportedContinuousMap.inf_apply, CategoryTheory.Limits.CompleteLattice.pullback_eq_inf, sup_inf_assoc_of_le, Nucleus.inf_apply, mul_min, NNRat.cast_min, CategoryTheory.MorphismProperty.inf, inf_lt_left, min_top_right, CategoryTheory.Subobject.inf_map, Hyperreal.coe_min, CategoryTheory.MorphismProperty.RespectsRight.inf, bihimp_of_ge, AlgebraicGeometry.Scheme.basicOpen_appLE, CategoryTheory.ObjectProperty.InheritedFromSource.instMin, Set.Ioc_inter_Ioc, MeasurableSpace.inf_le_invariants_comp, compl_compl_inf_distrib, InfHom.withBot'_toFun, compl_sup_distrib, RegularSpace.inf, Set.Ico_disjoint_Ico, Finset.iInf_insert_update, bihimp_inf_sup, Codisjoint.himp_inf_cancel_right, bihimp_right_involutive, Function.support_inf, Units.topology_eq_inf, MeasureTheory.IsStoppingTime.measurableSet_inter_le, List.le_min_of_forall_le, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivFunctor_obj_π_app, inf_covBy_of_covBy_sup_left, Setoid.inf_def, ClosedSubmodule.coe_inf, AntitoneOn.inf, GaloisConnection.u_inf, AlgebraicGeometry.isPreimmersion_eq_inf, min_le_mul_of_one_le_left, Set.Ioc_diff_Ioi, infIooOrderIsoIooSup_apply_coe, EReal.max_neg_neg, sdiff_inf, MeasureTheory.IsStoppingTime.min_const, le_inf_sup, bihimp_eq_inf, DFA.acceptsFrom_inter, IsGLB.insert, SemilatInfCat.Iso.mk_inv_toFun, iInf_union, Subalgebra.LinearDisjoint.rank_inf_eq_one_of_flat_left_of_inj, BoxIntegral.Prepartition.splitMany_insert, AlgebraicGeometry.IsOpenImmersion.ΓIso_inv, Finset.image_subset_infs_right, leOnePart_min, FrameHomClass.toInfTopHomClass, MeasureTheory.progMeasurable_min_stopping_time, inf_sup_left, AlgebraicGeometry.isProper_eq, bihimp_self, NucleusClass.toInfHomClass, Sublocale.inf_mem, min_lt_of_mul_lt_sq, inf_sSup_eq_iSup_inf_sup_finset, AffineSubspace.map_inf_le, iInf_dite, DFinsupp.inf_apply, inf_add, CompleteLattice.ωScottContinuous.inf, FiniteMulArchimedeanClass.min_le_mk_mul, min_mul_distrib, InfHom.coe_const, Monotone.map_min, List.prod_min_le, Filter.isBoundedUnder_ge_inf, CategoryTheory.GrothendieckTopology.intersection_covering, inf_right_comm, DFinsupp.support_sup_union_support_inf, inv_inf, negPart_min, InfHom.withTop_id, sup_inf_le_assoc_of_le, compl_bihimp_self, gc_inf_himp, Mathlib.Meta.Positivity.le_min_of_le_of_lt, AlgebraicGeometry.IsOpenImmersion.app_ΓIso_hom_assoc, IntermediateField.relfinrank_mul_relfinrank_eq_inf_relfinrank, Set.coe_projIic, OpenSubgroup.toOpens_inf, inf_eq_top_iff, TopologicalSpace.Opens.functor_map_eq_inf, CategoryTheory.Subfunctor.Subpresheaf.iSup_min, AddValuation.map_sub, AlgebraicGeometry.universallyClosed_eq_universallySpecializing, Set.Icc.coe_inf, Finset.infs_singleton, Finset.min'_pair, ofBoolRing_mul, Finset.biUnion_image_inf_right, sdiff_sdiff_right', ContinuousMap.coe_inf, symmDiff_symmDiff_left, LatticeHom.coe_toInfHom, min_le_min_left, Antitone.map_inf, iSup_inf_le_iSup_inf, compl_sup, min_div_div_right, CategoryTheory.Pretopology.mem_inf, sup_bihimp_bihimp, completelyRegularSpace_inf, AlgebraicGeometry.IsOpenImmersion.map_ΓIso_inv, CategoryTheory.Regular.exists_inf_pullback_eq_exists_inf, CategoryTheory.Subobject.inf_def, AlgebraicGeometry.RingedSpace.basicOpen_mul, OrderHom.coe_inf, AlgebraicGeometry.Flat.surjective_descendsAlong_surjective_inf_flat_inf_quasicompact, Multiset.inf_eq_inter, MonotoneOn.map_min, IntermediateField.relfinrank_inf_mul_relfinrank_of_le, AlgebraicGeometry.IsProper.eq_valuativeCriterion, Set.inf_mem_infs, max_div_div_right_of_nonpos, min_mul_max, CategoryTheory.Subobject.inf_arrow_factors_left, sdiff_compl, Filter.inf_liminf, inf_sdiff_sup_right, IsMaxFilter.min, AlgebraicGeometry.IsClosedImmersion.eq_isFinite_inf_mono, AlgebraicGeometry.Scheme.basicOpen_mul, DFinsupp.coe_inf, sup_eq_inf, compl_inf_self, Booleanisation.comp_sup_comp, inf_right_idem, Set.Ico_inter_Iio, IntermediateField.relrank_inf_mul_relrank_of_le, norm_inf_sub_inf_le_norm, IsCompl.inf_left_le_of_le_sup_right, IsMaxOn.min, CategoryTheory.MorphismProperty.IsStableUnderComposition.inf, himp_inf_self, CategoryTheory.Regular.frobeniusMorphism_isPullback, Finset.Ioo_filter_lt, AlgebraicGeometry.UniversallyClosed.eq_valuativeCriterion, Language.mem_inf, AlgebraicGeometry.IsOpenImmersion.app_ΓIso_hom, LatticeHom.coe_comp_inf_hom, CategoryTheory.Limits.CompleteLattice.prod_eq_inf, MeasureTheory.stoppedProcess_stoppedProcess', inf_lt_right, Left.min_le_max_of_mul_le_mul, disjointed_eq_inf_compl, sInf_insert, inf_eq_left, inf_eq_iff_sup_eq, MeasureTheory.AEFinStronglyMeasurable.inf, inf_sup_symmDiff, Set.Ioc_union_Ioc_union_Ioc_cycle, Nucleus.toFun_eq_coe, BoxIntegral.integralSum_sub_partitions, Finset.sup'_inf_distrib_left, tsub_min, InfTopHom.coe_top, TopCat.Sheaf.objSupIsoProdEqLocus_hom_snd, inf_lt_iff, MvPowerSeries.weightedOrder_add_of_weightedOrder_ne, AlgebraicGeometry.isomorphisms_eq_isOpenImmersion_inf_surjective, JordanHolderLattice.isMaximal_inf_right_of_isMaximal_sup, SemilatInfCat.dual_map, bihimp_left_inj, inf_left_right_swap, posPart_inf_negPart_eq_zero, CategoryTheory.MorphismProperty.instHasOfPostcompPropertyMin, min_add_min_le_min_add_add, inf_bot_eq, bihimp_left_injective, CategoryTheory.ObjectProperty.instIsStableUnderShiftMin, MeasureTheory.IsStoppingTime.measurableSet_stopping_time_le_min, Finsupp.support_inf_union_support_sup, cauchy_davenport_minOrder_add, inf_right_le_sup_right, min_le_of_right_le, Finset.Ico_diff_Ico_right, disjoint_inf_sdiff, AlgebraicGeometry.Scheme.Hom.preimage_inf, sup_inf_sdiff, bihimp_bihimp_cancel_left, Subalgebra.LinearDisjoint.rank_inf_eq_one_of_flat_right_of_inj, NonUnitalAlgebra.inf_toSubmodule, inf_sdiff, sdiff_inf_distrib, IsGLB.union, min_div_div_right', LatticeHomClass.map_inf, StarSubalgebra.coe_inf, AlgebraicGeometry.IsOpenImmersion.app_ΓIso_hom_apply, inf_eq_inf_iff_left, min_zero, symmDiff_symmDiff_right', continuousVAdd_inf, sup_inf_le, sInfHomClass.toInfTopHomClass, LowerAdjoint.closure_inf_le, AlgebraicGeometry.geometrically_inf, Set.inf_eq_inter, tsub_tsub_eq_min, Subalgebra.centralizer_coe_sup, csInf_union, IsWeakLowerModularLattice.inf_covBy_of_covBy_covBy_sup, DirectedOn.inf_sSup_eq, Multiset.inf_union, himp_bihimp_eq_inf, List.foldr_min_of_ne_nil, SemilatInfCat.Iso.mk_hom_toFun, AlgebraicGeometry.Scheme.Hom.appLE_appIso_inv_apply, inf_lt_of_left_lt, InfHom.withBot_comp, Finset.card_infs_iff, AlgebraicGeometry.IsFinite.eq_isProper_inf_isAffineHom, Codisjoint.bihimp_inf_bihimp_le_left, min_cases, inf_sdiff_distrib_right, two_nsmul_inf_eq_add_sub_abs_sub, Codisjoint.himp_inf_cancel_left, Monotone.map_inf_le, NonUnitalStarAlgebra.coe_inf, mul_inf, toDual_bihimp, sup_inf_bihimp, iInf_or, Directed.inf_iSup_eq, Set.Ioc_union_Ioi, ClosureOperator.closure_inf_le, Finset.min_insert, HahnSeries.min_orderTop_le_orderTop_sub, min_lt_max, CategoryTheory.Regular.frobeniusStrongEpiMonoFactorisation_m, ofDual_symmDiff, ConcaveOn.min_le_of_mem_segment, biInf_inf, min_lt_min, csSup_inter_le, AntitoneOn.map_inf, smul_max_of_nonpos, ProbabilityTheory.condExpKernel_eq, AlgebraicGeometry.Scheme.basicOpen_res, Booleanisation.lift_inf_lift, TopCat.Sheaf.objSupIsoProdEqLocus_inv_fst, map_bihimp, sdiff_eq_sdiff_iff_inf_eq_inf, mabs_min_le_max_mabs_mabs, Subalgebra.map_comap_eq, maximal_subtype, inf_sup_le_assoc_of_le, min_mul_mul_right, inf_eq_half_smul_add_sub_abs_sub, Ideal.quotientInfEquivQuotientProd_fst, CategoryTheory.Subobject.inf_comp_left_assoc, Nucleus.map_inf, symmDiff_sdiff_inf, Monotone.inf, BoundedContinuousFunction.coe_inf, Con.inf_iff_and, Pi.mulSingle_inf, CategoryTheory.ObjectProperty.instContainsZeroMinOfIsClosedUnderIsomorphisms, Filter.bliminf_not_inf, symmDiff_symmDiff_inf, AlgebraicGeometry.Scheme.IdealSheafData.ideal_inf, BoxIntegral.Prepartition.mem_inf, LowerSet.coe_iicInfHom, min_add_add_left, generateFrom_union_isOpen, codisjoint_inf_left, LinearMap.rank_comp_le, MeasureTheory.stoppedValue_stoppedProcess_ae_eq, List.min_le_of_le', Set.Iio_inter_Iio, bot_bihimp, inf_sdiff_left_comm, inf_eq_half_smul_add_sub_abs_sub', himp_bihimp, Algebra.coe_inf, BoxIntegral.Prepartition.inf_def, sdiff_sdiff_right_self, IsCompl.inf_right_eq_bot_iff, inf_strictMonoOn_Icc_sup, zero_min, MvPowerSeries.order_add_of_order_ne, BoundedLatticeHom.coe_toInfTopHom, BoxIntegral.Prepartition.inf_splitMany, LatticeHom.coe_comp_inf_hom', SSet.stdSimplex.face_inter_face, Set.Ici.isCompl_iff, GeneralizedBooleanAlgebra.sup_inf_sdiff, FiniteGaloisIntermediateField.instIsGaloisSubtypeMemIntermediateFieldMin, bihimp_bihimp_bihimp_comm, IntermediateField.lift_relrank_comap_comap_eq_lift_relrank_inf, Finset.sup_inf_sup, UniformSpace.toTopologicalSpace_inf, min_eq_left_iff, inf_le_left, Set.singleton_infs, ArchimedeanClass.min_le_mk_sub, Sym2.inf_mk, TopologicalSpace.Opens.infLELeft_apply, Interval.coe_inf, IntermediateField.inf_toSubfield, BddLat.coe_forget_to_semilatInf, sup_himp_bihimp, CategoryTheory.MorphismProperty.instHasTwoOutOfThreePropertyMin, NonemptyInterval.fst_sup, min_le_emultiplicity_add, Filter.Germ.const_min, Multiset.toDFinsupp_inter, AffineSubspace.mem_inf_iff, negPart_eq_neg_inf_zero, sdiff_symmDiff_left, Order.Frame.MinimalAxioms.inf_sSup_le_iSup_inf, Filter.Tendsto.min, NonUnitalStarAlgebra.map_inf, CategoryTheory.Subobject.inf_comp_right, CategoryTheory.MorphismProperty.precoverage_inf, FrameHom.toFun_eq_coe, min_le_of_add_le_two_nsmul, CategoryTheory.Sieve.inter_apply, CategoryTheory.MorphismProperty.IsStableUnderCobaseChange.inf, List.minimum_concat, Multiset.sum_min_le, instAssociativeMin, m_Birkhoff_inequalities, min_mabs_mabs_le_mabs_max, StarSubalgebra.mem_inf, Antitone.map_min, CategoryTheory.ObjectProperty.instIsTriangulatedMinOfIsClosedUnderIsomorphisms, FiniteGaloisIntermediateField.instIsSeparableSubtypeMemIntermediateFieldMin, Finset.inf_disjSum, Lattice.BicartSq.min_eq, Finset.Ico_filter_lt, FiniteArchimedeanClass.min_le_mk_add, Finset.mem_infs, AlgebraicGeometry.isomorphisms_eq_stalkwise, min_le_add_of_nonneg_left, disjoint_iff_inf_le, CategoryTheory.Subobject.inf_eq_map_pullback, HahnSeries.min_le_min_add, DFA.accepts_inter, BotHom.inf_apply, inf_inf_distrib_right, AlgebraicGeometry.IsFinite.eq_inf, Set.Iio.coe_inf, sup_sub_inf_eq_abs_sub, Filter.cardinalInterFilter_inf, InfHom.coe_bot, inf_div, Mathlib.Meta.Positivity.le_min_of_lt_of_le, AlgebraicGeometry.IsOpenImmersion.map_ΓIso_hom, WithTop.coe_min, min_le_max_of_add_le_add, Set.Ioo_disjoint_Ioo, MeasureTheory.IsStoppingTime.measurableSet_min_const_iff, BoundedLatticeHom.coe_comp_inf_hom', AlgebraicGeometry.GeometricallyIntegral.eq_geometricallyReduced_inf_geometricallyIrreducible, isModularLattice_iff_inf_sup_inf_assoc, IntermediateField.map_inf, TopologicalSpace.Opens.coe_inf, Finsupp.support_sup_union_support_inf, iSup_inf_of_monotone, UpperSemicontinuousAt.inf, GaloisInsertion.l_inf_u, compl_bihimp_compl, OrderEmbedding.map_inf_le, CategoryTheory.ObjectProperty.prop_inf_iff, Codisjoint.inf_left, iInf_insert, bihimp_fst, CategoryTheory.ObjectProperty.instSmallMin_1, PowerSeries.order_add_of_order_ne, SemilatSupCat_dual_comp_forget_to_partOrd, Ideal.fst_comp_quotientInfEquivQuotientProd, Measurable.min, CategoryTheory.Subobject.inf_pullback, Set.IccExtend_apply, IntermediateField.relfinrank_comap_comap_eq_relfinrank_inf, inf_sdiff_right, bihimp_isCommutative, InfHom.coe_inf, Filter.Germ.min_def, norm_inf_le_add, left_eq_inf, CategoryTheory.Subobject.inf_comp_right_assoc, IntermediateField.inf_relfinrank_left, WithTop.coe_inf, AddValuation.map_add, Finset.Ioc_disjoint_Ioc, sSup_inter_le, norm_inf_sub_inf_le_add_norm, continuous_inf_rng, Set.image_subset_infs_right, BoundedLatticeHom.coe_comp_inf_hom, UpperSemicontinuousWithinAt.inf, minimal_subtype, inf_assoc, DFinsupp.support_inf_union_support_sup, inf_eq_right, CompleteLattice.MulticoequalizerDiagram.min_eq, Finsupp.support_inf, bihimp_eq', cauchy_davenport_minOrder_mul, IntermediateField.inf_relrank_left, Sum.Lex.inl_inf, LatticeHomClass.toInfHomClass, abs_min_sub_min_le_max, MulArchimedeanClass.min_le_mk_div, Set.Ioc_union_Ioi', strictMono_inf_prod_sup, IsLocalMax.inf, BoundedLatticeHomClass.toInfTopHomClass, min_mabs_mabs_le_mabs_min, infIccOrderIsoIccSup_symm_apply_coe, PUnit.inf_eq, Coheyting.boundary_sup_sup_boundary_inf, AlgebraicGeometry.isPullback_opens_inf_le, IntermediateField.relrank_inf_mul_relrank, Algebra.mem_inf, sup_himp_distrib, MeasureTheory.Filtration.coeFn_inf, BoxIntegral.Prepartition.eventually_splitMany_inf_eq_filter, CompleteBooleanAlgebra.inf_compl_le_bot, Tropical.trop_inf, BoxIntegral.TaggedPrepartition.infPrepartition_toPrepartition, min_div_div_right_of_nonpos, NNRat.coe_min, CategoryTheory.Subfunctor.Subpresheaf.max_min, MeasureTheory.Integrable.inf, AlgebraicGeometry.Scheme.IdealSheafData.support_sup, MeasureTheory.Lp.coeFn_inf, min_inv_inv', bihimp_isAssociative, Ideal.snd_comp_quotientInfEquivQuotientProd, instCommutativeMin_mathlib, bihimp_hnot_self, GaloisCoinsertion.u_inf_l, Finset.fold_inf_univ, LowerSet.Iic_inf, AntitoneOn.map_sup, neg_inf, abs_min_le_max_abs_abs, inf_symmDiff_symmDiff, ConcaveOn.min_le_of_mem_Icc, Nat.factorization_gcd, MeasureTheory.AEStronglyMeasurable.inf, Finset.biUnion_image_inf_left, OrderHom.map_inf_fixedPoints_le, inf_sdiff_distrib_left, compl_bihimp, InfTopHom.coe_inf, TopCat.Sheaf.interUnionPullbackCone_pt, Filter.liminf_piecewise, Function.locallyFinsuppWithin.min_apply, sSup_inf_eq, inf_idem, IsCompl.inf_sup, InfTopHom.top_apply, bihimp_top, Set.Icc_union_Icc', BotHom.coe_inf, AlgebraicGeometry.IsIntegralHom.eq_universallyClosed_inf_isAffineHom, IsLeast.union, sdiff_sdiff_left', le_min_iff, bihimp_snd, IntermediateField.relrank_mul_relrank_eq_inf_relrank, add_inf, instLawfulOrderInf_mathlib, Continuous.min, Heyting.IsRegular.inf, Finset.inf_cons, iInf_inf_eq, UpperSemicontinuous.inf, inf_himp_le, MvPowerSeries.min_order_le_add, AlgebraicGeometry.Scheme.pretopology_eq_inf, right_eq_inf, WithZero.min_le_iff, Disjoint.inf_left', MeasurableSpace.measurableSet_inf, min_eq_top, Finset.infs_subset_iff, Monotone.map_inf, biSup_inter_of_pairwise_disjoint, TwoSidedIdeal.inf_ringCon, PowerSeries.order_add_of_order_eq, HasCompactSupport.inf, min_add, Ne.inf_lt_or_inf_lt, Associates.FactorSet.sup_add_inf_eq_add, Codisjoint.bihimp_eq_inf, inf_eq_minDefault, PolynormableSpace.inf, inf_sdiff_left, IsModularLattice.exists_inf_eq_and_codisjoint, Disjoint.eq_bot, inf_mul_sup, min_add_distrib, le_bihimp_iff, Algebra.inf_toSubsemiring, bihimp_eq_top, Finset.Iic_diff_Ioc, MulArchimedeanClass.min_le_mk_of_le_of_le, iSup_inf_of_antitone, Set.Ioo_inter_Ioo, CompleteDistribLattice.MinimalAxioms.inf_sSup_le_iSup_inf, NonUnitalAlgebra.inf_toNonUnitalSubsemiring, pow_inf_le, CategoryTheory.MorphismProperty.IsLocalAtTarget.inf, HahnSeries.min_orderTop_le_orderTop_add, Set.Ico.disjoint_iff, bihimp_bot, sdiff_inf_sdiff, liminf_min, instAssociativeMin_mathlib, Finset.inf_mem_infs, min_bot_right, Disjoint.inf_right, csInf_pair, iInf_pair, MeasureTheory.condExp_min_stopping_time_ae_eq_restrict_le, Set.Ioo_union_Ioo', bihimp_himp_right, InfHom.withTop_comp, OrderIsoClass.toInfTopHomClass, Finset.inf'_insert, inf_compl_eq_bot, bihimp_assoc, Finsupp.toMultiset_inf, AddUnits.topology_eq_inf, Right.min_le_max_of_add_le_add, Complementeds.mk_inf_mk, min_left_commutative, Finset.inf'_union, AlgebraicGeometry.ValuativeCriterion.eq, iInf_split_single, min_lt_of_left_lt, abs_inf_sub_inf_le_abs, Coheyting.boundary_le_boundary_sup_sup_boundary_inf_right, sdiff_symmDiff_right, Nucleus.le_apply', Cardinal.lift_min, posPart_min, continuous_inf_dom_left, bot_inf_eq, NonUnitalAlgebra.map_inf, toBoolAlg_mul, Tropical.inf_eq_add, Set.iUnion_image_inf_left, Function.mulSupport_inf, Finset.sum_min_le, NonUnitalStarAlgebra.mem_inf, CauSeq.coe_inf, lt_min_iff, analyticOrderAt_add_of_ne, AddUnits.min_val, InfHom.coe_top, IsComplemented.inf, AlgebraicGeometry.descendsAlong_universallyOpen_surjective_inf_flat_inf_quasicompact, InfPrime.inf_le, ConcaveOn.ge_on_segment, bihimp_eq_bot, CategoryTheory.Dial.tensorObj_rel, Finpartition.parts_inf, Set.iUnion_image_inf_right, Multiset.inf_ndinsert, Filter.IsBoundedUnder.inf, min_le_min, Finset.mem_uIcc, Affine.Simplex.altitude_def, LinearMap.lift_rank_comp_le, sup_sdiff_symmDiff, IsLocalMin.min, Antitone.map_sup, InfHom.withBot_id, Multiset.prod_min_le, AffineSubspace.comap_inf, CategoryTheory.SemilatticeInf.tensorObj, iSup_inf_iSup, UpperSemicontinuousOn.inf, AddCon.coe_inf, AlgebraicGeometry.IsOpenImmersion.map_ΓIso_inv_apply, AlgebraicGeometry.descendsAlong_universallyInjective_surjective_inf_flat_inf_quasicompact, Set.Ico_union_Ici, NonUnitalStarAlgebra.inf_toNonUnitalSubalgebra, Set.image_inf_prod, Finset.image_inf_product, ProbabilityTheory.condExpKernel_apply_eq_condDistrib, inf_ind, Set.Ioc_inter_Iic, TopologicalSpace.Opens.mk_inf_mk, Set.Iio_inter_Ioo, inf_left_comm, Disjoint.inf_left, MeasureTheory.stoppedProcess_eq_stoppedValue, bihimp_right_injective, MonotoneOn.min, Antitone.min, himp_eq_sSup
toPartialOrder 📖	CompOp	4773 math math: countable_image_lt_image_Ioi_within, SuccOrder.hasBasis_nhds_Ioc, PredOrder.nhdsGT_eq_nhdsNE, HahnSeries.order_lt_iff_exists, RatFunc.instFaithfulSMulPolynomialLaurentSeries, Affine.Simplex.sSameSide_affineSpan_faceOpposite_point_left_iff, units_inv_smul, Function.Embedding.encard_le, LinearOrder.isSuccArchimedean_iff_isPredArchimedean, le_iff_forall_lt_one_mul_le, RingCone.nonneg.isMaxCone, Set.finite_diff_iUnion_Ioo, tsub_lt_self_iff, HurwitzZeta.hasSum_int_hurwitzZetaOdd, Multiset.Ico_sub_Ico_right, AddUnits.orderEmbeddingVal_apply, one_le_div_iff, oneLePart_mono, AffineSubspace.sOppSide_iff_exists_right, GenContFract.IntFractPair.nth_stream_fr_nonneg_lt_one, Int.ceil_lt_iff, negPart_nonpos, isCompl_toDual_iff, Mathlib.Meta.NormNum.isNNRat_lt_false, ENat.add_lt_top, HahnSeries.SummableFamily.powerSeriesFamily_add, instPosSMulStrictMonoIntOfIsOrderedAddMonoid, continuousOn_ceil, PNat.bot_eq_one, Set.pairwiseDisjoint_range_iff, Valuation.IsRankOneDiscrete.generator_lt_one, mul_self_nonneg, nhds_basis_one_mabs_lt, sign_intCast, Cardinal.natCast_lt_toENat_iff, Nucleus.instTopHomClass, Finset.coe_inf', hasSum_mellin_pi_mul_sq', Ordinal.toNimber_eq_zero, mul_nonpos_iff_neg_imp_nonneg, IsCompact.bddBelow, AddCircle.coe_equivIco_mk_apply, mapClusterPt_atTop_pow_tfae, PNat.addLeftMono, ENat.toENNReal_lt_top, Set.Ioo_subset_Ioo_union_Ico, Valued.isOpen_closedball, emultiplicity_le_emultiplicity_of_dvd_left, DivisibleHull.archimedeanClassMk_mk_eq, Set.pairwise_disjoint_Ioc_zpow, codisjoint_iff_compl_le_right, Set.Iio_union_Ici, oneLePart_eq_one, Affine.Simplex.wOppSide_affineSpan_faceOpposite_point_left_iff, nsmul_nonneg_iff, abs_sub_abs_le_abs_add, HahnEmbedding.IsPartial.baseEmbedding_le, Finpartition.empty_parts, Set.pairwise_disjoint_Ioo_add_zsmul, Rat.intCast_lt_cast, CompositionSeries.le_last, zpow_right_strictAnti, Valuation.IsTrivialOn.valuation_algebraMap_le_one, ArchimedeanClass.FiniteResidueField.mk_ratCast, Irreducible.maximalIdeal_eq_setOf_le_v_coe, IsPreconnected.intermediate_value_Ico, CompositionSeries.last_eraseLast_le, RootPairing.coxeterWeight_nonneg, NNRat.coe_floor, ProbabilityTheory.gaussianReal_map_const_mul, Continuous.strictMono_of_inj_boundedOrder', IsDedekindDomain.HeightOneSpectrum.adicValued.has_uniform_continuous_const_smul', SignType.neg_one_lt_iff, Set.Ici_add_one_eq_Ioi, min_eq_bot, Int.lt_succ_floor, Finsupp.Colex.addLeftStrictMono, ENat.top_pos, Mathlib.Meta.NormNum.IsNNRat.natFloor, strictConvexOn_iff_slope_strict_mono_adjacent, Set.functorToTypes_obj, closure_interior_Icc, Order.Ioo_succ_right, NNRat.cast_strictMono, Fin.addNatOrderEmb_toEmbedding, LinearOrderedAddCommGroup.wellFoundedOn_setOf_le_lt_iff_nonempty_discrete, Dense.exists_ge, ValuationSubring.valuation_lt_one_iff, TopCat.Sheaf.interUnionPullbackCone_snd, OrderIso.pnatIsoNat_symm_apply, Heyting.isRegular_top, Set.notMem_Ioi, Valuation.FiniteField.algebraMap_le_one, Finset.le_fold_min, LinearOrderedAddCommGroupWithTop.sub_pos, ArchimedeanClass.FiniteElement.instIsStrictOrderedRing, Polynomial.cardPowDegree_zero, tendsto_inv_atTop_zero, Int.lt_ceil, neg_le_self_iff, tendsto_const_mul_pow_nhds_iff', Valuation.HasExtension.val_map_le_iff, Set.compl_ordConnectedSection_ordSeparatingSet_mem_nhdsGE, ENat.lt_add_one_iff', OrderEmbedding.birkhoffFinset_inf, Orientation.ne_iff_eq_neg, CategoryTheory.Limits.Types.binaryCofan_isColimit_iff, Valuation.isEquiv_iff_val_sub_one_lt_one, HahnSeries.mem_cardSuppLTSubfield, Valuation.one_apply_lt_one_iff, nhds_bot_basis, dense_iff_exists_between, countable_image_gt_image_Ioi_within, sign_mul_self, Finset.exists_one_lt_of_prod_one_of_exists_ne_one', quasiconcaveOn_iff_min_le, Set.abs_sub_right_of_mem_uIcc, not_isCofinal_iff, Sym2.disjoint_diagSet_fromRel, AbsoluteValue.isEquiv_trivial_iff_eq_trivial, CategoryTheory.Pairwise.diagram_obj, Set.toENat_cardinalMk_subtype, convexHull_insert, Set.Ioi_subset_Ioo_union_Ici, Set.Infinite.exists_gt, ENat.self_le_mul_left, ValuationSubring.integralClosure_algebraMap_injective, PNat.map_subtype_embedding_Ico, MeasureTheory.aecover_Ioi_of_Ici, Cardinal.toENat_eq_natCast_iff, cocompact_le_atBot, Set.disjoint_compl_left_iff_subset, MonotoneOn.of_map_inf, PowerSeries.heval_C, inv_atBot₀, Polynomial.isEquivalent_atBot_div, inv_le_mabs, ENat.card_le_card_of_injective, tendsto_ceil_right', Valuation.mem_maximalIdeal_iff, LinOrd.ofHom_apply, convex_iff_ordConnected, RootPairing.RootPositiveForm.zero_lt_posForm_apply_root, le_sdiff_right, MeasureTheory.integrable_iff_integrableAtFilter_atBot, convexHull_multiset_sum, FiniteArchimedeanClass.mem_addSubgroup_iff, Nucleus.monotone, abs_sub_round, partialSups_succ', WellOrderExtension.wellFoundedLT, Valuation.mem_leSubmodule_iff, isPiSystem_image_Iic, abs_add_eq_add_abs_iff, Multiset.Ico_sub_Ico_left, Left.pow_lt_one_iff', Set.pairwise_disjoint_Ico_zsmul, ArchimedeanClass.mk_intCast, WithBot.orderIsoPUnitSumLex_symm_inl, Set.disjoint_or_nonempty_inter, Finset.prod_one_sub_ordered, PredOrder.isOpen_iff, disjoint_sdiff_self_right, Cardinal.ofENat_lt_ofNat, ProbabilityTheory.gaussianReal_const_mul, Mathlib.Meta.Positivity.pos_of_isNNRat, Finset.le_fold_max, deriv_abs, Finset.Ioi_disjUnion_Iio, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivInverse_obj_π_app, NumberField.FinitePlace.mk_apply, isOpen_lt_prod, NNRat.le_def, IsCompact.exists_isLeast, InfTopHom.inf_apply, MeasureTheory.aecover_Ioi_of_Ioi, lt_compl_self, NNRat.not_cast_lt_zero, Finset.Icc_add_one_left_eq_Ioc, WithTop.continuousOn_untopD, MulArchimedeanClass.subgroup_strictAntiOn, nsmul_neg_iff, concaveOn_iff_slope_anti_adjacent, strictConvex_Iic, sub_le_neg_add_iff, min_bot_left, nhdsSet_Ioo, right_lt_lineMap_iff_one_lt, AffineSubspace.setOf_sSameSide_eq_image2, Set.Intersecting.isUpperSet, Nat.Ioc_filter_modEq_cast, List.sortedLE_mergeSort, Hyperreal.epsilon_lt_of_pos, Finset.uIcc_toDual, Finset.Ico_subset_Ico_union_Ico, Lattice.BicartSq.commSq, lowerClosure_infs, Finset.le_inf_div, OrderEmbedding.mulRight_apply, Nat.succPNat_mono, List.getD_max?_eq_unbotD_maximum, IsNonarchimedean.multiset_powerset_image_add, Set.Ioc_union_Ioc_left, Set.Iio_succ_eq_Iic, Padic.withValUniformEquiv_norm_le_one_iff, Int.cast_one_le_of_pos, Valued.toNormedField.norm_le_one_iff, ArchimedeanOrder.le_def, Rat.padicValuation_cast, nullMeasurableSet_Ioc, Finset.image_orderEmbOfFin_univ, ProbabilityTheory.Kernel.partialTraj_succ_of_le, Int.preimage_Ioc, CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.ofComposableArrows_incl_app, PNat.find_le, Finset.Iio_filter_lt, one_le_pow_mul_abs_eval_div, Set.tsub_encard_le_encard_diff, IsCauSeq.bounded', ConvexCone.canLift, Matrix.eRank_le_card_width, Ordinal.liftOnWellOrder_type, finSumEquivOfFinset_inr, InfPrime.finset_inf_le, MeasureTheory.ae_le_const_iff_forall_gt_measure_zero, Seminorm.finset_sup_apply, Polynomial.div_tendsto_atTop_leadingCoeff_div_of_degree_eq, Set.pairwise_disjoint_Ioo_mul_zpow, AddCircle.card_torsion_le_of_isSMulRegular, min_lt_min_right_iff, Finset.dens_map_le, Order.succ_lt_succ_iff, SuccOrder.limitRecOn_succ, List.maximum_cons, Finset.Colex.toColex_univ, Ordinal.iSup_typein_succ, Affine.Simplex.sign_excenterWeights_singleton_pos, CauSeq.le_lim, Int.instIsStrictOrderedRing, HahnSeries.leadingCoeff_mul, ENat.card_lt_top, Finset.uIcc_map_sectR, Set.range_IciExtend, LinearOrderedCommGroup.tendsto_nhds, Finset.le_sup'_iff, AddMonoidAlgebra.le_infDegree_add, ArchimedeanClass.closedBallAddSubgroup_top, ValuationSubring.valuation_le_iff, List.foldr_max_of_ne_nil, ArchimedeanClass.addSubgroup_antitone, Nat.succPNat_le_succPNat, Finset.min_eq_inf_withTop, Nat.ceil_pos, Set.iUnion_Ioc_eq_Ioi_self_iff, Polynomial.exists_partition_polynomial, mabs_le, add_right_strictMono_of_ne_top, mapClusterPt_leftLim, le_mabs', Finset.addConst_le_inv_dens, convex_iff_sum_mem, sdiff_le_iff', Finset.card_Ico_mul_right, Finset.fold_min_lt, MvPowerSeries.le_order_mul, Sublattice.map_equiv_eq_comap_symm, OrderRingHom.eq_id, mem_nhdsLT_iff_exists_Ico_subset, Cardinal.ofENat_le_ofNat, QuadraticMap.linMulLinSelfPosDef, sup_compl_le_himp, Cardinal.toENat_ofENat, PNat.Icc_eq_finset_subtype, Set.Ici.coe_inf, Valuation.IsRankOneDiscrete.exists_generator_lt_one', Finset.supIndep_univ_fin_two, signHom_apply, Set.sdiff_singleton_wcovBy, Polynomial.div_tendsto_atBot_leadingCoeff_div_of_degree_eq, Ordinal.toNatOrdinal_eq_one, Set.ncard_le_encard, himp_triangle, List.max_prod_le, CategoryTheory.Limits.MultispanIndex.toLinearOrderMultispanIso_inv_app, Opens.pretopology_toGrothendieck, HahnSeries.instIsStrictOrderedRingLexOfIsDomain, continuousOn_floor, Finset.Icc_min_max, LaurentSeries.LaurentSeriesRingEquiv_def, Field.Emb.Cardinal.directed_filtration, Set.Ioc_union_Ioc_right, Set.Intersecting.isUpperSet', AbsoluteValue.map_units_intCast, instIsCountablyGenerated_atBot, Polynomial.eventually_atBot_not_isRoot, Complementeds.coe_le_coe, Finset.inf_eq_top_iff, HahnEmbedding.Partial.orderTop_eq_archimedeanClassMk, Set.OrdConnected.IicExtend, Int.strictAntiOn_natAbs, Finset.uIcc_eq_union, Continuous.upperSemicontinuous, tendsto_smul_comp_nat_floor_of_tendsto_mul, List.minimum_of_length_pos_le_iff, Field.Emb.Cardinal.instInverseSystemWithTopToTypeOrdRankAlgHomSubtypeMemIntermediateFieldCoeOrderEmbeddingFiltrationAlgebraicClosureEmbFunctor, exists_seq_strictMono_tendsto_nhdsWithin, Hyperreal.neg_lt_of_tendsto_zero_of_pos, nhdsWithin_Ioi_isMeasurablyGenerated, HahnSeries.SummableFamily.powers_zero, Module.length_of_free, isLocallyClosed_Ioi, PNat.Ioo_eq_finset_subtype, lowerClosure_eq_top_iff, WithZeroTopology.nhds_zero, codisjoint_bihimp_sup, Set.Icc_succ_left_eq_Ioc, Field.Emb.Cardinal.filtration_succ, Set.unit_eq, ArchimedeanClass.FiniteResidueField.ofArchimedean_apply, Finset.inf_lt_iff, AddCircle.equivIccQuot_comp_mk_eq_toIcoMod, Set.IciExtend_self, Valuation.mem_ltIdeal_iff, CauSeq.abv_pos_of_not_limZero, Valuation.val_le_one_or_val_inv_lt_one, Mathlib.Tactic.Order.ToInt.toInt_le_toInt, Matrix.eRank_le_card_height, Padic.instCompatibleWithZeroMultiplicativeIntMulValuation, Nonneg.nontrivial, Module.End.independent_genEigenspace, NumberField.FinitePlace.norm_def', negPart_eq_zero', ENat.card_pos, BoundedLatticeHom.coe_comp_sup_hom', smulPosStrictMono_iff_SMulPosReflectLE, Valuation.leSubmodule_monotone, Int.fract_add_fract_le, sum_div_card_sq_le_sum_sq_div_card, Set.Icc_min_max, PredOrder.isPredLimit_of_mem_frontier, two_mul_le_add_sq, IsDedekindDomain.HeightOneSpectrum.mem_adicCompletionIntegers, SetTheory.PGame.grundyValue_eq_iff_equiv_nim, interior_Ici, ENat.toENNReal_strictMono, Int.cast_le_neg_one_of_neg, FunctionField.inftyValuation.X_inv, Set.Icc_subset_Ico_union_Icc, LinOrd.hom_id, Set.Ioo_inter_Iio, CategoryTheory.Limits.MultispanIndex.toLinearOrderMultispanIso_hom_app, WithBot.le_of_forall_lt_iff_le, Set.Ioi_diff_Ici, Finset.disjoint_coe, posPart_eq_self, Int.padicValuation_lt_one_iff, HahnSeries.single_zero_ofScientific, Finset.pairwiseDisjoint_coe, Finset.set_encard_biUnion_le, Nat.floor_div_natCast, ENat.one_lt_card_iff_nontrivial, isCompl_ofDual_iff, IsDedekindDomain.HeightOneSpectrum.intValuation_if_neg, Set.projIic_surjective, CategoryTheory.Limits.CompleteLattice.hasFiniteLimits_of_semilatticeInf_orderTop, monotone_transfiniteIterate, invOf_pos, le_abs_self, PNat.instIsOrderedCancelMonoid, NumberField.FinitePlace.embedding_apply, min_lt_min_left_iff, Ordinal.toNimber_symm_eq, Finset.Icc_succ_succ, IsDedekindDomain.HeightOneSpectrum.valuation_of_algebraMap, Set.disjoint_union_right, nhds_basis_Icc_pos, Finset.prod_Icc_eq_prod_Ico_mul, nullMeasurableSet_Ioo, Valuation.Integers.isPrincipal_iff_exists_isGreatest, Set.disjoint_of_subset_iff_left_eq_empty, VertexOperator.of_coeff_apply_coeff, Set.encard_preimage_val_le_encard_left, nhds_basis_abs_sub_lt, Finset.one_le_mulConst_self, instWellQuasiOrderedLEOfWellFoundedLT, Set.strictMonoOn_projIic, inv_atTop₀, LinearOrderedCommGroupWithZero.inl_mul_inr_eq_coe_toLex, LaurentSeries.valuation_le_iff_coeff_lt_eq_zero, instIsDiscreteValuationRingSubtypeMemSubringIntegerWithZeroMultiplicativeIntValuation, Finpartition.IsEquipartition.card_biUnion_offDiag_le', BoundedLatticeHom.dual_id, OrderIso.isNormal, exists_seq_strictAnti_tendsto, CategoryTheory.Functor.WellOrderInductionData.Extension.map_zero, Lattice.BicartSq.le₁₂, Int.card_Ioo, orderBornology_isBounded, lowerSemicontinuous_iff_isClosed_preimage, Set.ordConnected_iff_uIcc_subset_left, isGLB_infClosure, lt_tsub_iff_right, NatOrdinal.toOrdinal_min, LaurentSeries.valuation_single_zpow, FiniteArchimedeanClass.mk_lt_mk, infPrime_iff_not_isMax, SetRel.core_mono, max_add_add_le_max_add_max, Finset.sum_Ico_le_sum, tendsto_fract_left', AbsoluteValue.abs_abv_sub_le_abv_sub, ContinuousAt.finset_inf, monovary_iff_mul_rearrangement, SetTheory.PGame.grundyValue_nim_add_nim, Finset.map_truncatedInf, NNRat.instStarOrderedRing, Nimber.succ_def, sbtw_midpoint_of_ne, IsDedekindDomain.HeightOneSpectrum.intValuation_le_one, sameRay_or_ne_zero_and_sameRay_neg_iff_not_linearIndependent, le_iff_forall_rat_lt_imp_le, Affine.Simplex.wSameSide_affineSpan_faceOpposite_iff, smul_nonneg_iff_neg_imp_nonpos, Affine.Simplex.wOppSide_affineSpan_faceOpposite_point_right_iff, WeierstrassCurve.valuation_Δ_aux_eq_of_isIntegral, Nat.preimage_Iio, Finset.Nonempty.sup_eq_top_iff, MonomialOrder.degree_sub_le, Orientation.eq_or_eq_neg, negPart_eq_neg', IsNonarchimedean.apply_sum_le_sup_of_isNonarchimedean, le_of_toZ_le, Finset.inf'_lt_iff, CategoryTheory.TransfiniteCompositionOfShape.fac_assoc, Polynomial.exists_min_root, Hyperreal.infinitesimal_def, isPiSystem_Ioi, Finset.sum_Ico_int_sub, ContFract.convs_eq_convs', MeasureTheory.Filtration.rightCont_eq_self, min_mul_min_le_min_mul_mul', ArchimedeanClass.FiniteResidueField.mk_eq_zero, le_zero_iff, Finset.lubell_yamamoto_meshalkin_inequality_sum_card_div_choose, List.foldr_inf_eq_inf_toFinset, convexJoin_segments, Affine.Simplex.sign_signedInfDist_lineMap_incenter_touchpoint, Coheyting.boundary_top, Finset.Colex.toColex_lt_toColex_iff_max'_mem, Nat.measurable_floor, StieltjesFunction.measure_Ioo, EReal.sign_eq_and_abs_eq_iff_eq, starConvex_iff_ordConnected, AddGroupSeminormClass.toNonnegHomClass, Valuation.Compatible.srel_iff_lt, one_lt_mabs, exists_pos_right_iff_sameRay, Finset.lt_sup'_iff, NNRat.cast_le, Valuation.IsEquiv.valuedCompletion_le_one_iff, antivaryOn_comm, codisjoint_inf_right, disjoint_left_comm, hnot_le_iff_codisjoint_left, NNRat.floor_coe, Order.Ioo_eq_empty_iff_le_succ, mul_self_le_one_iff, WithBot.orderIsoPUnitSumLex_symm_inr, Set.Iic_diff_Iio, Order.Ideal.IsProper.notMem_or_compl_notMem, Coheyting.boundary_le_hnot, OrderEmbedding.preimage_uIoc, CategoryTheory.Functor.WellOrderInductionData.surjective, LieModule.genWeightSpaceChain_def', Module.End.genEigenspace_directed, Valuation.isEquiv_iff_val_lt_val, Finset.subConst_le_addConst_sq, Polynomial.exists_partition_polynomial_aux, le_iff_forall_pos_le_add, lt_emultiplicity_of_lt_multiplicity, ENat.monotone_map_iff, Finset.le_inf'_iff, leOnePart_le_one, mul_nonpos_iff_pos_imp_nonpos, InnerProductSpace.gramSchmidt_bot, himp_inf_le, Set.Ioc_subset_uIoc', Set.isCompl_range_some_none, Set.disjoint_singleton_right, Submodule.spanRank_toENat_eq_iInf_encard, isLeast_sdiff, SimpleGraph.hasse_preconnected_of_pred, max_lt_max_left_iff, variationOnFromTo.antitoneOn, Nat.ceil_int, Finset.sortedGT_sort, Finset.mem_uIcc', sign_nonneg_iff, min_abs_abs_le_abs_min, SimpleGraph.regularityReduced_adj, Hyperreal.coe_lt_omega, Finset.card_Ico_add_right, LinOrd.dual_map, nhds_basis_Ioo_one_lt, Pi.instNoMinOrderLexForallOfWellFoundedLTOfNonempty, OrderIso.sumLexIioIci_symm_apply_Ici, Finsupp.Lex.addLeftMono, Ioo_subset_closure_interior, Set.bounded_gt_inter_ge, AbsoluteValue.abs_isEuclidean, Zsqrtd.instIsStrictOrderedRingCastInt, pow_le_pow_iff_left, Finsupp.Lex.single_strictAnti, Valuation.isNontrivial_iff_exists_lt_one, ArchimedeanClass.mk_pow, ArchimedeanClass.isAddRegular_mk, nullMeasurableSet_Ioi, IsDedekindDomain.HeightOneSpectrum.instIsNontrivialWithZeroMultiplicativeIntValuation, Valuation.Integers.valuation_irreducible_lt_one, WithZeroTopology.nhds_zero_of_units, Set.Ico_subset_Icc_union_Ico, AddValuation.map_add', mem_nhdsGT_iff_exists_Ioc_subset, borel_eq_generateFrom_Ici, Topology.RelCWComplex.coe_skeletonLT, Num.cast_le, invOf_nonneg, Filter.tendsto_mabs_atTop_atTop, Finpartition.disjoint, strictConvex_Icc, antivary_iff_smul_rearrangement, Nonneg.mk_nnratCast, Set.Ioo_inter_Ioi, zpow_two_nonneg, GenContFract.succ_nth_fib_le_of_nth_den, Module.End.maxGenEigenspace_eq, one_le_mul_self_iff, List.coe_maximum_of_length_pos, Finset.Colex.le_iff_max'_mem, negPart_anti, SemilatInfCat_dual_comp_forget_to_partOrd, lt_inv_self_iff, ArchimedeanClass.mk_le_mk, NNRat.lt_def, exists_lub_Iio, Polynomial.div_tendsto_zero_iff_degree_lt, tendsto_floor_right_pure, MeasureTheory.aecover_Iio_of_Iic, Nat.preimage_Ici, upperSemicontinuousAt_iff_frequently, Finsupp.Colex.isStrictOrder, Int.padicValuation_eq_one_iff, smul_nonpos_iff, smul_inf_le, isClosed_nonneg, mabs_div_le, segment_eq_uIcc, Nat.count_le_setENCard, Nat.one_div_le_one_div, IsPreconnected.intermediate_value_Ioo, MvPowerSeries.le_weightedOrder_mul, PowerSeries.coe_add, Set.unbounded_gt_inter_gt, RootPairing.RootPositiveForm.zero_lt_posForm_iff, MvPolynomial.supDegree_esymmAlgHomMonomial, partialSups_add_one', sup_le_inf, pairwise_disjoint_fiber, LinearOrderedField.lt_inducedMap_iff, Finset.max_sum_le, MvPolynomial.schwartz_zippel_totalDegree, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivCounitIso_hom_app_hom, Finset.max'_le_iff, Right.pow_lt_one_iff, isOpen_lt, PowerSeries.coeff_heval, continuousOn_fract, Cardinal.toENat_eq_zero, Affine.Simplex.sign_touchpointWeights_empty, HahnSeries.ofSuppBddBelow_zero, ProbabilityTheory.HasSubgaussianMGF.const_mul, StieltjesFunction.mono', hnot_hnot_le, MvPowerSeries.le_order_prod, CategoryTheory.Functor.WellOrderInductionData.sectionsMk_val_op_bot, BoundedLENhdsClass.of_closedIciTopology, inf_le_right, MulArchimedeanClass.top_eq_mk_iff, Ioc_subset_biUnion_Ioc, OrderRingHom.apply_eq_self, Topology.CWComplex.iUnion_openCell_eq_skeletonLT, CategoryTheory.SmallObject.SuccStruct.Iteration.mkOfLimit.inductiveSystem_obj, Hyperreal.InfiniteNeg.lt_zero, Sym2.sortEquiv_apply_coe, Finset.orderIsoOfFin_symm_apply, tsub_pos_iff_lt, emultiplicity_lt_iff_not_dvd, Cardinal.toENat_eq_ofNat, CauSeq.const_lt, CanonicallyOrderedAdd.toOrderedSub, Nat.image_cast_int_Icc, exists_nonneg_left_iff_sameRay, Valuation.Integers.map_le_one, TopCat.Sheaf.interUnionPullbackCone_fst, emultiplicity_le_emultiplicity_of_dvd_right, Nat.image_cast_int_Iic, leOnePart_eq_one', InnerProductSpace.gramSchmidt_def, Orientation.map_eq_neg_iff_det_neg, neg_abs_le_neg, Finset.inf_id_eq_sInf, IsDedekindDomain.HeightOneSpectrum.intValuation_le_pow_iff_mem, Finset.mulConst_le_card, Finset.Icc_subset_uIcc', Int.preimage_Ioi, MonomialOrder.degree_reduce_lt, IsNonarchimedean.finset_image_add, Archimedean.embedReal_apply, Order.Ici_pred, Set.covBy_iff_exists_sdiff_singleton, le_himp_comm, Polynomial.abs_div_tendsto_atTop_of_degree_gt, LaurentSeries.ofPowerSeries_powerSeriesPart, instWellFoundedLTSubtypeSetFinite, IsDedekindDomain.HeightOneSpectrum.intValuation_singleton, Module.End.maxGenEigenspace_eq_genEigenspace_finrank, Ordinal.toNimber_min, emultiplicity_pos_of_dvd, CategoryTheory.TransfiniteCompositionOfShape.iic_isoBot, LaurentSeries.single_order_mul_powerSeriesPart, HahnEmbedding.Partial.archimedeanClassMk_eq_iff, exists_rat_gt, LinearOrderedCommGroup.Subgroup.genLTOne_lt_one, Module.End.mapsTo_genEigenspace_of_comm, HahnSeries.support_abs, ValuativeRel.ValueGroupWithZero.mk_pos, MonoidWithZeroHom.fst_mono, le_mabs, Odd.pow_nonneg_iff, Topology.IsUpper.isTopologicalBasis_insert_univ_subbasis, IsNonarchimedean.apply_natCast_le_one_of_isNonarchimedean, NNRat.cast_mono, disjoint_compl_right_iff, inf_left_le_sup_left, PowerSeries.order_mul_ge, SimpleGraph.farFromTriangleFree_iff, Nat.lt_succ_floor, MonomialOrder.zero_le, CompositionSeries.lt_last_of_mem_eraseLast, Finset.Colex.lt_iff_exists_forall_lt, sbtw_iff_left_ne_and_right_mem_image_Ioi, Complementeds.mk_bot, FunctionField.instIsNontrivialRatFuncWithZeroMultiplicativeIntInftyValuation, MultilinearMap.map_piecewise_sub_map_piecewise, Set.notMem_Iic, ArchimedeanClass.mk_natCast, CategoryTheory.TransfiniteCompositionOfShape.ofArrowIso_isoBot, CategoryTheory.Limits.HasIterationOfShape.hasColimitsOfShape, Nat.ceil_eq_zero, SetRel.prod_comp_prod, Even.pow_nonneg, zpow_neg_two_nonneg, Multiset.le_inf, Int.floor_eq_zero_iff, MeasureTheory.meas_le_ae_eq_meas_lt, Set.uIoo_eq_union, AffineBasis.convexHull_eq_nonneg_coord, Nat.floor_sub_one, codisjoint_iff_compl_le_left, AffineSubspace.sSameSide_iff_exists_left, IsModularLattice.complementedLattice_Ici, Set.disjoint_image_left, HeytAlg.Iso.mk_inv, InitialSeg.isNormal, pos_add_self_iff, mfderivWithin_projIcc_one, ENat.forall_natCast_le_iff_le, WithBot.lt_add_one_iff, Finset.min'_le, Set.Infinite.exists_lt, Cardinal.ofENat_mono, tendsto_ceil_left_pure_ceil, Int.comap_cast_atTop, le_himp_himp, measurable_lt, Valuation.ltAddSubgroup_monotone, Rat.padicValuation_self, OrderIso.infIrredUpperSet_symm_apply, hasBasis_nhdsSet_Ici_Ioi, Polynomial.tendsto_atTop_iff_leadingCoeff_nonneg, BoundedLatticeHom.symm_dual_comp, Polynomial.IsDistinguishedAt.degree_eq_coe_lift_order_map, OrderIso.map_inf, Set.encard_preimage_val_le_encard_right, Set.Iio_inj, MeasureTheory.aecover_Ioo_of_Ioc, HahnEmbedding.Seed.baseEmbedding_strictMono, PNat.le_of_dvd, Mathlib.Meta.NormNum.isRat_lt_true, Booleanisation.comp_lt_comp, Mathlib.Tactic.Order.ToInt.toInt_nle_toInt, ProbabilityTheory.Kernel.indep_limsup_atBot_self, CategoryTheory.TransfiniteCompositionOfShape.ofOrderIso_incl, HasStrictFDerivAt.abs, RatFunc.coe_X, PowerSeries.le_order_smul, convexHull_toCone_eq_sInf, le_iff_forall_one_lt_lt_mul', max_bot_left, CategoryTheory.TransfiniteCompositionOfShape.isWellOrderContinuous, PowerSeries.coeff_coe, Valued.isClopen_ball, frontier_Ici, Set.sdiff_singleton_covBy, Set.Icc.disjoint_iff, tendsto_ceil_atTop, Heyting.IsRegular.disjoint_compl_right_iff, Finset.max_mono, NonemptyFinLinOrd.epi_iff_surjective, ValuativeRel.ValueGroupWithZero.embed_strictMono, AffineSubspace.wOppSide_iff_exists_wbtw, Valuation.IsEquiv.pos_iff, PNat.card_Icc, Types.monoOverEquivalenceSet_inverse_map, Fin.castSuccOrderEmb_toEmbedding, Set.monotone_projIic, List.mem_argmin_iff, disjoint_symmDiff_inf, exists_lt_mul_self, MonomialOrder.toSyn_strictMono, inf_sup_le, complementedLattice_iff, PowerSeries.order_finite_iff_ne_zero, Finset.Ico_diff_Ico_left, FiniteArchimedeanClass.val_mk, Int.self_le_zpow_clog, Polynomial.isEquivalent_atTop_lead, Order.IsNormal.monotone, SimpleGraph.posSemidef_lapMatrix, Monotone.of_map_inf_le_left, Polynomial.le_trailingDegree_C, Set.bounded_ge_inter_not_ge, Finset.card_div_choose_le_card_shadow_div_choose, MonomialOrder.div_single, LinearOrder.supConvergenceClass, LinOrd.hom_inv_apply, LaurentSeries.coe_algebraMap, exists_isLocalExtr_Ioo, Polynomial.isLittleO_atTop_of_degree_lt, Set.unbounded_le_inter_le, Nimber.toOrdinal_max, Nonneg.segment_eq_uIcc, Monotone.of_map_inf, codisjoint_hnot_right, Nat.image_cast_int_Ioc, Finset.Colex.mem_initSeg, ArchimedeanClass.mk_add_lt_mk_left_iff, pow_two_nonneg, Tuple.monotone_proj, FiniteArchimedeanClass.mem_ballAddSubgroup_iff, Finset.mem_convexHull', MulArchimedeanClass.mk_eq_mk, MvPowerSeries.le_weightedOrder_prod, RatFunc.coe_coe, Multiset.inf_le, MeasureTheory.aecover_Ioc_of_Ioo, Set.indicator_le_indicator_nonneg, Finset.orderEmbOfFin_eq_orderEmbOfFin_iff, div_neg_iff, intermediate_value_Icc', AffineSubspace.sOppSide_iff_exists_left, Polynomial.abs_div_tendsto_atBot_atTop_of_degree_gt, Finsupp.disjoint_iff, measurableSet_Ico, Valuation.Integers.le_of_dvd, geom_sum_pos_iff, NumberField.FinitePlace.norm_embedding_eq, OrderRingIso.eq_refl, div_le_one_iff, GenContFract.abs_sub_convergents_le', isClosed_Ioc_iff, Finpartition.mem_avoid, abs_sub_le, NNRat.num_pos, partialSups_add_one, eVariationOn.nonempty_monotone_mem, intermediate_value_Ioo', Polynomial.valuation_of_mk, RootedTree.mem_subtrees_disjoint_iff, Mathlib.Tactic.Qify.nnratCast_le, isOpen_Ioo, Rat.intCast_le_cast, mabs_le', MulArchimedeanClass.mk_left_le_mk_mul_iff, Field.Emb.Cardinal.two_le_deg, RootPairing.exists_ge_zero_eq_rootForm, AbsoluteValue.isEquiv_iff_lt_one_iff, Finset.inf_prodMap, Int.le_ceil, MulArchimedeanClass.mem_subgroup_iff, AddSubmonoid.closure_image_isAddIndecomposable_baseOf, SemilatInfCat.dual_obj_isOrderBot, HahnSeries.order_mul, Nat.Prime.emultiplicity_le_emultiplicity_choose_add, tendsto_zpow_atTop_zero, Valuation.val_lt_one_iff, Set.pairwise_disjoint_Ioc_zsmul, Quaternion.normSq_le_zero, MulArchimedeanClass.subsemigroup_strictAnti, Finset.local_lubell_yamamoto_meshalkin_inequality_div, abs_le, Odd.zpow_nonpos_iff, isCoatom_compl, Int.fract_pos, Finpartition.parts_map, GroupSeminormClass.toNonnegHomClass, nhds_basis_zero_abs_lt, nhds_eq_iInf_abs_sub, Valuation.val_le_one_or_val_inv_le_one, Set.Icc_subset_uIcc, Fin.natAddOrderEmb_toEmbedding, measurableSet_Iio, WithTop.tendsto_untop, mabs_inf_div_inf_le_mabs, TopHom.coe_inf, RootPairing.RootPositiveForm.posForm_apply_root_root_le_zero_iff, ArchimedeanClass.mk_left_le_mk_sub_iff, Set.subset_compl_iff_disjoint_right, ENat.map_natCast_strictMono, Nimber.toOrdinal_min, Polynomial.cardPowDegree_isEuclidean, Polynomial.abs_div_tendsto_atTop_atTop_of_degree_gt, leOnePart_lt, Field.Emb.Cardinal.isLeast_leastExt, sub_half_lt_round, ValuativeRel.nonempty_orderIso_withZeroMul_int_iff, Finset.divConst_le_card, Finset.one_le_mulConst, LaurentSeries.inducing_coe, Set.Ioc_disjoint_Ioc, cmp_add_left, le_hnot_inf_hnot, exists_isExtrOn_Ioo_of_tendsto, Ordinal.enum_le_enum', PowerSeries.coe_smul, Finset.le_inf_image₂, Set.Ioo_subset_Ioc_union_Ico, Valuation.map_add, sdiff_le_hnot, Set.disjoint_left, ArchimedeanClass.mk_le_mk_smul, CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.ofComposableArrows_isColimit_desc, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivInverseObj_π_app, MulArchimedeanClass.mk_lt_mk, pred_min, div_le_inv_mul_iff, Set.disjoint_singleton_left, LaurentSeries.continuous_coe, PNat.factorMultiset_le_iff, convexJoin_segment_singleton, Finset.Colex.toColex_le_toColex_iff_max'_mem, min_eq_right_iff, HahnEmbedding.Partial.toOrderAddMonoidHom_apply, Set.disjoint_right, monovaryOn_comm, Valuation.HasExtension.val_map_lt_iff, LaurentSeries.algebraMap_C_mem_adicCompletionIntegers, PNat.tendsto_comp_val_iff, Order.IsNormal.ext, openSegment_eq_Ioo', cocompact_le_atTop, MvPowerSeries.lexOrder_def_of_ne_zero, MonomialOrder.degree_add_le, Valued.is_topological_valuation, InfHomClass.toOrderHomClass, CategoryTheory.TransfiniteCompositionOfShape.ici_F, HahnEmbedding.Seed.strictMono_coeff, interior_Iio, Finset.le_inf_add, min_le_max, instIsCodirectedOrder, one_le_mul_mabs, Nat.floor_div_ofNat, Set.Ioi_diff_Ioi, negPart_pos_iff, isPiSystem_image_Ioi, Order.Iio_succ_eq_insert, IsValuativeTopology.isOpen_ball, NatOrdinal.succ_def, continuous_iff_lower_upperSemicontinuous, Topology.RelCWComplex.iUnion_openCell_eq_skeleton, convexJoin_singleton_segment, CompositionSeries.lt_succ, MvPowerSeries.le_weightedOrder_map, Hyperreal.not_infinite_iff_exist_lt_gt, AffineSubspace.wOppSide_self_iff, le_emultiplicity_map, Dense.Iio_eq_biUnion, ENNReal.bot_eq_zero, Stream'.Seq.length'_le_iff, Hyperreal.archimdeanClassMk_coe, Int.floor_lt, mul_nonneg_iff, IsAbsoluteValue.abs_isAbsoluteValue, Pi.toLex_update_lt_self_iff, Order.lt_succ_iff_eq_or_gt, Field.Emb.Cardinal.succEquiv_coherence, hasDerivWithinAt_abs, NNRat.floor_cast, NNRat.coe_pos, Cardinal.noMaxOrder, abs_sub, Cardinal.ofENat_lt_aleph0, Hyperreal.tendsto_iff_forall, mapClusterPt_atTop_nsmul_tfae, MvPowerSeries.nat_le_order, inf_top_eq, Valuation.one_lt_val_iff, Orientation.map_eq_iff_det_pos, smul_nonpos_iff_pos_imp_nonpos, LatticeHom.withTopWithBot'_toFun, archimedean_iff_nat_le, SetRel.image_core_gc, SuccOrder.nhdsLE_eq_nhds, le_iff_forall_neg_add_le, HahnEmbedding.ArchimedeanStrata.ball_sup_stratum_eq, compl_sup_compl_le, DFinsupp.lt_of_forall_lt_of_lt, generateFrom_Icc_mem_le_borel, Set.disjoint_sdiff_inter, ContinuousOn.finset_inf, Quaternion.normSq_nonneg, Nat.le_floor_iff', countable_setOf_isolated_right, OrderRingIso.subsingleton_right, sup_strictMonoOn_Icc_inf, not_infIrred, Padic.norm_eq_zpow_log_mulValuation, mabs_mul_three, ENat.one_le_card_iff_nonempty, disjoint_sup_right, Nat.image_cast_int_Ici, MeasureTheory.AEEqFun.inf_le_left, ValuationSubring.valuation_lt_one_or_eq_one, Set.Icc_subset_Icc_union_Ioc, compl_anti, HahnSeries.instIsCancelMulZeroOfIsCancelAdd, Set.unbounded_lt_inter_le, Set.pairwise_disjoint_Ioo_add_intCast, PowerSeries.intValuation_eq_of_coe, Set.Ico_succ_succ_eq_Ioc, LocallyFiniteOrder.orderAddMonoidHom_bijective, HahnSeries.orderTop_mul_of_nonzero, List.minimum_of_length_pos_le_of_mem, Nat.ceil_mono, Tuple.sort_eq_refl_iff_monotone, le_iff_posPart_negPart, convexHull_add, Set.Ioo_add_one_right_eq_Ioc, Finset.divConst_le_mulConst_sq, FiniteMulArchimedeanClass.withTopOrderIso_apply_coe, WithTop.instBorelSpace, Finsupp.Lex.isStrictOrder, Finset.inf_sup, EReal.abs_mul_sign, Set.Iio_subset_Iic_iff, Finsupp.Colex.addRightMono, OrderEmbedding.coe_birkhoffFinset, PNat.lt_add_right, RootPairing.zero_lt_pairingIn_iff', Nat.preimage_floor_of_ne_zero, Set.Ioc_subset_Ioc_union_Icc, HahnEmbedding.Partial.isWF_support_evalCoeff, Set.projIci_eq_self, Set.antitone_setOf, CategoryTheory.OrthogonalReflection.iteration_map_succ, Set.covBy_insert, HahnEmbedding.Partial.orderTop_eq_iff, Mathlib.Meta.Positivity.nonneg_of_isNNRat, Polynomial.tendsto_atBot_iff_leadingCoeff_nonpos, List.coe_le_maximum_iff, Mathlib.Tactic.ENatToNat.not_lt_top, Finset.lubell_yamamoto_meshalkin_inequality_sum_inv_choose, disjoint_sdiff_comm, le_himp_iff_left, PNat.find_mono, Order.lt_succ_iff_eq_or_lt, Continuous.exists_forall_le_of_hasCompactSupport, ArchimedeanClass.top_eq_mk_iff, IsDedekindDomain.HeightOneSpectrum.equivHeightOneSpectrum_symm_apply, LowerSet.total_le, OrderMonoidWithZeroHom.mul_comp, compl_lt_self, tendsto_ceil_right_pure_add_one, ENat.card_le_one_iff_subsingleton, Finset.inf_apply, ArchimedeanClass.instIsOrderedAddMonoid, Hyperreal.isSt_iff_abs_sub_lt_delta, nhds_top_basis_Ici, Cardinal.toENat_lt_natCast_iff, abs_max_sub_max_le_abs, Finsupp.DegLex.single_lt_iff, Set.projIic_surjOn, LaurentSeries.val_le_one_iff_eq_coe, HasSubset.Subset.disjoint_compl_right, zpow_right_strictMono, Nucleus.idempotent', ProbabilityTheory.Kernel.HasSubgaussianMGF.const_mul, disjoint_compl_compl_left_iff, PrimeSpectrum.isIdempotentElemEquivClopens_symm_bot, DistLat.Iso.mk_inv, Polynomial.le_trailingDegree_monomial, sdiff_le_iff_left, ContinuousOn.strictMonoOn_of_injOn_Icc', MonomialOrder.le_degree, Set.Iio_diff_Iio, nhds_basis_Icc_one_lt, Module.Basis.orientation_eq_iff_det_pos, sq_le_sq, List.sum_min_le, LinOrd.inv_hom_apply, max_lt_max_right_iff, ArchimedeanClass.mk_ofNat, mul_nonneg_iff_pos_imp_nonneg, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquiv_counitIso, Polynomial.degree_comp, Finset.pluennecke_ruzsa_inequality_nsmul_add, ADEInequality.lt_six, MeasureTheory.AEEqFun.inf_le_right, IsDedekindDomain.HeightOneSpectrum.valuation_exists_uniformizer, Finset.abs_sum_le_sum_abs, Finpartition.ofErase_parts, Order.krullDim_int, Finsupp.Colex.addRightStrictMono, Function.locallyFinsuppWithin.posPart_add, frontier_Ioi, Set.Finite.encard_lt_top, invOf_lt_zero, FloorRing.gc_ceil_coe, IsDiscreteValuationRing.isRankOneDiscrete, instIsStrictOrderedRingNNRat, disjoint_of_sSup_disjoint, ENat.card_lt_top_of_finite, leOnePart_le_one', PredOrder.nhdsGE_eq_nhds, continuousWithinAt_iff_lower_upperSemicontinuousWithinAt, Submodule.inf_genEigenspace, Int.ceil_eq_iff, ArchimedeanClass.mk_lt_mk, posPart_nonneg, Set.disjoint_singleton, ZMod.valMinAbs_mem_Ioc, Finset.truncatedInf_le, add_left_strictMono_of_ne_top, neg_abs_le, oneLePart_eq_ite_lt, MvPowerSeries.nat_le_weightedOrder, Rat.toNNRat_lt_toNNRat_iff', upperBounds_Iio, Set.encard_union_le, MeasureTheory.aecover_Icc_of_Ioc, PrimeMultiset.prod_dvd_iff', ValuativeExtension.mapValueGroupWithZero_strictMono, borel_eq_generateFrom_Icc, Module.End.genEigenspace_top_eq_maxUnifEigenspaceIndex, le_of_inf_eq', Set.encard_strictMono, Polynomial.trailingDegree_le_trailingDegree, IsDedekindDomain.HeightOneSpectrum.adicCompletionIntegers.integers, Ordinal.toNatOrdinal_min, CategoryTheory.Triangulated.TStructure.le_monotone, exists_wellOrder, PowerSeries.coe_mul, unitInterval.symm_projIcc, Rat.preimage_cast_Ioi, sdiff_lt_left, cocompact_eq_atTop, ArchimedeanClass.FiniteElement.not_isUnit_iff_mk_pos, exists_lt_add_iff_lt_left, Hyperreal.archimedeanClassMk_neg_of_tendsto_atBot, HahnSeries.order_single_mul_of_isRegular, Polynomial.abs_tendsto_atTop_iff, Order.Ideal.coe_sup_eq, Finset.min_le, Cardinal.toENat_lift, PNat.Ico_eq_finset_subtype, CategoryTheory.SmallObject.SuccStruct.restrictionLTOfCoconeIso_inv_app, Int.instIsSuccArchimedean, hasDerivAt_iff_tendsto_slope_left_right, sign_zero, Function.Lex.wellFoundedLT, min_le_iff, disjoint_partialSups_right, tendsto_floor_right_pure_floor, Finset.Ioc_sub_one_left_eq_Icc, IsOpen.exists_Ioo_subset, WithZero.lt_mul_exp_iff_le, CauSeq.bounded', SimpleGraph.edgeSet_eq_iff, convexHull_basis_eq_stdSimplex, Hyperreal.isSt_sSup, Filter.tendsto_const_mul_atBot_iff, Field.Emb.Cardinal.noMaxOrder_rank_toType, Order.Ioo_pred_left, Set.biUnion_Ico_eq_Iio_self_iff, Convex.radon_partition, Finset.Ico_add_one_left_eq_Ioo, Units.orderEmbeddingVal_apply, Continuous.exists_forall_ge_of_hasCompactSupport, HahnSeries.SummableFamily.hsum_powerSeriesFamily_mul, NNRat.one_le_cast, Finset.max'_subset, List.minimum_append, PosSMulMono.nnrat_of_rat, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivFunctorObj_π_app, List.le_maximum_of_length_pos_of_mem, MeasureTheory.aecover_Ioc_of_Icc, Set.pairwise_disjoint_Ioc_add_zsmul, OrderMonoidIso.withZeroUnits_symm_apply, Finset.isGLB_inf, ENat.add_one_le_iff, Set.Ioi_inj, Int.card_Ioc, ArchimedeanClass.orderHom_zero, Int.preimage_Iio, FunctionField.valuedFqtInfty.def, Polynomial.exists_max_root, Int.floor_le_iff, Rat.preimage_cast_Icc, LinOrd.Iso.mk_hom, Set.Ico_subset_Ico_union_Ico, Finset.prod_sub_ordered, MonoidWithZeroHom.inl_strictMono, PowerSeries.heval_apply, mapClusterPt_atTop_zsmul_iff_nsmul, ENat.instOrderTopology, generateFrom_Ico_mem_le_borel, units_smul_eq_self_iff, NormedSpace.normalize_smul, MvPowerSeries.one_le_order_iff_constCoeff_eq_zero, Nonneg.coe_nnratCast, sign_mul_abs, HahnSeries.addVal_le_of_coeff_ne_zero, Set.Icc_pred_right_eq_Ico, SimpleGraph.farFromTriangleFree.le_card_sub_card, PowerSeries.coe_sub, min_eq_iff, Set.Ici_subset_Icc_union_Ici, WithBot.ge_of_forall_gt_iff_ge, Affine.Simplex.ExcenterExists.sign_signedInfDist_touchpoint, WithZeroMulInt.toNNReal_lt_one_iff, nhdsGT_basis, PrimeSpectrum.isIdempotentElemEquivClopens_one_sub, MulArchimedeanClass.liftOrderHom_mk, ArchimedeanClass.mem_ball_iff, NucleusClass.idempotent, PNat.sub_coe, SimpleGraph.isUniform_singleton, IsNonarchimedean.multiset_image_add_of_nonempty, Int.floor_le_sub_one_iff, OrderMonoidIso.withZeroUnits_apply, CategoryTheory.TransfiniteCompositionOfShape.ofComposableArrows_F, Cardinal.toENat_le_ofNat, Asymptotics.isEquivalent_nat_ceil, InverseSystem.PEquivOn.nat, units_smul_eq_neg_iff, inf_le_left, isPiSystem_Ioc, nonempty_orderEmbedding_of_finite_infinite, Profinite.NobelingProof.Products.eval_eq, le_iff_exists_inf, WithTop.orderIsoSumLexPUnit_toLex, succ_min, ArchimedeanClass.mk_monotoneOn, WithBot.succ_eq_bot, Set.disjoint_powerset_insert, LaurentSeries.algebraMap_apply, Int.floor_nonneg, Valuation.IsEquiv.one_lt_iff_one_lt, ArchimedeanClass.mk_sub_lt_mk_right_iff, Polynomial.div_tendsto_atBot_zero_of_degree_lt, IsDedekindDomain.HeightOneSpectrum.intValuation_le_pow_iff_dvd, Iio_mem_nhdsSet_Iic_iff, PNat.addLeftReflectLT, abs_sub_le_iff, Set.disjoint_toFinset, nhdsWithinLE_sup_nhdsWithinGT, midpoint_le_right, Int.cast_strictMono, Set.projIic_coe, GenContFract.IntFractPair.nth_stream_fr_lt_one, AddGroupCone.nonneg.hasMemOrNegMem, SMulPosMono.toSMulPosReflectLT, Set.unbounded_inter_ge, covBy_iff_lt_iff_le_left, LipschitzWith.projIcc, min_lt_iff, le_of_inf_eq, MvPowerSeries.le_weightedOrder_pow, bihimp_le_iff_left, iSupIndep.supIndep', Ordinal.toType_noMax_of_succ_lt, RootPairing.zero_lt_pairingIn_iff, IsDedekindDomain.HeightOneSpectrum.valuation_def, le_emultiplicity_of_le_multiplicity, Order.Ioi_pred, Polynomial.abs_tendsto_atTop, MvPolynomial.leadingCoeff_esymmAlgHomMonomial, CategoryTheory.Limits.MultispanIndex.toLinearOrder_fst, MeasureTheory.Measure.pi_prod_map_IocProdIoc, Set.Ioi_subset_Ioc_union_Ioi, CauSeq.lt_lim, lineMap_lt_right_iff_lt_one, AddMonoidAlgebra.le_inf_support_add, iSupIndep.supIndep, tendsto_fract_right', Set.vadd_Icc, ValuationClass.map_add_le_max, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivCounitIso_inv_app_hom, Matrix.IsIrreducible.nonneg, sign_pos, isPiSystem_Ico_mem, Set.Ioo_min_max, IsCompact.exists_isLUB, ValuationSubring.valuation_le_one, CategoryTheory.Limits.MultispanIndex.toLinearOrder_snd, PNat.natPred_monotone, SuccOrder.nhds_eq_pure, PowerSeries.le_order_map, Affine.Simplex.wSameSide_affineSpan_faceOpposite_point_left_iff, CategoryTheory.Limits.instHasIterationOfShapeElemIic, lineMap_le_lineMap_iff_of_lt', BoundedLatticeHom.coe_comp_lattice_hom', Set.pairwise_disjoint_Ioc_mul_zpow, inv_le_self_iff, monovaryOn_iff_forall_smul_nonneg, Finset.dens_le_one, ArchimedeanClass.FiniteElement.mk_intCast, Int.ceil_eq_zero_iff, Finset.le_prod_max_one, Set.pairwise_disjoint_Ico_mul_zpow, CategoryTheory.TransfiniteCompositionOfShape.iic_isColimit, HahnEmbedding.IsPartial.strictMono, Multiset.inf_zero, MonomialOrder.lex_lt_iff_of_unique, emultiplicity_le_emultiplicity_iff, Finset.le_max_of_eq, isLocallyClosed_Ico, inf_le_ite, frontier_lt_subset_eq, Lattice.BicartSq.le₂₄, Nat.floor_natCast, iUnion_Icc_intCast, Set.coe_projIci, MvPowerSeries.min_weightedOrder_le_add, SignType.neg_one_lt_one, Set.eq_empty_or_encard_eq_top_or_encard_diff_singleton_lt, Nat.one_le_floor_iff, PNat.ofNat_lt_ofNat, RootPairing.zero_le_rootForm, ZNum.isOrderedAddMonoid, Int.card_fintype_Ioo_of_lt, Dense.exists_le', MonomialOrder.degLex_le_iff, Filter.tendsto_zpow_atTop_atTop, Set.Ico_inter_Ico, instMulArchimedeanNNRat, tendsto_PNat_val_atTop_atTop, Tuple.graphEquiv₂_apply, le_oneLePart, WithTop.orderIsoSumLexPUnit_symm_inl, denselyOrdered_units_iff, Nat.measurable_ceil, HahnSeries.cardSuppLTSubfield_carrier, AffineSubspace.wOppSide_iff_exists_left, OrderIso.withZeroUnits_symm_apply, ENat.eq_top_iff_forall_gt, Int.card_box, LaurentSeries.derivative_iterate_coeff, Finset.coe_orderIsoOfFin_apply, NNRat.coe_lt_coe, Valuation.nonempty_rankOne_iff_mulArchimedean, QuadraticMap.toBilin_apply, Order.Ideal.IsMaximal.isPrime, MulArchimedeanClass.min_le_mk_mul, disjoint_iff, atBot_atTop_le_cocompact, tendsto_floor_atTop, MonomialOrder.bot_eq_zero, Finset.uIcc_product_uIcc, Set.ordConnected_iff_disjoint_Ioo_empty, Function.locallyFinsuppWithin.instIsOrderedAddMonoid, ValuativeRel.IsDiscrete.has_maximal_element, Int.floor_mono, ArchimedeanClass.mk_add_lt_mk_right_iff, LinearMap.finrank_genEigenspace_le, FunctionField.InftyValuation.map_add_le_max', mabs_mul_le, Set.offDiag_mono, MulArchimedeanClass.mem_closedBallSubgroup_iff, FiniteMulArchimedeanClass.mem_ballSubgroup_iff, Finsupp.lt_of_forall_lt_of_lt, WithTop.isOpenEmbedding_coe, bihimp_le_iff_right, inv_mabs_le, MonomialOrder.toSyn_lt_iff_ne_zero, WeierstrassCurve.IsMinimal.val_Δ_maximal, tendsto_inv_nhdsGT_zero, abs_sub_lt_iff, HasFDerivAt.abs, supPrime_iff_not_isMin, ArchimedeanClass.stdPart_eq_sInf, AffineSubspace.setOf_wOppSide_eq_image2, iUnion_Ioc_add_intCast, LinearOrderedField.cutMap_coe, Nat.floor_int, AbsoluteValue.abs_apply, Finset.sup'_lt_iff, AntitoneOn.of_map_sup, Hyperreal.stdPart_coe, HasFDerivWithinAt.abs, NatOrdinal.toOrdinal_max, Odd.pow_neg_iff, OrderEmbedding.birkhoffSet_inf, Nonneg.instNontrivialSubtypeLeOfNatOfAddLeftMono, Module.End.iSup_genEigenspace_eq, projIcc_eq_one, HasSSubset.SSubset.lt, Hyperreal.infinitePos_iff_infinite_and_pos, Finset.lt_fold_min, strictConvex_Ioo, ArchimedeanClass.ballAddSubgroup_top, LaurentSeries.exists_ratFunc_val_lt, sameRay_smul_left_iff, Finpartition.parts_eq_empty_iff, Set.Ico.coe_inf, AffineSubspace.wSameSide_and_wOppSide_iff, Int.Ioo_eq_finset_map, List.exists_map_eq_of_sorted_nonempty_iff_sbtw, Int.lt_floor_add_one, Multiset.Ico_filter_lt, SimpleGraph.disjoint_edgeSet, LinOrd.id_apply, inf_le_right, AlgebraicGeometry.IsOpenImmersion.map_ΓIso_inv_assoc, Module.End.genEigenspace_inf_le_add, interior_Icc, FiniteArchimedeanClass.liftOrderHom_mk, Finset.addConst_le_subConst_sq, Field.Emb.Cardinal.instIsSeparableSubtypeMemIntermediateFieldAdjoinImageToTypeOrdRankCompCoeBasisWellOrderedBasisLeastExtIioSingletonSet, Finset.prod_Ico_int_div, HahnSeries.embDomainOrderEmbedding_apply, ArchimedeanClass.mk_map_nonneg_of_archimedean, LinearOrderedCommMonoidWithZero.toIsOrderedMonoid, ENat.coe_toNat_le_self, Set.IicExtend_apply, Module.End.eigenspace_le_genEigenspace, UV.le_of_mem_compression_of_notMem, LocallyFiniteOrder.orderAddMonoidHom_strictMono, Order.isGLB_Ioi_iff_isPredPrelimit, FiniteMulArchimedeanClass.mem_closedBallSubgroup_iff, Valued.hasBasis_nhds_zero, Lat.Iso.mk_inv, Finset.supIndep_iff_pairwiseDisjoint, MonomialOrder.degree_le_iff, ArchimedeanClass.FiniteResidueField.ofArchimedean_inj, Affine.Simplex.wOppSide_affineSpan_faceOpposite_iff, Set.indicator_nonpos_le_indicator, PrimitiveSpectrum.hull_finsetInf, Hyperreal.epsilon_lt_pos, abs_lt_iff_mul_self_lt, NonemptyFinLinOrd.hom_comp, Hyperreal.coe_nonneg, Finset.isGreatest_max', GenContFract.zero_le_of_den, Heyting.Regular.coe_le_coe, OrderIso.sumLexIioIci_symm_apply_Iio, Int.card_Ico_of_le, HahnEmbedding.ArchimedeanStrata.disjoint_ball_stratum, lowerSemicontinuous_iff_frequently, infIccOrderIsoIccSup_apply_coe, HahnEmbedding.ArchimedeanStrata.archimedeanClassMk_of_mem_stratum, Finset.uIcc_subset_uIcc_iff_le', PUnit.isOrderedCancelAddMonoid, WithTop.continuous_coe, Nat.one_div_cast_pos, Set.Ioc_subset_Ioc_union_Ioc, Finset.Ico_inter_Ico, Padic.mulValuation_toFun, Finset.uIcc_subset_uIcc_iff_le, zpow_two_pos_of_ne_zero, SimpleGraph.FarFromTriangleFree.nonpos, IsDedekindDomain.HeightOneSpectrum.valuation_div_le_one_iff, CategoryTheory.SmallObject.SuccStruct.Iteration.mkOfLimit.inductiveSystem_map, Cardinal.one_le_ofENat, Int.sub_one_lt_floor, Set.projIci_surjective, Ideal.height_le_spanRank_toENat_of_mem_minimal_primes, ArchimedeanClass.stdPart_map_real, Finset.prod_one_add_ordered, Tropical.add_eq_left_iff, instModuleFinite, Hyperreal.infinitePos_iff_infinitesimal_inv_pos, IsValuativeTopology.mem_nhds_iff', not_infPrime_top, HahnEmbedding.IsPartial.truncLT_mem_range, IsDedekindDomain.HeightOneSpectrum.valuation_lt_one_iff_dvd, Complementeds.coe_top, NNRat.cast_nonneg, PrimeSpectrum.isIdempotentElemEquivClopens_symm_inf, SignType.not_one_lt, ContinuousOn.strictMonoOn_of_injOn_Ioo, LinOrd.ofHom_id, WithZero.withZeroUnitsEquiv_symm_strictMono, iUnion_Ico_add_intCast, mapClusterPt_rightLim, CategoryTheory.Pairwise.cocone_pt, Coheyting.boundary_sup_le, Affine.Simplex.wSameSide_affineSpan_faceOpposite_point_right_iff, AffineMap.lineMap_mono, isLUB_Iio, Set.Icc_succ_pred_eq_Ioo, IsDedekindDomain.HeightOneSpectrum.intValuation.map_add_le_max', BoundedLatticeHom.coe_comp_sup_hom, exists_isLocalExtr_Ioo_of_tendsto, Opens.pretopology_ofGrothendieck, Set.right_mem_uIoc, ENat.epow_right_mono, LaurentSeries.derivative_apply, Finsupp.Colex.wellFoundedLT_of_finite, Rat.cast_lt_natCast, LinearOrderedAddCommGroupWithTop.neg_pos, Valuation.isEquiv_iff_val_le_one, Finset.inf'_Ici, Padic.comap_mulValuation_eq_padicValuation, CategoryTheory.SmallObject.SuccStruct.Iteration.obj_bot, Set.Iic.coe_inf, Set.exists_min_image, disjointed_add_one, Polynomial.abs_tendsto_atBot_iff, DivisibleHull.instIsStrictOrderedModuleNNRat, Finset.SupIndep.disjoint_sup_sup, Filter.tendsto_const_mul_pow_atTop_iff, PowerSeries.le_order_mul, BddLat.forget_semilatInf_partOrd_eq_forget_bddOrd_partOrd, Finset.disjoint_sup_left, wellQuasiOrderedLE_iff_wellFoundedLT, Mathlib.Meta.NormNum.IsNat.natCeil, NumberField.FinitePlace.norm_lt_one_iff_mem, disjoint_compl_left, posSMulStrictMono_iff_PosSMulReflectLE, Set.pairwise_disjoint_Ico_add_intCast, lowerSemicontinuous_iff_isClosed_epigraph, hasBasis_nhdsSet_Iic_Iic, PNat.find_le_iff, CategoryTheory.instIsCardinalFilteredToTypeOrd, Valuation.Integers.not_denselyOrdered_of_isPrincipalIdealRing, isCompact_Ioo_iff, Module.Basis.orientation_eq_or_eq_neg, VertexOperator.ncoeff_apply, tendsto_ceil_right_pure_floor_add_one, Rat.preimage_cast_Ico, Set.Ioc_subset_uIoc, quasiconvexOn_iff_le_max, HahnSeries.order_abs, Set.encard_lt_top_iff, Valuation.HasExtension.val_map_le_one_iff, AddCircle.equivIccQuot_comp_mk_eq_toIocMod, le_iff_forall_pos_lt_add', isComplemented_bot, Valuation.map_sub, FixedDetMatrices.reps_entries_le_m', Hyperreal.coe_pos, Rat.valuation_le_one_iff_den, BoundedLatticeHom.coe_toSupBotHom, infIooOrderIsoIooSup_symm_apply_coe, supIrred_iff_not_isMin, PosSMulReflectLT.toPosSMulMono, EReal.sign_mul, Hyperreal.archimedeanClassMk_neg_of_tendsto_atTop, MulArchimedeanClass.mk_mul_lt_mk_left_iff, Nat.floor_div_eq_div, Valuation.mem_valuationSubring_iff, Complementeds.codisjoint_coe, LinearOrderedAddCommGroupWithTop.sub_left_strictMono_of_ne_top, Pi.card_uIcc, List.argmax_cons, Set.IicExtend_coe, tendsto_ceil_left, inv_le_leOnePart, continuousWithinAt_iff_continuous_left'_right', ArchimedeanClass.mk_natCast_nonneg, LaurentSeries.powerSeriesPart_coeff, isGreatest_himp, Finset.orderEmbOfFin_zero, Set.Icc_inter_Icc, WithZero.le_max_iff, Set.encard_le_card, SimpleGraph.hasse_preconnected_of_succ, segment_eq_Icc', Order.PartialIso.exists_across, ProbabilityTheory.Kernel.partialTraj_le_def, NNRat.nonpos_iff_eq_zero, disjoint_compl_compl_right_iff, leOnePart_eq_ite_lt, Ioc_subset_closure_interior, Set.subset_diff, Valuation.Integers.isIntegral_iff_v_le_one, disjointed_le_id, Set.sep_infs_le, partialSups_succ, Set.monotoneOn_or_antitoneOn_iff_uIcc, sbtw_iff_right_ne_and_left_mem_image_Ioi, ArchimedeanClass.mk_right_le_mk_sub_iff, Set.uIcc_subset_uIcc_iff_le', upperSemicontinuous_iff_frequently, tendsto_pow_div_pow_atTop_zero, Multiset.max_sum_le, IsCauSeq.bounded, Set.not_disjoint_iff_nonempty_inter, Booleanisation.lift_le_lift, Valuation.Integers.isPrincipalIdealRing_iff_not_denselyOrdered, isOpen_Iio, WeierstrassCurve.isGoodReduction_iff, Rat.toNNRat_lt_toNNRat_iff_of_nonneg, nhds_basis_Ioo_pos, nullMeasurableSet_le, NNRat.preimage_cast_Iic, Int.isCompl_even_odd, ArchimedeanClass.FiniteResidueField.ofArchimedean_injective, lineMap_le_left_iff_nonpos, Finset.exists_max_image, Set.Iic.complementedLattice_iff, hnot_top, lt_tsub_comm, inf_le_sup, inf_left_le_sup_right, Set.Finite.encard_lt_encard, EReal.sign_coe, AddCircle.continuous_equivIoc_symm, Ordinal.toNatOrdinal_one, Affine.Simplex.sign_excenterWeights_singleton_neg, NonemptyFinLinOrd.Iso.mk_inv, BoundedLatticeHomClass.toBoundedOrderHomClass, SSet.stdSimplex.nonDegenerateEquiv_apply_apply, Rat.cast_lt_intCast, Valuation.RankOne.strictMono, tendsto_inv_atBot_nhdsLT_zero, Nat.floor_lt', Valuation.Integers.le_iff_dvd, SimpleGraph.IsUniform.pos, himp_le, CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.instIsIsoAppIncl, posPart_nonpos, four_mul_le_sq_add, le_sup_sdiff, Set.Icc_diff_pi_univ_Ioc_subset, LaurentSeries.exists_Polynomial_intValuation_lt, LinearOrderedAddCommGroupWithTop.top_pos, Hyperreal.infiniteNeg_iff_infinite_and_neg, MonomialOrder.degree_sum_le, tendsto_ceil_atBot, himp_eq_top_iff, isGLB_pair, Ioc_diff_botSet, round_le, LinearOrderedCommGroup.wellFoundedOn_setOf_ge_gt_iff_nonempty_discrete, LinearOrderedField.inducedOrderRingHom_toFun, ValuationSubring.valuation_le_one_iff, Field.Emb.Cardinal.strictMono_leastExt, NNRat.natCast_le_cast, ArchimedeanClass.mk_zero, Finset.Ioc_inter_Ioc, CategoryTheory.TransfiniteCompositionOfShape.map_isoBot, Int.injOn_natAbs_Iic, Set.Ioc_diff_Iic, mem_segment_iff_sameRay, Set.exists_max_image, Set.disjoint_insert_left, ComplementedLattice.exists_isCompl, IsDedekindDomain.HeightOneSpectrum.valuedAdicCompletion_eq_valuation', mem_extremePoints_iff_forall_segment, Nat.preimage_ceil_of_ne_zero, compl_lt_compl_iff_lt, Orientation.map_eq_det_inv_smul, top_inf_eq, PNat.map_subtype_embedding_Icc, MeasureTheory.integrable_iff_integrableAtFilter_atBot_atTop, HahnSeries.orderTop_le_of_coeff_ne_zero, Finset.le_inf'_image₂, Finset.Ioi_sub_one_eq_Ici, Set.unbounded_gt_inter_not_gt, Order.exists_orderEmbedding_insert, sdiff_sdiff_sdiff_le_sdiff, NNRat.coe_ceil, Hyperreal.lt_of_tendsto_atTop, NNRat.preimage_cast_Ioi, Rat.natCast_le_cast, isCompact_Ioc_iff, Finset.nonneg_addConst, Set.exists_lower_bound_image, lowerSemicontinuousOn_iff_isClosed_epigraph, OrderType.type_eq_type, CircleDeg1Lift.iterate_monotone, toIcoDiv_zero_one, concaveOn_iff_div, lt_add_iff_lt_left_or_exists_lt, Finsupp.card_uIcc, Dense.exists_ge', grade_le_grade_iff, Tropical.add_eq_iff, ValuationSubring.instIsScalarTowerSubtypeMemValuationSubringWithZeroMultiplicativeInt, Order.Ideal.isPrime_iff_mem_or_compl_mem, Set.Iic_diff_Ioc, Int.orderedSMul, Valuation.map_add_le_max', minimal_iff_isLeast, add_abs_nonneg, inv_nhdsGT_zero, Sublattice.prodEquiv_toEquiv, Rat.cast_lt, Finset.Ioc_sub_one_right_eq_Ioo, Finset.Icc_succ_pred_eq_Ioo, Hyperreal.archimedeanClassMk_pos_of_tendsto, Finsupp.DegLex.single_antitone, WithTop.pred_eq_top, Finsupp.Lex.single_lt_iff, Nimber.add_nat, RootPairing.posRootForm_posForm_pos_of_ne_zero, tendsto_abs_nhdsNE_zero, monovary_iff_forall_smul_nonneg, exists_isExtrOn_uIoo_of_tendsto, closure_openSegment, Affine.Simplex.ExcenterExists.sign_signedInfDist_lineMap_excenter_touchpoint, Int.Ioc_filter_modEq_card, SimpleGraph.nonuniformWitnesses_spec, Polynomial.isBigO_atBot_of_degree_le, CategoryTheory.TransfiniteCompositionOfShape.fac, Finset.prod_add_ordered, lt_abs, Set.not_monotoneOn_not_antitoneOn_iff_exists_le_le, Finset.dens_strictMono, eventually_nhdsWithin_sign_eq_of_deriv_neg, CategoryTheory.Pairwise.diagram_map, OrderRingIso.subsingleton_left, exists_abs_lt, LinearOrderedAddCommGroupWithTop.strictMono_add_left_of_ne_top, borel_eq_generateFrom_Ioc, Valued.isClosed_ball, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivFunctor_obj_pt, covBy_iff_le_iff_lt_left, WithZero.exists_ne_zero_and_le_and_le, Tuple.self_comp_sort, BoundedLatticeHom.map_top', disjoint_disjointed_of_lt, StieltjesFunction.measurableSet_Ioi, Set.bdd_below_bdd_above_iff_subset_uIcc, disjoint_map_orderIso_iff, Finset.Ioo_succ_right_eq_Ioc, List.sortedLE_insertionSort, IsCompact.bddAbove, Set.bounded_ge_inter_ge, Even.pow_pos, le_abs, sameRay_smul_left_iff_of_ne, Finset.filter_infs_le, Finset.Colex.ofColex_top, IicProdIoc_def, PNat.ofNat_le_ofNat, Finset.orderEmbOfFin_last, strictConvex_Iio, HahnSeries.order_mul_of_nonzero, Set.lt_eq_ssubset, List.exists_map_eq_of_sorted_nonempty_iff_wbtw, FiniteMulArchimedeanClass.withTopOrderIso_symm_apply, Finset.sum_Icc_eq_sum_Ico_add, FiniteArchimedeanClass.mem_closedBallAddSubgroup_iff, not_bddAbove_iff_isCofinal, Int.card_Ico, Set.Icc_diff_pi_univ_Ioo_subset, PseudoMetric.IsUltra.isTransitiveRel_ball, Set.nsmul_right_monotone, HahnModule.coeff_smul_order_add_order, Module.Basis.orientation_ne_iff_eq_neg, Valuation.srel_iff_lt, abs_mul_sign, MeasureTheory.Measure.pi_prod_map_IicProdIoc, Int.card_Ioc_of_le, Set.iUnion_Ico_eq_Iio_self_iff, LinearOrderedAddCommGroup.discrete_iff_not_denselyOrdered, Finset.Ioc_succ_succ, ENat.natCast_lt_succ, upperSemicontinuousOn_iff_preimage_Iio, FiniteArchimedeanClass.mem_ball_iff, not_isCofinal_iff_bddAbove, Int.image_Ico_emod, PNat.equivNonZeroDivisorsNat_symm_apply_coe, grade_eq_grade_iff, WithZero.exists_ne_zero_and_lt_and_lt, CategoryTheory.TransfiniteCompositionOfShape.map_isColimit, TopCat.Sheaf.interUnionPullbackConeLift_right, ComplementedLattice.isStronglyCoatomic', PowerSeries.one_le_order_iff_constCoeff_eq_zero, continuousAt_iff_continuous_left'_right', OrderIso.subsingleton_of_wellFoundedGT', Profinite.NobelingProof.Products.eval_πs_image', MulArchimedeanClass.mk_le_mk_iff_lt, himp_inf_himp_inf_le, Filter.tendsto_mabs_atBot_atTop, OrderIso.sumLexIicIoi_symm_apply_Iic, Nat.succPNat_lt_succPNat, le_mabs_self, HahnSeries.SummableFamily.powerSeriesFamily_hsum_zero, HahnSeries.archimedeanClassMk_eq_archimedeanClassMk_iff, JordanHolderLattice.lt_of_isMaximal, LinearOrderedAddCommGroupWithTop.add_lt_top, Affine.Simplex.face_points, Filter.tendsto_abs_atBot_atTop, Finset.range_orderEmbOfFin, tendsto_nat_floor_div_atTop, Order.PFilter.inf_mem_iff, Units.mem_posSubgroup, FiniteMulArchimedeanClass.liftOrderHom_mk, tendsto_inv_atTop_nhdsGT_zero, Filter.comap_abs_atTop, compl_sup_le_himp, MulArchimedeanOrder.lt_def, ValuativeRel.ValueGroupWithZero.mk_lt_mk, ENat.toENNRealOrderEmbedding_apply, NNRat.natCast_lt_cast, Order.coheight_int, monovaryOn_iff_exists_monotoneOn, strictConvex_iff_convex, intermediate_value_Ioo, Set.Ioc_pred_right_eq_Ioo, ContinuousWithinAt.finset_inf, DivisibleHull.mk_le_mk, max_le_iff, one_lt_div_iff, Multiset.inf_coe, TopologicalSpace.Closeds.coe_finset_inf, Continuous.bddBelow_range_of_hasCompactSupport, HurwitzZeta.hasSum_int_completedHurwitzZetaOdd, CategoryTheory.SimplicialThickening.functor_map, BoundedLatticeHom.dual_symm_apply_toFun, MonomialOrder.degree_mul_lt_iff_left_lt_of_ne_zero, Sublattice.prodEquiv_apply, Field.Emb.Cardinal.equivSucc_coherence, NNRat.cast_le_one, Finpartition.default_eq_empty, Finset.Iio_add_one_eq_Iic, Finset.sup_eq_top_iff, hnot_bot, LinearOrderedCommGroupWithZero.inl_eq_coe_inlₗ, WithTop.orderIsoSumLexPUnit_top, Nat.emultiplicity_two_factorial_lt, convexJoin_assoc, disjoint_right_comm, MonomialOrder.degree_smul_le, Rat.comap_cast_atBot, max_eq_left_iff, CategoryTheory.Limits.CompleteLattice.finiteLimitCone_isLimit_lift, Finset.Colex.lt_iff_exists_filter_lt, Polynomial.cyclotomic_pos_and_nonneg, WithZeroMulInt.toNNReal_le_one_iff, le_compl_self, max_lt_iff, Set.Ioc_sub_one_right_eq_Ioo, Set.Iic.disjoint_iff, le_emultiplicity_of_pow_dvd, Finset.orderEmbOfFin_singleton, OrderIso.compl_symm_apply, Tuple.antitone_pair_of_not_sorted, tendsto_inv_atBot_zero, ContinuousOn.upperSemicontinuousOn, nhdsLT_sup_nhdsGE, IsNonarchimedean.nmul_le, Finset.inf_eq_bot_iff, le_sdiff, Int.card_fintype_Icc_of_le, right_mem_openSegment_iff, Finset.Icc_sub_one_right_eq_Ico, Order.isSuccLimitRecOn_succ, antivaryOn_iff_exists_monotoneOn_antitoneOn, HahnSeries.leadingCoeff_pos_iff, abs_max_sub_max_le_max, countable_image_lt_image_Iio_within, CategoryTheory.Limits.MultispanShape.ofLinearOrder_L, MvPowerSeries.le_weightedOrder_smul, ofBoolRing_le_ofBoolRing_iff, orderEmbeddingOfInjective_apply, Polynomial.isBigO_of_degree_le, lt_subset_interior_le, Finset.pluennecke_ruzsa_inequality_pow_div_pow_mul, ofBoolAlg_mul_ofBoolAlg_eq_left_iff, HahnSeries.instNoZeroDivisors, HasCountableSeparatingOn.range_Ioi, IsDedekindDomain.HeightOneSpectrum.valuation_of_mk', HasCountableSeparatingOn.range_Iio, HahnSeries.leadingCoeff_mul_of_ne_zero, Set.Ioo_subset_uIoo, isLocallyClosed_Ioc, Finset.Ioc_sub_one_sub_one_eq_Ico, not_linearIndependent_iffₒₛ, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquiv_inverse, Multiset.exists_max_image, ArchimedeanClass.min_le_mk_add, HahnSeries.order_le_of_coeff_ne_zero, Polynomial.le_trailingDegree_mul, Finset.addConst_le_card, div_nonpos_iff, sameRay_of_mem_orbit, Units.inv_pos, Set.Ioi_sub_one_eq_Ici, ArchimedeanClass.mk_le_mk_iff_lt, tendsto_floor_right, SemilatInfCat.coe_forget_to_partOrd, WithVal.lt_def, Order.isNormal_iff_strictMono_and_continuous, PNat.factorMultiset_le_iff', antivary_iff_exists_monotone_antitone, Set.bounded_gt_inter_gt, HahnSeries.order_ofForallLtEqZero, LaurentSeries.of_powerSeries_localization, Finset.le_inf_mul, Set.powersetCard.ofFinEmbEquiv_symm_apply, IsValuativeTopology.mem_nhds_zero_iff, Finset.one_le_divConst, HahnSeries.coeff_mul_order_add_order, HahnEmbedding.Partial.eval_smul, himp_le_left, nsmul_le_nsmul_iff_right, Order.Ico_succ_right, Int.le_ceil_iff, Finset.Iic_pred_eq_Iio, MulArchimedeanClass.mk_antitoneOn, iSupIndep_iff_supIndep_of_injOn, MulArchimedeanClass.mk_monotoneOn, Nat.ceil_le_floor_add_one, MonomialOrder.degree_mul_le, Valuation.apply_posSubmonoid_pos, Finset.truncatedInf_empty, hasStrictDerivAt_abs, one_le_sq_iff_one_le_abs, Set.disjoint_prod, Valuation.one_srel_iff, Pi.Colex.isStrictOrder, midpoint_le_left, RatFunc.valuation_eq_LaurentSeries_valuation, CategoryTheory.SmallObject.ιFunctorObj_eq, monovary_iff_smul_rearrangement, leOnePart_eq_one, List.minimum_cons, sum_Ioo_inv_sq_le, le_himp_iff', negPart_eq_ite, Nat.succPNat_strictMono, Set.compl_Ioi, Ordinal.le_enum_succ, monovary_comm, FiniteArchimedeanClass.subsemigroup_eq_addSubgroup, inf_lt_left_or_right, HahnSeries.orderTop_mul_of_ne_zero, Stream'.Seq.at_least_as_long_as_coind, Finite.exists_max, NNRat.preimage_cast_Icc, bihimp_triangle, exists_Ioo_extr_on_Icc, continuousOn_iff_lower_upperSemicontinuousOn, toZ_iterate_pred_ge, MeasureTheory.partialTraj_const, monovary_iff_exists_antitone, Set.left_mem_uIoc, Module.End.disjoint_genEigenspace, MvPolynomial.supDegree_esymm, Set.mem_Icc_iff_abs_le, FloorRing.archimedean, Int.gc_coe_floor, ProbabilityTheory.gaussianReal_mul_const, PosSMulStrictMono.toPosSMulReflectLE, ENat.one_le_iff_ne_zero_withTop, add_le_add_iff_left_of_ne_top, WithZeroTopology.isClosed_iff, List.minimum_of_length_pos_le_getElem, strictConvex_Ici, le_compl_iff_le_compl, TopologicalSpace.Opens.coe_finset_inf, TopHom.inf_apply, Hyperreal.archimedeanClassMk_nonneg_of_tendsto, gc_sdiff_sup, mul_pos_iff, Order.not_isMin_succ, Continuous.if_le, Mathlib.Meta.NormNum.IsRat.natFloor, Function.isMinimalFor_argminOn, Set.indicator_eq_zero', Nat.choose_lt_pow_div, ArchimedeanClass.mem_addSubgroup_iff, Function.isMinimalFor_argmin, WithZeroTopology.hasBasis_nhds_zero, CategoryTheory.isCofilteredOrEmpty_of_semilatticeInf, ArchimedeanClass.addSubgroup_eq_bot, Hyperreal.epsilon_lt_of_neg, Valuation.mem_leAddSubgroup_iff, Submodule.inf_iSup_genEigenspace, tendsto_nat_ceil_atTop, Nat.floor_ofNat, Polynomial.trailingDegree_le_of_ne_zero, MeasureTheory.integrable_iff_integrableAtFilter_atTop, exists_nonneg_right_iff_sameRay, MonomialOrder.le_add_right, FiniteMultiplicity.emultiplicity_le_of_multiplicity_le, AddCircle.coe_image_Icc_eq, CharP.intCast_injOn_Ico, Finset.max_le_iff, Polynomial.isEquivalent_atTop_div, Set.Ici.disjoint_iff, isLocallyClosed_Iio, Archimedean.embedReal_injective, IsPreconnected.ordConnected, min_abs_abs_le_abs_max, semilatticeSup_mk'_partialOrder_eq_semilatticeInf_mk'_partialOrder, abs_sub_abs_le_abs_sub, exteriorPower.ιMultiDual_apply_ιMulti, nonemptyFinLinOrd_dual_comp_forget_to_linOrd, Topology.IsLower.tendsto_nhds_iff_lt, List.getD_min?_eq_untopD_minimum, LinearOrderedField.coe_mem_cutMap_iff, Valuation.vle_iff_le, Module.End.genEigenspace_eq_genEigenspace_maxUnifEigenspaceIndex_of_le, Order.Ioi_pred_eq_insert, SimpleGraph.not_isUniform_iff, Set.disjoint_image_iff, disjoint_assoc, OrderIso.sumLexIicIoi_symm_apply_Ioi, MonomialOrder.degree_pow_le, cmp_mul_right', mapClusterPt_atTop_zpow_iff_pow, mul_self_pos, ValuationSubring.monotone_mapOfLE, List.exists_map_eq_of_sorted_iff_sbtw, measurableSet_Ioi, PNat.add_one_le_iff, bddBelow_iff_exists_le, Int.preimage_Iic, Valued.toNormedField.norm_le_iff, Valuation.map_add', Set.disjoint_pi, InfClosed.codirectedOn, map_pos_of_ne_zero, Orientation.oangle_sign_smul_left, exists_isLocalExtr_uIoo_of_tendsto, iUnion_Icc_add_intCast, Cardinal.ofENat_le_ofENat, Int.Icc_eq_finset_map, BddDistLat.dual_map, ProbabilityTheory.Kernel.partialTraj_succ_self, ENat.toENNReal_lt, Nucleus.coe_lt_coe, MulArchimedeanClass.ballSubgroup_antitone, Finset.uIcc_prod_def, Pi.uIcc_eq, IsDedekindDomain.HeightOneSpectrum.valuation_lt_one_iff_mem, countable_image_gt_image_Iio_within, Mathlib.Meta.Positivity.nonneg_of_isRat, bot_eq_one', Polynomial.le_trailingDegree_C_mul_X_pow, DivisibleHull.instIsOrderedCancelAddMonoid, not_infPrime, Valuation.ltSubmodule_monotone, Pi.lt_toColex_update_self_iff, Cardinal.ofNat_lt_ofENat, Cardinal.card_typein_toType_lt, LaurentSeries.coe_X_compare, Set.indicator_eq_zero, Finset.dens_biUnion_le, HahnSeries.finiteArchimedeanClassOrderIsoLex_apply_snd, instArchimedeanNNRat, Int.card_fintype_Ioc_of_le, Module.Basis.orientation_comp_linearEquiv_eq_iff_det_pos, LaurentSeries.hasseDeriv_comp_coeff, PNat.card_Ico, sameRay_neg_smul_left_iff_of_ne, sub_one_lt, le_symmDiff_iff_right, Set.empty_covBy_singleton, continuousAt_iff_continuous_left_right, symmDiff_triangle, HahnSeries.cardSupp_div_le, CategoryTheory.SmallObject.instIsIsoRightAppArrowMapToTypeOrdFunctorIterationFunctor, Finset.inf_dite_neg_le, CategoryTheory.Pairwise.cocone_ι_app, NumberField.RingOfIntegers.HeightOneSpectrum.adicAbv_def, Fin.castLEOrderEmb_toEmbedding, Orientation.oangle_sign_smul_add_smul_smul_add_smul, ValuativeRel.RankLeOneStruct.strictMono, Birkhoff_inequalities, GroupCone.oneLE.hasMemOrInvMem, Finset.Ici_succ_eq_Ioi, MonomialOrder.toSyn_monotone, Valued.integer.mulArchimedean_mrange_of_isCompact_integer, eventually_nhdsWithin_sign_eq_of_deriv_pos, Valuation.Integers.dvdNotUnit_iff_lt, nhds_eq_iInf_mabs_div, exists_le_mul_self, Padic.valuation_p_lt_one, Finset.dens_le_dens_sdiff_add_dens, disjoint_of_sSup_disjoint_of_le_of_le, LaurentSeries.intValuation_le_iff_coeff_lt_eq_zero, Tropical.addLeftMono, sdiff_le_inf_hnot, TopCat.Presheaf.IsSheaf.isSheafPreservesLimitPairwiseIntersections, PointedCone.tmul_subset_maxTensorProduct, BooleanAlgebra.le_iff_atom_le_imp, Finset.uIcc_map_sectL, Fin.attachFin_uIcc, MvPowerSeries.weightedOrder_mul_ge, Valuation.IsEquiv.lt_iff_lt, convexJoin_convexJoin_convexJoin_comm, MvPowerSeries.le_order, Nat.ceil_intCast, bddLat_dual_comp_forget_to_semilatSupCat, Finset.dens_lt_dens, Function.argminOn_le, RootPairing.zero_le_posForm, StieltjesFunction.mono, Finset.Iio_succ_eq_Iic, Set.one_le_encard_insert, RatFunc.algebraMap_apply_div, Int.Ico_filter_dvd_card, PNat.map_subtype_embedding_Ioo, Set.Nonempty.encard_pos, Set.compl_ordConnectedSection_ordSeparatingSet_mem_nhdsLE, convexHull_sum, PowerSeries.le_order_pow_of_constantCoeff_eq_zero, LinearOrderedSemiring.toOrderedSMul, Set.monotone_or_antitone_iff_uIcc, MonomialOrder.degLex_single_le_iff, ArchimedeanClass.mk_mul, strictConcaveOn_iff_slope_strict_anti_adjacent, HahnSeries.addVal_apply_of_ne, tendsto_ratCast_atBot_iff, MeasureTheory.aecover_Icc_of_Icc, Set.pow_right_monotone, LinearOrderedCommGroup.wellFoundedOn_setOf_le_lt_iff_nonempty_discrete, posPart_pos_iff, Order.Iio_succ, Nimber.instWellFoundedLT, MvPolynomial.leadingCoeff_toLex_C, AddCircle.coe_image_Ioc_eq, Finset.Ico_succ_succ, Filter.tendsto_mul_const_atTop_iff, Finset.SupIndep.le_sup_iff, interior_Ioc, ArchimedeanClass.map_mk_eq, Set.Ioi_pred_eq_Ici, MvPowerSeries.order_le, Multiset.Ico_inter_Ico, Finset.Colex.toColex_lt_toColex_iff_exists_forall_lt, Rat.preimage_cast_Iic, Finset.max'_eq_sorted_last, Finset.min'_subset, LinearLocallyFiniteOrder.instIsPredArchimedeanOfLocallyFiniteOrder, PredOrder.nhds_eq_pure, add_lt_add_iff_left_of_ne_top, hasBasis_nhdsSet_Iic_Iio, NatOrdinal.toOrdinal_natCast, Set.Ioc_pred_left_eq_Icc, PowerSeries.coe_zero, Module.End.mem_genEigenspace_top, Valued.closure_coe_completion_v_lt, List.minimum_eq_coe_iff, Module.Basis.orientation_adjustToOrientation, MulArchimedeanClass.mk_div_lt_mk_left_iff, Pi.Lex.wellFoundedLT, sign_mul, grade_lt_grade_iff, BoundedLatticeHom.symm_dual_id, countable_setOf_covBy_left, posPart_eq_ite, Polynomial.isEquivalent_atBot_lead, Module.End.injOn_genEigenspace, Finset.mem_convexHull, OrderEmbedding.preimage_uIcc, Set.intersecting_iff_pairwise_not_disjoint, ZNum.cast_le, IsDiscreteValuationRing.addVal_add, SetTheory.PGame.equiv_nim_grundyValue, Mathlib.Meta.NormNum.isRat_lt_false, Nonneg.coe_nnqsmul, Module.Basis.orientation_comp_linearEquiv_eq_neg_iff_det_neg, mul_neg_iff, PrimeSpectrum.isIdempotentElemEquivClopens_symm_sup, Finset.nonneg_addConst_self, Finset.Icc_pred_right_eq_Ico, AbsoluteValue.map_units_int_smul, Module.End.genEigenspace_one, Profinite.NobelingProof.Products.lt_iff_lex_lt, Int.padicValuation_self, mabs_div, Valued.closure_coe_completion_v_mul_v_lt, compl_le_self, Set.encard_iUnion_le_of_finite, mul_self_lt_one_iff, Nat.ceil_one, RootPairing.RootPositiveForm.rootLength_pos, measurable_IicProdIoc, Int.Ioc_eq_finset_map, Hyperreal.infinitesimal_neg_iff_infiniteNeg_inv, Set.uIcc_eq_union, Set.disjoint_compl_right_iff_subset, Set.pairwise_disjoint_Ioo_zpow, HahnSeries.isUnit_iff, Int.instIsPredArchimedean, inf_lt_sup, Hyperreal.infiniteNeg_def, MulArchimedeanClass.mk_right_le_mk_mul_iff, IsMulIndecomposable.baseOf_subset_one_lt, isAtomic_of_isCoatomic_of_complementedLattice_of_isModular, gc_Ici_sInf, smul_nonpos_iff_neg_imp_nonneg, Set.Ico_diff_Iio, Set.unbounded_ge_iff_unbounded_inter_ge, isPiSystem_Ico, Set.finite_iff_bddBelow, Valued.cauchy_iff, AffineSubspace.wSameSide_iff_exists_left, Nat.ceil_ofNat, MvPolynomial.schwartz_zippel_sup_sum, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.map_f', Asymptotics.IsEquivalent.tendsto_atBot_iff, Set.disjoint_image_image, Valuation.one_apply_le_one, Cardinal.toENatAux_gc, AddCircle.card_torsion_le_of_isSMulRegular_int, EReal.sign_bot, LinearOrderedAddCommGroup.Subgroup.negGen_neg, HahnSeries.min_order_le_order_add, LaurentSeries.exists_powerSeries_of_memIntegers, sbtw_pointReflection_of_ne, PointedCone.minTensorProduct_le_maxTensorProduct, transfiniteIterate_bot, CategoryTheory.TransfiniteCompositionOfShape.ici_isoBot, Set.compl_Iic, Nat.ceil_sub_natCast, Filter.comap_mabs_atTop, nhdsWithin_Iio_isMeasurablyGenerated, comap_coe_nhdsLT_eq_atTop_iff, Cardinal.toNat_toENat, PNat.Ioc_eq_finset_subtype, ArchimedeanClass.mk_left_le_mk_add_iff, Finset.sort_sorted_lt, Finset.le_card_falling_div_choose, MulArchimedeanClass.mk_one, NonemptyInterval.snd_sup, eq_compl_iff_isCompl, lt_sup_iff, Finset.Ioc_pred_right_eq_Ioo, exists_pos_left_iff_sameRay, Function.disjoint_mulSupport_iff, MvPolynomial.monic_esymm, Finset.prod_min_le, Set.Ico_succ_left_eq_Ioo, Int.floor_eq_iff, subsingleton_floorSemiring, ArchimedeanClass.FiniteResidueField.mk_eq_mk, ArchimedeanClass.stdPart_monotoneOn, SimpleGraph.compl_neighborSet_disjoint, abs_nonpos_iff, Ordinal.toNimber_one, Convex.min_le_combo, Polynomial.cardPowDegree_apply, monovaryOn_iff_smul_rearrangement, Odd.strictMono_pow, NNRat.instCanonicallyOrderedAdd, IsDedekindDomain.HeightOneSpectrum.adicValued_apply, InfHom.withTop'_toFun, Finset.prod_prod_Ioi_mul_eq_prod_prod_off_diag, InnerProductSpace.gramSchmidt_def', Finset.toDual_inf, closure_Iio, Set.not_disjoint_iff, Int.card_Icc_of_le, RootPairing.pairingIn_le_zero_iff, CategoryTheory.SmallObject.SuccStruct.extendToSucc.obj_eq, NumberField.FinitePlace.norm_def_int, LowerSet.iicInfHom_apply, WithTop.tendsto_untopA, Nat.Ico_filter_modEq_cast, CategoryTheory.TransfiniteCompositionOfShape.iic_F, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.w, Set.disjoint_iff_inter_eq_empty, le_inf_iff, Finset.expect_mul_sq_le_sq_mul_sq, NNRat.coe_le_coe, CategoryTheory.SmallObject.SuccStruct.restrictionLTOfCoconeIso_hom_app, tendsto_ceil_left_pure, self_mul_sign, ContinuousWithinAt.lowerSemicontinuousWithinAt, Set.uIcc_subset_uIcc_iff_le, convexHullAddMonoidHom_apply, cocompact_eq_atBot, RingSeminormClass.toNonnegHomClass, vectorSpan_segment, HahnSeries.binomial_power, ENat.toENNReal_mono, OrderTopology.to_orderClosedTopology, Ordinal.cof_eq_cof_toType, RootPairing.pairingIn_lt_zero_iff, LinearLocallyFiniteOrder.succFn_spec, List.argmax_eq_some_iff, Heyting.Regular.coe_top, MonoidWithZeroHom.inr_mono, Coheyting.boundary_inf_le, IsValuativeTopology.hasBasis_nhds_zero', inf_le_bihimp, Set.Icc.isCompl_iff, PowerSeries.coe_C, codisjoint_hnot_left, Finset.convexHull_eq, Mathlib.Meta.NormNum.isRat_le_false, Set.Infinite.exists_lt_map_eq_of_mapsTo, Set.Iic_sub_one_eq_Iio, sdiff_eq_bot_iff, Polynomial.div_tendsto_leadingCoeff_div_of_degree_eq, PNat.find_lt_iff, inf_eq_inf_iff_right, Filter.not_tendsto_pow_atTop_atBot, Set.Ioc_union_Ioc_symm, le_neg_self_iff, upperSemicontinuousOn_iff_frequently, sdiff_le, Finset.orderEmbOfCardLe_mem, exists_isLocalExtr_uIoo, pow_dvd_iff_le_emultiplicity, ENat.epow_left_mono, Dense.borel_eq_generateFrom_Ico_mem, Mathlib.Meta.NormNum.isNNRat_le_true, tendsto_intCast_atTop_iff, PointedCone.tmul_subset_minTensorProduct, Nonneg.coe_inv, Polynomial.eventually_atTop_not_isRoot, Finset.fold_max_le, Order.lt_succ_iff, LinearOrderedField.inducedMap_mono, Polynomial.natTrailingDegree_le_trailingDegree, CategoryTheory.Limits.CompleteLattice.finite_limit_eq_finset_univ_inf, ValuativeRel.isRankLeOne_iff_mulArchimedean, Valuation.Integers.maximalIdeal_eq_setOf_le_v_algebraMap, nhdsSet_Iic, Finset.sup_inf, exteriorPower.pairingDual_apply_apply_eq_one, OrderIso.sumLexIicIoi_apply_inr, ArchimedeanClass.mk_ratCast, CategoryTheory.isCofiltered_of_semilatticeInf_nonempty, Order.isLUB_Iio_iff_isSuccPrelimit, PowerSeries.coe_neg, BoundedLatticeHom.map_bot', LinearOrderedAddCommGroup.wellFoundedOn_setOf_ge_gt_iff_nonempty_discrete, pred_max, Set.exists_upper_bound_image, tendsto_floor_left', RootPairing.coxeterWeightIn_le_four, Finset.pluennecke_ruzsa_inequality_pow_div, Set.antitone_bforall, Order.succ_injective, MulArchimedeanClass.map_mk_eq, ProbabilityTheory.gaussianReal_map_mul_const, MeasureTheory.stoppedProcess_eq'', Nat.orderedSMul, Set.Iic_union_Ioi, Finset.truncatedInf_singleton, MeasureTheory.integrableOn_Ioi_iff_integrableAtFilter_atTop_nhdsWithin, PowerSeries.min_order_le_order_add, bddLat_dual_comp_forget_to_semilatInfCat, CategoryTheory.OrthogonalReflection.iteration_map_succ_assoc, cmp_sub_zero, zsmul_left_strictMono, ValuationSubring.isIntegral_of_mem_ringOfIntegers', TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivUnitIso_inv_app_hom, LaurentSeries.hasseDeriv_coeff, Set.zero_mem_neg_add_iff, Rat.preimage_cast_Ici, Set.disjoint_insert_right, lowerBounds_infClosure, Set.pairwise_disjoint_Ioc_intCast, ArchimedeanClass.ballAddSubgroup_antitone, AddCircle.openPartialHomeomorphCoe_source, sign_apply, HahnSeries.embDomainOrderAddMonoidHom_injective, PosNum.cast_le, sq_lt_one_iff_abs_lt_one, Set.subset_compl_iff_disjoint_left, Polynomial.exists_approx_polynomial, Finite.exists_min, Profinite.NobelingProof.Products.lt_nil_empty, sq_sum_le_card_mul_sum_sq, tendsto_nat_floor_atTop, ValuativeRel.instIsOrderedMonoidValueGroupWithZero, Nimber.toOrdinal_eq_one, Tuple.comp_sort_eq_comp_iff_monotone, Set.Ici_diff_Ioi, Finset.Ico_add_one_right_eq_Icc, Sym2.sortEquiv_symm_apply, Ico_mem_nhds_iff, Types.monoOverEquivalenceSet_functor_map, Finset.supIndep_pair, intermediate_value_Ioc', toENat_rank_span_set, le_sup_inf, Finset.min'_lt_max', oneLePart_le_one, Int.comap_cast_atBot, GenContFract.of_den_mono, SuccOrder.isOpen_iff, DivisibleHull.qsmul_def, MvPolynomial.supDegree_toLex_C, Finset.mulConst_le_inv_dens, Finset.Ioc_pred_pred_eq_Ico, ArchimedeanClass.out_top, sign_one, ValuativeRel.uniformizer_inv_le_iff, Valuation.one_vlt_iff, DFinsupp.card_uIcc, neg_lt_self_iff, IsValuativeTopology.isClopen_ball, IsValuativeTopology.hasBasis_nhds, Set.Iic_pred_eq_Iio, Finset.le_inf_iff, Set.encard_mono, AbsoluteValue.IsAdmissible.exists_approx, abs_cases, Polynomial.tendsto_nhds_iff, Affine.Simplex.sSameSide_affineSpan_faceOpposite_iff, dvd_iff_emultiplicity_pos, AddCircle.measurePreserving_equivIoc, PrimitiveSpectrum.preimage_upperClosure_compl_finset, Rat.castOrderEmbedding_apply, ENat.add_lt_add_iff_left, BoolAlg.dual_map, ArchimedeanClass.subsemigroup_strictAnti, Set.encard_singleton_inter, Matrix.IsIrreducible.exists_pos, Int.instStarOrderedRing, QuotientAddGroup.btw_coe_iff, Finset.sum_card_slice_div_choose_le_one, IsDedekindDomain.HeightOneSpectrum.intValuation_lt_one_iff_dvd, Filter.Eventually.exists_Ioo_subset, wbtw_iff_right_eq_or_left_mem_image_Ici, Mathlib.Meta.NormNum.isRat_le_true, CauSeq.const_le, FiniteMulArchimedeanClass.mk_le_mk, archimedean_iff_nat_lt, Finset.inf_mono, disjoint_compl_left_iff, Rat.toNNRat_pos, tendsto_pow_neg_atTop, Asymptotics.IsEquivalent.tendsto_atTop_iff, WithZero.denselyOrdered_set_iff_subsingleton, Set.Iic_subset_Iic_union_Icc, IsConnected.Icc_subset, abs_pos, Set.subsingleton_Icc_iff, Set.bounded_lt_inter_lt, aemeasurable_uIoc_iff, infIrred_iff_not_isMax, Set.pairwise_disjoint_Ioo_zsmul, IsDiscreteValuationRing.map_algebraMap_eq_valuationSubring, LinearLocallyFiniteOrder.instIsSuccArchimedeanOfLocallyFiniteOrder, OrderIso.subsingleton_of_wellFoundedLT', Valuation.one_vle_iff, ENat.one_le_epow, lowerSemicontinuousOn_iff_frequently, Filter.tendsto_const_mul_pow_atBot_iff, wbtw_iff_left_eq_or_right_mem_image_Ici, Ioo_subset_openSegment, Set.unbounded_lt_iff, abs_sub_map_le_div, convexHull_pi, ArchimedeanClass.ball_top, Cardinal.toENat_strictMonoOn, InnerProductSpace.span_gramSchmidt_Iic, HahnSeries.pow_add, Fin.castAddOrderEmb_toEmbedding, CategoryTheory.Limits.Types.isPushout_of_bicartSq, Set.Nontrivial.exists_lt, SimpleGraph.FarFromTriangleFree.lt_half, Finset.Nonempty.inf_eq_bot_iff, round_eq_zero_iff, Pi.support_single_disjoint, NNRat.preimage_cast_Ici, abs_sup_sub_sup_le_abs, Finset.min_eq_bot, HasSubset.Subset.disjoint_compl_left, FiniteArchimedeanClass.mk_le_mk, Coheyting.boundary_hnot_le, CategoryTheory.SmallObject.iterationFunctorMapSuccAppArrowIso_hom_right_right_comp_assoc, HahnSeries.orderTop_mul, Ordinal.ToType.mk_symm_apply_coe, MonomialOrder.wf, ArchimedeanClass.FiniteElement.isUnit_iff_mk_eq_zero, Finset.fold_min_le, Hyperreal.instIsStrictOrderedRing, frontier_Ici_subset, Set.projIic_self, Valued.toNormedField.one_lt_norm_iff, LinOrd.forget_map, Finset.inf_dite_pos_le, Field.Emb.Cardinal.filtration_apply, PrimeMultiset.prod_dvd_iff, Set.Ioc_pred_pred_eq_Ico, Coheyting.boundary_le_boundary_sup_sup_boundary_inf_left, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.sq, Finset.Ioo_pred_left_eq_Ioc, Affine.Simplex.ExcenterExists.sign_touchpointWeights, SimpleGraph.fromEdgeSet_disjoint, Rat.cast_mono, NNRat.ceil_coe, Nat.image_cast_int_Ioi, IsDedekindDomain.HeightOneSpectrum.intValuation_zero_lt, sq_lt_sq, Int.lt_zpow_succ_log_self, add_sq_le, Finset.le_dens_sdiff, strictConvex_Ioc, Finset.min'_lt_max'_of_card, toZ_iterate_succ, IsValuativeTopology.hasBasis_nhds_zero, AffineMap.lineMap_anti, LaurentSeries.LaurentSeriesRingEquiv_mem_valuationSubring, nhdsWithinLT_sup_nhdsWithinGT, IsDedekindDomain.HeightOneSpectrum.valuedAdicCompletion_eq_valuation, posSMulMono_iff_posSMulReflectLT, AddSubmonoid.mem_closure_image_pos_iff, Valuation.IsNontrivial_iff_exists_one_lt, Matroid.ExchangeProperty.encard_diff_le_aux, LinOrd.ext_iff, isOpen_Ioi, Affine.Simplex.sign_touchpointWeights_singleton_pos, NonemptyFinLinOrd.hom_hom_id, Padic.toEquiv_withValUniformEquiv_eq_toEquiv_withValRingEquiv, nhdsSet_Ici, isCompact_Ico_iff, AddCircle.eq_coe_Ico, SetRel.image_mono, Set.Iio_subset_Iio_iff, Orientation.oangle_sign_smul_right, TopCat.Sheaf.interUnionPullbackConeLift_left, disjointed_le, Odd.zpow_nonneg_iff, Finset.Ioi_pred_eq_Ici, Function.Injective.image_strictMono, Asymptotics.isEquivalent_nat_floor, Module.End.genEigenspace_eq_iSup_genEigenspace_nat, Finset.min'_lt_of_mem_erase_min', Valuation.mem_ltAddSubgroup_iff, le_iff_forall_pos_lt_add, mabs_mabs_div_mabs_le_mabs_div, Cardinal.ofNat_le_ofENat, CategoryTheory.TransfiniteCompositionOfShape.ici_isColimit, Set.Iic_inter_Iic, IsCompact.bddAbove_image, PNat.succ_eq_add_one, Lattice.isStronglyAtomic, Ordinal.enum_succ_eq_top, Nimber.toOrdinal_one, iSupIndep.sup_indep_univ, doublyStochastic_eq_convexHull_permMatrix, mul_smul_one_lt_iff, PNat.factorMultiset_mono, LaurentSeries.valuation_LaurentSeries_equal_extension, cocompact_eq_atBot_atTop, floorDiv_le_ceilDiv, Set.disjoint_univ, LaurentSeries.hasseDeriv_single_add, ENat.addLECancellable_coe, le_himp_iff, Interval.disjoint_coe, Set.disjoint_image_right, SetLike.coe_strictMono, Types.monoOverEquivalenceSet_functor_obj, nhdsLT_basis, Submodule.spanRank_toENat_eq_iInf_finset_card, Order.succ_le_succ_iff, CompositionSeries.strictMono, LucasLehmer.two_lt_q, HahnSeries.orderTop_nsmul_le_orderTop_pow, variationOnFromTo.sub_self_monotoneOn, WeierstrassCurve.isMinimal_iff, Finset.pluennecke_ruzsa_inequality_nsmul_sub_nsmul_sub, CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.instIsIsoMapF, Set.Iio_ssubset_Iio_iff, trichotomy_of_mul_eq_mul, CategoryTheory.Limits.CompleteLattice.pullback_eq_inf, Dense.borel_eq_generateFrom_Ico_mem_aux, RatFunc.v_def, DFinsupp.Lex.wellFoundedLT_of_finite, Function.mulSupport_disjoint_iff, Function.locallyFinsuppWithin.negPart_add, ArchimedeanClass.FiniteResidueField.mk_ne_zero, Finset.coe_inf_of_nonempty, Nat.one_sub_one_div_cast_nonneg, map_pos_of_ne_one, zsmul_left_strictAnti, Set.Icc_add_one_left_eq_Ioc, Rat.padicValuation_eq_zero_iff, Set.OrdConnected.IciExtend, Int.floor_toNat, NonemptyFinLinOrd.dual_map, LaurentSeries.LaurentSeries_coe, strictConvex_Ico, MeasureTheory.integrableOn_Iio_iff_integrableAtFilter_atBot_nhdsWithin, PNat.addLeftReflectLE, ENat.pow_lt_top_iff, CategoryTheory.SimplicialThickening.Path.left_le, CategoryTheory.SmallObject.SuccStruct.ofCocone_obj_eq_pt, Finsupp.DegLex.single_le_iff, Finset.centroid_mem_convexHull, ComplementedLattice.isStronglyCoatomic, compl_le_himp, Int.existsUnique_mem_box, IsDedekindDomain.HeightOneSpectrum.intValuation_eq_one_iff, Set.Iio_add_one_eq_Iic, inf_lt_left, HahnSeries.archimedeanClassOrderIsoWithTop_apply, max_eq_bot, Set.OrdConnected.restrict, FiniteMulArchimedeanClass.mem_subgroup_iff, CategoryTheory.TransfiniteCompositionOfShape.ofOrderIso_isoBot, Set.Ico_add_one_left_eq_Ioo, Valuation.Integers.wfDvdMonoid_iff_wellFounded_gt_on_v, Set.encard_le_coe_iff_finite_ncard_le, Rat.preimage_cast_Iio, Finset.Ico_filter_le, Set.unbounded_gt_iff, CategoryTheory.SemilatticeInf.tensorUnit, Rat.cast_nonneg, AbsoluteValue.IsAdmissible.exists_partition, MvPowerSeries.le_order_smul, NNRat.toNNRat_mono, Heyting.Regular.coe_toRegular, WithTop.isEmbedding_coe, Set.monotone_setOf, oneTangentSpaceIcc_def, LaurentSeries.powerSeries_ext_subring, Set.unit_valuation_eq_one, Set.Ioc_inter_Ioc, himp_le_himp_himp_himp, Finset.min'_eq_sorted_zero, VertexOperator.ext_iff, PowerSeries.le_order_pow, Polynomial.isBoundedUnder_abs_atBot_iff, OrderEmbedding.addRight_apply, negPart_lt, IsNonarchimedean.finset_image_add_of_nonempty, DivisibleHull.coeOrderAddMonoidHom_apply, PosSMulStrictMono.nnrat_of_rat, emultiplicity_prime_le_emultiplicity_image_by_factor_orderIso, BoundedLatticeHom.dual_apply_toFun, InfHom.withBot'_toFun, stdSimplex.barycenter_apply, mul_nonpos_iff, Nat.floor_le_ceil, ProbabilityTheory.indep_limsup_atBot_self, Finset.min'_le_max', Int.one_le_ceil_iff, Hyperreal.lt_neg_of_pos_of_infinitesimal, Set.Iio_union_Ioi, Ordinal.iSup_typein_limit, nhdsSet_Iio, IsNonarchimedean.nsmul_le, Set.pairwise_disjoint_Ioc_add_intCast, AbsoluteValue.hasBasis_uniformity, squarefree_iff_emultiplicity_le_one, ArchimedeanClass.mk_le_mk_iff_ratCast, InnerProductSpace.gramSchmidtOrthonormalBasis_inv_blockTriangular, NNRat.one_lt_cast, geom_sum_neg_iff, Set.Ico_disjoint_Ico, sdiff_sdiff_le, ValuativeRel.IsNontrivial.exists_lt_one, Set.unbounded_le_iff, Order.lt_add_one_iff, Rat.toNNRat_add_le, Tuple.eq_sort_iff, MeasureTheory.stoppedProcess_eq_of_mem_finset, sign_neg, CategoryTheory.Triangulated.TStructure.ge_antitone, Cardinal.continuum_toENat, inv_nhdsLT_zero, Nat.range_cast_int, OrderIso.sumLexIicIoi_apply_inl, IsPreconnected.intermediate_value_Ioc, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivFunctor_obj_π_app, CompositionSeries.head_le_of_mem, SuccOrder.nhdsGT, ValuativeRel.le_uniformizer_iff, LinearOrderedCommGroupWithZero.inr_eq_coe_inrₗ, Ioc_mem_nhds_iff, Finset.Icc_succ_left_eq_Ioc, Field.Emb.Cardinal.deg_lt_aleph0, CategoryTheory.Functor.IsWellOrderContinuous.restriction_setIci, tendsto_const_mul_pow_nhds_iff, isPiSystem_image_Iio, DFinsupp.Lex.isStrictOrder, signedDist_smul, max_sub_max_le_max, iUnion_Ico_intCast, GenContFract.le_of_succ_succ_get?_contsAux_b, Finset.max_eq_top, ProbabilityTheory.gaussianPDFReal_inv_mul, nhdsGE_basis_Icc, Valuation.integer.v_irreducible_pos, Set.Ioo_subset_Ioc_union_Ioo, StieltjesFunction.measure_Icc, Finsupp.Lex.addRightStrictMono, Set.Ioi_subset_Ioi_iff, LieModule.genWeightSpaceChain_def, ConvexCone.isGenerating_iff_isReproducing, isGreatest_compl, Sublattice.comap_equiv_eq_map_symm, Valuation.leIdeal_mono, Set.Ioc_diff_Ioi, FunctionField.inftyValuation.X_zpow, PNat.card_fintype_Ioo, LaurentSeries.hasseDeriv_comp, infIooOrderIsoIooSup_apply_coe, CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.ofComposableArrows_F, FiniteMulArchimedeanClass.congrOrderIso_symm, Int.ceil_le, Finset.Icc_subset_uIcc, Set.strictMonoOn_projIci, Booleanisation.lift_lt_lift, Tuple.antitone_pair_of_not_sorted', Polynomial.trailingDegree_lt_wf, le_iff_forall_one_lt_lt_mul, Set.finite_diff_iUnion_Ioo', antivaryOn_iff_smul_rearrangement, Finset.inf_of_mem, bihimp_eq_inf, CauSeq.lim_lt, mabs_div_pos, OrderEmbedding.birkhoffSet_sup, SetRel.preimage_mono, SemilatInfCat.Iso.mk_inv_toFun, Set.Iic_subset_Iic_union_Ioc, Finset.subConst_le_card, LaurentSeries.powerSeriesRingEquiv_coe_apply, PredOrder.nhdsLT, CategoryTheory.Limits.CompleteLattice.finiteLimitCone_cone_pt, Set.ordConnected_of_uIcc_subset_left, PNat.Prime.one_lt, RieszExtension.step, AbsoluteValue.IsAdmissible.exists_partition', Finset.disjoint_sup_right, PrimeSpectrum.isIdempotentElemEquivClopens_apply_toOpens, Topology.RelCWComplex.iUnion_openCell_eq_skeletonLT, PrimeSpectrum.basicOpen_isIdempotentElemEquivClopens_symm, SignType.neg_lt_neg_iff, sq_nonpos_iff, Set.Ioo_pred_left_eq_Ioc, Int.fract_add_le, HahnSeries.orderTop_add_le_mul, Set.range_projIic, LinOrd.Iso.mk_inv, CategoryTheory.TransfiniteCompositionOfShape.ofArrowIso_incl, Module.End.genEigenspace_le_genEigenspace_maxUnifEigenspaceIndex, HurwitzZeta.hasSum_nat_hurwitzZetaOdd, MeasureTheory.ae_restrict_uIoc_iff, LinearOrderedCommGroupWithZero.fst_comp_inl, upperClosure_eq_bot_iff, ENat.le_coe_iff, IsCompact.exists_isMinOn, abs_pow_sub_pow_le, Int.ceil_lt_add_one, HahnEmbedding.ArchimedeanStrata.isInternal_stratum', Dense.borel_eq_generateFrom_Ioc_mem_aux, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivFunctor_map_hom, le_symmDiff_sup_left, Int.image_fract, Multiset.exists_min_image, OrderRingIso.apply_eq_self, Nimber.instZeroLEOneClass, Set.Iic_union_Ici, Fin.succAboveOrderEmb_toEmbedding, PrincipalSeg.isNormal, inv_mabs_le_inv, Positive.coe_inv, Rat.cast_nonpos, Finset.sortedLT_sort, Set.mulIndicator_eq_one', Hyperreal.lt_of_pos_of_infinitesimal, Finset.supIndep_iff_disjoint_erase, archimedean_iff_rat_le, one_lt_sq_iff_one_lt_abs, ArchimedeanClass.FiniteResidueField.mk_le_mk, OrderIso.subsingleton_of_wellFoundedLT, Filter.tendsto_pow_atTop_iff, Set.encard_le_encard_iff_encard_diff_le_encard_diff, mem_nhdsGE_iff_exists_Ico_subset, Affine.Simplex.sign_touchpointWeights_singleton_neg, LaurentSeries.powerSeriesEquivSubring_apply, Set.Ico_add_one_add_one_eq_Ioc, MvPowerSeries.map_iterateFrobenius_expand, Function.support_disjoint_iff, Order.succ_eq_succ_iff, Finset.sum_sum_Ioi_add_eq_sum_sum_off_diag, Valuation.IsNontrivial.exists_one_lt, IsDedekindDomain.HeightOneSpectrum.intValuation_def, AddMonoidAlgebra.le_infDegree_mul, CategoryTheory.Limits.WalkingMultispan.inclusionOfLinearOrder_obj, OrderIso.pnatIsoNat_apply, LocallyFiniteOrder.orderAddMonoidHom_apply, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivInverse_obj_pt, not_lt_zero', Set.isCompl_range_inl_range_inr, SimpleGraph.le_card_nonuniformWitness, CategoryTheory.SmallObject.SuccStruct.transfiniteCompositionOfShapeιIteration_incl, Coheyting.boundary_le, FunctionField.inftyValuation.X, InnerProductSpace.gramSchmidt_def'', RingCone.nonneg.hasMemOrNegMem, Set.unbounded_ge_inter_gt, StieltjesFunction.length_eq, mem_nhdsLT_iff_exists_Ioo_subset, FiniteMulArchimedeanClass.min_le_mk_mul, MonomialOrder.degree_prod_le, LinearOrderedSemifield.toPosSMulStrictMono_rat, Module.End.genEigenspace_zero_nat, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivUnitIso_hom_app_hom, antivary_iff_mul_rearrangement, MeasureTheory.Filtration.rightCont_eq, Set.infinite_iff_exists_gt, FiniteMultiplicity.emultiplicity_lt_of_multiplicity_lt, HahnSeries.leadingCoeff_nonneg_iff, WithZeroTopology.isOpen_iff, Measurable.nat_floor, toZ_iterate_pred, CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.ofComposableArrows_isoBot_inv, ENat.lt_add_one_iff, ENat.addLECancellable_of_ne_top, RootedTree.isPredArchimedean, tendsto_intCast_atBot_iff, List.prod_min_le, Nimber.instNoMaxOrder, Filter.isBoundedUnder_ge_inf, ArchimedeanClass.archimedean_of_mk_eq_mk, Finset.max'_eq_iff, tendsto_nat_ceil_div_atTop, Finsupp.DegLex.isStrictOrder, Cardinal.ofENat_lt_ofENat, Finset.dens_mono, ArchimedeanClass.mk_eq_mk, NNRat.instOrderedSub, EReal.sign_top, Matrix.IsPrimitive.exists_pos_pow, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivUnitIsoApp_hom_hom, Valuation.srel_one_iff, Finset.inf_empty, max_mul_mul_le_max_mul_max', Set.one_notMem_inv_mul_iff, LinearOrder.isSuccArchimedean_of_isPredArchimedean, Continuous.strictMono_of_inj, MonomialOrder.div_set, List.mem_argmax_iff, MulArchimedeanClass.mk_mul_lt_mk_right_iff, right_le_lineMap_iff_one_le, MonoidWithZeroHom.snd_mono, neg_le_negPart, nullMeasurableSet_lt', Module.End.genEigenspace_top, Ordinal.toNatOrdinal_zero, Set.preimage_eq_empty_iff, BoundedLatticeHomClass.map_top, gc_inf_himp, symmDiff_le_sup, Int.Icc_eq_pair, CategoryTheory.SmallObject.iterationFunctorMapSuccAppArrowIso_hom_left, HahnEmbedding.Partial.orderTop_eq_finiteArchimedeanClassMk, Valuation.IsUniformizer.val_pos, Set.Ioi_subset_Ici_iff, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivFunctorObj_pt, Finset.orderEmbOfFin_apply, bot_himp, AlgebraicGeometry.IsOpenImmersion.app_ΓIso_hom_assoc, Set.unbounded_ge_inter_not_ge, MeasureTheory.aecover_Ioo_of_Ioo, intermediate_value_Ico', List.exists_map_eq_of_sorted_iff_wbtw, Odd.pow_pos_iff, PointedCone.minTensorProduct_comm, fderiv_norm_smul, Set.disjoint_iff_forall_ne, abs_add', LinOrd.ofHom_comp, HasFDerivAt.hasFDerivAt_norm_smul, NNRat.cast_pos, borel_eq_generateFrom_Ico, Set.coe_projIic, NatOrdinal.toOrdinal_eq_zero, tendsto_floor_atBot, Finset.bddBelow, inf_eq_top_iff, QuotientAddGroup.btw_coe_iff', Multiset.Ico_filter_le, CategoryTheory.IsGrothendieckAbelian.generatingMonomorphisms.functorToMonoOver_map, List.le_maximum_of_mem', negPart_nonpos', MeasureTheory.aecover_Ioc_of_Ioc, PNat.instWellFoundedLT, Order.isNormal_iff', Cardinal.ofENat_strictMono, Pi.lt_toLex_update_self_iff, Int.preimage_Ioo, OrderType.type_le_type_iff, FunctionField.inftyValuedFqt.def, one_lt_oneLePart_iff, CategoryTheory.SmallObject.πFunctorObj_eq, isPiSystem_Iio, isLeast_hnot, Set.abs_sub_le_of_uIcc_subset_uIcc, Mathlib.Tactic.Qify.nnratCast_lt, NonemptyFinLinOrd.id_apply, LTSeries.head_add_length_le_int, tendsto_ceil_left', hahnEmbedding_isOrderedModule_rat, AddValuation.map_sub, Set.Icc.coe_inf, Affine.Simplex.sign_signedInfDist_touchpoint_empty, Finsupp.Lex.addLeftStrictMono, FiniteArchimedeanClass.congrOrderIso_symm, Valuation.RankOne.strictMono', mabs_mul_eq_mul_mabs_iff, mabs_div_mabs_le_mabs_mul, PNat.lt_add_left, WithBot.orderIsoPUnitSumLex_toLex, SimpContFract.of_isContFract, tendsto_const_mul_zpow_atTop_zero, AffineIndependent.convexHull_inter', ComplementedLattice.isStronglyAtomic', Int.addSubmonoid_closure_range_pow, Set.Ioi_inter_Ioo, AffineSubspace.sOppSide_pointReflection, max_eq_right_iff, Set.Ici_subset_Icc_union_Ioi, Finset.le_max', PredOrder.hasBasis_nhds_Ioc, Filter.tendsto_Ioc_uIcc_uIcc, GenContFract.of_one_le_get?_partDen, Valuation.vle_one_iff, sign_nonpos_iff, Set.Finite.exists_lt_map_eq_of_forall_mem, disjoint_partialSups_left, smul_nonneg_iff, Cardinal.toENat_le_iff_of_le_aleph0, PNat.sub_le, Finset.intervalGapsWithin_snd_of_lt, one_le_leOnePart, Valuation.IsEquiv.val_sub_one_lt_one_iff, Nat.one_div_cast_nonneg, Set.Icc_sub_one_right_eq_Ico, Finset.supIndep_univ_bool, ENat.coe_lt_coe, sign_pow, Finset.exists_inf_le, Set.powersetCard.mem_ofFinEmbEquiv_iff_mem_range, PowerSeries.order_le, measurableSet_Ioo, Valuation.Integers.coe_span_singleton_eq_setOf_le_v_algebraMap, LinearOrderedAddCommGroup.discrete_or_denselyOrdered, MonomialOrder.degLex_lt_iff, IsDedekindDomain.HeightOneSpectrum.adicValued.uniformContinuousConstSMul, IsValuativeTopology.hasBasis_nhds', LinearOrder.infConvergenceClass, ContinuousOn.surjOn_Icc, emultiplicity_lt_top, Finset.Ioo_add_one_right_eq_Ioc, Multiset.max_prod_le, AlgebraicGeometry.IsOpenImmersion.map_ΓIso_inv, isAtomic_iff_isCoatomic, HahnModule.orderTop_vAdd_le_orderTop_smul, strictConvex_iff_ordConnected, Int.card_Icc, Set.disjoint_image_inl_image_inr, NNRat.ofNat_le_cast, Cardinal.toENat_eq_top, sameRay_smul_right_iff_of_ne, extremePoints_doublyStochastic, Valuation.Integers.valuation_pos_iff_ne_zero, Multiset.inf_mono, hasDerivAt_abs, Valued.isOpen_closedBall, Finset.lt_inf'_iff, OrderHom.coe_inf, lineMap_le_right_iff_le_one, Int.floor_le_neg_one_iff, invOf_nonpos, exists_square_le, negPart_nonneg, Affine.Simplex.sign_excenterWeights_empty, IsPreconnected.mapsTo_Ioi_or_Iio, Finset.intervalGapsWithin_succ_fst_of_lt, Field.Emb.Cardinal.strictMono_filtration, convexHull_eq_union_convexHull_finite_subsets, tendsto_fract_left, compl_antitone, Finset.sort_sorted_gt, PNat.card_Ioo, GenContFract.fib_le_of_contsAux_b, Set.disjoint_sdiff_left, compl_strictAnti, Complementeds.mk_top, leOnePart_eq_inv, Finset.le_min_iff, ENat.coe_le_coe, Int.cast_mono, gc_sSup_Iic, upperSemicontinuous_iff_isClosed_preimage, Hyperreal.lt_of_tendsto_atBot, max_bot_right, Nat.one_sub_one_div_cast_le_one, MvPowerSeries.weightedOrder_le, Mathlib.Meta.NormNum.IsRat.natCeil, Finset.Ioc_pred_left_eq_Icc, Valuation.IsEquiv.one_le_iff_one_le, Set.Ioo_succ_right_eq_Ioc, Int.ceil_toNat, SignType.not_lt_neg_one, HahnEmbedding.Seed.truncLT_mem_range_baseEmbedding, NNRat.ceil_cast, Set.pairwise_disjoint_Ico_zpow, Nat.cast_div_le, Set.Iio_diff_Iic, AntitoneOn.of_map_inf, Positive.isOrderedCancelMonoid, Int.floor_pos, Valued.mem_nhds_zero, Odd.zpow_pos_iff, abs_eq_neg_self, sign_eq_zero_iff, sameRay_neg_smul_right_iff_of_ne, HahnSeries.orderTop_le_orderTop_smul, PNat.equivNonZeroDivisorsNat_apply_coe, Int.preimage_Ici, PseudoMetric.IsUltra.isTrans_ball, Finset.Colex.lt_iff_max'_mem, Set.intersecting_insert, Valued.isOpen_ball, ENat.add_one_pos, sup_lt_iff, HahnSeries.orderTop_lt_iff_exists, AddCircle.liftIoc_eq_lift_Icc, Nimber.lt_wf, abs_sub_nonpos, ArchimedeanClass.mk_map_of_archimedean, CategoryTheory.IsGrothendieckAbelian.generatingMonomorphisms.instIsWellOrderContinuousFunctor, Dense.exists_le, CauSeq.lim_le, SuccOrder.isOpen_singleton_iff, ValuationSubring.mem_principalUnitGroup_iff, LocallyBoundedVariationOn.exists_monotoneOn_sub_monotoneOn, monovary_iff_forall_mul_nonneg, pow_lt_one_iff, ArchimedeanClass.FiniteResidueField.instArchimedean, Valued.mem_nhds, Mathlib.Meta.Positivity.abs_pos_of_ne_zero, Ordinal.lsub_typein, OrderMonoidWithZeroHom.coe_mul, abs_sub_map_le_sub, Set.Ico_inter_Iio, punctured_nhds_eq_nhdsWithin_sup_nhdsWithin, Nat.one_div_pos_of_nat, FiniteArchimedeanClass.withTopOrderIso_symm_apply, Set.disjoint_preimage_iff, Archimedean.exists_orderAddMonoidHom_real_injective, AddMonoidAlgebra.supDegree_sub_lt_of_leadingCoeff_eq, Finset.abs_expect_le, Order.embedding_from_countable_to_dense, HahnEmbedding.Partial.mem_domain, Ordinal.toNatOrdinal_eq_zero, Cardinal.one_lt_ofENat, Even.add_pow_le, intermediate_value_univ, Filter.tendsto_Icc_uIcc_uIcc, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivInverse_map_hom, Topology.CWComplex.iUnion_openCell_eq_skeleton, Finset.Ioo_filter_lt, sq_pos_iff, Hyperreal.infinite_iff_abs_lt_abs, EReal.le_iff_sign, BoundedLatticeHom.coe_toBoundedOrderHom, LaurentSeries.powerSeriesEquivSubring_coe_apply, AlgebraicGeometry.IsOpenImmersion.app_ΓIso_hom, FloorSemiring.eventually_mul_pow_lt_factorial_sub, WithTop.tendsto_untopD, Finset.nonneg_subConst_self, Pi.Colex.wellFoundedLT, max_cases, Ordinal.enum_zero_eq_bot, Polynomial.isBoundedUnder_abs_atTop_iff, IsDedekindDomain.HeightOneSpectrum.valuationOfNeZero_eq, Finset.min'_eq_iff, LinOrd.coe_id, Nat.ceil_sub_ofNat, Function.argmin_le, HahnSeries.embDomainOrderAddMonoidHom_apply, Set.Ici_diff_Ici, MulArchimedeanClass.out_top, NNRat.coe_mono, sq_nonneg, CategoryTheory.Limits.CompleteLattice.prod_eq_inf, convexOn_pow, Set.abs_sub_left_of_mem_uIcc, HahnEmbedding.Seed.mem_domain_baseEmbedding, one_le_pow_iff, MulArchimedeanClass.mk_left_le_mk_div_iff, Finset.isGLB_iff_isLeast, le_compl_iff_disjoint_left, inf_lt_right, le_symmDiff_iff_left, SimpleGraph.IsCompleteBetween.disjoint, Nat.ceil_sub_one, Finset.sum_Icc_of_even_eq_range, BoundedLatticeHomClass.toSupBotHomClass, Heyting.Regular.coe_lt_coe, Finsupp.Lex.single_antitone, Topology.RelCWComplex.skeleton_monotone, Set.disjoint_sdiff_right, sameRay_neg_smul_right_iff, RootPairing.RootPositiveForm.exists_pos_eq, symmDiff_le_iff, Set.finite_iff_bddBelow_bddAbove, PowerSeries.coe_X, Valued.integer.locallyFiniteOrder_units_mrange_of_isCompact_integer, AffineSubspace.sSameSide_iff_exists_right, NNRat.preimage_cast_Ico, inf_eq_left, codisjoint_hnot_hnot_left_iff, SMulPosReflectLT.toSMulPosMono, FiniteDimensional.exists_relation_sum_zero_pos_coefficient_of_finrank_succ_lt_card, mem_convexHull_iff_exists_fintype, UV.disjoint_of_mem_compression_of_notMem, Hyperreal.ofSeq_le_ofSeq, Ico_subset_closure_interior, MeasureTheory.Measure.measure_Ioo_eq_zero, Set.mem_uIoc, Complementeds.coe_bot, Set.Ioc_union_Ioc_union_Ioc_cycle, Booleanisation.lift_lt_comp, neg_le_abs, SuccOrder.isSuccLimit_of_mem_frontier, Set.univ_disjoint, le_iff_forall_lt_rat_imp_le, toZ_iterate_succ_le, PNat.card_fintype_Ioc, LaurentSeries.instLaurentSeriesComplete, InfTopHom.coe_top, round_le_add_half, Cardinal.ofENat_lt_nat, LinearOrderedCommGroup.to_noMinOrder, Odd.zpow_neg_iff, AbsoluteValue.map_units_int, nullMeasurableSet_Iio, Set.encard_image_le, sdiff_le_comm, convexHull_toCone_isLeast, sameRay_or_sameRay_neg_iff_not_linearIndependent, IsDedekindDomain.HeightOneSpectrum.valuation_surjective, NNRat.cast_nonpos, Set.Ioc_sub_one_sub_one_eq_Ico, Int.le_floor, Hyperreal.omega_pos, Valuation.rel_one_iff, Rat.cast_lt_zero, Int.fract_eq_self, List.minimum_anti, Set.Ico_add_one_right_eq_Icc, lowerSemicontinuousAt_iff_frequently, CategoryTheory.TransfiniteCompositionOfShape.ofComposableArrows_isoBot, Set.projIci_self, Rat.cast_strictMono, convex_iff_div, HahnSeries.single_div_single, exists_pred_iterate_or, LinearOrderedCommGroupWithZero.wellFoundedOn_setOf_ge_gt_iff_nonempty_discrete_of_ne_zero, Padic.withValUniformEquiv_cast_apply, Module.End.generalized_eigenvec_disjoint_range_ker, Nucleus.coe_le_coe, NonemptyFinLinOrd.comp_apply, ComplementedLattice.isStronglyAtomic, Cardinal.ofENat_le_one, SimpleGraph.right_nonuniformWitnesses_card, Hyperreal.infiniteNeg_iff_infinitesimal_inv_neg, ArchimedeanClass.mk_intCast_nonneg, countable_image_lt_image_Ioi, tendsto_inv_nhdsLT_zero, DFinsupp.Colex.wellFoundedLT_of_finite, convexIndependent_iff_finset, pow_div_pow_eventuallyEq_atTop, HahnSeries.archimedeanClassMk_le_archimedeanClassMk_iff, LaurentSeries.valuation_coe_ratFunc, Set.zero_notMem_sub_iff, DivisibleHull.archimedeanClassOrderIso_apply, Int.fract_lt_one, SemilatInfCat.dual_map, Hyperreal.archimedeanClassMk_omega_neg, frontier_le_subset_eq, Set.one_notMem_div_iff, posPart_lt, Valuation.Integers.isPrincipal_iff_exists_eq_setOf_valuation_le, zsmul_lt_zsmul_iff_right, PNat.card_fintype_Ico, Hyperreal.archimedeanClassMk_coe_nonneg, Matrix.mem_glpos, CategoryTheory.TransfiniteCompositionOfShape.iic_incl_app, IsValuativeTopology.isClosed_ball, min_add_min_le_min_add_add, inf_bot_eq, AddCircle.continuous_equivIco_symm, nhdsWithinLE_sup_nhdsWithinGE, HahnSeries.inv_def, intermediate_value_Icc, Cardinal.ofENat_pos, Padic.coe_withValRingEquiv, Int.Ico_filter_modEq_card, Valuation.Integer.not_isUnit_iff_valuation_lt_one, Int.pred_eq_pred, CategoryTheory.TransfiniteCompositionOfShape.ofOrderIso_F, Matrix.IsPrimitive.nonneg, Finset.Ioo_sub_one_left_eq_Ioc, Padic.comap_mulValuation_eq_int_padicValuation, Fintype.exists_disjointed_le, Nat.floor_sub_natCast, Finset.one_le_divConst_self, Nat.image_cast_int_Ioo, Int.Ioc_filter_dvd_eq, OrderIso.asBoolAlgAsBoolRing_apply, Int.preimage_Icc, MeasureTheory.ae_const_le_iff_forall_lt_measure_zero, AffineSubspace.wSameSide_iff_exists_right, continuousAt_sign_of_neg, Affine.Simplex.sSameSide_affineSpan_faceOpposite_point_right_iff, isPiSystem_Ioc_mem, div_pos_iff, measurableSet_lt, AddCircle.continuousAt_equivIoc, ENat.add_le_add_iff_right, OrderEmbedding.addLeft_apply, Iic_mem_nhdsSet_Iic_iff, Rat.cast_pos_of_pos, Nat.Prime.emultiplicity_factorial_le_div_pred, UniqueFactorizationMonoid.le_emultiplicity_iff_replicate_le_normalizedFactors, LinearOrderedCommGroupWithZero.fst_apply, variationOnFromTo.monotoneOn, Cardinal.toENat_le_natCast_iff, Set.toENat_cardinalMk, inf_right_le_sup_right, NumberField.FinitePlace.norm_eq_one_iff_notMem, MulArchimedeanClass.ballSubgroup_top, grade_injective, Finset.Ico_diff_Ico_right, ArchimedeanClass.mem_closedBall_iff, Polynomial.div_tendsto_atBot_zero_iff_degree_lt, Finset.inf_erase_top, disjoint_inf_sdiff, Set.bounded_le_inter_lt, countable_of_isolated_left', Dense.exists_seq_strictAnti_tendsto, Set.range_projIci, Set.Ici_subset_Ico_union_Ici, Valuation.vlt_one_iff, Finset.le_min'_iff, abs_abs_sub_abs_le_abs_sub, extremePoints_convexHull_subset, ENat.mul_left_strictMono, Set.Finite.disjoint_toFinset, Finset.intervalGapsWithin_fst_of_lt_lt, Module.End.mem_genEigenspace_one, mabs_mul', LaurentSeries.valuation_compare, mem_segment_iff_div, Cardinal.enat_gc, Padic.isUniformInducing_cast_withVal, le_iff_oneLePart_leOnePart, IsModularLattice.isModularLattice_Ici, MeasureTheory.aecover_Ico_of_Ioo, ArchimedeanClass.mk_ratCast_nonneg, PrimeSpectrum.isIdempotentElemEquivClopens_symm_top, Hyperreal.tendsto_atBot_iff, FiniteArchimedeanClass.addSubgroup_strictAnti, Nat.one_le_ceil_iff, PowerSeries.le_order, leOnePart_eq_ite, Orientation.someBasis_orientation, Set.pairwiseDisjoint_range_singleton, Even.zpow_pos_iff, HahnEmbedding.ArchimedeanStrata.archimedean_stratum, exposedPoints_subset_extremePoints, SimpleGraph.nonuniformWitness_spec, Right.nsmul_neg_iff, Set.isPWO_iff_isWF, le_symmDiff_sup_right, two_mul_le_add_pow_two, LieAlgebra.IsKilling.rootSpace_zsmul_add_ne_bot_iff_mem, PNat.find_min', Int.ceil_pos, PointedCone.maxTensorProduct_comm, Finset.fold_max_lt, WithTop.tendsto_coe_atTop, AlgebraicGeometry.IsOpenImmersion.app_ΓIso_hom_apply, Set.disjoint_empty, Tuple.eq_sort_iff', inf_eq_inf_iff_left, abs_lt, Set.one_lt_encard_iff, Set.Icc_add_one_sub_one_eq_Ioo, Continuous.finset_inf, negPart_eq_zero, MvPowerSeries.order_mul_ge, FiniteMulArchimedeanClass.ballSubgroup_strictAnti, Finpartition.le, HahnSeries.lt_iff, HahnSeries.instIsOrderedAddMonoidLex, instIsCountablyGenerated_atTop, Module.End.IsFinitelySemisimple.genEigenspace_eq_eigenspace, ArchimedeanClass.mk_le_mk_add_of_archimedean, DivisibleHull.mk_lt_mk, sup_inf_le, LowerAdjoint.closure_inf_le, Submonoid.closure_image_isMulIndecomposable_baseOf, ArchimedeanOrder.lt_def, Rat.toNNRat_le_toNNRat_iff, IsCompact.exists_isGLB, AbsoluteValue.IsAdmissible.toIsEuclidean, Rat.le_toNNRat_iff_coe_le, Cardinal.toENatAux_le_nat, Finsupp.Colex.addLeftMono, Hyperreal.lt_of_tendsto_zero_of_pos, Set.disjoint_diagonal_offDiag, SetRel.gc_leftDual_rightDual, Finset.Icc_add_one_sub_one_eq_Ioo, Cardinal.toENat_le_nat, Rat.toNNRat_le_iff_le_coe, Rat.cast_le_intCast, Complex.UnitDisc.tendsto_pow_atTop_nhds_zero, Set.encard_pos, mem_nhdsLE_iff_exists_Icc_subset, WithZeroMulInt.toNNReal_strictMono, NNRat.instOrderTopology, Int.preimage_floor_singleton, RatFunc.single_one_eq_pow, Finset.Ioo_succ_succ, Finset.map_orderEmbOfFin_univ, sdiff_eq_self_iff_disjoint, closure_Ico, LaurentSeries.tendsto_valuation, abs_max_le_max_abs_abs, HahnSeries.SummableFamily.powers_toFun, Tropical.add_eq_right_iff, nhdsLT_eq_bot_iff, left_le_midpoint, Module.End.genEigenspace_div, Finset.exists_min_image, Set.unbounded_le_inter_lt, List.Perm.maximum_eq, Int.mem_box, Ordinal.typein_lt_self, LocallyConvexSpace.convex_open_basis_zero, Valuation.IsEquiv.le_one_iff_le_one, Set.encard_le_coe_iff, countable_setOf_isolated_left_within, Set.Iic_diff_Iic, isPiSystem_Icc, Zsqrtd.instIsOrderedAddMonoidCastInt, PowerSeries.heval_unit, List.maximum_mono, Units.inv_neg, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivUnitIsoApp_inv_hom, Ioi_mem_nhdsSet_Ici_iff, MeasureTheory.Measure.measure_Ioo_pos, hasBasis_nhdsSet_Ici_Ici, not_bddAbove_iff, pos_invOf_of_invertible_cast, Polynomial.abs_tendsto_atBot, List.foldr_min_of_ne_nil, Set.infinite_iff_exists_lt, Valuation.integer.coe_span_singleton_eq_setOf_le_v_coe, Nat.choose_le_pow_div, DFinsupp.Colex.total_le, Valuation.Integers.wellFounded_gt_on_v_iff_discrete_mrange, SemilatInfCat.Iso.mk_hom_toFun, oneLePart_lt, PUnit.canonicallyOrderedAdd, StieltjesFunction.measure_Ioc, LinearOrder.bot_topologicalSpace_eq_generateFrom, strictConvex_iff_div, zpow_right_mono, PNat.natPred_strictMono, pow_div_pow_eventuallyEq_atBot, ContinuousOn.lowerSemicontinuousOn, LaurentSeries.coe_range_dense, CategoryTheory.Limits.MultispanShape.ofLinearOrder_fst, InnerProductSpace.span_gramSchmidt_Iio, Odd.pow_lt_pow, Field.Emb.Cardinal.iSup_adjoin_eq_top, MeasureTheory.integrableOn_Ici_iff_integrableAtFilter_atTop, toWellOrderExtension_strictMono, Set.notMem_Iio, FiniteArchimedeanClass.coe_congrOrderIso_apply, disjoint_compl_right, MeasureTheory.integrableOn_Iic_iff_integrableAtFilter_atBot, Nat.nth_eq_orderEmbOfFin, compl_le_compl_iff_le, TopCat.Presheaf.IsSheaf.isSheafPairwiseIntersections, zero_le', MvPowerSeries.le_weightedOrder, Module.End.genEigenspace_eq_genEigenspace_finrank_of_le, NonemptyFinLinOrd.hom_hom_comp, nhdsLE_basis_Icc, OrderIso.compl_apply, tendsto_floor_left_pure_ceil_sub_one, Set.compl_Iio, SimpleGraph.FarFromTriangleFree.lt_one, Ordinal.toNatOrdinal_natCast, le_compl_comm, HahnSeries.orderTop_self_sub_one_pos_iff, min_cases, SimpleGraph.left_nonuniformWitnesses_card, AbsoluteValue.map_prod, Finset.lt_min'_iff, PowerSeries.intValuation_X, mabs_eq_inv_self, IsSumSq.nonneg, pow_two_pos_of_ne_zero, Set.Ioc_subset_Ioo_union_Icc, AddCircle.continuousAt_equivIco, isCofinal_setOf_imp_lt, TopCat.Presheaf.isGluing_iff_pairwise, SimplexCategory.toCat_obj, Finset.lt_sup_iff, Set.projIci_surjOn, Finpartition.mk_mem_sparsePairs, Set.mulIndicator_eq_one, continuousAt_sign_of_pos, ENNReal.monotone_zpow, Set.Icc_subset_uIcc', Int.floor_lt_self_iff, le_sup_iff, NatOrdinal.toOrdinal_symm_eq, CategoryTheory.SmallObject.SuccStruct.iterationCocone_pt, Polynomial.div_tendsto_atTop_zero_of_degree_lt, LocallyFiniteOrder.denselyOrdered_iff_subsingleton, toIcoMod_zero_one, Int.Ico_eq_finset_map, IsDedekindDomain.HeightOneSpectrum.adicValued_apply', instSMulPosStrictMonoIntOfIsOrderedAddMonoid, compl_le_hnot, Hyperreal.stdPart_of_tendsto, Polynomial.cardPowDegree_nonzero, OrderRingHom.subsingleton, MulArchimedeanClass.mem_ballSubgroup_iff, PredOrder.nhdsLE, Finset.min_le_of_eq, midpoint_mem_segment, CompositionSeries.toList_sorted, Set.encard_lt_encard_iff_encard_diff_lt_encard_diff, isLocallyClosed_Ioo, strictConcaveOn_iff_div, Int.gc_ceil_coe, LocallyFiniteOrder.orderAddMonoidHom_toAddMonoidHom, trichotomy_of_add_eq_add, ArchimedeanClass.mk_eq_top_iff, NatOrdinal.toOrdinal_one, ArchimedeanClass.mk_le_add_mk_of_archimedean, Pi.instNoMaxOrderColexForallOfWellFoundedGTOfNonempty, Heyting.Regular.toRegular_coe, Order.isNormal_iff, Finset.inf'_le_iff, sdiff_top, PowerSeries.IsWeierstrassFactorization.degree_eq_coe_lift_order_map, isGreatest_pair, OrderIso.subsingleton_of_wellFoundedGT, ArchimedeanClass.mk_right_le_mk_add_iff, Rat.cast_le_natCast, mabs_max_le_max_mabs_mabs, archimedean_iff_int_lt, Set.Ico_succ_right_eq_Icc, ArchimedeanClass.FiniteResidueField.mk_lt_mk, Finset.SupIndep.pairwiseDisjoint, ClosureOperator.closure_inf_le, stdSimplex.barycenter_eq_centerMass, NNRat.Nonneg.coe_ofScientific, tendsto_const_mul_zpow_atTop_nhds_iff, HahnSeries.min_orderTop_le_orderTop_sub, Ordinal.toNimber_zero, CategoryTheory.SmallObject.iterationFunctorObjObjRightIso_ιIteration_app_right, Polynomial.div_tendsto_zero_of_degree_lt, cocompact_le_atBot_atTop, nhdsGT_eq_bot_iff, IsPreconnected.Icc_subset, Finsupp.DegLex.instIsOrderedCancelAddMonoidDegLexNat, cmp_mul_left', Mathlib.Meta.Positivity.pos_of_isRat, min_lt_max, NatOrdinal.toOrdinal_toNatOrdinal, FiniteMulArchimedeanClass.subgroup_eq_bot, interior_Ico, SMulPosStrictMono.toSMulPosReflectLE, RootPairing.rootForm_pos_of_ne_zero, Set.ordConnected_iff_uIcc_subset_right, OrderIso.withZeroUnits_apply, LinOrd.hom_comp, AffineSpace.asymptoticNhds_eq_smul, exteriorPower.pairingDual_apply_apply_eq_one_zero, exists_seq_strictMono_tendsto, IsRealClosed.nonneg_iff_isSquare, MulArchimedeanClass.subgroup_antitone, WithZeroTopology.Iio_mem_nhds_zero, AddCircle.openPartialHomeomorphCoe_symm_apply, le_compl_compl, lt_mabs, Types.monoOverEquivalenceSet_inverse_obj, GenContFract.IntFractPair.succ_nth_stream_b_le_nth_stream_fr_inv, SignType.pos_iff, SuccOrder.prelimitRecOn_succ, frontier_Iic, AbsoluteValue.IsAdmissible.exists_approx_aux, Finset.subConst_le_inv_dens, upperSemicontinuous_iff_IsClosed_hypograph, NatOrdinal.instWellFoundedLT, Nat.preimage_floor_zero, Module.End.genEigenspace_nat, Order.height_int, Affine.Simplex.ExcenterExists.signedInfDist_excenter, Icc_mem_nhds_iff, antivaryOn_iff_forall_mul_nonpos, IsSquare.nonneg, Padic.coe_withValRingEquiv_symm, MulArchimedeanClass.closedBallSubgroup_top, Dense.exists_lt, SuccOrder.nhdsGE, HahnSeries.leadingCoeff_mul_of_nonzero, Mathlib.Tactic.Order.ToInt.toInt_nlt_toInt, Int.abs_sub_lt_one_of_floor_eq_floor, frontier_Iic_subset, archimedean_iff_rat_lt, mabs_min_le_max_mabs_mabs, Valuation.HasExtension.mk_smul_mk, Nat.floor_eq_zero, Finset.inf_eq_sInf_image, BoundedLatticeHom.dual_comp, WithTop.denselyOrdered_set_iff_subsingleton, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.w_assoc, compl_eq_iff_isCompl, ValuationSubring.mem_nonunits_iff, Cardinal.toENat_comp_ofENat, one_lt_leOnePart_iff, symmDiff_eq_top, Real.Angle.sign_toReal, IsAbsoluteValue.abs_abv_sub_le_abv_sub, Valued.toNormedField.norm_lt_iff, MeasureTheory.aecover_Ioc_of_Ico, PseudoMetric.coe_finsetSup, NNRat.preimage_cast_Ioo, Int.floor_le, Set.one_mem_div_iff, PowerSeries.IsWeierstrassFactorizationAt.degree_eq_coe_lift_order_map_of_ne_top, Valuation.rel_iff_le, sq_le_one_iff_abs_le_one, Polynomial.abs_isBoundedUnder_iff, Finset.inf_eq_iInf, HahnSeries.order_pow, MulArchimedeanClass.mk_le_mk, StieltjesFunction.iInf_Ioi_eq, Set.Ici_succ_eq_Ioi, quasilinearOn_iff_mem_uIcc, lt_add_iff_lt_right_or_exists_lt, sign_eq_sign_or_eq_neg, Finset.prod_Icc_succ_eq_mul_endpoints, Hyperreal.lt_of_st_lt, MulArchimedeanClass.mk_eq_top_iff, OrderEmbedding.birkhoffSet_apply, Pi.instNoMaxOrderLexForallOfWellFoundedLTOfNonempty, LocallyFiniteOrder.orderMonoidHom_strictMono, Rat.toNNRat_lt_iff_lt_coe, Set.Ico_subset_Icc_union_Ioo, countable_image_gt_image_Ioi, ENat.strictMono_map_iff, MonomialOrder.lex_lt_iff, Nat.lt_ceil, FloorRing.gc_coe_floor, CategoryTheory.TransfiniteCompositionOfShape.ofArrowIso_isColimit, MonomialOrder.eq_zero_iff, VertexOperator.ncoeff_of_coeff, CompositionSeries.total, PNat.natPred_lt_natPred, Filter.tendsto_div_const_atBot_iff, CircleDeg1Lift.pow_monotone, ENat.one_lt_top, Valuation.Integers.valuation_irreducible_pos, Module.End.genEigenspace_le_maximal, nhdsLE_sup_nhdsGT, LaurentSeries.comparePkg_eq_extension, Set.pairwise_disjoint_Ico_intCast, NumberField.toNNReal_valued_eq_adicAbv, HahnSeries.finiteArchimedeanClassOrderIsoLex_apply_fst, Valuation.vlt_iff_lt, le_compl_iff_disjoint_right, Cardinal.toENat_le_iff_of_lt_aleph0, lowerSemicontinuousOn_iff_preimage_Iic, MonoidWithZeroHom.inr_strictMono, nullMeasurableSet_Ico, convexJoin_left_comm, FiniteArchimedeanClass.ballAddSubgroup_strictAnti, LowerSet.coe_iicInfHom, one_lt_pow_iff, codisjoint_inf_left, compl_top, instArchimedeanInt, CategoryTheory.HasLiftingProperty.transfiniteComposition.sqFunctor_obj, Nat.sub_one_lt_floor, Order.iso_of_countable_dense, disjoint_disjointed, Rat.preimage_cast_Ioo, DivisibleHull.archimedeanClassOrderIso_symm_apply, Ordinal.ToType.mk_apply, Nonneg.coe_div, borel_eq_generateFrom_Ioc_le, iInter_Iic_eq_empty_iff, Valued.hasBasis_uniformity, LinearOrderedField.coe_lt_inducedMap_iff, Sym2.inf_le_sup, Set.Iic.isCompl_iff, ArchimedeanClass.addSubgroup_strictAntiOn, isCompl_compl, Nat.floor_mono, ArchimedeanClass.FiniteResidueField.ordConnected_preimage_mk, Valuation.mem_ltSubmodule_iff, nhds_basis_Ioo, one_lt_mul_self_iff, SimpleGraph.disjoint_fromEdgeSet, StieltjesFunction.outer_Ioc, Module.End.mem_genEigenspace_nat, IsPreconnected.intermediate_value, Set.Iio_inter_Iio, sdiff_eq_left, List.minimum_le_of_mem', Nat.le_ceil, Finset.inf'_mono, RatFunc.single_zpow, PNat.instNoMaxOrder, isPiSystem_Ici, FiniteArchimedeanClass.submodule_strictAnti, MeasureTheory.aecover_Ioo_of_Ico, symmDiff_eq_sup, PNat.lt_add_one_iff, ArchimedeanClass.mk_one, HahnSeries.orderTop_abs, Set.compl_Ici, NNRat.cast_lt_one, Field.Emb.Cardinal.adjoin_image_leastExt, Complementeds.isCompl_coe, div_nonneg_iff, CategoryTheory.Limits.CompleteLattice.instHasBinaryProductsOfOrderTop, Set.pairwiseDisjoint_fiber, mul_nonneg_iff_neg_imp_nonpos, borel_eq_generateFrom_Ioi, LaurentSeries.valuation_def, OrderIso.sumLexIioIci_apply_inl, zero_lt_iff, Set.projIci_coe, Mathlib.Tactic.Order.ToInt.exists_translation, HahnSeries.le_order_iff_forall, Valuation.integer.v_irreducible_lt_one, Cardinal.ofENat_toENat_le, sum_Ioc_inv_sq_le_sub, EReal.sign_mul_inv_abs, WithTop.orderIsoSumLexPUnit_symm_inr, Int.natCast_strictMono, Left.pow_lt_one_iff, Nat.ceil_zero, Ordinal.typein_one_toType, MeasureTheory.aecover_Iio_of_Iio, disjoint_sup_left, NNRat.floor_def, PNat.card_Ioc, ArchimedeanClass.mem_ballAddSubgroup_iff, HahnSeries.forallLTEqZero_supp_BddBelow, LaurentSeries.derivative_iterate, directedOn_of_inf_mem, Convex.combo_le_max, convexHull_prod, instWellFoundedGTUnit, Set.bounded_le_inter_le, Filter.isBoundedUnder_le_abs, IsModularLattice.isModularLattice_Iic, PNat.natPred_le_natPred, LinearOrderedCommMonoidWithZero.toMulPosStrictMono, inf_strictMonoOn_Icc_sup, Rat.cast_pos, Set.encard_insert_le, Nat.pow_le_choose, FunctionField.inftyValuation.C, EisensteinSeries.tendsto_tsum_one_div_linear_sub_succ_eq, BoundedLatticeHom.coe_toInfTopHom, Nat.map_cast_int_atTop, OrderTopology.of_discreteTopology, Finset.isGLB_inf_id, NNRat.preimage_cast_Ioc, Valuation.IsNontrivial.exists_lt_one, Set.Ici.isCompl_iff, HahnSeries.instIsOrderedRingLexOfNoZeroDivisors, Even.zpow_nonneg, mem_nhds_iff_exists_Ioo_subset, Set.encard_le_one_iff, Ordinal.toNimber_toOrdinal, Cardinal.toENat_le_one, interior_Ioo, Field.Emb.Cardinal.instFiniteDimensionalSubtypeMemIntermediateFieldAdjoinImageToTypeOrdRankCompCoeBasisWellOrderedBasisLeastExtIioSingletonSet, neg_one_lt_zero, Affine.Simplex.sign_signedInfDist_incenter, Affine.Simplex.ExcenterExists.sign_signedInfDist_excenter, LinearOrderedAddCommGroup.to_noMaxOrder, Finsupp.Colex.single_le_iff, MeasureTheory.aecover_Icc_of_Ioo, Ordinal.cof_type_lt, Nat.ceil_natCast, LinearOrderedAddCommGroup.isAddCyclic_iff_not_denselyOrdered, round_eq_iff, PNat.lt_find_iff, FiniteMulArchimedeanClass.subsemigroup_eq_subgroup, Set.Iio_subset_Iio_union_Ico, isCompl_bot_top, Finset.pluennecke_ruzsa_inequality_pow_div_pow_div, Ordinal.toNimber_max, mem_segment_add_sub, OrderTopology.of_linearLocallyFinite, Filter.tendsto_div_const_atTop_iff, isClosed_Ico_iff, MeasureTheory.countable_meas_le_ne_meas_lt, Set.encard_le_encard_of_injOn, Complementeds.coe_lt_coe, min_eq_left_iff, sdiff_le_iff, Set.Iio_subset_Iic_union_Ico, frontier_Iio, le_sup_sdiff_sup_sdiff, Hyperreal.IsSt.lt, denselyOrdered_set_iff_subsingleton, Set.zero_notMem_neg_add_iff, NNRat.cast_lt, inf_le_left, Set.encard_tsub_one_le_encard_diff_singleton, Set.disjoint_image_inl_range_inr, pow_pos_iff, ENat.mul_le_mul_right_iff, CompleteLatticeHom.toOrderIsoRangeOfInjective_apply, HomotopicalAlgebra.RelativeCellComplex.Cells.hj, convexHull_eq_union, subsingleton_setOf_mem_iff_pairwise_disjoint, EReal.sign_mul_abs, Order.Ioo_eq_empty_iff_pred_le, DistLat.Iso.mk_hom, Set.pairwiseDisjoint_image_right_iff, Cardinal.toENat_injOn, ArchimedeanClass.min_le_mk_sub, PredOrder.isOpen_singleton_iff, LinearIndepOn.encard_le_toENat_rank, Ordinal.sup_typein_limit, Int.preimage_ceil_singleton, antivary_iff_forall_mul_nonpos, pow_le_one_iff, Rat.HeightOneSpectrum.valuation_equiv_padicValuation, DivisibleHull.instIsStrictOrderedModuleRat, le_inv_self_iff, LaurentSeries.valuation_le_iff_coeff_lt_log_eq_zero, Interval.coe_inf, convexHull_eq, Types.monoOverEquivalenceSet_unitIso, GenContFract.le_of_succ_get?_den, RootPairing.RootPositiveForm.zero_lt_apply_root_root_iff, Cardinal.toENat_eq_nat, exists_seq_strictAnti_tendsto_nhdsWithin, BddLat.coe_forget_to_semilatInf, Pi.instNoMinOrderColexForallOfWellFoundedGTOfNonempty, convexJoin_assoc_aux, isPiSystem_Ioo, Orientation.oangle_sign_smul_add_smul_right, MeasureTheory.aecover_Ico_of_Ioc, borel_eq_generateFrom_Iio, Rat.lt_toNNRat_iff_coe_lt, div_le_div_flip, codisjoint_himp_self_left, CategoryTheory.HasLiftingProperty.transfiniteComposition.sqFunctor_map, HasSolidNorm.orderClosedTopology, Set.one_lt_encard_iff_nontrivial, LaurentSeries.uniformContinuous_coeff, CategoryTheory.MorphismProperty.IsCardinalForSmallObjectArgument.preservesColimit, GenContFract.zero_le_of_contsAux_b, Mathlib.Meta.NormNum.IsInt.natCeil, Finsupp.DegLex.wellFoundedLT, LinearOrderedAddCommGroup.Subgroup.exists_neg_generator, AddSubgroup.isLeast_of_closure_iff_eq_abs, negPart_eq_neg, ArchimedeanClass.eq_zero_or_top_of_archimedean, tendsto_pow_div_pow_atTop_atTop, mabs_lt, NonemptyInterval.fst_sup, Nucleus.coe_top, LinearLocallyFiniteOrder.le_succFn, HeytAlg.Iso.mk_hom, PowerSeries.coe_one, CategoryTheory.IsGrothendieckAbelian.generatingMonomorphisms.functorToMonoOver_obj, HasStrictFDerivAt.hasStrictFDerivAt_norm_smul, min_le_emultiplicity_add, Polynomial.signVariations_eq_eraseLead_add_ite, List.sortedGE_mergeSort, Ordinal.toNimber_eq_one, Valuation.mem_leIdeal_iff, FinBoolAlg.hasForgetToFinPartOrd_forget₂_map, WithZeroTopology.tendsto_zero, LinearOrderedAddCommGroupWithTop.sub_le_sub_iff_left_of_ne_top, Int.card_fintype_Ico_of_le, LaurentSeries.hasseDeriv_zero, IsNonarchimedean.multiset_image_add, BooleanSubalgebra.mem_map_equiv, Padic.norm_rat_le_one_iff_padicValuation_le_one, emultiplicity_pos_iff, Sublattice.map_symm_eq_iff_eq_map, LinearOrderedSemiring.toLocallyConvexSpace, Finset.exists_pos_of_sum_zero_of_exists_nonzero, Nonneg.Icc_subset_segment, Set.nontrivial_iff_exists_lt, Set.bounded_ge_inter_gt, posPart_mono, Set.notMem_Ici, Valued.isClosed_closedBall, SignType.lt_one_iff, ENat.succ_def, Finpartition.bot_notMem, mem_nhdsGT_iff_exists_Ioo_subset, ComplementedLattice.instOrderDual, Cardinal.nat_le_ofENat, Set.smul_Icc, Lat.Iso.mk_hom, Finset.Ico_succ_left_eq_Ioo, Set.integer_valuation_le_one, grade_covBy_grade_iff, CategoryTheory.SmallObject.SuccStruct.instIsWellOrderContinuousIterationFunctor, interior_Iic, Valuation.coe_ltAddSubgroup, Cardinal.ofENat_toENat_eq_self, AddCircle.coe_image_Ico_eq, Finset.sum_sym2_filter_not_isDiag, Finset.Iic_sub_one_eq_Iio, Order.le_succ_bot_iff, IsDedekindDomain.HeightOneSpectrum.coe_smul_adicCompletion, List.max_sum_le, Finsupp.DegLex.le_iff, Rat.surjective_padicValuation, interior_Ioi, Real.smoothTransition.projIcc, Set.Finite.convexHull_eq_image, MonoidWithZeroHom.inl_mono, convexJoin_right_comm, nhdsWithinLT_sup_nhdsWithinGE, Affine.Simplex.sOppSide_affineSpan_faceOpposite_point_right_iff, wellFounded_gt_exact_sequence, antivaryOn_iff_exists_antitoneOn_monotoneOn, Matrix.isIrreducible_iff, MvPolynomial.schwartz_zippel_sum_degreeOf, Mathlib.Meta.NormNum.IsInt.natFloor, FiniteMulArchimedeanClass.val_mk, Set.range_injOn_strictMono, FiniteArchimedeanClass.ball_strictAnti, right_le_midpoint, compl_le_iff_compl_le, Int.ceil_mono, CategoryTheory.TransfiniteCompositionOfShape.ofComposableArrows_incl_app, not_denselyOrdered_withZero_int, Continuous.exists_forall_le_of_hasCompactMulSupport, ArchimedeanClass.orderHom_top, ENat.exists_nat_gt, Topology.IsLower.isTopologicalBasis_insert_univ_subbasis, mem_openSegment_iff_div, HahnEmbedding.Partial.eval_zero, nhdsGE_basis, measurable_IocProdIoc, Cardinal.ofENat_toENat, Ordinal.typein_le_typein', StieltjesFunction.measure_Ico, Left.nsmul_neg_iff, IsNonarchimedean.apply_intCast_le_one_of_isNonarchimedean, Set.ordConnected_iff_uIcc_subset, Finset.exists_inf_eq_iInf, le_himp, NNRat.cast_le_natCast, antivaryOn_iff_forall_smul_nonpos, List.minimum_concat, Finset.inf_le, tendsto_floor_left, CategoryTheory.Limits.MultispanIndex.toLinearOrder_left, Multiset.sum_min_le, abs_add_le, OrderEmbedding.isEmbedding_of_ordConnected, LinearOrderedCommGroup.to_noMaxOrder, convexHull_rangle_single_eq_stdSimplex, Opens.toPretopology_grothendieckTopology, Hyperreal.InfinitePos.pos, Function.Injective.encard_range, Set.biUnion_Ioc_eq_Ioi_self_iff, Set.encard_le_one_iff_eq, sameRay_smul_right_iff, HahnSeries.finiteArchimedeanClassOrderIso_apply, LaurentSeries.ratfuncAdicComplRingEquiv_apply, LinearOrderedAddCommGroupWithTop.strictMono_add_right_of_ne_top, instIsLocalizationIntPosRat, BoundedLatticeHomClass.map_bot, WithTop.tendsto_nhds_top_iff, Polynomial.isLittleO_atBot_of_degree_lt, m_Birkhoff_inequalities, min_mabs_mabs_le_mabs_max, AffineSpace.asymptoticNhds_eq_smul_vadd, MonomialOrder.div, Int.strictMonoOn_natAbs, Finset.pluennecke_ruzsa_inequality_pow_mul, Nimber.toOrdinal_symm_eq, convexHull_union, sq_pos_of_ne_zero, convexHull_sub, Hyperreal.infinitePos_def, Topology.RelCWComplex.skeletonLT_I, Cardinal.aleph_toENat, maximal_iff_isGreatest, cmp_div_one', WithZeroTopology.orderClosedTopology, Int.cast_le_neg_one_or_one_le_cast_of_ne_zero, Irreducible.maximalIdeal_pow_eq_setOf_le_v_coe_pow, Finset.lt_fold_max, tendsto_ceil_right, PowerSeries.coeff_heval_zero, Finset.inf_univ_eq_iInf, MeasureTheory.Measure.measure_Ioi_pos, smul_nonneg_iff_pos_imp_nonneg, MonomialOrder.lex_le_iff, oneLePart_eq_self, exists_pos_left_iff_sameRay_and_ne_zero, HahnSeries.instIsDomainOfIsCancelAdd, abs_add_three, sameRay_neg_smul_left_iff, Nat.floor_zero, CategoryTheory.SmallObject.prop_iterationFunctor_map_succ, Rat.cast_le, Order.not_isMax_pred, ProbabilityTheory.condIndep_limsup_atBot_self, Set.functorToTypes_map, zsmul_le_zsmul_iff_right, antivary_iff_forall_smul_nonpos, Finset.Ico_filter_lt, le_posPart, FiniteArchimedeanClass.min_le_mk_add, Finset.min_mono, Set.lt_iff_ssubset, IsDedekindDomain.HeightOneSpectrum.intValuation_exists_uniformizer, Continuous.bddBelow_range_of_hasCompactMulSupport, antivaryOn_iff_mul_rearrangement, Set.Ioo_sub_one_left_eq_Ioc, Nat.inv_pos_of_nat, disjoint_iff_inf_le, HahnSeries.min_le_min_add, convexHull_list_sum, Set.not_monotoneOn_not_antitoneOn_iff_exists_lt_lt, iSupIndep_iff_supIndep, Nat.floor_one, BotHom.inf_apply, Nat.floor_sub_ofNat, exists_Icc_mem_subset_of_mem_nhds, measurableSet_Ioc, Filter.Eventually.intCast_atBot, MonomialOrder.degree_sPolynomial_le, OrderEmbedding.range_inj, AffineSubspace.wOppSide_iff_exists_right, EReal.sign_neg, LinearOrderedField.cutMap_self, add_self_nonpos_iff, GroupCone.oneLE.isMaxMulCone, WithVal.le_def, HasCountableSeparatingOn.range_Ici, Finset.pluennecke_ruzsa_inequality_nsmul_sub, Hyperreal.stdPart_omega, Set.Ioc_inter_Ioi, Nat.floor_eq_iff', List.argmin_eq_some_iff, IsDiscreteValuationRing.addVal_le_iff_dvd, Mathlib.Meta.NormNum.isNNRat_le_false, isPiSystem_Icc_mem, Set.Iio.coe_inf, ArchimedeanClass.liftOrderHom_mk, Nat.isCompl_even_odd, Valuation.HasExtension.val_map_lt_one_iff, LinearOrderedAddCommGroupWithTop.sub_self_nonneg, LinearOrderedField.cutMap_bddAbove, CategoryTheory.TransfiniteCompositionOfShape.map_incl, ArchimedeanClass.orderHom_mk, WithBot.denselyOrdered_set_iff_subsingleton, Set.Ici.subtype_functor_final, Metric.isBounded_of_abs_le, Set.Iic_subset_Iio_union_Icc, one_le_mabs, IicProdIoc_comp_restrict₂, CategoryTheory.SimplicialThickening.Path.le_right, StieltjesFunction.length_Ioc, Order.lt_succ_bot_iff, Continuous.lowerSemicontinuous, MvPolynomial.IsSymmetric.antitone_supDegree, Set.encard_le_encard, AlgebraicGeometry.IsOpenImmersion.map_ΓIso_hom, ENat.toENNReal_le, Valuation.one_le_val_iff, Cardinal.toENat_eq_iff_of_le_aleph0, FiniteMulArchimedeanClass.mk_lt_mk, Set.zero_mem_sub_iff, Submonoid.closure_image_one_lt_and_isMulIndecomposable, Set.Ioo_disjoint_Ioo, MulArchimedeanClass.mk_right_le_mk_div_iff, IsCompact.bddBelow_image, BoundedLatticeHom.coe_comp_inf_hom', Finset.prod_Icc_of_even_eq_range, four_mul_le_pow_two_add, leOnePart_eq_inv', Valuation.Compatible.vle_iff_le, Mathlib.Tactic.PNatToNat.coe_le_coe, SetTheory.PGame.nim_grundyValue, Iotop_subset_Ioc, PNat.le_one_iff, atTop_le_cocompact, WithZeroTopology.isOpen_Iio, iSupIndep_iff_supIndep_univ, NNRat.floor_natCast_div_natCast, Finsupp.Lex.addRightMono, Int.fract_nonneg, MonomialOrder.degree_sub_leadingTerm_lt_degree, Int.Ico_filter_modEq_eq, NonemptyInterval.coe_sup_interval, projIcc_eq_zero, nhds_bot_basis_Iic, Set.integer_eq, mabs_div_lt_iff, measurableSet_lt', Ici_mem_nhdsSet_Ici_iff, Positive.coe_zpow, Int.injOn_natAbs_Ici, WithTop.continuousOn_untopA, Set.pairwiseDisjoint_image_left_iff, OrderEmbedding.map_inf_le, nhds_top_basis, Hyperreal.abs_lt_real_iff_infinitesimal, Int.preimage_fract, zpow_le_zpow_iff_left, inv_lt_self_iff, instLawfulOrderSup_mathlib, Set.monotone_image, SubRootedTree.bot_mem_iff, Int.Ioc_filter_modEq_eq, Finset.inf_top, Int.addSubmonoid_closure_range_mul_self, AffineIndependent.not_wbtw_of_injective, Hyperreal.infinitesimal_pos_iff_infinitePos_inv, Multiset.abs_sum_le_sum_abs, AddGroupCone.nonneg.isMaxCone, oneLePart_eq_ite, Module.End.hasGenEigenvector_iff, MulArchimedeanClass.orderHom_mk, SemilatSupCat_dual_comp_forget_to_partOrd, Module.Basis.orientation_neg_single, IsCompact.exists_isGreatest, MvPolynomial.leadingCoeff_toLex, LinearOrder.isPredArchimedean_of_isSuccArchimedean, Ico_subset_biUnion_Ico, Set.wcovBy_insert, hnot_anti, ArchimedeanClass.mk_div, abs_le_one_iff_mul_self_le_one, nullMeasurableSet_lt, Set.range_IicExtend, CategoryTheory.TransfiniteCompositionOfShape.map_F, antivary_comm, HahnSeries.leadingCoeff_neg_iff, CategoryTheory.SimplicialThickening.Path.le, ENat.tendsto_nhds_top_iff_natCast_lt, Order.IsNormal.strictMono, iUnion_Ioc_intCast, convexOn_iff_div, Booleanisation.lift_le_comp, left_eq_inf, Nonneg.coe_zpow, left_mem_openSegment_iff, MonomialOrder.degree_monomial_le, CategoryTheory.SimplicialThickening.functor_id, HahnSeries.order_mul_of_ne_zero, Units.zero_lt, Set.range_injOn_strictAnti, OrderMonoidWithZeroHom.comp_mul, AffineSubspace.setOf_sOppSide_eq_image2, AddValuation.map_add, Module.End.mem_genEigenspace_zero, Finset.Ioc_disjoint_Ioc, Valuation.ltIdeal_mono, Valuation.IsEquiv.lt_one_iff_lt_one, Set.encard_iUnion_le_of_fintype, ProbabilityTheory.gaussianPDFReal_mul, Even.convexOn_pow, abs_sub_pos, Finset.le_inf_const_le, Set.one_le_encard_iff_nonempty, Int.sign_eq_sign, Ideal.height_le_spanRank_toENat, Archimedean.embedReal_one, BoundedLatticeHom.coe_comp_inf_hom, borel_eq_generateFrom_Iic, MonomialOrder.degLex_single_lt_iff, CategoryTheory.OrthogonalReflection.iteration_map_succ_surjectivity, Set.unbounded_ge_iff, strictConvexOn_iff_div, nhdsLE_sup_nhdsGE, mabs_mabs_div_mabs_le, NNRat.bddAbove_coe, CategoryTheory.Limits.WalkingMultispan.inclusionOfLinearOrder_map, PointedCone.mem_maxTensorProduct, MeasureTheory.aecover_Ico_of_Icc, Finset.isGLB_inf', List.getElem_le_maximum_of_length_pos, lineMap_lt_lineMap_iff_of_lt', Int.padicValuation_le_one, inf_eq_right, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.w₁, ArchimedeanClass.addValuation_apply, MeasureTheory.aecover_Ico_of_Ico, Nucleus.top_apply, Valuation.isEquiv_iff_val_lt_one, Cardinal.natCast_eq_toENat_iff, le_max_iff, IsDedekindDomain.HeightOneSpectrum.embedding_mul_absNorm, nsmul_pos_iff, Set.not_equitableOn, AffineSubspace.not_sOppSide_self, HahnSeries.inv_single, Preorder.instHasBinaryProducts, Valuation.IsUniformizer.val_lt_one, CompositionSeries.le_last_of_mem, ENat.eq_top_iff_forall_ge, MultilinearMap.map_sub_map_piecewise, Cardinal.ofENat_le_nat, Finsupp.Colex.single_lt_iff, ContinuousAt.lowerSemicontinuousAt, segment_subset_closure_openSegment, CategoryTheory.SmallObject.iterationFunctorMapSuccAppArrowIso_hom_right_right_comp, IsNonarchimedean.finset_powerset_image_add, ringHom_monotone, SMulPosReflectLE.toSMulPosStrictMono, Mathlib.Tactic.PNatToNat.coe_lt_coe, monovaryOn_iff_exists_antitoneOn, MonomialOrder.degree_sub_LTerm_lt, HahnModule.instIsTorsionFree, wbtw_pointReflection, Set.instPreservesColimitsOfShapeFunctorToTypesOfIsFilteredOrEmpty, NNRat.cast_lt_natCast, linOrd_dual_comp_forget_to_Lat, instNonemptySeedRatReal, abs_min_sub_min_le_max, countable_setOf_isolated_left, Finset.pluennecke_ruzsa_inequality_nsmul_sub_nsmul_add, Hyperreal.coe_le_coe, MulArchimedeanClass.min_le_mk_div, CategoryTheory.TransfiniteCompositionOfShape.ofComposableArrows_isColimit, LocallyFiniteOrder.orderMonoidWithZeroHom_strictMono, sdiff_eq_self_iff_disjoint', Nimber.toOrdinal_zero, monovaryOn_iff_mul_rearrangement, ENat.mul_le_mul_left_iff, AffineSubspace.setOf_wSameSide_eq_image2, strictMono_inf_prod_sup, NatOrdinal.toOrdinal_zero, BoundedLatticeHomClass.toInfTopHomClass, mul_nonneg_of_three, Module.End.genEigenspace_le_genEigenspace_finrank, MonomialOrder.sPolynomial_lt_of_degree_ne_zero_of_degree_eq, mabs_div_mabs_le_mabs_div, hnot_le_comm, NumberField.FinitePlace.norm_le_one, min_mabs_mabs_le_mabs_min, infIccOrderIsoIccSup_symm_apply_coe, CategoryTheory.Limits.MultispanShape.ofLinearOrder_snd, Order.Iic_succ, isCompl_top_bot, PseudoMetric.finsetSup_apply, add_self_neg_iff, Dense.exists_seq_strictMono_tendsto, Module.End.mem_genEigenspace, Collinear.wbtw_or_wbtw_or_wbtw, Heyting.IsRegular.disjoint_compl_left_iff, Valuation.mem_integer_iff, Set.covBy_iff_exists_insert, Set.disjoint_range_inl_image_inr, FinBddDistLat.dual_map, Nat.cast_mul_floor_div_cancel, Units.mulArchimedean_iff, PowerSeries.coe_pow, Nat.mul_cast_floor_div_cancel, Set.powersetCard.mem_range_ofFinEmbEquiv_symm_iff_mem, nsmul_nonpos_iff, Finsupp.DegLex.monotone_degree, Finset.card_uIcc_prod, le_emultiplicity_iff_replicate_subperm_primeFactorsList, ArchimedeanClass.mk_antitoneOn, partialSups_add_one_eq_sup_disjointed, isOrderBornology_iff_eq_orderBornology, Int.succ_eq_succ, Rat.toNNRat_lt_toNNRat_iff, isPiSystem_Iic, Affine.Simplex.face_points', Finset.codisjoint_inf_left, nhdsGT_sup_nhdsWithin_singleton, HahnSeries.addVal_apply, tendsto_fract_right, Cardinal.toENat_nat, tendsto_floor_left_pure_sub_one, Hyperreal.coe_lt_coe, LinearOrderedCommGroup.Subgroup.exists_generator_lt_one, HahnEmbedding.Partial.exists_domain_eq_top, LaurentSeries.mem_integers_of_powerSeries, cmp_add_right, Topology.RelCWComplex.skeletonLT_monotone, div_lt_one_iff, FiniteMulArchimedeanClass.subgroup_strictAnti, PowerSeries.nat_le_order, WeierstrassCurve.IsGoodReduction.goodReduction, LinearOrderedCommGroupWithZero.discrete_iff_not_denselyOrdered, FinBoolAlg.hasForgetToFinPartOrd_forget₂_obj_str, abs_abs_sub_abs_le, LaurentSeries.instIsFractionRingPowerSeries, LinearOrderedCommGroup.discrete_or_denselyOrdered, SubRootedTree.mem_iff, Finset.dens_union_le, Polynomial.roots_countP_pos_le_signVariations, Valued.isClopen_closedBall, ArchimedeanClass.mk_eq_zero_of_archimedean, Set.pairwise_disjoint_Ico_add_zsmul, PNat.map_subtype_embedding_Ioc, SimplexCategory.toCat_map, Dense.Ioi_eq_biUnion, upperSemicontinuousOn_iff_isClosed_hypograph, Nimber.toOrdinal_toNimber, HahnSeries.cardSupp_hsum_powers_le, posPart_eq_zero, abs_eq_self, tendsto_intCast_atTop_atTop, NonemptyFinLinOrd.mono_iff_injective, lt_neg_self_iff, nhdsLT_sup_nhdsGT, Rat.preimage_cast_Ioc, iUnion_Iio_eq_univ_iff, LinearOrderedCommGroupWithZero.inl_apply, Set.bounded_lt_inter_le, nhdsLT_neBot, ArchimedeanClass.mk_sub_lt_mk_left_iff, WithTop.continuous_untop, CategoryTheory.SmallObject.preservesColimit, Filter.tendsto_abs_atTop_atTop, Orientation.eq_or_eq_neg_of_isEmpty, Valuation.leAddSubgroup_monotone, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquiv_functor, LinearOrderedCommGroupWithZero.inr_apply, Finsupp.Lex.single_le_iff, isPiSystem_Ioo_mem, Orientation.oangle_sign_smul_add_smul_left, Finset.le_inf_sub, Dense.exists_gt, convexOn_zpow, RootPairing.posRootForm_rootFormIn_posDef, Finset.fold_inf_univ, Finpartition.parts_extendOfLE_of_eq, LowerSet.Iic_inf, Module.End.genEigenspace_zero, not_linearIndepOn_finset_iffₒₛ, Polynomial.le_trailingDegree_X_pow, continuousWithinAt_iff_continuous_left_right, Matroid.toENat_cRank_eq, mabs_sup_div_sup_le_mabs, List.minimum_le_coe_iff, measurableSet_bddBelow_range, ValuationSubring.algebraMap_injective, Hyperreal.st_eq_sSup, Nonneg.toNonneg_lt, PosSMulMono.toPosSMulReflectLT, abs_min_le_max_abs_abs, Finset.orderEmbOfFin_mem, Ordinal.toNatOrdinal_toOrdinal, Set.Finite.encard_biUnion_le, Finset.max_prod_le, InfHom.mk_le_mk, ContinuousWithinAt.upperSemicontinuousWithinAt, MvPowerSeries.le_order_pow, MeasureTheory.aecover_Icc_of_Ico, Set.projIic_eq_self, continuousAt_sign_of_ne_zero, AffineSubspace.wOppSide_pointReflection, tendsto_floor_right', InfTopHom.coe_inf, TopCat.Sheaf.interUnionPullbackCone_pt, IsValuativeTopology.mem_nhds_iff, abs_nonneg, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquiv_unitIso, RatFunc.single_inv, PowerSeries.heval_mul, Int.lt_floor_iff, lowerSemicontinuousWithinAt_iff_frequently, MulArchimedeanClass.subgroup_eq_bot, nhds_basis_mabs_div_lt, Valuation.pos_iff, LinearOrderedCommGroup.discrete_iff_not_denselyOrdered, Valued.norm_pos_iff_valuation_pos, wbtw_midpoint, codisjoint_himp_self_right, Nat.ceil_eq_iff, Set.bounded_gt_inter_not_gt, exists_zero_lt, List.maximum_eq_coe_iff, Rat.natCast_lt_cast, HahnSeries.SummableFamily.support_powerSeriesFamily_subset, InfTopHom.top_apply, CategoryTheory.Limits.CompleteLattice.finiteLimitCone_cone_π_app, disjoint_sdiff_self_left, Ordinal.enum_zero_le', HahnSeries.zero_ofSuppBddBelow, smulPosMono_iff_smulPosReflectLT, TopCat.Presheaf.SheafConditionPairwiseIntersections.coneEquivInverseObj_pt, MeasureTheory.IsSetSemiring.Ioc, List.sortedGE_insertionSort, Types.monoOverEquivalenceSet_counitIso, LocallyFiniteOrder.orderAddMonoidEquiv_apply, Right.sign_neg, List.le_maximum_of_length_pos_iff, Set.compl_Ioc, AffineIndependent.convexHull_inter, IsModularLattice.complementedLattice_Iic, List.coe_minimum_of_length_pos, exists_le_add_iff_le_right, LinOrd.comp_apply, NatOrdinal.toOrdinal_eq_one, Finset.Ici_add_one_eq_Ioi, isPiSystem_image_Ici, ArchimedeanClass.FiniteElement.mk_natCast, Odd.geom_sum_pos, abs_le', LinOrd.coe_comp, IsDedekindDomain.HeightOneSpectrum.valuation_le_one, AddMonoidAlgebra.infDegree_withTop_some_comp, BotHom.coe_inf, ENat.one_lt_card, ENat.self_le_mul_right, LaurentPolynomial.degree_T_le, ENat.add_le_add_iff_left, PosSMulMono.toPosSMulReflectLE, Order.Ideal.IsPrime.isMaximal, Filter.Tendsto.finset_inf_nhds, tendsto_pow_atTop_nhds_zero_iff, Set.Ioi_inter_Ioi, Dense.borel_eq_generateFrom_Ioc_mem, ENat.mul_right_strictMono, CategoryTheory.SmallObject.iterationFunctorObjObjRightIso_ιIteration_app_right_assoc, instIsPrincipalIdealRingSubtypeMemSubringIntegerWithZeroMultiplicativeIntValuation, CompositionSeries.head_le, Finset.max'_lt_iff, comap_coe_nhdsGT_eq_atBot_iff, Finset.listMap_orderEmbOfFin_finRange, FinBoolAlg.dual_map, strictConvex_Ioi, Ordinal.familyOfBFamily_enum, Polynomial.div_tendsto_atTop_zero_iff_degree_lt, Valued.toNormedField.norm_lt_one_iff, le_min_iff, IsSimpleOrder.instIsAtomic, CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.ofComposableArrows_isoBot_hom, Finset.inf_Ici, OrderIso.asBoolAlgAsBoolRing_symm_apply, PrimeSpectrum.isIdempotentElemEquivClopens_mul, UpperSet.total_le, instLawfulOrderInf_mathlib, Nat.add_one_le_ceil_iff, HahnSeries.mem_orderTopSubOnePos_iff, Continuous.exists_forall_ge_of_hasCompactMulSupport, denselyOrdered_iff_denselyOrdered_units_and_nontrivial_units, Measurable.nat_ceil, SuccOrder.nhdsLT_eq_nhdsNE, CategoryTheory.TransfiniteCompositionOfShape.ici_incl, IsDedekindDomain.HeightOneSpectrum.valuationOfNeZeroToFun_eq, Order.sub_one_lt_iff, ZSpan.mem_fundamentalDomain, exists_succ_iterate_or, MeasureTheory.aecover_Ioo_of_Icc, Set.Iio_subset_Iic_union_Ioo, Set.Ici_eq_singleton_iff_isTop, Real.log_of_ne_zero, Set.disjoint_range_iff, ArchimedeanClass.mk_map_of_archimedean', Module.End.genEigenspace_le_smul, CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.mem_map, Order.lt_one_iff_nonpos, inf_himp_le, Subgroup.isLeast_of_closure_iff_eq_mabs, MvPowerSeries.min_order_le_add, Nonneg.orderedSub, AddCircle.liftIco_eq_lift_Icc, PNat.card_fintype_Icc, right_eq_inf, MeasureTheory.ae_restrict_uIoc_eq, Finset.Nonempty.dens_pos, succ_max, LaurentSeries.coeff_coe_powerSeries, FiniteArchimedeanClass.addSubgroup_eq_bot, WithZero.min_le_iff, mabs_div_le_iff, WithZeroTopology.nhds_eq_update, ValuativeRel.uniformizer_lt_one, nhdsGT_neBot, archimedean_iff_int_le, countable_setOf_covBy_right, PowerSeries.le_order_prod, ValuativeRel.uniformizer_pos, HahnEmbedding.Partial.exists_isMax, sup_sdiff_injOn, Archimedean.mkRat_mem_ratLt, CauSeq.bounded, NNRat.cast_le_ofNat, exists_uIoo_isExtrOn_uIcc, Ordinal.type_toType, le_add_iff_lt_right_or_exists_le, Pi.mulSupport_mulSingle_disjoint, LinearOrderedAddCommGroup.isAddCyclic_iff_nonempty_equiv_int, HahnSeries.orderTop_embDomain, Valuation.IsRankOneDiscrete.exists_generator_lt_one, Set.prod_subset_compl_diagonal_iff_disjoint, SignType.neg_iff, Ordinal.nmul_eq_mul, Set.Finite.convexHull_eq, BoundedGENhdsClass.of_closedIicTopology, Archimedean.embedRealFun_strictMono, hnot_le_iff_codisjoint_right, HahnSeries.cardSupp_inv_le, MeasureTheory.Measure.measure_Iio_pos, Hyperreal.stdPart_epsilon, Set.IsPWO.of_linearOrder, Profinite.NobelingProof.Products.instWellFoundedLT, mabs_div_le_one, Sublattice.prodEquiv_symm_apply, ZNum.isStrictOrderedRing, MulArchimedeanClass.mk_div_lt_mk_right_iff, Matrix.eRank_submatrix_le, Ne.inf_lt_or_inf_lt, Finset.dens_le_dens, BooleanAlgebra.eq_iff_atom_le_iff, DFinsupp.Lex.total_le, inf_eq_minDefault, Complex.sum_div_factorial_le, Set.empty_disjoint, Hyperreal.ofSeq_lt_ofSeq, Module.End.genEigenspace_restrict, ContinuousAt.upperSemicontinuousAt, orderTopology_of_ordConnected, finSumEquivOfFinset_inl, exists_one_lt', CategoryTheory.TransfiniteCompositionOfShape.ofOrderIso_isColimit, BddLat.dual_map, exists_rat_lt, CategoryTheory.SimplicialThickening.functor_obj_as, Set.Ioo_subset_uIoo', Set.Ioc_sub_one_left_eq_Icc, Archimedean.of_locallyFiniteOrder, VertexOperator.coeff_eq_ncoeff, FunctionField.inftyValuation_apply, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.w₂, IsCompact.exists_isMaxOn, PrimeSpectrum.coe_isIdempotentElemEquivClopens_apply, MulArchimedeanClass.mulArchimedean_of_mk_eq_mk, Order.Ioc_pred_left, isClosed_Ioo_iff, MulArchimedeanOrder.le_def, Fintype.not_linearIndependent_iffₒₛ, nonneg_add_self_iff, zpow_lt_zpow_iff_left, sub_le_sub_flip, Odd.pow_nonpos_iff, Polynomial.cyclotomic_pos, le_bihimp_iff, Dense.borel_eq_generateFrom_Icc_mem, Finset.Iic_diff_Ioc, Set.disjoint_union_left, ValuativeRel.instMulArchimedeanValueGroupWithZeroOfIsRankLeOne, ArchimedeanClass.ball_antitone, Set.Ioo_inter_Ioo, Finset.Ico_succ_succ_eq_Ioc, Int.Ico_filter_dvd_eq, starConvex_iff_div, nhdsSet_Ioi, pow_inf_le, Mathlib.Meta.NormNum.IsNat.natFloor, Lattice.isStronglyCoatomic, Left.sign_neg, Affine.Simplex.sOppSide_affineSpan_faceOpposite_iff, measurableSet_bddAbove_range, Finset.le_max, HahnSeries.min_orderTop_le_orderTop_add, instWellFoundedGTWithZeroMultiplicativeIntLeOne, Set.Ico.disjoint_iff, Profinite.NobelingProof.Products.eval_πs_image, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.w₁_assoc, Finset.ofDual_sup, PNat.one_le_find, LaurentSeries.powerSeriesPart_zero, Finset.sum_Icc_succ_eq_add_endpoints, Valuation.val_le_one_iff, Finset.sum_le_sum_Ioc, isCoatomic_of_isAtomic_of_complementedLattice_of_isModular, Filter.tendsto_mul_const_atBot_iff, HahnSeries.leadingCoeff_nonpos_iff, StieltjesFunction.right_continuous, Odd.pow_le_pow, Set.instOrdConnectedOrdConnectedComponent, LaurentSeries.exists_ratFunc_eq_v, HahnSeries.SummableFamily.powerSeriesFamily_smul, Finpartition.exists_le_of_le, Cardinal.natCast_le_toENat_iff, Polynomial.trailingDegree_one_le, Set.Ioi_subset_Ioc_union_Ici, min_bot_right, PrimeSpectrum.isIdempotentElemEquivClopens_symm_compl, Int.card_Ioo_of_lt, Valued.toNormedField.one_le_norm_iff, Pi.Lex.isStrictOrder, Sublattice.mem_map_equiv, EReal.sign_mul_inv_abs', countable_image_gt_image_Iio, Stream'.Seq.lt_length'_iff, Set.Finite.encard_strictMonoOn, le_iff_forall_one_lt_le_mul, Lattice.BicartSq.le₃₄, ENat.add_lt_add_iff_right, wellFoundedLT_toType, LinearPMap.domain_mono, one_lt_ltOnePart_iff, IsModularLattice.complementedLattice_Icc, openSegment_subset_union, Nat.cast_inv_le_one, Finset.divConst_le_inv_dens, multiplicity_le_emultiplicity, ZMod.valMinAbs_spec, Hyperreal.gt_of_neg_of_infinitesimal, LinearOrderedCommGroupWithZero.wellFoundedOn_setOf_le_lt_iff_nonempty_discrete_of_ne_zero, Int.add_one_le_ceil_iff, Nat.lt_floor_add_one, Finsupp.Lex.wellFoundedLT_of_finite, OrderIso.sumLexIioIci_apply_inr, Rat.comap_cast_atTop, OrderIsoClass.toInfTopHomClass, MonomialOrder.degree_sPolynomial_lt_sup_degree, Padic.isDenseInducing_cast_withVal, left_lt_lineMap_iff_pos, add_lt_add_iff_right_of_ne_top, Set.encard_le_one_iff_subsingleton, HahnEmbedding.Seed.domain_baseEmbedding, NNRat.cast_lt_ofNat, Nat.one_div_lt_one_div, Booleanisation.comp_le_comp, wellFounded_lt_exact_sequence, Set.monotone_powerset, abs_le_iff_mul_self_le, PNat.mod_le, Continuous.bddAbove_range_of_hasCompactSupport, ArchimedeanClass.mem_closedBallAddSubgroup_iff, Finset.disjiUnion_Iic_disjointed, sign_eq_neg_one_iff, FiniteArchimedeanClass.withTopOrderIso_apply_coe, CategoryTheory.SimplicialThickening.functor_comp, LinearOrderedField.mem_cutMap_iff, Module.End.pos_finrank_genEigenspace_of_hasEigenvalue, Set.Iio_injective, Finset.orderEmbOfFin_compl_singleton_apply, ENat.lt_coe_add_one_iff, Dense.borel_eq_generateFrom_Icc_mem_aux, Dense.topology_eq_generateFrom, Asymptotics.isLittleO_pow_pow_atTop_of_lt, DFinsupp.Colex.isStrictOrder, CircleDeg1Lift.translationNumber_mono, Metric.isBounded_of_abs_lt, Finset.mulConst_le_divConst_sq, le_sdiff_sup, ENat.card_le_one, negPart_eq_ite_lt, Polynomial.le_trailingDegree_X, Module.length_eq_rank, zsmul_left_mono, Coheyting.boundary_bot, WithTop.nhds_coe, CategoryTheory.Limits.CompleteLattice.finite_product_eq_finset_inf, FiniteMulArchimedeanClass.coe_congrOrderIso_apply, Nat.image_cast_int_Ico, SetTheory.PGame.nim_add_nim_equiv, intermediate_value_Ioc, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.w₂_assoc, NNRat.preimage_cast_Iio, CauSeq.const_pos, PseudoMetric.nonneg, Ioo_subset_Iotop, intermediate_value_Ico, MonomialOrder.degree_sub_leadingTerm_lt_iff, NNRat.ofNat_lt_cast, abs_inf_sub_inf_le_abs, Set.pairwise_disjoint_Ioo_intCast, sign_eq_one_iff, exists_le_add_iff_le_left, Set.Ioi_injective, Set.unbounded_lt_inter_lt, Subfield.toIsStrictOrderedRing, ArchimedeanClass.FiniteResidueField.instIsOrderedRing, Cardinal.toENat_lt_top, MonomialOrder.degree_sub_leadingTerm_le, Coheyting.boundary_le_boundary_sup_sup_boundary_inf_right, Valuation.exists_div_eq_of_surjective, le_abs', Valuation.Integers.maximalIdeal_pow_eq_setOf_le_v_algebraMap_pow, Submonoid.mem_closure_image_one_lt_iff, compl_bot, IsDedekindDomain.HeightOneSpectrum.intValuation_apply, Nucleus.le_apply', nhdsLE_basis, isAtom_compl, Int.preimage_Ico, le_add_iff_lt_left_or_exists_le, HahnSeries.le_orderTop_iff_forall, SetLike.coe_mono, MvPowerSeries.le_order_pow_of_constantCoeff_eq_zero, ArchimedeanClass.mk_inv, Valuation.Integers.isPrincipalIdealRing_iff_not_denselyOrdered_mrange, NucleusClass.le_apply, bot_inf_eq, Complementeds.disjoint_coe, Finsupp.DegLex.single_strictAnti, List.trop_minimum, Set.Icc_subset_Icc_union_Icc, Finset.lt_max'_of_mem_erase_max', Ordinal.toNatOrdinal_max, upperSemicontinuousWithinAt_iff_frequently, Set.IciExtend_apply, Set.uIoc_eq_union, not_infIrred_top, Set.IicExtend_self, convexHull_range_eq_exists_affineCombination, mabs_le_one, Matrix.isPrimitive_iff, Real.arcsin_projIcc, wbtw_iff_sameRay_vsub, NonemptyFinLinOrd.Iso.mk_hom, LaurentSeries.valuation_X_pow, LaurentPolynomial.degree_C_le, Set.ordConnected_uIoc, Order.le_succ_iff_eq_or_le, Nimber.toOrdinal_eq_zero, countable_setOf_isolated_right_within, tendsto_mabs_nhdsNE_one, lt_max_iff, HahnSeries.le_order_smul, Finset.sum_mul_sq_le_sq_mul_sq, IsDedekindDomain.HeightOneSpectrum.intValuation_lt_one_iff_mem, DistribLattice.mem_ideal_sup_principal, Set.monotone_projIci, Int.padicValuation_eq_zero_iff, LaurentSeries.hasseDeriv_single, Valuation.Integers.dvd_iff_le, List.maximum_concat, Cardinal.toENat_congr, CategoryTheory.Limits.instIsWellOrderContinuousCompOfPreservesWellOrderContinuousOfShape, OrderMonoidWithZeroHom.mul_apply, ENat.range_natCast, Order.Ideal.isPrime_iff_mem_or_mem, Finset.sum_min_le, Polynomial.eventually_no_roots, NumberField.FinitePlace.norm_def, lt_min_iff, FiniteArchimedeanClass.mem_closedBall_iff, antivary_iff_exists_antitone_monotone, Even.pow_pos_iff, Int.Ioc_filter_dvd_card, discreteTopology_iff_orderTopology_of_pred_succ, toZ_le_iff, Valuation.one_rel_iff, MulArchimedeanClass.orderHom_top, Valuation.le_one_of_subsingleton, NonnegSpectrumClass.iff_spectrum_nonneg, Set.Intersecting.bot_notMem, Finset.codisjoint_inf_right, mabs_cases, Nat.preimage_Ico, GenContFract.abs_sub_convs_le, CategoryTheory.Functor.WellOrderInductionData.Extension.zero_val, OrderEmbedding.birkhoffFinset_sup, NNRat.castOrderEmbedding_apply, continuousAt_iff_lower_upperSemicontinuousAt, Filter.Eventually.intCast_atTop, ArchimedeanClass.closedBall_top, PosSMulStrictMono.toPosSMulReflectLT, ENat.one_le_iff_ne_zero, Finsupp.Colex.single_strictMono, NonarchimedeanHomClass.map_add_le_max, PNat.addLeftStrictMono, countable_image_lt_image_Iio, InfPrime.inf_le, mem_segment_sub_add, monovary_iff_exists_monotone, Pi.toColex_update_lt_self_iff, Order.Ideal.IsPrime.mem_or_compl_mem, WithZero.withZeroUnitsEquiv_strictMono, LinearOrderedAddCommGroupWithTop.sub_lt_sub_iff_left_of_ne_top, hahnEmbedding_isOrderedAddMonoid, List.maximum_append, ENat.lt_one_iff_eq_zero, Matroid.toENat_cRk_eq, HasCountableSeparatingOn.range_Iic, LinearOrderedCommGroupWithZero.discrete_or_denselyOrdered, IsSimpleOrder.instIsCoatomic, GenContFract.IntFractPair.nth_stream_fr_nonneg, Function.disjoint_support_iff, Finset.isLeast_min', bihimp_eq_bot, isComplemented_top, List.argmin_cons, Tuple.monotone_sort, Set.Ioi_ssubset_Ioi_iff, Set.encard_le_encard_diff_add_encard, ProbabilityTheory.Kernel.partialTraj_eq_prod, Finpartition.parts_inf, Icc_subset_segment, Finset.mem_uIcc, LinearOrderedAddCommGroup.to_noMinOrder, Filter.tendsto_const_mul_atTop_iff, PNat.le_find_iff, contMDiffOn_projIcc, Mathlib.Meta.NormNum.isNNRat_lt_true, Cardinal.toENat_eq_one, Order.isSuccPrelimitRecOn_succ, Finset.inf'_le, Ordinal.toNatOrdinal_symm_eq, NonemptyFinLinOrd.hom_id, OrderIso.isCompl_iff, MonomialOrder.iocam, posPart_eq_ite_lt, Finset.max_abv_sum_one_le, mem_nhdsLE_iff_exists_Ioc_subset, ENat.not_lt_zero, MonomialOrder.degree_sub_LTerm_le, Rat.padicValuation_le_one_iff, Finset.Ico_succ_right_eq_Icc, codisjoint_hnot_hnot_right_iff, HahnSeries.leadingCoeff_abs, left_le_lineMap_iff_nonneg, exists_lt_add_iff_lt_right, MonomialOrder.lex_le_iff_of_unique, lineMap_lt_left_iff_neg, LinearOrderedCommGroup.isCyclic_iff_nonempty_equiv_int, Measurable.lt, tendsto_ratCast_atTop_iff, Set.disjoint_iff, ArchimedeanClass.stdPart_eq_sSup, OrderEmbedding.mulLeft_apply, max_eq_iff, IsDedekindDomain.HeightOneSpectrum.notMem_adicCompletionIntegers, Set.one_mem_inv_mul_iff, bot_eq_zero', tendsto_smul_comp_nat_floor_of_tendsto_nsmul, Hyperreal.gt_of_tendsto_zero_of_neg, Cardinal.mk_Iio_ord_toType, Hyperreal.epsilon_pos, PosSMulReflectLE.toPosSMulStrictMono, LaurentPolynomial.degree_C_mul_T_le, Multiset.prod_min_le, Set.IciExtend_coe, LinearOrderedCommGroup.isCyclic_iff_not_denselyOrdered, instDenselyOrderedUnits, upperSemicontinuousOn_iff_preimage_Ici, Hyperreal.archimedeanClassMk_epsilon_pos, Finset.dens_pos, Set.mem_uIcc, CategoryTheory.SemilatticeInf.tensorObj, Profinite.NobelingProof.Products.head_lt_ord_of_isGood, disjoint_sdiff_sdiff, Finpartition.avoid_parts_val, Finset.nonneg_subConst, NNRat.cast_lt_zero, CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.mem_incl_app, Set.Nonempty.not_disjoint, WithBot.orderIsoPUnitSumLex_bot, Ordinal.sup_typein_succ, exists_pos_right_iff_sameRay_and_ne_zero, Hyperreal.tendsto_atTop_iff, IsAddIndecomposable.baseOf_subset_pos, Set.powersetCard.ofFinEmbEquiv_apply, LinearOrderedCommMonoidWithZero.toZeroLeOneClass, AlgebraicGeometry.IsOpenImmersion.map_ΓIso_inv_apply, Set.notMem_uIoc, Topology.IsUpper.tendsto_nhds_iff_lt, Mathlib.Tactic.Order.ToInt.toInt_lt_toInt, LaurentSeries.powerSeriesPart_eq_zero, LinearOrderedField.toPosSMulStrictMono_rat, ENat.coe_lt_top, MonomialOrder.degree_sPolynomial, Polynomial.isBigO_atTop_of_degree_le, one_le_oneLePart, Nat.preimage_ceil_zero, nhdsGE_basis_Ico, Ordinal.nadd_eq_add, HahnSeries.BddBelow_zero, Continuous.bddAbove_range_of_hasCompactMulSupport, Cardinal.nat_lt_ofENat, polynomialFunctions.comap_compRightAlgHom_iccHomeoI, Polynomial.valuation_X_eq_neg_one, hahnEmbedding_isOrderedModule, Ordinal.one_toType_eq, List.Perm.minimum_eq, LinearOrderedAddCommGroup.tendsto_nhds, Nat.ceil_add_le, AbsoluteValue.eq_trivial_of_isEquiv_trivial, closure_Ioc, Finset.Ico_add_one_add_one_eq_Ioc, Set.Ioc_inter_Iic, Set.Iio_inter_Ioo, restrict₂_comp_IicProdIoc, Finset.isLUB_iff_isGreatest, ProbabilityTheory.Kernel.traj_eq_prod, MonomialOrder.degree_X_le_single, NatOrdinal.lt_wf, PNat.lt_succ_self, WithBot.add_one_le_iff, tendsto_zero_geometric_tsum_pnat, IsNonarchimedean.add_pow_le, Int.fract_eq_iff, Nucleus.le_apply, closure_Ioi, Set.disjoint_univ_pi, convexOn_iff_slope_mono_adjacent, ArchimedeanClass.mk_zpow, lt_tsub_iff_left, Lattice.BicartSq.le₁₃, Nat.image_cast_int_Iio, Set.ordConnected_uIcc, mem_nhdsGE_iff_exists_Icc_subset, Affine.Simplex.sOppSide_affineSpan_faceOpposite_point_left_iff, mabs_eq_self, MeasureTheory.AEStronglyMeasurable.aestronglyMeasurable_uIoc_iff, Int.instIsOrderedAddMonoid, add_le_add_iff_right_of_ne_top, closure_Ioo, MvPowerSeries.le_order_map, atBot_le_cocompact, MulArchimedean.of_locallyFiniteOrder, Set.pairwiseDisjoint_singleton_iff_injOn, Hyperreal.coeRingHom_toFun, Even.zpow_pos, Nat.floor_pos, StieltjesFunction.right_continuous', sdiff_triangle, leOnePart_anti, HahnEmbedding.Partial.toOrderAddMonoidHom_injective, monovaryOn_iff_forall_mul_nonneg

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
dual_dual 📖	mathematical	—	OrderDual.instSemilatticeInf OrderDual OrderDual.instSemilatticeSup	—	ext
ext 📖	—	Preorder.toLE PartialOrder.toPreorder toPartialOrder	—	—	PartialOrder.ext ext_inf
ext_inf 📖	mathematical	Preorder.toLE PartialOrder.toPreorder toPartialOrder	toMin	—	eq_of_forall_le_iff le_inf_iff
inf_le_left 📖	mathematical	—	Preorder.toLE PartialOrder.toPreorder toPartialOrder inf	—	—
inf_le_right 📖	mathematical	—	Preorder.toLE PartialOrder.toPreorder toPartialOrder inf	—	—
le_inf 📖	mathematical	Preorder.toLE PartialOrder.toPreorder toPartialOrder	inf	—	—

SemilatticeSup

Definitions

Name	Category	Theorems
mk' 📖	CompOp	1 math math: semilatticeSup_mk'_partialOrder_eq_semilatticeInf_mk'_partialOrder
sup 📖	CompOp	3 math math: le_sup_left, sup_le, le_sup_right
toMax 📖	CompOp	1902 math math: max_choice, max_sub_min_eq_abs', NonUnitalSubalgebra.coe_starClosure, IsLocalMaxOn.max, LatticeHom.toFun_eq_coe, MeasureTheory.Measure.MeasureDense.approx, iSup_insert, Submodule.finrank_sup_add_finrank_inf_eq, sub_sup, CategoryTheory.extensive_regular_generate_coherent, IsLUB.union, Finset.disjSups_subset_iff, IsWeakUpperModularLattice.covBy_sup_of_inf_covBy_covBy, Multiset.sup_ndinsert, csSup_pair, map_symmDiff', Filter.Tendsto.max_left, LinearMap.quotientInfEquivSupQuotient_symm_apply_eq_zero_iff, WithTop.coe_max, MonomialOrder.sPolynomial_leadingTerm_mul', Ideal.radical_sup, iSup_pair, Pi.symmDiff_def, sdiff_sup_cancel, AffineSubspace.direction_sup_eq_sup_direction, DFinsupp.toMultiset_sup, Module.End.isSemisimple_restrict_iff, Set.inter_symmDiff_distrib_left, continuous_sup_rng_right, sup_div_inf_eq_mabs_div, Nat.iSup_lt_succ', Algebra.lift_cardinalMk_adjoin_le, DoubleQuot.liftSupQuotQuotMkₐ_toRingHom, OrderIsoClass.toSupHomClass, Measurable.max, SymmetricAlgebra.rank_eq, Codisjoint.sup_left, Finset.max_union, Subgroup.sup_eq_closure_mul, compl_symmDiff_self, Mathlib.Tactic.Order.ToInt.toInt_sup_toInt_eq_toInt, TopCat.Sheaf.interUnionPullbackCone_snd, instCommutativeMax_mathlib, Set.smul_set_symmDiff, Cardinal.powerlt_max, Subgroup.exists_mem_sup, max_div_div_right, Sublattice.sup_mem, min_sub_sub_left, LinearMap.map_le_map_iff, IsCompl.sup_eq_top, LatticeCon.r_inf_sup_iff, biSup_le_eq_sup, AddQuantale.add_sup_distrib, sup_himp_self_right, MeasureTheory.Integrable.sup, AlgebraicGeometry.Scheme.IdealSheafData.radical_sup, Monotone.sup, add_eq_sup, ofBoolRing_sub, MonomialOrder.degree_add_of_ne, sup_le_sup_left, posPart_max, BiheytingHom.map_sdiff', Ordinal.max_zero_left, AddSubgroup.map_eq_map_iff, partialSups_succ', Multiset.Ico_sub_Ico_left, IntermediateField.extendScalars_sup, Cardinal.mk_list_eq_max_mk_aleph0, add_max, Finset.le_fold_max, AddSubgroup.exists_mem_sup, Set.mem_sups, AddSubmonoid.sup_eq_closure, Cardinal.mk_list_le_max, Equiv.Perm.support_prod_of_pairwise_disjoint, inf_right_le_sup_left, CategoryTheory.ObjectProperty.HasCardinalLT.sup, Subalgebra.LinearDisjoint.sup_free_of_free, PseudoMetric.IsUltra.sup, NonUnitalStarAlgebra.mem_sup_right, continuous_sup_dom, Monoid.Coprod.range_inl_sup_range_inr, List.getD_max?_eq_unbotD_maximum, Multiset.sup_eq_union, SupHom.bot_apply, StarSubalgebra.mem_sup_left, MeasureTheory.measureReal_symmDiff_le, symmDiff_eq', Finset.inf'_sup_inf', CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.D₁_W, Cardinal.mk_multiset_of_nonempty, Submodule.mem_sup', iSup_bool_eq, MeasureTheory.NullMeasurableSet.exists_isOpen_symmDiff_lt, sup_left_right_swap, ContinuousMap.sup_apply, List.maximum_cons, MeasureTheory.exists_measure_symmDiff_lt_of_generateFrom_isSetRing, Set.Ioc_union_Ioc', sup_inf_inf_compl, List.foldr_max_of_ne_nil, OrderHom.le_map_sup_fixedPoints, mabs_le_max_mabs_mabs, instCommutativeMax, MeasureTheory.MemLp.sup, iSup_split, sdiff_le_iff', IsModularLattice.sup_inf_le_assoc_of_le, Sublattice.map_equiv_eq_comap_symm, OrderEmbedding.le_map_sup, TopologicalSpace.Opens.mem_sup, LinearPMap.domain_supSpanSingleton, inf_symmDiff_distrib_right, CompleteBooleanAlgebra.himp_eq, sup_compl_le_himp, Multiset.sup_cons, Subgroup.map_sup, Subalgebra.comap_map_eq, Function.support_max, Subalgebra.finrank_sup_eq_finrank_right_mul_finrank_of_free, not_supPrime, List.max_prod_le, Finset.Icc_min_max, abs_le_max_abs_abs, Set.image_symmDiff, Set.Ioc_union_Ioc_right, sdiff_symmDiff, CategoryTheory.Subfunctor.Subpresheaf.max_obj, AddCon.sup_def, Submodule.isOrtho_sup_right, Subsemiring.map_sup, Submonoid.comap_sup_map_of_injective, ClosedSubmodule.toSubmodule_sup, Submodule.fst_sup_snd, IsMinFilter.sup, two_nsmul_sup_eq_add_add_abs_sub, GaloisInsertion.l_sup_u, NonUnitalAlgebra.mem_sup_left, FirstOrder.Language.Substructure.map_sup, sup_eq_sup_iff_left, codisjoint_bihimp_sup, Pi.symmDiff_apply, DualNumber.range_lift, bihimp_bihimp_sup, iInf_sup_iInf, Subgroup.map_eq_map_iff, max_neg_neg, BoundedLatticeHom.coe_comp_sup_hom', WithTop.coe_sup, Cardinal.mul_le_max_of_aleph0_le_right, compl_inf, sup_sdiff_right_self, Set.Icc_min_max, Finset.sup_eq_union', max_le_max_left, AddSubgroup.mem_sup_left, sup_le_sup, symmDiff_compl_self, SupHom.withBot_id, IsUpperModularLattice.covBy_sup_of_inf_covBy, Cardinal.sum_pow_le_max_aleph0, Con.sup_eq_conGen, FiniteGaloisIntermediateField.instIsGaloisSubtypeMemIntermediateFieldMax, MonotoneOn.max, AddSubmonoid.op_sup, MonoidAlgebra.cardinalMk_of_infinite, DoubleQuot.coe_quotLeftToQuotSupₐ, inf_himp_bihimp, IsModularLattice.exists_disjoint_and_sup_eq, Set.Iio_union_Ioo, AddSubgroup.comap_map_eq, Set.sup_mem_sups, Finset.symmDiff_eq_union_iff, sdiff_sdiff_sup_sdiff', max_add_add_le_max_add_max, Measurable.sup_of_right, Finset.sup_insert, Filter.bliminf_sup_le_and, AddSubgroup.normal_add, Subsemiring.op_sup, MeasureTheory.measure_symmDiff_eq_top, Cardinal.mul_eq_max_of_aleph0_le_right, AEMeasurable.max, MonomialOrder.degree_sub_le, Ne.lt_sup_or_lt_sup, cbiSup_eq_of_not_forall, symmDiff_symmDiff_self', Finset.Colex.toColex_lt_toColex_iff_max'_mem, instAssociativeMax, lt_max_of_lt_left, Set.toFinset_symmDiff, instAssociativeMax_mathlib, sup_iSup, LieSubalgebra.span_union, symmDiff_top, Set.coe_projIcc, Subalgebra.rank_sup_eq_rank_left_mul_rank_of_free, sup_inf_inf_sdiff, Cardinal.mk_finsupp_lift_of_infinite, sup_le_sup_right, sup_biInf_le_biInf_sup, isLeast_sdiff, max_lt_max_left_iff, Submodule.coe_sup, Set.singleton_sups_singleton, Finset.disjSups_singleton, ExpGrowth.expGrowthSup_add, TensorProduct.quotientTensorQuotientEquiv_symm_apply_mk_tmul, Subfield.map_sup, AddSubgroup.add_normal, Disjoint.sup_sdiff_cancel_left, AddSubgroup.mem_sup_of_normal_left, hnot_symmDiff_self, Order.Ideal.coe_sup, Set.indicator_symmDiff, Subgroup.mul_normal, SupHom.coe_bot, Set.Ioo_inter_Ioi, min_le_max_of_mul_le_mul, IsCompl.symmDiff_eq_top, Finset.Colex.le_iff_max'_mem, SemilatInfCat_dual_comp_forget_to_partOrd, AlgebraicGeometry.Scheme.IdealSheafData.support_mul, symmDiff_right_comm, IsCompl.le_sup_right_iff_inf_left_le, Mathlib.Tactic.Bound.lt_max_of_lt_left_or_lt_right, List.le_max_of_le', IsGreatest.insert, inf_eq_sup, max_inv_one, AddMonoidAlgebra.supDegree_add_le, Finset.inf_sup_distrib_right, partialSups_add_one', sup_le_inf, ofDual_min, Finset.max_sum_le, Subfield.cardinalMk_closure_le_max, Subgroup.coe_mul_of_left_le_normalizer_right, Cardinal.mul_eq_left_iff, NumberField.isTotallyReal_sup, Algebra.map_sup, le_sup_left, sup_sup_sup_comm, AddSubmonoid.sup_mul, Submonoid.map_sup_comap_of_surjective, sInf_sup_le_iInf_sup, TopCat.Sheaf.interUnionPullbackCone_fst, Set.symmDiff_def, Disjoint.le_symmDiff_sup_symmDiff_right, Submonoid.mem_sup, irreducible_pow_sup_of_ge, right_eq_sup, LowerAdjoint.closure_sup_closure_right, isOpen_sup, lt_sup_of_lt_right, Sylow.normalizer_sup_eq_top', SemilatSupCat.Iso.mk_inv_toFun, NonUnitalAlgebra.mem_sup_right, Subalgebra.unop_sup, inf_left_le_sup_left, symmDiff_top', LinearMap.range_domRestrict_eq_range_iff, sSup_insert, TopologicalSpace.Closeds.instContinuousSup, Submodule.comap_map_sup_of_comap_le, HeytAlg.Iso.mk_inv, NNRat.coe_max, LinearMap.span_singleton_sup_orthogonal_eq_top, Projectivization.Subspace.span_sup, MeasureTheory.measureReal_symmDiff_eq, Left.min_le_max_of_add_le_add, symmDiff_of_ge, max_inv_inv', Algebraic.cardinalMk_le_max, FirstOrder.Language.Substructure.map_sup_comap_of_surjective, Ideal.gcd_eq_sup, max_bot_left, UniformContinuous.sup_closeds, bihimp_himp_left, symmDiff_left_inj, NonUnitalSubsemiring.closure_union, negPart_max, disjoint_symmDiff_inf, inf_sup_le, oneLePart_max, Submonoid.mrange_inl_sup_mrange_inr, Finset.Ico_diff_Ico_left, sSup_union, AddSubsemigroup.map_sup, DistribLattice.le_sup_inf, top_symmDiff, Submonoid.prod_bot_sup_bot_prod, symmDiff_assoc, max_mul_min, Ideal.sup_eq_top_iff_isCoprime, AddSubmonoid.smul_sup, Ideal.smul_sup, Nimber.toOrdinal_max, IsModularLattice.exists_inf_eq_and_sup_eq, abs_eq_max_neg, Algebra.IsAlgebraic.cardinalMk_le_max, hasCardinalLT_subtype_max, LeftOrdContinuous.map_sup, FirstOrder.Language.Substructure.comap_sup_map_of_injective, Subgroup.normal_subgroupOf_sup_of_le_normalizer, Tropical.untrop_max, partialSups_add_one, sdiff_sup, Submodule.neg_sup, IsLocalMin.sup, Submodule.sup_eq_range, Subring.op_sup, sub_inf, Submodule.sub_mem_sup, sup_eq_mul_oneLePart_div, Subsemigroup.mul_mem_sup, Filter.EventuallyLE.sup_le, Algebra.adjoin_union, sdiff_symmDiff', AddMonoid.Coprod.mrange_lift, biSup_symmDiff_biSup_le, himp_eq, Ideal.mem_sup_left, Monotone.le_map_sup, max_mul_of_nonneg, Valuation.map_add_of_distinct_val, RingCon.sup_def, CategoryTheory.Subfunctor.max_obj, lipschitzWith_sup_right, Set.Ioc_disjoint_Ioc, CompletelyDistribLattice.sdiff_le_iff, le_hnot_inf_hnot, Valuation.map_add, ite_le_sup, AddSubgroup.relIndex_map_map, Ideal.map_sup_mem_minimalPrimes_of_map_quotientMk_mem_minimalPrimes, Finset.Colex.toColex_le_toColex_iff_max'_mem, lt_max_of_sq_lt_mul, IsMaxOn.sup, Finset.Ico_union_Ico', codisjoint_assoc, openSegment_eq_Ioo', AffineSubspace.direction_affineSpan_insert, MonomialOrder.degree_add_le, AffineSubspace.vectorSpan_union_of_mem_of_mem, PseudoMetric.IsUltra.bot, Finset.smul_finset_symmDiff, Set.mem_symmDiff, beattySeq'_symmDiff_beattySeq_pos, BddLat.forget_semilatSup_partOrd_eq_forget_bddOrd_partOrd, IsAddFoelner.tendsto_meas_vadd_symmDiff_vadd, min_le_max, Monoid.Coprod.mrange_eq, CauSeq.coe_sup, IdemSemiring.add_eq_sup, BooleanSubalgebra.sup_mem, max_div_min_eq_mabs, MonoidHom.noncommCoprod_range, MeasureTheory.abs_measureReal_sub_le_measureReal_symmDiff', instIdempotentOpMax_mathlib, compl_symmDiff, fn_min_add_fn_max, Order.Coframe.MinimalAxioms.iInf_sup_eq, Ordinal.card_omega0_opow, Codisjoint.top_le, List.max_le_of_forall_le, IsCoatom.sup_eq_top_of_ne, Submodule.smul_sup', HahnEmbedding.ArchimedeanStrata.ball_sup_stratum_eq, compl_sup_compl_le, min_lt_max_of_add_lt_add, sup_strictMonoOn_Icc_inf, DoubleQuot.quotQuotToQuotSupₐ_toRingHom, disjoint_sup_right, ofBoolRing_add, IntermediateField.sup_toSubalgebra_of_isAlgebraic_left, abs_sub_sup_add_abs_sub_inf, Subrepresentation.toSubmodule_sup, JordanHolderLattice.sup_eq_of_isMaximal, IntermediateField.restrictScalars_sup, Finset.max_pair, UV.compress_of_disjoint_of_le', Submodule.submoduleOf_sup_of_le, IsFoelner.tendsto_meas_smul_symmDiff, Set.Icc.codisjoint_iff, CategoryTheory.Subfunctor.max_min, UpperSet.Ici_sup, Lattice.BicartSq.max_eq, Filter.isBoundedUnder_le_sup, Dynamics.coverEntropyEntourage_union, Finset.inf_sup_distrib_left, Finset.card_sups_iff, MeasurableSpace.generateFrom_sup_generateFrom, inv_sup, Multiset.sup_coe, IsCompl.sup_inf, symmDiff_fst, Submonoid.sup_eq_closure_mul, Monotone.map_sup, abs_max_sub_max_le_abs, sup_lt_of_lt_sdiff_left, DistLat.Iso.mk_inv, MeasureTheory.OuterMeasure.trim_sup, Monotone.max, isLUB_pair, Submonoid.mem_sup_left, sup_top_eq, AddSubgroup.relIndex_sup_left, max_lt_max_right_iff, Ideal.sup_pow_add_le_pow_sup_pow, FractionalIdeal.coeIdeal_sup, Finset.singleton_sups_singleton, bot_symmDiff, Submodule.finiteDimensional_sup, FreeAlgebra.cardinalMk_le_max, Finset.forall_sups_iff, LinearMap.map_coprod_prod, Cardinal.aleph_add_aleph, codisjoint_iff, Finset.image_subset_sups_left, Order.Ideal.coe_sup_eq, MeasureTheory.Measure.MeasureDense.fin_meas_approx, Antitone.le_map_inf, Finset.inf'_sup_distrib_right, MeasureTheory.edist_indicatorConstLp_eq_enorm, MonoidAlgebra.cardinalMk_lift_of_infinite, symmDiff_comm, UV.sup_sdiff_mem_of_mem_compression_of_notMem, sup_lt_sup_of_lt_of_inf_le_inf, inf_sup_assoc_of_le, DFinsupp.coe_sup, Set.Iio_union_Ico, AddSubgroup.add_mem_sup, Subalgebra.LinearDisjoint.rank_sup_of_free, Ordinal.iSup_sum, Ideal.mul_left_self_sup, Finset.sups_singleton, StarSubalgebra.mul_mem_sup, symmDiff_sdiff_right, max_add_add_left, PrimeSpectrum.sup_vanishingIdeal_le, AddSubmonoid.closure_union, Subring.comap_map_eq, sup_eq_iff_inf_eq, Multiset.toFinsupp_union, sup_eq_iSup, WType.cardinalMk_le_max_aleph0_of_finite', QuasiconvexOn.sup, max_top_right, Algebra.TensorProduct.map_ker, Submodule.map_sup, le_iff_eq_sup_sdiff, SupBotHom.bot_apply, ConvexOn.le_max_of_mem_Icc, StarAlgebra.adjoin_nonUnitalStarSubalgebra_eq_span, Filter.Tendsto.max, Finset.max'_pair, max_one_div_max_inv_one_eq_self, max_sub_sub_left, symmDiff_left_involutive, Dynamics.coverEntropy_union, NonUnitalAlgebra.mul_mem_sup, WeierstrassCurve.Affine.CoordinateRing.XYIdeal_add_eq, symmDiff_sdiff_left, Order.Coframe.MinimalAxioms.sup_iInf_eq, sup_add, FirstOrder.Language.card_functions_sum_skolem₁_le, Finset.vadd_finset_symmDiff, sup_biSup, PSet.rank_insert, fixedPoints_submonoid_sup, ValuationClass.map_add_le_max, LinearMap.comap_leq_ker_subToSupQuotient, Set.Ioo_min_max, sup_sdiff_cancel_right, toDual_max, OrderIsoClass.toSupBotHomClass, BoundedLatticeHom.coe_comp_lattice_hom', symmDiff_symmDiff_right, Submodule.map_mkQ_eq_top, Subring.closure_union, IntermediateField.isCyclotomicExtension_lcm_sup, max_add_min, Finset.le_prod_max_one, Submodule.eq_top_of_disjoint, Subsemigroup.map_sup, BoolAlg.hasForgetToHeytAlg_forget₂_map, IntermediateField.sup_toSubalgebra_of_isAlgebraic, SimpleGraph.chromaticNumber_sum, max_min_distrib_left, bot_sup_eq, iInf_sup_of_monotone, AddSubmonoid.neg_sup, Set.coe_projIci, IsLocalMinOn.max, max_div_min_eq_mabs', MeasureTheory.measure_symmDiff_le, fn_max_add_fn_min, AddSubsemigroup.comap_sup_map_of_injective, Set.Ico_inter_Ico, Subsemiring.unop_sup, AddSubsemigroup.mem_sup_left, max_zero_add_max_neg_zero_eq_abs_self, Filter.limsup_sup_filter, Coheyting.hnot_hnot_sup_boundary, FunctionField.InftyValuation.map_add_le_max', AddMonoidAlgebra.cardinalMk_of_infinite', Submonoid.smul_sup, AffineSubspace.span_union, Cardinal.mul_eq_max, List.le_max_of_le, LinearMap.quotientInfEquivSupQuotient_apply_mk, NatOrdinal.toOrdinal_max, Filter.Tendsto.max_right, le_pow_sup, smul_max_of_nonneg, AddSubgroup.mem_sup', Cardinal.mk_freeMonoid, Set.sup_eq_union, Cardinal.mk_bounded_set_le, rel_sup_mul, TopHom.sup_apply, inf_add_sup, MeasureTheory.measure_neg_vadd_symmDiff, AddSubsemigroup.unop_sup, Lat.Iso.mk_inv, Subgroup.comap_sup_eq, biSup_ge_eq_sup, symmDiff_right_inj, Finset.fold_max_add, IntermediateField.fg_sup, Set.Iic_union_Ioc, MeasurableSpace.cardinal_generateMeasurableRec_le, Filter.tendsto_nhds_max_left, infIccOrderIsoIccSup_apply_coe, Finset.uIcc_subset_uIcc_iff_le', sup_eq_sdiff_sup_sdiff_sup_inf, smul_min_of_nonpos, toBoolAlg_add, Finset.Ico_inter_Ico, right_lt_sup, Finset.uIcc_subset_uIcc_iff_le, Algebra.sup_toSubsemiring, WithZero.coe_sup, AddSubgroup.coe_add_of_left_le_normalizer_right, Set.Iio_union_Ioo', beattySeq_symmDiff_beattySeq'_pos, SupHom.coe_top, Irrational.beattySeq_symmDiff_beattySeq_pos, Set.Ioc_inter_Ioo_of_right_le, Subalgebra.mem_starClosure, Coheyting.boundary_sup_le, AddSubgroup.map_le_map_iff, Nat.cast_max, Complementeds.mk_sup_mk, Set.union_symmDiff_subset, IsDedekindDomain.HeightOneSpectrum.intValuation.map_add_le_max', BoundedLatticeHom.coe_comp_sup_hom, iSup_split_single, Filter.IsBoundedUnder.sup, ScottContinuousOn.sup₂, le_sup_of_le_left, Subalgebra.finrank_right_dvd_finrank_sup_of_free, IsModularLattice.inf_sup_inf_assoc, NumberField.Units.dirichletUnitTheorem.map_logEmbedding_sup_torsion, sup_eq_and_inf_eq_iff, sup_hnot_self, WType.cardinalMk_le_max_aleph0_of_finite, Finset.image_subset_sups_right, ConvexOn.le_on_segment, Subalgebra.mul_toSubmodule, Finset.symmDiff_nonempty, ofBoolAlg_sup, Algebra.adjoin_nonUnitalSubalgebra_eq_span, Ideal.mul_sup, TopCat.Sheaf.objSupIsoProdEqLocus_hom_fst, quasiconvexOn_iff_le_max, Polynomial.sup_aeval_range_eq_top_of_isCoprime, sup_inf_right, IsFractional.sup, Valuation.map_sub, BoundedLatticeHom.coe_toSupBotHom, infIooOrderIsoIooSup_symm_apply_coe, LowerAdjoint.closure_sup_closure_left, sup_eq_half_smul_add_add_abs_sub', AddSubgroup.index_map, Rat.cast_max, symmDiff_snd, Disjoint.symmDiff_eq_sup, Cardinal.mk_list_eq_max, IsSemisimpleModule.sup, Setoid.sup_eq_eqvGen, Set.Icc_inter_Icc, WithZero.le_max_iff, segment_eq_Icc', NonUnitalSubring.map_sup, Finset.mem_disjSups, Finsupp.supported_union, EReal.min_neg_neg, partialSups_succ, AntitoneOn.map_min, Subgroup.relIndex_map_map, AddMonoid.Coprod.range_eq, Set.uIcc_subset_uIcc_iff_le', Set.Ioo_inter_Ioc_of_left_le, Polynomial.sup_ker_aeval_eq_ker_aeval_mul_of_coprime, Multiset.max_sum_le, max_idem, min_div_div_left', TopologicalSpace.Closeds.lipschitz_sup, Cardinal.mk_freeAddGroup, Ideal.mem_minimalPrimes_sup, Set.Iic.complementedLattice_iff, inf_le_sup, inf_left_le_sup_right, AddSubmonoid.sup_eq_range, UpperSet.coe_iciSupHom, sup_eq_half_smul_add_add_abs_sub, CompactlySupportedContinuousMap.sup_apply, mabs_div_sup_mul_mabs_div_inf, LatticeHom.withBot_toFun, Submodule.mul_sup, Disjoint.sup_left, le_sup_sdiff, AddSubgroup.op_sup, Order.Coframe.MinimalAxioms.sup_iInf₂_eq, Set.Ici.coe_sup, sup_eq_left, Max.left_comm, LowerSemicontinuousAt.sup, CategoryTheory.ObjectProperty.instEssentiallySmallMax, Finset.Ioc_inter_Ioc, Submonoid.map_sup, Set.Ioc_diff_Iic, sup_right_idem, WeierstrassCurve.Affine.CoordinateRing.degree_norm_smul_basis, mabs_div_le_max_div, Finset.sup'_insert, sdiff_sdiff_right, LinearMap.sup_range_inl_inr, LatticeHom.map_inf', Cardinal.mk_finsupp_nat, StrictConvexOn.lt_on_openSegment, LinearMap.span_singleton_sup_ker_eq_top, Finset.smul_finset_symmDiff₀, max_eq_top, Topology.IsGeneratedBy.sup, Valuation.map_add_le_max', IsModularLattice.sup_inf_sup_assoc, Filter.blimsup_sup_not, Monotone.map_max, toBoolAlg_add_add_mul, inf_eq_and_sup_eq_iff, Set.Finite.toFinset_symmDiff, max_div_div_left', BoundedLatticeHom.map_top', DoubleQuot.ker_quotQuotMk, SemilatSupCat.dual_map, sup_idem, AddMonoidAlgebra.cardinalMk_lift_of_infinite, Ideal.sup_mul_right_self, sup_sdiff_inf, IsLocalMin.max, le_sInf_inter, codisjoint_iff_le_sup, Subgroup.mem_sup_of_normal_right, Submodule.comap_sup_map_of_injective, Int.cast_max, inf_sdiff_sup_left, Subalgebra.mulMap'_surjective, le_sup_right, AddSubgroup.comap_sup_eq_of_le_range, CoheytingHom.map_top', AddSubgroup.closure_add_le, Finset.fold_sup_univ, TopCat.Sheaf.interUnionPullbackConeLift_right, Lattice.BicartSq.sup_eq, DoubleQuot.coe_quotQuotEquivQuotSupₐ, left_or_right_lt_sup, inf_sup_self, Pi.single_sup, AddSubsemigroup.op_sup, sup_sdiff_right, symmDiff_eq_right, Subgroup.relIndex_sup_right, min_max_distrib_right, fn_min_mul_fn_max, Filter.EventuallyLE.le_sup_of_le_right, compl_sup_le_himp, Tropical.trop_sup_def, symmDiff_eq, MeasurableSpace.comap_prodMk, IsMinOn.max, MeasureTheory.le_measure_symmDiff, max_le_iff, symmDiff_eq_sup_sdiff_inf, ClosureOperator.closure_sup_closure_right, Set.mulIndicator_symmDiff, MeasureTheory.AEFinStronglyMeasurable.sup, max_eq_left_iff, IntermediateField.restrictScalars_adjoin_eq_sup, CategoryTheory.ObjectProperty.instIsClosedUnderIsomorphismsMax, max_lt_iff, AlgebraicGeometry.Scheme.basicOpen_add_le, iSup_dite, IsDedekindDomain.HeightOneSpectrum.intValuation.le_max_iff_min_le, IsPGroup.to_sup_of_normal_left', MeasureTheory.measure_symmDiff_inv_smul, Algebra.mem_sup_left, LinearMap.quotientInfEquivSupQuotient_injective, sup_inf_left, Subgroup.mem_sup_left, abs_max_sub_max_le_max, Set.Ico_inter_Ici, posPart_def, IntermediateField.cardinalMk_adjoin_le, Submodule.dualAnnihilator_sup_eq, Submonoid.inv_sup, Subsemigroup.closure_union, MeasureTheory.Lp.coeFn_sup, MeasureTheory.OuterMeasure.sup_apply, CompleteBooleanAlgebra.le_sup_inf, Subsemigroup.unop_sup, Subgroup.toSubmonoid_zpowers, Subalgebra.finrank_left_dvd_finrank_sup_of_free, left_lt_sup, sup_inf_self, Cardinal.mk_freeAddMonoid, Subsemigroup.comap_sup_map_of_injective, NumberField.Units.regOfFamily_div_regulator, CategoryTheory.ObjectProperty.prop_sup_iff, AddSubmonoid.mul_sup, CategoryTheory.MorphismProperty.HasCardinalLT.sup, Finset.symmDiff_subset_sdiff, Submodule.dualCoannihilator_sup_eq, QuotientAddGroup.comap_map_mk', Antitone.map_max, BooleanSubalgebra.mk_sup_mk, max_add_add_right, LowerSemicontinuousWithinAt.sup, Cardinal.mul_le_max_of_aleph0_le_left, fn_max_mul_fn_min, Cardinal.power_nat_le_max, mul_max_of_nonneg, sup_assoc, Subalgebra.mul_toSubmodule_le, AffineSubspace.direction_sup, max_mul_mul_right, CovBy.sup_of_inf_of_inf_left, Algebra.IsAlgebraic.lift_cardinalMk_le_max, sup_le_of_le_sdiff_left, Coheyting.boundary_inf, bihimp_eq, SSet.skeleton_succ, BoundedContinuousFunction.coe_sup, neg_sup, SupBotHom.coe_sup, Units.max_val, Finset.symmDiff_subset_union, gc_sdiff_sup, MonomialOrder.sPolynomial_def, Set.iUnion_image_sup_right, SupHom.coe_const, DFinsupp.sup_apply, SupHom.withTop'_toFun, AddSubmonoid.exists_mem_sup, AddSubgroup.coe_add_of_right_le_normalizer_left, Nat.factorization_lcm, fixedPoints_addSubmonoid_sup, sup_eq_bot_iff, FirstOrder.Language.isExtensionPair_iff_exists_embedding_closure_singleton_sup, Set.Ico_union_Ico', NumberField.IsCMField.closure_realFundSystem_sup_torsion, MonotoneOn.sup, Module.Basis.flag_succ, min_abs_abs_le_abs_max, AddSubgroup.unop_sup, IntermediateField.LinearDisjoint.finrank_sup, MeasureTheory.AEEqFun.coeFn_sup, iInf_sup_iInf_le, MonoidAlgebra.cardinalMk_of_infinite', TwoSidedIdeal.mem_sup_right, iSup_sup_eq, LinearGrowth.linearGrowthSup_sup, Subring.prod_bot_sup_bot_prod, Finset.max'_insert, sup_sup_distrib_left, Equiv.Perm.support_mul_le, WithTop.untop₀_max, UV.sup_sdiff_mem_of_mem_compression, Module.End.isFinitelySemisimple_iff, symmDiff_eq_iff_sdiff_eq, Subgroup.FG.sup, ENNReal.iSup_ennreal, SupHom.withTop_toFun, dist_mulIndicator, supsSupHom_apply, sup_left_idem, Algebra.TensorProduct.productMap_range, Subsemigroup.mem_sup_left, symmDiff_sup_inf, AlgebraicGeometry.Scheme.IdealSheafData.vanishingIdeal_sup, AddSubgroup.codisjoint_addSubgroupOf_sup, Subgroup.subgroupOf_sup, symmDiff_self, le_symmDiff_iff_right, symmDiff_triangle, HahnSeries.cardSupp_div_le, NonUnitalAlgebra.map_sup, LowerAdjoint.closure_sup_closure, IsNonarchimedean.add_eq_max_of_ne, norm_sup_le_add, Birkhoff_inequalities, LatticeCon.sup, iSup_ite, RelHomClass.map_sup, AddSubgroup.ofAddUnits_inf, sup_eq_maxDefault, ext_sup, Ideal.Filtration.sup_N, Right.min_le_max_of_mul_le_mul, isFoelner_iff, min_neg_neg, AlgebraicGeometry.Scheme.IdealSheafData.comap_sup, ofBoolAlg_symmDiff, Disjoint.right_lt_sup_of_left_ne_bot, Subgroup.comap_sup_comap_le, Fin.attachFin_uIcc, EReal.coe_toENNReal_eq_max, bddLat_dual_comp_forget_to_semilatSupCat, Submodule.sup_smul, Finset.sup_mem_sups, min_max_distrib_left, Ordinal.max_eq_zero, symmDiff_left_surjective, Subgroup.ofUnits_inf, LowerSemicontinuous.sup, BiheytingHom.toFun_eq_coe, leOnePart_max, iSup_option_elim, Finset.fold_sup_bot_singleton, max_sub_min_eq_abs, sup_mul₀, NumberField.Units.closure_fundSystem_sup_torsion_eq_top, Filter.sup_limsup, IsFoelner.tendsto_meas_smul_symmDiff_smul, lt_max_of_lt_right, Multiset.Ico_inter_Ico, FirstOrder.Language.Substructure.closure_insert, Cardinal.mk_freeRing, Monoid.Coprod.mrange_lift, Subsemigroup.op_sup, Set.apply_indicator_symmDiff, Ideal.mem_span_singleton_sup, LieSubmodule.sup_toSubmodule, le_max_of_two_nsmul_le_add, KaehlerDifferential.kerTotal_map, IsLUB.insert, sup_bot_eq, mul_max, Disjoint.le_symmDiff_sup_symmDiff_left, sdiff_sdiff_sup_sdiff, Module.End.invtSubmodule.sup_mem, sInf_sup_eq, max_zero_sub_max_neg_zero_eq_self, DoubleQuot.coe_quotQuotEquivQuotSupₐ_symm, IsLocalMaxOn.sup, Finset.truncatedSup_union, Cardinal.add_eq_max', IsCoprime.sup_eq, inf_symmDiff_distrib_left, Ordinal.card_opow_le_of_omega0_le_right, irreducible_pow_sup, IntermediateField.sup_def, ciSup_or', SupPrime.le_sup, IsPGroup.to_sup_of_normal_right, MeasurableSpace.CountablyGenerated.sup, symmDiff_isAssociative, AddSubmonoid.add_mem_sup, TensorProduct.quotientTensorQuotientEquiv_apply_tmul_mk_tmul_mk, inf_lt_sup, Cardinal.mul_mk_eq_max, Set.Ico_diff_Iio, inf_sup_right, Set.subset_symmDiff_union_symmDiff_right, Algebra.Generators.comp_localizationAway_ker, LSeries.abscissaOfAbsConv_binop_le, Set.symmDiff_subset_union, MeasureTheory.tendsto_measure_symmDiff_preimage_nhds_zero, IntermediateField.finrank_sup_le, Ideal.iSup_iInf_eq_top_iff_pairwise, Ideal.isCoprime_tfae, Ideal.map_sup_comap_of_surjective, Submonoid.op_sup, Cardinal.aleph_max, NonemptyInterval.snd_sup, lt_sup_iff, LSeries.abscissaOfAbsConv_add_le, Subgroup.map_le_map_iff, LatticeHom.coe_toSupHom, sup_mul, bihimp_eq_sup_himp_inf, covBy_sup_of_inf_covBy_left, OreLocalization.cardinalMk_le_max, hnot_inf_distrib, CategoryTheory.Limits.CompleteLattice.pushout_eq_sup, Set.uIcc_subset_uIcc_iff_le, HeytingHom.map_himp', Subgroup.normal_mul, CoheytingHom.map_sdiff', Coheyting.boundary_inf_le, max_le_mul_of_one_le, Set.Icc.isCompl_iff, Ordinal.card_opow_omega0, Quantale.sup_mul_distrib, Subgroup.comap_map_eq, div_sup, Cardinal.add_eq_max, max_mul_mul_left, negPart_def, Set.Ioc_union_Ioc_symm, Tropical.trop_max_def, Antitone.map_sup_le, sdiff_eq_sInf, NonUnitalStarAlgebra.mul_mem_sup, Finset.fold_max_le, Ideal.map_sup, Subgroup.mem_sup, FirstOrder.Language.Substructure.CG.sup, AffineSubspace.nonempty_sup_left, LinearMap.range_coprod, Subalgebra.finrank_sup_eq_finrank_left_mul_finrank_of_free, BoundedLatticeHom.map_bot', pred_max, Cardinal.preAleph_max, AddSubmonoid.mrange_inl_sup_mrange_inr, sup_of_le_right, Monoid.Coprod.range_lift, Subalgebra.finrank_sup_le_of_free, Ideal.comap_map_quotientMk, SupHom.withBot_comp, bddLat_dual_comp_forget_to_semilatInfCat, sup_mem_supClosure, Subalgebra.starClosure_toSubalgebra, max_min_distrib_right, sdiff_sup_self, DividedPowers.isSubDPIdeal_sup, ClosureOperator.closure_sup_closure_left, List.zipWith_swap_prod_support', Submodule.comap_map_mkQ, List.support_sum_eq, OpenAddSubgroup.toAddSubgroup_sup, Con.sup_def, ClosureOperator.closure_sup_closure, IsComplemented.sup, TopCat.Sheaf.objSupIsoProdEqLocus_inv_snd, le_sup_inf, Polynomial.degree_add_le_of_le, symmDiff_isCommutative, sup_iInf_le_iInf_sup, sdiff_sdiff, SupHom.const_apply, List.mem_foldr_sup_support_iff, nndist_mulIndicator, MeasureTheory.eLpNorm_indicator_sub_indicator, IsMaxFilter.max, NonUnitalStarAlgebra.mem_sup_left, Subgroup.map_le_map_iff', Set.Iic.coe_sup, AntitoneOn.map_max, AlexandrovDiscrete.sup, ExpGrowth.le_expGrowthInf_add, Submodule.inf_orthogonal, Finset.sup_union, Ideal.sup_mul_inf, Mathlib.Tactic.Bound.le_max_of_le_left_or_le_right, BoundedLatticeHom.toFun_eq_coe, LSeries.abscissaOfAbsConv_convolution_le, abs_sup_sub_sup_le_abs, Polynomial.cardinalMk_eq_max, sup_iSup_nat_succ, ClosedSubmodule.mem_sup, div_inf, AlgebraicGeometry.Scheme.Hom.preimage_sup, Subgroup.sup_subgroupOf_eq, compl_symmDiff_compl, DoubleQuot.ker_quotLeftToQuotSup, AntitoneOn.max, MeasurableSet.symmDiff, Finset.max'_union, Filter.EventuallyEq.symmDiff, Coheyting.boundary_le_boundary_sup_sup_boundary_inf_left, SupBotHom.sup_apply, Subalgebra.finite_sup, Function.support_sup, CauSeq.rat_sup_continuous_lemma, IsAlgClosed.cardinal_le_max_transcendence_basis', Ideal.comap_map_of_surjective, mul_sup, max_lt_max, AddSubmonoid.coe_sup, min_lt_max_of_mul_lt_mul, TopCat.Sheaf.interUnionPullbackConeLift_left, BotHom.sup_apply, AddSubgroup.sup_normal, sup_le_iff, Submodule.restrictScalars_sup, Set.singleton_sups, max_max_max_comm, max_one_mul_max_inv_one_eq_mabs_self, TopologicalSpace.Closeds.coe_sup, BooleanSubalgebra.val_sup, csSup_insert, Subalgebra.rank_sup_eq_rank_right_mul_rank_of_free, AlgebraicGeometry.Scheme.IdealSheafData.mul_inf, AddSubgroup.mem_sup_right, AddSubgroup.sup_eq_closure, min_add_max, SetTheory.PGame.birthday_def, sup_inf_assoc_of_le, exists_sSupIndep_disjoint_sSup_atoms, FirstOrder.Language.Term.card_sigma, CategoryTheory.Precoverage.sup_mem_coverings, Submonoid.unop_sup, LinearMap.eqOn_sup, SupHom.withBot_toFun, max_top_left, Submodule.add_mem_sup, Ideal.minimalPrimes_map_of_surjective, IsLocalMax.sup, max_eq_bot, Submodule.sup_orthogonal_inf_of_hasOrthogonalProjection, Algebra.TensorProduct.map_range, Order.Coframe.sdiff_le_iff, Finset.Ico_filter_le, Cardinal.mk_bounded_subset_le, Finset.sup_disjSum, Set.Ioc_inter_Ioc, CompleteLattice.ωScottContinuous.sup, MonomialOrder.sPolynomial_monomial_mul, Multiset.sup_ndunion, Finset.iSup_insert, DeltaGeneratedSpace.sup, AddSubsemigroup.mem_sup_right, Submodule.sup_dualAnnihilator_le_inf, compl_sup_distrib, UpperSet.iciSupHom_apply, UpperSemicontinuous.sup, sup_compl_eq_top, CategoryTheory.Precoverage.IsStableUnderSup.sup_mem_coverings, Set.Ico_disjoint_Ico, Submonoid.closure_mul_le, bihimp_inf_sup, Polynomial.coeff_divModByMonicAux_mem_span_pow_mul_span, AddCon.sup_eq_addConGen, IntermediateField.sup_toSubalgebra_of_left, NonUnitalSubring.closure_union, Submonoid.mul_mem_sup, IsLocalMax.max, Set.Finite.symmDiff_congr, SupHom.withBot'_toFun, Projectivization.Subspace.sup_span, Pi.mulSingle_sup, max_sub_max_le_max, Set.inter_symmDiff_distrib_right, Submodule.smul_sup, Cardinal.add_mk_eq_max, CompactlySupportedContinuousMap.coe_sup, Sublattice.comap_equiv_eq_map_symm, infIooOrderIsoIooSup_apply_coe, EReal.max_neg_neg, AddMonoidAlgebra.cardinalMk_lift_of_infinite', LinearPMap.domain_sup, sdiff_inf, le_inf_sup, PrimeMultiset.prod_sup, Finset.biUnion_image_sup_right, OrderEmbedding.birkhoffSet_sup, IntermediateField.LinearDisjoint.rank_sup, NNRat.cast_max, MeasureTheory.measure_inv_smul_symmDiff, HomogeneousIdeal.toIdeal_sup, IntermediateField.rank_sup_le_of_isAlgebraic, leOnePart_min, Subgroup.mul_mem_sup, inf_sup_left, sup_comm, abs_pow_sub_pow_le, Finset.coe_symmDiff, Subalgebra.FG.sup, le_symmDiff_sup_left, Submodule.isQuotientEquivQuotientPrime_iff, Subalgebra.LinearDisjoint.finrank_sup_of_free, sup_left_comm, ZFSet.rank_insert, MvPolynomial.degrees_add_le, Subgroup.smul_sup, FirstOrder.Language.Substructure.closure_union, TopHom.coe_sup, Submodule.span_union, Finset.image_sup_product, Submonoid.coe_sup, AntitoneOn.sup, AddSubmonoid.closure_add_le, Set.Ioo_inter_Ioc_of_right_lt, AffineSubspace.finiteDimensional_sup, AddSubgroup.mem_sup_of_normal_right, StarSubalgebra.map_sup, Submodule.rank_add_le_rank_add_rank, Submodule.sup_mul, sup_eq_right, sup_sdiff_left_self, sup_sdiff_self_left, DFinsupp.support_sup_union_support_inf, inv_inf, max_mul_mul_le_max_mul_max', DualNumber.range_inlAlgHom_sup_adjoin_eps, WCovBy.sup_eq, negPart_min, max_le_max, Submodule.spanRank_sup_le_sum_spanRank, sup_inf_le_assoc_of_le, symmDiff_sdiff, SemilatSupCat.Iso.mk_hom_toFun, Cardinal.mk_freeGroup, FirstOrder.Language.Substructure.FG.sup, symmDiff_sdiff_eq_sup, symmDiff_le_sup, Multiset.Ico_filter_le, Subgroup.comap_sup_eq_of_le_range, AddMonoid.Coprod.range_lift, Polynomial.degree_sub_le, Filter.EventuallyLE.le_sup_of_le_left, le_sup_of_le_right, SupHom.sup_apply, Ordinal.card_opow_eq_of_omega0_le_right, Equiv.Perm.support_prod_le, FractionalIdeal.coe_sup, iInf₂_sup_eq, MeasurableSpace.cardinal_measurableSet_le, CompleteDistribLattice.sdiff_le_iff, Set.Ioi_inter_Ioo, max_eq_right_iff, CategoryTheory.Sieve.functorPushforward_union, sdiff_sdiff_right', Subgroup.relIndex_sup_left, MeasurableSpace.cardinal_generateMeasurable_le, symmDiff_symmDiff_left, TwoSidedIdeal.mem_sup, Quantale.mul_sup_distrib, symmDiff_symmDiff_cancel_left, CompleteDistribLattice.MinimalAxioms.iInf_sup_le_sup_sInf, Antitone.map_inf, Finset.max_insert, compl_sup, IsMinOn.sup, IsAlgClosed.cardinal_le_max_transcendence_basis, Multiset.max_prod_le, sup_bihimp_bihimp, Setoid.sup_def, Polynomial.sup_ker_aeval_le_ker_aeval_mul, symmDiff_eq_bot, BooleanAlgebra.himp_eq, MeasureTheory.Filtration.coeFn_sup, Continuous.max, Set.Iic_union_Icc', AddSubgroup.mem_sup, AffineSubspace.nonempty_sup_right, Finset.sup_sup, max_bot_right, Ideal.ofList_append, SupHom.coe_sup, Finsupp.sup_apply, max_div_div_right_of_nonpos, min_mul_max, UpperSemicontinuousOn.sup, inf_sdiff_sup_right, CovBy.sup_of_inf_of_inf_right, sup_sq_eq_mul_mul_mabs_div, Topology.IsUpper.toContinuousInf, sup_eq_inf, Algebra.EssFiniteType.aux, Subgroup.closure_mul_le, MonotoneOn.map_sup, Finset.Colex.lt_iff_max'_mem, sup_lt_iff, Finset.biUnion_image_sup_left, AddSubmonoid.sup_eq_closure_add, BiheytingHom.map_himp', top_sup_eq, biInf_sup_le_biInf_sup, le_iff_exists_sup, MeasurableSpace.comap_sup, le_max_of_le_right, Booleanisation.comp_sdiff_lift, Submodule.sup_orthogonal_of_hasOrthogonalProjection, Subring.unop_sup, Measurable.sup_of_left, Set.apply_mulIndicator_symmDiff, Set.forall_sups_iff, MeasureTheory.MeasuredSets.dist_def, Subalgebra.rank_sup_le_of_free, UV.compress_of_disjoint_of_le, Set.Iic.codisjoint_iff, AddMonoid.Coprod.mrange_inl_sup_mrange_inr, Codisjoint.sup_right, max_cases, CategoryTheory.ObjectProperty.isoClosure_sup, Set.sups_singleton, iSup_sup, limsup_max, Algebra.isIntegral_sup, DoubleQuot.quotQuotEquivQuotSup_quotQuotMk, QuotientGroup.comap_map_mk', Finset.symmDiff_subset_sdiff', le_symmDiff_iff_left, BoundedLatticeHomClass.toSupBotHomClass, Left.min_le_max_of_mul_le_mul, symmDiff_le_iff, List.support_sum_subset, le_max_of_le_left, LatticeHom.coe_comp_sup_hom, inf_eq_iff_sup_eq, inf_sup_symmDiff, symmDiff_eq_Xor', Cardinal.aleph_mul_aleph, PseudoMetric.coe_sup, dist_indicator, LinearMap.comap_eq_sup_ker_of_disjoint, Set.Ioc_union_Ioc_union_Ioc_cycle, Algebra.Generators.ker_comp_eq_sup, GaloisCoinsertion.u_sup_l, ScottContinuous.sup₂, TopCat.Sheaf.objSupIsoProdEqLocus_hom_snd, Subalgebra.op_sup, MeasureTheory.FinStronglyMeasurable.sup, oneLePart_def, SSet.Subcomplex.preimage_max, OrderIso.map_sup, TwoSidedIdeal.sup_ringCon, IsPGroup.to_sup_of_normal_right', fixedPoints_subgroup_sup, Set.Iic_union_Icc, Submodule.finrank_add_le_finrank_add_finrank, Ordinal.card_opow_le_of_omega0_le_left, Ideal.mem_quotient_iff_mem_sup, symmDiff_right_surjective, Subalgebra.LinearDisjoint.val_mulMap_tmul, Disjoint.sup_right, sup_sInf_le_iInf_sup, ConvexOn.le_on_segment', Subgroup.sup_normal, DoubleQuot.coe_quotQuotToQuotSupₐ, Finset.iSup_insert_update, Subalgebra.mulMap_range, Submodule.lt_sup_iff_notMem, sup_sub, CategoryTheory.Sieve.pushforward_union, Max.right_comm, CircleDeg1Lift.sup_apply, sdiff_sdiff_left, Submonoid.mem_sup_right, Subfield.extendScalars_sup, Subsemigroup.mem_sup_right, FirstOrder.Language.Term.card_le, Finsupp.support_inf_union_support_sup, AddSubsemigroup.map_sup_comap_of_surjective, ConvexOn.sup, Set.Ioc_inter_Ioo_of_left_lt, Ideal.IsMaximal.coprime_of_ne, inf_right_le_sup_right, Ideal.map_eq_iff_sup_ker_eq_of_surjective, covBy_sup_of_inf_covBy_of_inf_covBy_right, Ideal.add_eq_sup, StrictConvexOn.sup, Ordinal.card_opow_eq_of_omega0_le_left, sup_inf_sdiff, Finset.sup_ite, sdiff_sup_sdiff_cancel, Codisjoint.sup_right', sdiff_inf_distrib, IntermediateField.isSeparable_sup, biInf_sup_biInf, Submonoid.FG.sup, le_symmDiff_sup_right, iInf_sup_eq, Filter.Germ.const_max, Submodule.IsLattice.sup, Finset.inf_sup_inf, Finset.fold_max_lt, CompleteBooleanAlgebra.top_le_sup_compl, DoubleQuot.quotQuotEquivQuotSupₐ_toRingEquiv, AlgebraicGeometry.Scheme.IdealSheafData.ideal_sup, Set.Iic_union_Ioc', AffineSubspace.sup_direction_le, BddLat.coe_forget_to_semilatSup, symmDiff_symmDiff_right', max_mul, sup_himp_self_left, sup_inf_le, leOnePart_def, Set.Finite.symmDiff, Submodule.map₂_sup_left, Subsemiring.closure_union, Submodule.sup_eq_top_iff, LinearMap.ker_sup_ker_le_ker_comp_of_commute, coinduced_sup, LinearMap.range_ofIsCompl, Polynomial.degree_add_le, abs_max_le_max_abs_abs, UpperSemicontinuousWithinAt.sup, ENat.toENNReal_max, Subalgebra.centralizer_coe_sup, max_mul_mul_le_max_mul_max, Hyperreal.coe_max, MeasureTheory.abs_measureReal_sub_le_measureReal_symmDiff, Cardinal.add_mk_eq_max', lt_sup_of_lt_left, AddSubmonoid.mem_sup, CategoryTheory.PreZeroHypercover.presieve₀_sum, MvPolynomial.cardinalMk_le_max_lift, Nonneg.coe_toNonneg, not_supIrred, Subalgebra.coe_starClosure, AddSubmonoid.map_sup_comap_of_surjective, MeasureTheory.measure_symmDiff_eq, MeasureTheory.AEEqFun.coeFn_posPart, MonomialOrder.sPolynomial_monomial_mul', Finset.sup_cons, Booleanisation.comp_inf_comp, Ideal.ofList_cons_smul, Filter.tendsto_nhds_max_right, AddMonoidAlgebra.sup_support_add_le, Sylow.normalizer_sup_eq_top, Set.symmDiff_eq_empty, sup_sdiff, CoheytingHom.toFun_eq_coe, symmDiff_hnot_self, Subring.smul_sup, abs_sub_le_max_sub, BooleanAlgebra.top_le_sup_compl, Monotone.disjointed_succ_sup, Finset.sup'_cons, max_aleph0_card_le_rank_fun_nat, FreeAlgebra.cardinalMk_le_max_lift, le_sup_iff, AddMonoidAlgebra.supDegree_sub_le, Subsemiring.prod_bot_sup_bot_prod, IntermediateField.lift_cardinalMk_adjoin_le, symmDiff_left_injective, MeasureTheory.SignedMeasure.of_symmDiff_compl_positive_negative, LinearMap.coe_quotientInfToSupQuotient, Subfield.closure_union, NonUnitalStarAlgebra.map_sup, sup_inf_bihimp, isGreatest_pair, mabs_max_le_max_mabs_mabs, Function.mulSupport_max, PNat.factorMultiset_lcm, min_lt_max, AntitoneOn.map_inf, AffineSubspace.map_sup, smul_max_of_nonpos, Submodule.map_sup_comap_of_surjective, Finset.symmDiff_eq_empty, le_csInf_inter, symmDiff_eq_left, Set.mabs_mulIndicator_symmDiff, Finset.sups_subset_iff, LSeries.abscissaOfAbsConv_sub_le, sSup_pair, Finset.max_abv_sum_one_le_of_isNonarchimedean, TopCat.Sheaf.objSupIsoProdEqLocus_inv_fst, MonotoneOn.map_max, hnot_sup_self, symmDiff_right_injective, AddSubgroup.ofAddUnits_sup_addUnits, mabs_min_le_max_mabs_mabs, Submodule.span_sup, Cardinal.powerlt_aleph0_le, StrictConvexOn.lt_on_open_segment', inf_sup_le_assoc_of_le, le_max_of_sq_le_mul, iInf_sup_le_iInf_sup, symmDiff_eq_top, EMetric.Closeds.lipschitz_sup, Finset.truncatedInf_sups, symmDiff_sdiff_inf, MonoidAlgebra.cardinalMk_lift_of_infinite', AddSubsemigroup.closure_union, Subgroup.op_sup, Algebra.mem_sup_right, Finset.sup'_union, TopologicalSpace.Opens.coe_sup, HeytingHom.map_bot', Projectivization.Subspace.span_union, IntermediateField.rank_sup_le, AddSubgroup.toAddSubmonoid_zmultiples, sup_sdiff_cancel', sup_le, max_le_add_of_nonneg, symmDiff_symmDiff_inf, MeasureTheory.ae_eq_set_symmDiff, MeasureTheory.measure_symmDiff_neg_vadd, left_eq_sup, symmDiff_of_le, LinearMap.coprod_map_prod, Multiset.max_le_of_forall_le, Cardinal.add_eq_left_iff, Set.Iic.isCompl_iff, sdiff_symmDiff_eq_sup, sup_sdiff_distrib, Order.Ideal.mem_sup, PUnit.sup_eq, TopologicalSpace.Closeds.uniformContinuous_sup, sup_eq_sup_iff_right, Cardinal.mk_finsupp_of_infinite, symmDiff_eq_sup, norm_sup_sub_sup_le_add_norm, MeasureTheory.IsStoppingTime.max, Polynomial.degree_update_le, Ideal.eq_prime_pow_mul_coprime, ProjectiveSpectrum.zeroLocus_sup_ideal, AddMonoid.Coprod.mrange_eq, BotHom.coe_sup, isArtinian_sup, Booleanisation.lift_sup_lift, AddQuantale.sup_add_distrib, Subsemiring.smul_sup, Heyting.Regular.coe_sup, nndist_indicator, Finset.mem_symmDiff, Submonoid.closure_union, disjoint_sup_left, mabs_eq_max_inv, Convex.combo_le_max, Subgroup.codisjoint_subgroupOf_sup, Set.Ioi.coe_sup, sup_sInf_eq, Subgroup.coe_mul_of_right_le_normalizer_left, inf_strictMonoOn_Icc_sup, Filter.limsup_piecewise, AddSubgroup.comap_sup_eq, CategoryTheory.Subobject.sup_factors_of_factors_left, GeneralizedBooleanAlgebra.sup_inf_sdiff, LatticeHom.coe_comp_sup_hom', Cardinal.mul_eq_max_of_aleph0_le_left, HeytingHom.toFun_eq_coe, Ordinal.toNimber_max, IsAddFoelner.tendsto_meas_vadd_symmDiff, sdiff_le_iff, LatticeHomClass.toSupHomClass, le_sup_sdiff_sup_sdiff, Finset.forall_disjSups_iff, TensorProduct.map_ker, DistLat.Iso.mk_hom, NonUnitalSubsemiring.map_sup, IntermediateField.adjoin_union, Filter.EventuallyLE.sup, UpperSemicontinuousAt.sup, Ordinal.omega_max, Finset.singleton_sups, Subgroup.mem_sup_of_normal_left, sup_himp_bihimp, WithBot.coe_max, CategoryTheory.Sieve.union_apply, List.foldr_sup_eq_sup_toFinset, Polynomial.cardinalMk_le_max, sup_div, HeytAlg.Iso.mk_hom, Submodule.sup_toAddSubmonoid, StarSubalgebra.mem_sup_right, SupBotHom.coe_bot, BooleanSubalgebra.map_sup, AddSubsemigroup.add_mem_sup, Sublattice.coe_sup, LinearMap.map_eq_top_iff, Sublattice.map_symm_eq_iff_eq_map, isNoetherian_sup, Multiset.sup_union, Lat.Iso.mk_hom, Submodule.mem_sup, sdiff_symmDiff_left, Sublattice.mk_sup_mk, List.max_sum_le, sup_sdiff_self_right, IntermediateField.lift_sup, Set.vadd_set_symmDiff, Order.Ideal.sup_mem, Algebra.cardinalMk_adjoin_le, Set.symmDiff_nonempty, Filter.blimsup_sup_le_or, add_sup, Algebra.mul_mem_sup, MeasureTheory.AEEqFun.posPart_mk, max_neg_zero, AlgebraicGeometry.Scheme.IdealSheafData.inf_mul, Ideal.le_comap_sup, Monoid.Coprod.range_eq, Nat.iSup_lt_succ, MeasureTheory.exists_measure_symmDiff_lt_of_generateFrom_isSetSemiring, Subgroup.closure_union, NumberField.Units.finiteIndex_iff_sup_torsion_finiteIndex, Filter.blimsup_not_sup, m_Birkhoff_inequalities, min_mabs_mabs_le_mabs_max, Set.preimage_symmDiff, CategoryTheory.Coverage.sup_covering, symmDiff_left_comm, Ideal.ofList_cons, iSup_option, Antitone.map_min, Sublattice.le_comap_sup, IdemCommSemiring.add_eq_sup, Finsupp.support_sup, Finset.lt_fold_max, AddSubgroup.sup_eq_closure_add, Submodule.exists_mem_sup, Subalgebra.val_mulMap'_tmul, Multiset.toDFinsupp_union, IntermediateField.sup_toSubalgebra_of_right, Submodule.span_insert, Ideal.comap_map_of_surjective', DoubleQuot.quotQuotEquivQuotSup_symm_quotQuotMk, Cardinal.sum_pow_eq_max_aleph0, Set.Ici_inter_Ici, AlgHom.eqOn_sup, sup_sdiff_eq_sup, WithBot.coe_sup, CategoryTheory.Subobject.sup_factors_of_factors_right, Submodule.FG.sup, IntermediateField.le_sup_toSubalgebra, isCoboundedUnder_le_max, MonomialOrder.degree_sPolynomial_le, AddSubmonoid.map_sup, irreducible_pow_sup_of_le, Set.Ioc_inter_Ioi, Set.Finite.sup, ofDual_bihimp, Set.subset_image_symmDiff, sup_sub_inf_eq_abs_sub, Finset.inf'_sup_distrib_left, Set.image_sup_prod, covBy_sup_of_inf_covBy_of_inf_covBy_left, ZFSet.rank_pair, BooleanSubalgebra.le_comap_sup, min_le_max_of_add_le_add, Set.Ioo_disjoint_Ioo, IsPGroup.to_sup_of_normal_left, sup_eq_prod_inf_factors, ExpGrowth.expGrowthSup_sup, iSup_symmDiff_iSup_le, sup_iInf₂_eq, Order.Ideal.sup_mem_iff, Filter.blimsup_or_eq_sup, isModularLattice_iff_inf_sup_inf_assoc, max_zero_sub_eq_self, MeasureTheory.Submartingale.sup, toDual_symmDiff, NonemptyInterval.coe_sup_interval, MonomialOrder.coeff_sPolynomial_sup_eq_zero, Finsupp.support_sup_union_support_inf, MonomialOrder.sPolynomial_mem_sup_ideal, CategoryTheory.ObjectProperty.instSmallMax, MeasureTheory.AEStronglyMeasurable.sup, instLawfulOrderSup_mathlib, Subgroup.index_map, CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.D₃_W, codisjoint_left_comm, Cardinal.mul_eq_max', AddMonoid.Coprod.range_inl_sup_range_inr, SemilatSupCat_dual_comp_forget_to_partOrd, IntermediateField.sup_toSubfield, Set.IccExtend_apply, Ideal.span_union, AddSubmonoid.addSubmonoid_smul_sup, CategoryTheory.MorphismProperty.toSet_max, IntermediateField.sup_toSubalgebra_of_isAlgebraic_right, symmDiff_right_involutive, fixedPoints_addSubgroup_sup, PrimeSpectrum.zeroLocus_sup, continuous_sup_rng_left, map_symmDiff, symmDiff_symmDiff_symmDiff_comm, GaloisConnection.l_sup, Finsupp.toMultiset_sup, Finset.Ioc_disjoint_Ioc, Disjoint.symmDiff_right, Ideal.IsHomogeneous.sup, CompleteLinearOrder.sdiff_le_iff, Ordinal.max_zero_right, IntermediateField.map_sup, AlgebraicGeometry.IsAffineOpen.sup_of_disjoint, IsTranscendenceBasis.lift_cardinalMk_eq_max_lift, DoubleQuot.quotQuotEquivQuotSup_quot_quot_algebraMap, IsTranscendenceBasis.lift_rank_eq_max_lift, List.zipWith_swap_prod_support, Submodule.rank_sup_add_rank_inf_eq, biSup_sup, Finset.sup_eq_union, MvRatFunc.rank_eq_max_lift, DFinsupp.support_inf_union_support_sup, LowerAdjoint.closure_sup_closure_le, max_left_commutative, bihimp_eq', covBy_sup_of_inf_covBy_right, le_max_iff, Submodule.finite_sup, SupHom.withTop_id, Antitone.max, MvPolynomial.cardinalMk_le_max, sup_sup_distrib_right, abs_min_sub_min_le_max, Subgroup.mem_sup_right, Submodule.mem_sup_left, strictMono_inf_prod_sup, Cardinal.mk_freeCommRing, infIccOrderIsoIccSup_symm_apply_coe, sup_sdiff_self, AddSubgroup.comap_sup_comap_le, IsLocalMinOn.sup, LowerSemicontinuousOn.sup, Coheyting.boundary_sup_sup_boundary_inf, Cardinal.mk_freeAbelianGroup, Subgroup.mem_sup', iInf_sup_of_antitone, MeasurableSet.exists_isOpen_symmDiff_lt, sup_ind, partialSups_add_one_eq_sup_disjointed, Submonoid.sup_eq_range, MvPolynomial.support_symmDiff_support_subset_support_add, sup_himp_distrib, MeasureTheory.MeasurePreserving.measure_symmDiff_preimage_iterate_le, codisjoint_right_comm, Submodule.mem_sup_right, TwoSidedIdeal.mem_sup_left, Submodule.sup_set_smul, Sum.Lex.inr_sup, min_div_div_right_of_nonpos, CategoryTheory.Subfunctor.Subpresheaf.max_min, HasSolidNorm.continuousSup, Submodule.sup_span, NonUnitalSubalgebra.starClosure_toNonUnitalSubalgebra, sup_sdiff_left, LinearPMap.supSpanSingleton_apply_mk, HahnSeries.cardSupp_hsum_powers_le, AlgebraicGeometry.Scheme.IdealSheafData.support_sup, sup_lt_of_lt_sdiff_right, Ideal.mem_sup_right, min_inv_inv', Ideal.sup_mul, Set.abs_indicator_symmDiff, EuclideanGeometry.orthogonalProjection_sup_of_orthogonalProjection_eq, Cardinal.add_le_max, Algebra.sup_def, Subsemigroup.map_sup_comap_of_surjective, Ideal.isCoprime_iff_sup_eq, Nat.iSup_le_succ', Polynomial.degree_sub_le_of_le, top_symmDiff', AntitoneOn.map_sup, mul_sup₀, mabs_sup_div_sup_le_mabs, neg_inf, IsDedekindDomain.exists_sup_span_eq, Polynomial.degree_add_eq_of_leadingCoeff_add_ne_zero, abs_min_le_max_abs_abs, inf_symmDiff_symmDiff, DoubleQuot.quotLeftToQuotSupₐ_toRingHom, Finset.max_prod_le, LieSubalgebra.add_eq_sup, sup_iInf_eq, Submodule.map_add_le, CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.D₄_W, compl_bihimp, TopCat.Sheaf.interUnionPullbackCone_pt, Submodule.covBy_span_singleton_sup, hnot_hnot_sup_distrib, IsCompl.inf_sup, Ordinal.card_opow_le, MeasureTheory.MeasuredSets.edist_def, ClosedSubmodule.coe_sup, AddSubmonoid.prod_bot_sup_bot_prod, PseudoMetric.sup_apply, tsub_add_eq_max, SemilatSupCat.coe_forget_to_partOrd, Set.Icc_union_Icc', Set.Icc.coe_sup, Ideal.sup_mul_left_self, MeasureTheory.measure_symmDiff_eq_zero_iff, Subgroup.IsComplement'.sup_eq_top, sup_of_le_left, Codisjoint.sup_left', Cardinal.mk_finsupp_lift_of_infinite', Submodule.wcovBy_span_singleton_sup, Set.Ioi_inter_Ioi, AddSubgroup.FG.sup, symmDiff_symmDiff_cancel_right, Subgroup.unop_sup, Cardinal.power_le_max_power_one, HasCompactMulSupport.sup, Set.Ioc.codisjoint_iff, AddSubgroup.closure_union, compl_sup_eq_top, NonUnitalAlgebra.adjoin_union, sdiff_sdiff_eq_sdiff_sup, ContinuousLinearMap.range_coprod, generateFrom_inter, DoubleQuot.quotQuotEquivQuotSupₐ_symm_toRingEquiv, Ideal.mul_right_self_sup, symmDiff_bot, Submodule.prod_sup_prod, succ_max, continuous_max, BiheytingAlgebra.sdiff_le_iff, Monoid.Coprod.mrange_inl_sup_mrange_inr, AddSubmonoid.FG.sup, iSup_union, AddSubmonoid.unop_sup, sup_sdiff_injOn, Cardinal.mul_le_max, sup_right_comm, HasCompactSupport.sup, MeasurableSpace.measurableSet_sup, ClosureOperator.closure_sup_closure_le, Finset.symmDiff_eq_union, Order.Coframe.MinimalAxioms.sup_sInf_eq, AddOreLocalization.cardinalMk_le_max, HahnSeries.cardSupp_inv_le, sSupHomClass.toSupBotHomClass, Filter.sup_liminf, RingCon.sup_eq_ringConGen, Associates.FactorSet.sup_add_inf_eq_add, Submodule.add_eq_sup, OrderHom.iterate_sup_le_sup_iff, IsLocalization.coeSubmodule_sup, max_le_max_right, Subring.map_sup, CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.D₂_W, Subspace.dualAnnihilator_inf_eq, TrivSqZeroExt.range_inlAlgHom_sup_adjoin_range_inr, inf_mul_sup, KaehlerDifferential.kerTotal_map', AddSubgroup.addSubgroupOf_sup, IntermediateField.normal_sup, edist_indicator, AddMonoidAlgebra.cardinalMk_of_infinite, AddSubmonoid.mem_sup_left, Set.Ioo_inter_Ioo, AddSubgroup.relIndex_sup_right, Submodule.sup_toAddSubgroup, AddSubgroup.map_sup, CategoryTheory.PreZeroHypercover.presieve₀_add, Ordinal.lsub_sum, Function.update_sup, MeasureTheory.OuterMeasure.map_sup, MeasureTheory.NullMeasurableSet.symmDiff, norm_sup_sub_sup_le_norm, IsMaxFilter.sup, max_sub_sub_right, isAddFoelner_iff, sup_Prop_eq, Filter.Germ.max_def, toBoolRing_symmDiff, Disjoint.symmDiff_left, iSup_sum, LinearMap.quotientInfEquivSupQuotient_surjective, Sublattice.mem_map_equiv, Finset.mem_sups, Set.Ioc.coe_sup, Order.Coframe.MinimalAxioms.iInf_sup_le_sup_sInf, CategoryTheory.Presheaf.isSheaf_sup, IsCyclotomicExtension.lcm_sup, SequentialSpace.sup, AffineSubspace.sup_direction_lt_of_nonempty_of_inter_empty, Set.Ioo_union_Ioo', Ideal.span_insert, bihimp_himp_right, sup_eq_add_posPart_sub, FreeAlgebra.cardinalMk_eq_max, MonomialOrder.degree_sPolynomial_lt_sup_degree, Submodule.map₂_sup_right, ZFSet.rank_union, Submonoid.sup_eq_closure, Set.smul_set_symmDiff₀, DoubleQuot.coe_liftSupQuotQuotMkₐ, csSup_union, IntermediateField.finiteDimensional_sup, Set.sups_subset_iff, Right.min_le_max_of_add_le_add, CovBy.sup_of_inf_left, Submodule.isOrtho_sup_left, lt_max_of_two_nsmul_lt_add, CovBy.sup_of_inf_right, Ordinal.preOmega_max, NonUnitalSubalgebra.mem_starClosure, le_sdiff_sup, IntermediateField.fixingSubgroup_sup, Set.symmDiff_union_subset, Submonoid.exists_mem_sup, MeasureTheory.dist_indicatorConstLp_eq_norm, Cardinal.add_eq_right_iff, CategoryTheory.Limits.CompleteLattice.coprod_eq_sup, SupHom.top_apply, Tropical.untrop_sup, OrderHom.coe_sup, OpenSubgroup.toSubgroup_sup, Function.locallyFinsuppWithin.max_apply, Subgroup.ofUnits_sup_units, Sym2.sup_mk, Multiset.sup_add, Coheyting.boundary_le_boundary_sup_sup_boundary_inf_right, sdiff_symmDiff_right, Codisjoint.eq_top, Cardinal.mk_finsupp_of_infinite', BoundedLatticeHom.coe_comp_lattice_hom, Antitone.sup, MvPolynomial.cardinalMk_eq_max_lift, iSup_or, Ordinal.toNatOrdinal_max, Set.IciExtend_apply, IsMaxOn.max, Set.image_subset_sups_left, lt_max_iff, Submodule.comap_sup_of_injective, LinearMap.range_add_le, DistribLattice.mem_ideal_sup_principal, FirstOrder.Language.Substructure.lift_card_closure_le, TopologicalLattice.toContinuousSup, GeneralizedCoheytingAlgebra.sdiff_le_iff, Order.Coframe.MinimalAxioms.sInf_sup_eq, Sublattice.map_sup, List.maximum_concat, IntermediateField.isPurelyInseparable_sup, AddSubgroup.map_le_map_iff', Submodule.small_sup, PSet.rank_pair, AddSubmonoid.comap_sup_map_of_injective, Complementeds.coe_sup, CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.Diagram.sup_W, OrderEmbedding.birkhoffFinset_sup, Disjoint.sup_sdiff_cancel_right, FreeAlgebra.cardinalMk_eq_max_lift, NonarchimedeanHomClass.map_add_le_max, Finset.image_symmDiff, IsGreatest.union, Cardinal.lift_max, Set.Iio_union_Ico', AddSubmonoid.mem_sup_right, DFinsupp.support_sup, List.maximum_append, Sum.Lex.inl_sup, IsMinFilter.max, LinearMap.prod_eq_sup_map, ConvexOn.le_max_of_mem_segment, AddSubgroup.normal_addSubgroupOf_sup_of_le_normalizer, CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.Diagram.sup_P, Nat.iSup_le_succ, Finset.mem_uIcc, MeasureTheory.IsStoppingTime.max_const, TrivSqZeroExt.range_liftAux, SSet.skeletonOfMono_succ, Monotone.disjointed_add_one_sup, Set.union_symmDiff_union_subset, Finset.max_abv_sum_one_le, sup_sdiff_symmDiff, max_add, MonomialOrder.sPolynomial_mul_monomial, SupHom.withTop_comp, max_div_div_right', LinearMap.surjective_domRestrict_iff, max_eq_iff, Finset.iSup_union, Antitone.map_sup, ContinuousMap.coe_sup, AlgebraicGeometry.Scheme.IdealSheafData.add_eq_sup, MvPolynomial.cardinalMk_eq_max, CategoryTheory.Presieve.isSheaf_sup, MonomialOrder.sPolynomial_leadingTerm_mul, CategoryTheory.Sieve.functorPullback_union, edist_mulIndicator, Set.subset_symmDiff_union_symmDiff_left, Algebra.Subalgebra.restrictScalars_adjoin, Algebraic.cardinalMk_lift_le_max, FirstOrder.Language.BoundedFormula.card_le, MonomialOrder.degree_sPolynomial, Function.mulSupport_sup, Algebra.rank_adjoin_le, LinearMap.ker_comp_eq_of_commute_of_disjoint_ker, Subgroup.sup_eq_closure, AddUnits.max_val, sInf_sup_sInf, add_tsub_eq_max, LinearMap.BilinForm.span_singleton_sup_orthogonal_eq_top, sup_le_of_le_sdiff_right, rel_sup_add, setOf_isOpen_sup, Submodule.comap_map_eq, sdiff_triangle
toPartialOrder 📖	CompOp	1618 math math: AlgebraicGeometry.Scheme.toSpecΓ_apply, partialSups_apply, upperBounds_supClosure, AlgebraicGeometry.Scheme.Opens.ι_image_basicOpen, AlgebraicGeometry.Γ_map_morphismRestrict, AlgebraicGeometry.Scheme.Hom.smoothLocus_eq_top_iff, IsCyclotomicExtension.adjoin_primitive_root_eq_top, Algebra.range_ofId, NonUnitalSubalgebra.center_eq_top, sInf_univ, CategoryTheory.sheafBotEquivalence_functor, Subalgebra.LinearDisjoint.inf_eq_bot, AlgebraicGeometry.Scheme.ΓSpecIso_inv_naturality_assoc, Submodule.rTensorOne_symm_apply, AlgebraicGeometry.Scheme.Hom.toPartialMap_hom, AlgebraicGeometry.Scheme.map_PrimeSpectrum_basicOpen_of_affine, coinduced_bot, AlgebraicGeometry.Scheme.bot_mem_grothendieckTopology, IntermediateField.finInsepDegree_top, Metric.cauchySeq_iff, LatticeHom.withTopWithBot_apply, SSet.Subcomplex.preimage_eq_top_iff, measurable_from_top, AlgebraicGeometry.IsAffineOpen.isoSpec_inv_appTop, AlgebraicGeometry.Scheme.germ_stalkClosedPointTo, le_sup_left, IntermediateField.adjoin_eq_top_iff_of_isAlgebraic, TopCat.Sheaf.interUnionPullbackCone_snd, iSupIndep.injOn_iInf, IntermediateField.LinearDisjoint.iff_inf_eq_bot, AlgebraicGeometry.ΓSpec.locallyRingedSpaceAdjunction_counit_app, MeasurableSpace.comap_const, AlgebraicGeometry.Scheme.IsQuasiAffine.toIsImmersion, AlgebraicGeometry.StructureSheaf.globalSectionsIso_inv, TopologicalSpace.Opens.mem_top, AlgebraicGeometry.iSup_affineOpens_eq_top, AlgebraicGeometry.isAffineOpen_top, Finset.truncatedSup_infs, AlgebraicGeometry.AffineSpace.isoOfIsAffine_inv, MeasureTheory.Measure.sub_top, AlgebraicGeometry.Scheme.support_nilradical, covBy_iff_le_iff_lt_right, partialSups_const_add, partialSups_succ', MeasureTheory.Egorov.tendstoUniformlyOn_diff_iUnionNotConvergentSeq, partialSups_mono, Submodule.comm_trans_lTensorOne, IntermediateField.coe_algebraMap_over_bot, RingCon.toCon_eq_bot, NonUnitalStarAlgebra.mem_bot, IsDedekindDomain.HeightOneSpectrum.iInf_localization_eq_bot, inf_right_le_sup_left, lt_compl_self, Algebra.adjoin_singleton_intCast, PseudoMetric.IsUltra.sup, Subalgebra.pi_top, AlgebraicGeometry.Scheme.Opens.toSpecΓ_SpecMap_presheaf_map_top, AlgebraicGeometry.LocallyRingedSpace.notMem_prime_iff_unit_in_stalk, sSup_univ, AlgebraicGeometry.Scheme.restrictFunctorΓ_inv_app, ContinuousAt.finset_sup, AddMonoidAlgebra.supDegree_single, AlgebraicGeometry.instIsDomainCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTopOfIsIntegral, MeasurableSpace.comap_bot, NormedCommGroup.cauchySeq_iff, MeasureTheory.Lp.cauchySeq_Lp_iff_cauchySeq_eLpNorm, MeasureTheory.OuterMeasure.mkMetric_top, GradedAlgebra.exists_finset_adjoin_eq_top_and_homogeneous_ne_zero, AffineBasis.tot, Algebra.mem_top, AlgebraicGeometry.AffineSpace.toSpecMvPolyIntEquiv_symm_apply, Filter.liminf_const_top, AlgebraicGeometry.Scheme.fromSpecStalk_toSpecΓ_assoc, AlgebraicGeometry.AffineSpace.SpecIso_hom_appTop, MeasureTheory.hittingAfter_bot_le_iff, AlgebraicGeometry.LocallyRingedSpace.basicOpen_eq_bot_iff_forall_evaluation_eq_zero, IsOpen.exists_subset_affineIndependent_span_eq_top, SSet.iSup_subcomplexOfSimplex_prod_eq_top, AlgebraicGeometry.Scheme.Hom.preimage_bot, OrderEmbedding.le_map_sup, IntermediateField.coe_bot, Submodule.mulMap_one_right_eq, OrdinalApprox.gfp_mem_range_gfpApprox, CompleteLattice.isCompactElement_finsetSup, not_supPrime, AlgebraicGeometry.Scheme.zeroLocus_eq_univ_iff_subset_nilradical, AlgebraicGeometry.Scheme.Opens.topIso_inv, CategoryTheory.Sieve.mem_iff_pullback_eq_top, bot_sdiff, IntermediateField.lift_insepDegree_bot', ciSup_partialSups_eq', NonUnitalAlgebra.coe_bot, bddAbove_iff_exists_ge, Metric.tendsto_atTop, iInf_of_empty, sSup_eq_bot, inseparable_top, TensorAlgebra.adjoin_range_ι, NonUnitalStarAlgebra.coe_bot, NonUnitalStarAlgebra.mem_top, sup_eq_sup_iff_left, AlgHom.equalizer_eq_top, IsCompl.bihimp_eq_bot, Finset.sup_add_le, iSup_false, algebraicClosure.algebraicClosure_eq_bot, AffineSubspace.comap_bot, PUnit.bot_eq, Filter.Tendsto.partialSups_apply, iInf_false, AlgebraicGeometry.Scheme.Hom.id_appTop, CategoryTheory.Presheaf.imageSieve_app, cauchySeq_iff_tendsto_dist_atTop_0, bot_lt_iSup, iInf_eq_top, ProbabilityTheory.indep_limsup_atTop_self, Filter.eventuallyConst_atTop, IsGaloisGroup.fixingSubgroup_top, Multiset.sup_zero, CategoryTheory.Presieve.isSheaf_bot, LatticeHom.coe_withTopWithBot, MeasurableSpace.generateFrom_empty, IsGaloisGroup.fixedPoints_top, RingCon.comap_bot, MeasureTheory.condLExp_bot', AlgebraicGeometry.Scheme.ideal_ker_le_ker_ΓSpecIso_inv_comp, Algebra.toSubsemiring_eq_top, IntermediateField.botEquiv_symm, Continuous.finset_sup, Subalgebra.op_bot, partialSups_eq_sup'_range, MeasureTheory.OuterMeasure.trim_top, IsLocalRing.closedPoint_mem_iff, AlgebraicGeometry.Scheme.isoSpec_inv_toSpecΓ, QuotientAddGroup.leftRel_eq_top, Finset.Nonempty.sup_eq_top_iff, Algebra.adjoin_singleton_algebraMap, RingCon.matrix_top, SSet.Subcomplex.range_eq_top, Multiset.le_sup, AlgHom.fieldRange_eq_map, IntermediateField.relfinrank_bot_right, Ne.lt_sup_or_lt_sup, Field.exists_primitive_element, isGalois_iff_isGalois_top, AlgebraicGeometry.isIso_ΓSpec_adjunction_unit_app_basicOpen, AlgebraicGeometry.isNoetherian_iff_of_finite_affine_openCover, Coheyting.boundary_top, AlgebraicGeometry.Scheme.ι_toIso_inv, Order.pred_injective, CategoryTheory.Subfunctor.range_toRange, UnitAddTorus.mFourierSubalgebra_closure_eq_top, CategoryTheory.Limits.CompleteLattice.finite_coproduct_eq_finset_sup, InfiniteGalois.mem_bot_iff_fixed, Frm.Iso.mk_hom, Algebra.toSubring_eq_top, AddCon.toSetoid_top, ProbabilityTheory.condIndep_bot_left, NumberField.adjoin_eq_top_of_infinitePlace_lt, Finset.sup'_Iic, Polynomial.IsSplittingField.splits_iff, AlgebraicGeometry.Scheme.IdealSheafData.equivOfIsAffine_apply, Partition.bot_notMem, SSet.Subcomplex.topIso_inv_app_coe, himp_bot, Finset.disjSups_singleton, bot_lt_affineSpan, ConditionallyCompleteLinearOrderedField.toZeroLEOneClass, Finset.ofDual_inf, biUnion_range_succ_disjointed, LatticeHom.withTopWithBot_id, polynomialFunctions.starClosure_topologicalClosure, Coheyting.hnot_boundary, Finset.le_truncatedSup, AlgebraicGeometry.Scheme.IdealSheafData.equivOfIsAffine_symm_apply, CategoryTheory.GrothendieckTopology.trivial_covering, hnot_symmDiff_self, AffineEquiv.span_eq_top_iff, Order.Ideal.coe_sup, AlgebraicGeometry.Scheme.SpecΓIdentity_hom_app, AffineSubspace.direction_eq_top_iff_of_nonempty, BooleanAlgebra.sdiff_eq, Filter.HasBasis.cauchySeq_iff, StarSubalgebra.bot_toSubalgebra, IsCompl.symmDiff_eq_top, SemilatInfCat_dual_comp_forget_to_partOrd, upperClosure_sups, Subfield.splits_bot, ConditionallyCompleteLinearOrder.compare_eq_compareOfLessAndEq, induced_const, Algebra.toSubring_bot, IdemCommSemiring.bot_le, affineSpan_singleton_union_vadd_eq_top_of_span_eq_top, AddMonoidAlgebra.supDegree_add_le, partialSups_add_one', integralClosure_eq_top_iff, interior_convexHull_nonempty_iff_affineSpan_eq_top, isGLB_Ioi, CompleteSublattice.top_mem, AlgebraicGeometry.Scheme.isoSpec_inv_preimage_zeroLocus, Subalgebra.LinearDisjoint.inf_eq_bot_of_commute, MvPolynomial.le_weightedTotalDegree, Coheyting.hnot_eq_top_iff_exists_boundary, TopologicalSpace.eq_top_iff_forall_inseparable, sSup_empty, AlgebraicGeometry.ProjectiveSpectrum.Proj.toOpen_toSpec_val_c_app_assoc, AlgebraicGeometry.PresheafedSpace.Γ_obj_op, le_sup_left, IntermediateField.adjoin_zero, TopCat.Sheaf.interUnionPullbackCone_fst, IntermediateField.adjoin_univ, AlgebraicGeometry.Scheme.Modules.toOpen_fromTildeΓ_app, TopCat.GlueData.MkCore.V_id, AffineSubspace.linear_topEquiv, Subalgebra.algebra_isAlgebraic_bot_right, UniformSpace.toTopologicalSpace_top, right_eq_sup, LowerAdjoint.closure_sup_closure_right, iSup_partialSups_eq, SemilatSupCat.Iso.mk_inv_toFun, CategoryTheory.Subfunctor.Subpresheaf.preimage_eq_top_iff, Subalgebra.comm_trans_rTensorBot, AffineSubspace.not_wSameSide_bot, AlgebraicGeometry.Scheme.bot_mem_precoverage, Finset.sup_erase_bot, symmDiff_top', CategoryTheory.Sieve.top_apply, Subalgebra.algebra_isAlgebraic_bot_left_iff, Algebra.EssFiniteType.adjoin_mem_finset, lt_inf_iff, AlgebraicGeometry.Scheme.Hom.preimage_top, partialSups_const_mul, Polynomial.IsSplittingField.adjoin_rootSet, AddCon.toSetoid_bot, AlgebraicGeometry.Scheme.isoSpec_hom, AlgebraicGeometry.Scheme.ι_toIso_inv_assoc, PseudoMetric.IsUltra.isTransitiveRel_closedBall, TopologicalSpace.Closeds.coe_eq_empty, AlgebraicGeometry.Proj.basicOpenToSpec_app_top, NonUnitalSubalgebra.prod_top, TopologicalSpace.NoetherianSpace.exists_finset_irreducible, AlgebraicGeometry.Scheme.Hom.image_top_eq_opensRange, ConditionallyCompleteLinearOrderedField.toPosMulStrictMono, MonotoneOn.of_map_sup, MeasurableSpace.map_const, Set.unbounded_le_inter_not_le, DistribLattice.le_sup_inf, NonUnitalStarAlgebra.coe_top, AlgebraicGeometry.Scheme.toSpecΓ_naturality_assoc, PseudoMetric.IsUltra.isTrans_closedBall, sSupHom.coe_bot, Sublocale.top_mem, AlgebraicGeometry.SurjectiveOnStalks.iff_of_isAffine, AlgebraicGeometry.SpecMap_ΓSpecIso_hom, Subalgebra.center_eq_top, CompleteBooleanAlgebra.sdiff_eq, NumberField.mixedEmbedding.exists_primitive_element_lt_of_isComplex, MeasureTheory.Egorov.measure_inter_notConvergentSeq_eq_zero, Nonneg.toNonneg_le, IsIntegrallyClosedIn.integralClosure_eq_bot, SSet.iSup_skeleton, integralClosure_idem, Set.bounded_lt_inter_not_lt, PrimeSpectrum.iSup_basicOpen_eq_top_iff, IsNormalClosure.adjoin_rootSet, partialSups_add_one, instIsAbelianGaloisSubtypeMemIntermediateFieldBot, AffineBasis.tot', LatticeHom.withTopWithBot_comp, CategoryTheory.Sieve.functorPullback_bot, himp_top, TopologicalSpace.Opens.isOpenEmbedding_obj_top, AlgebraicGeometry.LocallyRingedSpace.Γ_obj_op, Algebra.mem_bot, AlgebraicGeometry.AffineSpace.isoOfIsAffine_inv_appTop_coord, Fin.top_eq_last, Finset.sup_div_le, AlgebraicGeometry.AffineSpace.isoOfIsAffine_inv_over_assoc, CategoryTheory.Sieve.generate_bot, Metric.tendsto_atTop', SSet.Subcomplex.eq_top_iff_of_hasDimensionLT, AlgebraicGeometry.Scheme.isoSpec_hom_naturality, iInf₂_eq_top, induced_topology_pure, AlgebraicGeometry.Scheme.toSpecΓ_isoSpec_inv_assoc, FirstOrder.Language.Substructure.small_bot, CompletelyDistribLattice.sdiff_le_iff, WellFoundedGT.finite_ne_bot_of_iSupIndep, ite_le_sup, essInf_measure_zero, Polynomial.SplittingFieldAux.adjoin_rootSet, codisjoint_assoc, RingCon.subsingleton_quotient, PseudoMetric.IsUltra.bot, BddLat.forget_semilatSup_partOrd_eq_forget_bddOrd_partOrd, CategoryTheory.Sieve.generate_top, StarSubalgebra.mem_bot, SSet.Subcomplex.topIso_inv_ι, AlgebraicGeometry.Scheme.toSpecΓ_naturality, AlgebraicGeometry.Scheme.Hom.quasiFiniteLocus_eq_top, IntermediateField.fixingSubgroup_top, add_eq_left_iff_le, AffineSubspace.coe_eq_univ_iff, CategoryTheory.Sieve.equalizer_self, IntermediateField.bot_toSubalgebra, TopologicalSpace.Opens.mk_univ, top_bihimp, Algebra.toSubmodule_bot, Finset.sup'_mono, AlgebraicGeometry.LocallyRingedSpace.Γ_Spec_left_triangle, Algebra.map_bot, Subfield.mem_bot_iff_pow_eq_self, LatticeHom.withTopWithBot'_toFun, AlgebraicGeometry.RingedSpace.mem_top_basicOpen, Subfield.isTotallyReal_bot, PMF.toOuterMeasure_caratheodory, Set.bounded_le_inter_not_le, Fin.rev_top, IntermediateField.relfinrank_top_right, IndiscreteTopology.eq_top, Algebra.adjoin_singleton_zero, liminf_eq_top, Finset.inf_sup, AlgebraicGeometry.Scheme.Hom.toPartialMap_domain, Set.Icc.codisjoint_iff, UpperSet.Ici_sup, Algebra.coe_bot, CompleteLinearOrder.top_sdiff, Setoid.injective_iff_ker_bot, Submodule.toConvexCone_top, MeasureTheory.condLExp_bot, Filter.isBoundedUnder_le_sup, sSupHom.bot_apply, Order.pred_le_iff_eq_or_le, AlgebraicGeometry.IsAffineOpen.isoSpec_inv, Multiset.sup_coe, AlgebraicGeometry.Scheme.Γ_obj, CategoryTheory.Presieve.isSheafFor_top_sieve, OrderIso.supIrredLowerSet_symm_apply, AlgebraicGeometry.isLocallyNoetherian_iff_of_affine_openCover, ProbabilityTheory.condIndep_limsup_atTop_self, SSet.hasDimensionLT_subcomplex_top_iff, IntermediateField.restrictScalars_top, SSet.Subcomplex.instSubsingletonHomToSSetBot, Finset.isLUB_sup_id, EuclideanGeometry.Sphere.orthRadius_center, TopologicalSpace.isOpen_top_iff, AlgebraicGeometry.IsLocallyArtinian.isArtinianRing_of_isAffine, AlgebraicGeometry.StructureSheaf.toPushforwardStalkAlgHom_apply, AlgebraicGeometry.Scheme.preimage_basicOpen_top, isLUB_pair, Fin.top_eq_zero, MvPolynomial.adjoin_range_X, sup_top_eq, AlgebraicGeometry.Scheme.ΓSpecIso_inv, NonUnitalAlgebra.range_id, IntermediateField.mem_top, ENat.lift_one, bot_symmDiff, AlgebraicGeometry.Scheme.isoSpec_hom_naturality_assoc, AlgebraicGeometry.Scheme.isoSpec_inv_image_zeroLocus, Field.primitive_element_iff_algHom_eq_of_eval', Finset.bddAbove, sdiff_self, codisjoint_iff, Finset.le_sup_dite_pos, CategoryTheory.GrothendieckTopology.top_mem, IsDedekindDomain.integer_empty, AlgebraicGeometry.ΓSpec.locallyRingedSpaceAdjunction_counit_app', EMetric.cauchySeq_iff, AffineSubspace.not_sSameSide_bot, Subgroup.FG.finset_sup, adjoin_eq_top_of_conductor_eq_top, disjoint_partialSups_right, Subalgebra.eq_bot_of_finrank_one, AlgebraicGeometry.Scheme.Opens.ι_image_basicOpen_topIso_inv, IntermediateField.relrank_top_right, AlgebraicGeometry.SpecMap_ΓSpecIso_inv_toSpecΓ, AffineBasis.affineSpan_eq_top_of_toMatrix_left_inv, MeasureTheory.hittingBtwn_bot_le_iff, AlgebraicGeometry.Scheme.toSpecΓ_preimage_zeroLocus, Finset.truncatedSup_empty, continuous_bot, Algebra.coe_top, IntermediateField.LinearDisjoint.bot_left, TopologicalSpace.Opens.inclusion'_top_functor, FirstOrder.Language.Substructure.cg_bot, IntermediateField.isTotallyReal_bot, MeasureTheory.Measure.mkMetric_top, SSet.Subcomplex.eq_top_iff_contains_nonDegenerate, max_top_right, AlgebraicGeometry.Scheme.fromSpecStalk_appTop, ConditionallyCompleteLinearOrderedField.toIsOrderedCancelAddMonoid, Finset.sup_mul_le, Finset.max_eq_sup_coe, Subalgebra.unop_top, Filter.Tendsto.finset_sup_nhds, compl_inf_eq_bot, SupBotHom.bot_apply, AlgebraicGeometry.PresheafedSpace.Γ_map_op, Subalgebra.lTensorBot_one_tmul, ContinuousWithinAt.partialSups_apply, Projectivization.Subspace.span_empty, Order.pred_top_le_iff, SupClosed.directedOn, limsup_eq_bot, AlgebraicGeometry.Scheme.id_appTop, sSup_compact_eq_top, Subalgebra.mulMap_bot_left_eq, AlgebraicGeometry.Scheme.Opens.toSpecΓ_appTop_assoc, OrderIsoClass.toSupBotHomClass, AffineSubspace.bot_coe, Convex.interior_nonempty_iff_affineSpan_eq_top, IntermediateField.instFiniteSubtypeMemBot, NormedAddCommGroup.cauchySeq_iff, Polynomial.adjoin_rootSet_eq_range, AffineSubspace.parallel_bot_iff_eq_bot, CategoryTheory.Presheaf.equalizerSieve_self_eq_top, bot_sup_eq, essSup_const_bot, not_bddBelow_iff, AlgebraicGeometry.Scheme.fromSpecStalk_toSpecΓ, le_partialSups_of_le, AlgebraicGeometry.Scheme.ker_toSpecΓ, TopCat.Presheaf.map_germ_eq_Γgerm, Algebra.top_toSubmodule, comp_partialSups, SSet.Subcomplex.preimage_range, AlgebraicGeometry.Scheme.ker_of_isAffine, Subalgebra.fg_of_submodule_fg, AlgebraicGeometry.IsAffineOpen.algebraMap_Spec_obj, AlgebraicGeometry.isBasis_basicOpen, inf_le_iff, SupPrime.not_isMin, CompleteSublattice.bot_mem, AlgebraicGeometry.Scheme.Γevaluation_naturality_apply, partialSups_eq_sup_range, CliffordAlgebra.adjoin_range_ι, AlgebraicGeometry.Flat.flat_and_surjective_iff_faithfullyFlat_of_isAffine, CompleteLattice.isCompactElement_iff_exists_le_iSup_of_le_iSup, AntitoneOn.of_map_sup, AlgebraicGeometry.LocallyRingedSpace.coe_toΓSpecSheafedSpace_hom_base_hom_apply_asIdeal, le_pow_sup, CategoryTheory.Limits.CompleteLattice.finiteColimitCocone_cocone_ι_app, Polynomial.Splits.adjoin_rootSet_eq_range, IntermediateField.finrank_eq_one_iff, Setoid.top_def, AlgebraicGeometry.isIntegral_appTop_of_universallyClosed, IntermediateField.lift_top, min_top_left, IdemSemiring.toMulLeftMono, AddMonoidAlgebra.supDegree_zero, iSup_eq_top, TopHom.sup_apply, partialSups_monotone, ENNReal.tendsto_atTop, AlgebraicGeometry.ΓSpec.adjunction_counit_app, IntermediateField.eq_bot_of_isAlgClosed_of_isAlgebraic, AlgebraicGeometry.tilde.isoTop_hom, CategoryTheory.Subfunctor.range_eq_top, borel_eq_top_of_discrete, IntermediateField.insepDegree_bot', Filter.HasBasis.cauchySeq_iff', CoheytingHomClass.map_top, Submonoid.FG.finset_sup, AlgebraicGeometry.Scheme.Opens.toSpecΓ_appTop, CategoryTheory.Subfunctor.Subpresheaf.image_top, right_lt_sup, Order.pred_le_pred_iff, PrimeSpectrum.basicOpen_zero, AlgebraicGeometry.ProjectiveSpectrum.Proj.toStalk_stalkMap_toSpec_assoc, GradedAlgebra.exists_finset_adjoin_eq_top_and_homogeneous, Finset.sup_Iic, AlgebraicGeometry.Γ_restrict_isLocalization, IntermediateField.restrictScalars_eq_top_iff, CategoryTheory.GrothendieckTopology.bot_covers, AffineSubspace.smul_bot, isDenseEmbedding_pure, TopologicalSpace.Opens.coe_eq_empty, CategoryTheory.top_apply, AlgebraicGeometry.ProjectiveSpectrum.Proj.toStalk_stalkMap_toSpec, NonUnitalAlgebra.toSubmodule_bot, Finset.coe_sup', ScottContinuousOn.sup₂, AlgebraicGeometry.ΓSpecIso_obj_hom, not_supIrred_bot, CategoryTheory.GrothendieckTopology.Cover.preOneHypercover_sieve₁, sup_hnot_self, le_of_sup_eq, disjointed_add_one, AlgebraicGeometry.Spec.germ_stalkMapIso_hom_assoc, CauchySeq.comp_injective, Order.pred_lt_iff_eq_or_lt, PrimeSpectrum.iInf_localization_eq_bot, AlgebraicGeometry.Scheme.Hom.preimage_basicOpen_top, partialSups_mul_const, IntermediateField.bot_eq_top_of_finrank_adjoin_eq_one, Finset.sup_empty, Setoid.mk_eq_top, MeasureTheory.OuterMeasure.comap_top, TopCat.Sheaf.objSupIsoProdEqLocus_hom_fst, CategoryTheory.Sieve.overEquiv_top, ProbabilityTheory.iIndep_comap_mem_iff, IntermediateField.botContinuousSMul, Field.exists_primitive_element_of_finite_bot, CategoryTheory.GrothendieckTopology.close_eq_top_iff_mem, TopologicalSpace.Opens.functor_obj_map_obj, Subalgebra.unop_bot, AffineSubspace.parallel_iff_direction_eq_and_eq_bot_iff_eq_bot, CategoryTheory.Sieve.arrows_eq_top_iff, LowerAdjoint.closure_sup_closure_left, AlgebraicGeometry.exists_appTop_π_eq_of_isAffine_of_isLimit, CategoryTheory.Sieve.arrows_top, Finset.mem_disjSups, Frm.Iso.mk_inv, QuotientAddGroup.rightRel_eq_top, partialSups_succ, AlgebraicGeometry.Scheme.OpenCover.iSup_opensRange, AlgebraicGeometry.SheafedSpace.IsOpenImmersion.image_preimage_is_empty, Set.sep_sups_le, AffineSubspace.mem_top, Algebra.bijective_algebraMap_iff, Subalgebra.topEquiv_apply, BooleanAlgebra.inf_compl_le_bot, CategoryTheory.topologyOfClosureOperator_sieves, hnot_top, UpperSet.coe_iciSupHom, Field.exists_primitive_element_of_finite_top, IntermediateField.adjoin_simple_eq_top_iff_of_isAlgebraic, continuous_top, AlgebraicGeometry.Scheme.Γevaluation_naturality_assoc, essInf_const_top, AlgebraicGeometry.Scheme.IdealSheafData.coe_support_ofIdealTop, Set.Ici.coe_sup, SSet.instHasDimensionLTToSSetBotSubcomplex, sup_eq_left, himp_eq_top_iff, CategoryTheory.MorphismProperty.bot_mem_precoverage, IntermediateField.rank_adjoin_eq_one_iff, LatticeHom.withTop'_toFun, AlgebraicGeometry.ΓSpec.toOpen_comp_locallyRingedSpaceAdjunction_homEquiv_app, AddGroupTopology.toTopologicalSpace_top, sSup_diff_singleton_bot, AlgebraicGeometry.Scheme.Opens.toSpecΓ_top, TopologicalSpace.Closeds.coe_bot, IntermediateField.adjoin_one, IntermediateField.rank_top, CompleteDistribLattice.top_sdiff, directedOn_of_sup_mem, CategoryTheory.sheafBotEquivalence_inverse_map_val, OrdinalApprox.lfpApprox_ord_eq_lfp, CategoryTheory.Sieve.generate_of_singleton_isSplitEpi, AlgebraicGeometry.AffineSpace.SpecIso_inv_appTop_coord, CategoryTheory.Sieve.functorPullback_top, max_eq_top, Finset.truncatedSup_singleton, AlgebraicGeometry.germ_stalkClosedPointIso_hom_assoc, AlgebraicGeometry.Scheme.IdealSheafData.support_eq_top_iff, TopologicalSpace.Opens.coe_finset_sup, NonUnitalAlgebra.top_toNonUnitalSubsemiring, Quotient.subsingleton_iff, Setoid.bot_def, CategoryTheory.Subfunctor.Subpresheaf.bot_obj, Subfield.bot_eq_of_zMod_algebra, PowerBasis.adjoin_gen_eq_top, SemilatSupCat.dual_map, StarSubalgebra.eq_top_iff, IntermediateField.adjoin_root_eq_top, codisjoint_iff_le_sup, AffineSubspace.smul_top, ConvexCone.toPointedCone_top, MeasurableSpace.measurableSet_bot_iff, Subfield.map_bot, iInf_ne_top_subtype, CategoryTheory.GrothendieckTopology.discrete_eq_top, TopCat.Presheaf.map_germ_eq_Γgerm_assoc, le_sup_right, Submodule.comm_trans_rTensorOne, NonUnitalStarAlgebra.top_toNonUnitalSubalgebra, partialSups_eq_sUnion_image, CoheytingHom.map_top', MeasureTheory.OuterMeasure.zero_caratheodory, Finset.fold_sup_univ, TopCat.Sheaf.interUnionPullbackConeLift_right, ConvexCone.mem_top, left_or_right_lt_sup, CategoryTheory.Limits.CompleteLattice.finite_colimit_eq_finset_univ_sup, CategoryTheory.sheafBotEquivalence_unitIso, MeasureTheory.Content.innerContent_bot, IntermediateField.extendScalars_self, MeasureTheory.OuterMeasure.top_caratheodory, AlgebraicGeometry.StructureSheaf.globalSectionsIso_hom, Polynomial.degree_sum_le, ClosureOperator.closure_sup_closure_right, IntermediateField.finrank_top, Finset.sup_eq_top_iff, hnot_bot, KleeneAlgebra.one_le_kstar, le_compl_self, NonUnitalStarAlgebra.range_eq_top, Finset.sup_const_le, csSup_empty, separableClosure.eq_top_iff, ProbabilityTheory.iIndepSet.iIndep_comap_mem, Algebra.top_toSubring, Set.Ico_inter_Ici, AlgebraicGeometry.ΓSpec.left_triangle, CategoryTheory.Subfunctor.eq_top_iff_isIso, AlgebraicGeometry.Scheme.Modules.toOpen_fromTildeΓ_app_assoc, CategoryTheory.sheafBotEquivalence_inverse_obj_val, AlgebraicGeometry.AffineSpace.comp_homOfVector, IntermediateField.top_toSubalgebra, Subfield.roots_X_pow_char_sub_X_bot, untrop_sum, CompleteBooleanAlgebra.le_sup_inf, IntermediateField.relrank_top_left, left_lt_sup, Submodule.lTensorOne'_tmul, one_le_kstar, AlgebraicGeometry.Scheme.instIsOpenImmersionToSpecΓOfIsQuasiAffine, Finset.coe_sup_of_nonempty, AlgebraicGeometry.Scheme.homOfLE_appTop, Order.Frame.le_himp_iff, Submodule.rTensorOne'_tmul_one, WithTop.ge_of_forall_gt_iff_ge, IsGaloisGroup.fixedPoints_bot, AlgebraicGeometry.Scheme.isoSpec_inv_naturality_assoc, AlgebraicGeometry.IsAffineOpen.fromSpec_app_self, nhds_top, Con.toSetoid_eq_bot, MeasureTheory.condExp_bot, Submodule.rTensorOne'_tmul, TopologicalSpace.Opens.mem_bot, AlgebraicGeometry.PresheafedSpace.restrictTopIso_hom, Finset.sup_prodMap, exists_root_adjoin_eq_top_of_isCyclic, AlgebraicGeometry.AffineSpace.hom_ext_iff, iSupIndep.injOn, AlgebraicGeometry.ΓSpec.unop_locallyRingedSpaceAdjunction_counit_app', Heyting.Regular.coe_bot, Finset.exists_sup_ge, MeasurableSpace.generateFrom_singleton_univ, Quantale.mul_bot, AlgebraicGeometry.Scheme.isoSpec_Spec_hom, ENat.lift_zero, sSup_atoms_eq_top, IntermediateField.finrank_eq_one_iff_eq_top, SSet.Subcomplex.iSup_ofSimplex_nonDegenerate_eq_top, SupBotHom.coe_sup, Finset.sup_sub_le, AlgebraicGeometry.tilde.isIso_toOpen_top, SupHom.withTop'_toFun, CompleteLinearOrder.himp_bot, sup_eq_bot_iff, iSupIndep_ne_bot, Subfield.extendScalars_top, AlgebraicGeometry.HasRingHomProperty.appTop, AlgebraicGeometry.LocallyRingedSpace.basicOpen_zero, semilatticeSup_mk'_partialOrder_eq_semilatticeInf_mk'_partialOrder, AffineSubspace.mk'_top, Algebra.zariskisMainProperty_iff_exists_saturation_eq_top, NumberField.is_primitive_element_of_infinitePlace_lt, StarSubalgebra.coe_bot, Finset.max_eq_sup_withBot, UniformSpace.toTopologicalSpace_bot, CompHausLike.LocallyConstant.locallyConstantIsoContinuousMap_hom, Set.Ici.codisjoint_iff, CategoryTheory.Presheaf.isLocallySurjective_iff_range_sheafify_eq_top, MonoidAlgebra.exists_finset_adjoin_eq_top, AlgebraicGeometry.Scheme.isNilpotent_iff_basicOpen_eq_bot, IntermediateField.finrank_adjoin_eq_one_iff, IntermediateField.bot_eq_top_of_rank_adjoin_eq_one, sSup_eq_bot', SeparationQuotient.inseparableSetoid_eq_top_iff, AlgebraicGeometry.Scheme.isPullback_toSpecΓ_toSpecΓ, CompleteLinearOrder.le_himp_iff, AlgebraicGeometry.Scheme.instSubsingletonCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensBot, partialSups_eq_biSup, AlgebraicGeometry.Scheme.ΓSpecIso_naturality, MeasureTheory.Egorov.notConvergentSeqLTIndex_spec, AlgebraicGeometry.Scheme.restrictFunctorΓ_hom_app, add_le_iff, Partition.bot_notMem', IntermediateField.finrank_bot, symmDiff_self, sdiff_sdiff_self, LowerAdjoint.closure_sup_closure, PowerBasis.adjoin_eq_top_of_gen_mem_adjoin, NonUnitalAlgebra.eq_top_iff, AlgebraicGeometry.SheafedSpace.Γ_map, sup_eq_maxDefault, IsIntegrallyClosed.integralClosure_eq_bot, IsIntegrallyClosed.integralClosure_eq_bot_iff, Polynomial.IsSplittingField.adjoin_rootSet', IntermediateField.sepDegree_bot, AlgebraicGeometry.germ_stalkClosedPointIso_hom, bddLat_dual_comp_forget_to_semilatSupCat, ProbabilityTheory.Kernel.iIndep_comap_mem_iff, AddQuantale.add_bot, Set.unbounded_le_Ioi, AlgebraicGeometry.Scheme.toSpecΓ_isoSpec_inv, Submodule.rTensorOne_tmul, AlgebraicGeometry.IsFinite.instHasAffinePropertyAndIsAffineFiniteCarrierObjOppositeOpensCarrierCarrierCommRingCatPresheafOpOpensTopHomAppTop, isLeast_pair, AlgebraicGeometry.IsAffineOpen.instIsAffineToSchemeBasicOpen, IntermediateField.finInsepDegree_bot', OrdinalApprox.gfpApprox_ord_eq_gfp, CategoryTheory.Coverage.eq_top_pullback, IntermediateField.restrictScalars_bot_eq_self, sup_bot_eq, Asymptotics.isBigO_atTop_iff_eventually_exists, SupHomClass.toOrderHomClass, AlgebraicGeometry.Scheme.toIso_inv_ι_assoc, AlgebraicGeometry.SheafedSpace.restrictTopIso_inv, AlgebraicGeometry.Scheme.toSpecΓ_appTop, Asymptotics.isBigO_atTop_iff_eventually_exists_pos, Order.Coframe.top_sdiff, IntermediateField.fg_bot, Finset.image_subset_Iic_sup, Filter.limsInf_top, SupPrime.le_sup, Finset.sup'_le_iff, ContinuousWithinAt.finset_sup, AlgebraicGeometry.Scheme.IdealSheafData.support_eq_bot_iff, add_eq_right_iff_le, CategoryTheory.Presheaf.isLocallySurjective_iff_range_sheafify_eq_top', GroupTopology.toTopologicalSpace_bot, AlgHom.range_eq_top, Algebra.adjoin_singleton_one, CategoryTheory.Subfunctor.Subpresheaf.epi_iff_range_eq_top, NonUnitalAlgebra.mem_top, NonUnitalStarAlgebra.toNonUnitalSubalgebra_eq_top, SSet.Subcomplex.image_top, CompleteSublattice.coe_bot, AffineSubspace.affineSpan_eq_top_iff_vectorSpan_eq_top_of_nonempty, IntermediateField.adjoin_empty, AffineSubspace.topEquiv_symm_apply_coe, FrameHom.coe_toInfTopHom, ciSup_of_empty, Fin.bot_eq_zero, Field.Emb.Cardinal.eq_bot_of_not_nonempty, AlgebraicGeometry.StructureSheaf.algebraMap_obj_top_bijective, TopologicalSpace.Opens.inclusion'_map_eq_top, IntermediateField.rank_bot, Subalgebra.centralizer_eq_top_iff_subset, AlgebraicGeometry.IsAffineOpen.fromSpec_preimage_self, iSup_eq_dif, CategoryTheory.Limits.CompleteLattice.pushout_eq_sup, separableClosure_inf_perfectClosure, inf_compl_self, MeasureTheory.Measure.add_top, biUnion_Iic_disjointed, AlgebraicGeometry.LocallyRingedSpace.Γevaluation_naturality_apply, Algebra.top_toSubsemiring, Subalgebra.rTensorBot_tmul_one, EMetric.tendsto_atTop, sdiff_eq_bot_iff, AlgebraicGeometry.Spec_zeroLocus_eq_zeroLocus, AlgebraicGeometry.Scheme.Opens.ι_appTop, MeasureTheory.hitting_bot_le_iff, ContinuousWithinAt.partialSups, Finset.sup_inf, cauchySeq_const, LatticeHom.withTopWithBot_toFun, Subfield.bot_eq_of_charZero, IsIntegrallyClosedIn.integralClosure_eq_bot_iff, CompletelyDistribLattice.le_himp_iff, AffineMap.map_top_of_surjective, AlgebraicGeometry.Scheme.map_basicOpen, bddLat_dual_comp_forget_to_semilatInfCat, CategoryTheory.Subfunctor.Subpresheaf.top_obj, MeasureTheory.IsSetRing.partialSups_mem, ClosureOperator.closure_sup_closure_left, NonUnitalAlgebra.adjoin_univ, AlgebraicGeometry.isRetrocompact_basicOpen, GeneralizedBooleanAlgebra.inf_inf_sdiff, Order.pred_top_lt_iff, AlgebraicGeometry.Scheme.isoSpec_inv_naturality, IntermediateField.bot_eq_top_iff_finrank_eq_one, FrameHom.map_sSup', ContinuousOn.partialSups, ClosureOperator.closure_sup_closure, TopCat.Sheaf.objSupIsoProdEqLocus_inv_snd, PseudoMetric.IsUltra.finsetSup, IntermediateField.adjoin_eq_bot_iff, MeasureTheory.SimpleFunc.simpleFunc_bot', Submodule.rTensorOne_tmul_one, AlgebraicGeometry.Scheme.Hom.quasiFiniteLocus_eq_top_iff, AlgebraicGeometry.instQuasiSeparatedToSpecΓOfQuasiSeparatedSpaceCarrierCarrierCommRingCat, CategoryTheory.Sieve.pullback_eq_top_of_mem, CategoryTheory.GrothendieckTopology.trivial_eq_bot, AlgebraicGeometry.Scheme.comp_appTop_assoc, FirstOrder.Language.Substructure.closure_empty, AlgebraicGeometry.Proj.basicOpen_one, KleeneAlgebra.mul_kstar_le_kstar, Filter.limsup_bot, Set.Iic.coe_sup, ciSup_partialSups_eq, IntermediateField.lift_sepDegree_bot', CompletelyDistribLattice.top_sdiff, GeneralizedHeytingAlgebra.le_himp_iff, Subalgebra.op_top, AlgebraicGeometry.Scheme.isoSpec_Spec, CategoryTheory.Subfunctor.Subpresheaf.range_id, AffineSubspace.coe_eq_bot_iff, iSup₂_eq_bot, essSup_measure_zero, Algebra.adjoin_singleton_natCast, IntermediateField.LinearDisjoint.inf_eq_bot, Order.isPredLimitRecOn_pred, Field.exists_primitive_element_iff_finite_intermediateField, AlgebraicGeometry.IsClosedImmersion.hasAffineProperty, Field.Emb.Cardinal.filtration_apply, SupBotHom.sup_apply, FirstOrder.Language.Substructure.map_bot, AlgebraicGeometry.Scheme.preimage_opensRange_toSpecΓ, indiscreteTopology_iff, AlgebraicGeometry.Scheme.Spec.algebraMap_residueFieldIso_inv, Subalgebra.bot_eq_top_iff_finrank_eq_one, Subalgebra.mulMap_bot_right_eq, ContinuousAt.partialSups, EMetric.cauchySeq_iff_le_tendsto_0, AlgebraicGeometry.Scheme.eq_zeroLocus_of_isClosed_of_isAffine, Finset.isLUB_sup', Preorder.instHasBinaryCoproducts, AddMonoidAlgebra.exists_finset_adjoin_eq_top, TopCat.Sheaf.interUnionPullbackConeLift_left, AlgebraicGeometry.Scheme.Opens.ι_preimage_self, CategoryTheory.Subfunctor.instIsIsoFunctorTypeιTop, BotHom.sup_apply, sup_le_iff, trop_iInf, AddSubgroup.FG.finset_sup, CategoryTheory.Subfunctor.bot_obj, AlgebraicGeometry.Scheme.toSpecΓ_image_zeroLocus, AlgebraicGeometry.PresheafedSpace.ofRestrict_top_c, partialSups_zero, Finset.sup_eq_iSup, AlgebraicGeometry.toSpecΓ_SpecMap_ΓSpecIso_inv_assoc, AlgebraicGeometry.SheafedSpace.Γ_obj_op, Algebra.isAlgebraic_iff, TopologicalSpace.Closeds.coe_top, Subalgebra.lTensorBot_symm_apply, AlgebraicGeometry.IsAffineOpen.fromSpec_app_self_apply, NonUnitalStarAlgebra.comap_top, FreeAlgebra.adjoin_range_ι, ContinuousMap.subalgebra_topologicalClosure_eq_top_of_separatesPoints, max_top_left, Con.toSetoid_bot, min_top_right, Finset.untrop_sum, MeasureTheory.sigmaFinite_bot_iff, SSet.Subcomplex.topIso_inv_ι_assoc, AlgebraicGeometry.Scheme.inv_appTop, IntermediateField.finrank_top', Order.Coframe.sdiff_le_iff, AlgebraicGeometry.isLocalization_away_of_isAffine, instIsDirectedOrder, Finset.map_truncatedSup, AlgebraicGeometry.IsAffineOpen.ι_basicOpen_preimage, iSup_neg, CategoryTheory.Limits.CompleteLattice.hasFiniteColimits_of_semilatticeSup_orderBot, AffineSubspace.direction_top, Affine.Simplex.span_eq_top, IntermediateField.lift_bot, NumberField.mixedEmbedding.exists_primitive_element_lt_of_isReal, IsGalois.fixedField_top, WithBot.sInf_empty, UpperSet.iciSupHom_apply, TopologicalSpace.Opens.eq_bot_or_top, map_partialSups, AlgebraicGeometry.morphismRestrict_appTop, IsLocalRing.closed_point_mem_iff, CompleteLinearOrder.compare_eq_compareOfLessAndEq, IdemSemiring.toCanonicallyOrderedAdd, AlgebraicGeometry.Scheme.IdealSheafData.ofIdealTop_ideal, Algebra.IsAlgebraic.isNormalClosure_iff, iInf_top, Finset.isLUB_sup, MeasureTheory.hittingAfter_eq_sInf, MeasureTheory.condLExp_bot_ae_eq, AlgebraicGeometry.Scheme.Hom.preimage_opensRange, StarSubalgebra.toSubalgebra_eq_top, AlgebraicGeometry.ΓSpecIso_hom_stalkClosedPointIso_inv, StarSubalgebra.mem_top, AlgebraicGeometry.AffineSpace.toSpecMvPolyIntEquiv_apply, CategoryTheory.GrothendieckTopology.bot_covering, SupHom.withBot'_toFun, Submodule.mulMap_one_left_eq, AffineSubspace.isEmpty_bot, Set.finite_iff_bddAbove, AlgebraicGeometry.LocallyRingedSpace.Γ_map, IntermediateField.adjoin_simple_eq_bot_iff, IntermediateField.relfinrank_bot_left, AlgebraicGeometry.isCompactOpen_iff_eq_basicOpen_union, exists_subset_affineIndependent_affineSpan_eq_top, AlgebraicGeometry.Spec.algebraMap_stalkIso_inv, le_inf_sup, RingCon.matrix_bot, CompleteLinearOrder.le_total, Algebra.adjoin_adjoin_coe_preimage, TopologicalSpace.Closeds.coe_finset_sup, HeytingHomClass.map_bot, AlgebraicGeometry.eq_top_of_sigmaSpec_subset_of_isCompact, Algebra.adjoin_top, TopologicalSpace.Opens.mk_empty, FrameHomClass.toInfTopHomClass, bihimp_self, iSup_ne_bot_subtype, AlgebraicGeometry.PresheafedSpace.Γ_obj, AffineSubspace.perpBisector_eq_top, IntermediateField.adjoin_intCast, Algebra.adjoin_root_eq_top_of_isSplittingField, Finset.filter_sups_le, inf_sSup_eq_iSup_inf_sup_finset, ContinuousOn.finset_sup, AlgebraicGeometry.PresheafedSpace.toRestrictTop_c, Algebra.surjective_algebraMap_iff, IntermediateField.sepDegree_bot', Polynomial.supDegree_eq_degree, CategoryTheory.Presheaf.isSheaf_bot, AlgebraicGeometry.Scheme.isoSpec_inv_toSpecΓ_assoc, TopHom.coe_sup, IntermediateField.LinearDisjoint.bot_right, Filter.limsSup_bot, Finset.sup_eq_bot_of_isEmpty, AffineSubspace.pointwise_vadd_bot, Field.primitive_element_iff_minpoly_degree_eq, Algebra.toSubmodule_eq_top, AlgHom.fieldRange_eq_top, Order.pred_lt_pred_iff, iSup_emptyset, WithSeminorms.tendsto_nhds_atTop, discreteTopology_bot, sup_eq_right, DualNumber.range_inlAlgHom_sup_adjoin_eps, AlgebraicGeometry.Scheme.toOpen_eq, isPurelyInseparable_iff_perfectClosure_eq_top, Fin.cast_top, SemilatSupCat.Iso.mk_hom_toFun, compl_bihimp_self, RingCon.coe_bot, IntermediateField.rank_eq_one_iff, bot_himp, Subalgebra.fg_bot, Algebra.adjoin_univ, AlgHom.equalizer_same, IntermediateField.eq_bot_of_isPurelyInseparable_of_isSeparable, CategoryTheory.Subfunctor.image_top, PUnit.top_eq, TopologicalSpace.Closeds.coe_eq_univ, AffineIndependent.affineSpan_eq_top_iff_card_eq_finrank_add_one, ProjectiveSpectrum.basicOpen_zero, IntermediateField.adjoin_root_eq_top_of_isSplittingField, CompleteDistribLattice.sdiff_le_iff, AlgebraicGeometry.ΓSpecIso_inv_ΓSpec_adjunction_homEquiv, algebraicClosure.eq_top_iff, AffineSubspace.not_sOppSide_bot, disjoint_partialSups_left, LatticeHom.withBot'_toFun, CompleteDistribLattice.MinimalAxioms.iInf_sup_le_sup_sInf, IsOpen.exists_between_affineIndependent_span_eq_top, Setoid.eq_top_iff, AffineSubspace.top_coe, AlgebraicGeometry.toSpecΓ_SpecMap_ΓSpecIso_inv, Field.primitive_element_iff_minpoly_natDegree_eq, sInfHom.coe_top, AlgebraicGeometry.instIsIsoModulesSpecOfCarrierFromTildeΓUnitOpensCarrierCarrierCommRingCatRingCatSheaf, Subalgebra.fg_top, NonUnitalAlgebra.toSubmodule_eq_top, isDenseInducing_pure, symmDiff_eq_bot, Finset.toDual_sup, AlgebraicGeometry.Scheme.Hom.inv_appTop, SSet.iSup_skeletonOfMono, affineSpan_coe_preimage_eq_top, AffineSubspace.pointwise_vadd_top, IntermediateField.isScalarTower_over_bot, ProbabilityTheory.condVar_bot', ProbabilityTheory.Kernel.indep_limsup_atTop_self, MeasureTheory.AEEqFun.le_sup_right, TwoSidedIdeal.top_ringCon, SupIrred.not_isMin, AffineSubspace.perpBisector_self, AntitoneOn.of_map_inf, AlgebraicGeometry.Spec_zeroLocus, IntermediateField.bot_toSubfield, AlgebraicGeometry.Scheme.ΓSpecIso_inv_naturality, compl_inf_self, IntermediateField.topEquiv_symm_apply_coe, AffineSubspace.span_empty, top_sup_eq, NonUnitalStarAlgebra.map_bot, AffineSubspace.map_bot, le_iff_exists_sup, affineSpan_eq_top_of_nonempty_interior, Subalgebra.lTensorBot_tmul, NonUnitalAlgebra.adjoin_empty, SSet.iSup_range_eq_top_of_isColimit, IntermediateField.rank_top', Subalgebra.topEquiv_symm_apply_coe, TopCat.Presheaf.isSheaf_on_punit_iff_isTerminal, upperBounds_range_partialSups, AlgebraicGeometry.Scheme.SpecΓIdentity_inv_app, partialSups_eq_ciSup_Iic, MeasureTheory.OuterMeasure.boundedBy_top, kstar_mono, AlgebraicGeometry.Scheme.Pullback.diagonalCoverDiagonalRange_eq_top_of_injective, iInf_eq_dif, Set.Iic.codisjoint_iff, CompleteSublattice.coe_top, CategoryTheory.Sieve.functorPushforward_bot, ConditionallyCompleteLinearOrder.le_total, IntermediateField.topEquiv_apply, partialSups_iff_forall, ProbabilityTheory.condIndep_bot_right, Order.Frame.himp_bot, mem_bot_iff_intCast, AlgebraicGeometry.basicOpen_eq_of_affine', IntermediateField.adjoin_natCast, AlgebraicGeometry.AffineSpace.isoOfIsAffine_hom_appTop, TopologicalSpace.Opens.coe_bot, AffineSubspace.topEquiv_apply, AlgebraicGeometry.instIsDominantToSpecΓOfCompactSpaceCarrierCarrierCommRingCat, PseudoMetric.coe_sup, AlgebraicGeometry.Scheme.preimage_eq_top_of_closedPoint_mem, Lattice.inf_le_left, iInf_extend_top, ScottContinuous.sup₂, TopologicalSpace.Closeds.isClopen_singleton_bot, IsCyclotomicExtension.singleton_one, MeasureTheory.hittingBtwn_eq_sInf, TopCat.Sheaf.objSupIsoProdEqLocus_hom_snd, SSet.finite_subcomplex_top_iff, inf_lt_iff, AlgebraicGeometry.Scheme.isoSpec_Spec_inv, Algebra.adjoin_restrictScalars, OrderIso.map_sup, Set.partialSups_eq_accumulate, NonUnitalAlgebra.coe_top, QuotientGroup.rightRel_eq_top, NonUnitalAlgebra.map_top, IntermediateField.isPurelyInseparable_bot, AddQuantale.bot_add, AlgebraicGeometry.Scheme.germ_stalkClosedPointTo_assoc, AlgebraicGeometry.Scheme.topIso_hom, MeasurableSpace.generateFrom_singleton, AlgebraicGeometry.finite_appTop_of_universallyClosed, AffineSubspace.span_univ, IntermediateField.top_toSubfield, TopologicalSpace.IsOpenCover.iSup_eq_top, AffineSubspace.map_eq_bot_iff, NonUnitalAlgebra.to_subring_eq_top, PointwiseConvergenceCLM.tendsto_nhds_atTop, RingOfIntegers.exponent_eq_one_iff, disjointed_succ, sSup_eq_top, AlgebraicGeometry.specTargetImageFactorization_app_injective, Subalgebra.rTensorBot_symm_apply, Algebra.comap_top, Finset.sup_mono, AlgebraicGeometry.PresheafedSpace.Γ_map, MeasureTheory.tendstoUniformlyOn_of_ae_tendsto_of_measurable_edist, NonUnitalAlgebra.toNonUnitalSubring_eq_top, codisjoint_map_orderIso_iff, ProbabilityTheory.indep_bot_right, AlgebraicGeometry.StructureSheaf.toOpenₗ_top_bijective, ProbabilityTheory.condVar_bot_ae_eq, AffineSubspace.direction_bot, Set.unbounded_lt_inter_not_lt, CategoryTheory.Sieve.functorInclusion_top_isIso, MeasureTheory.upperCrossingTime_zero', MaximalSpectrum.iInf_localization_eq_bot, CompleteBooleanAlgebra.top_le_sup_compl, AffineBasis.isUnit_toMatrix_iff, Algebra.IsCentral.center_eq_bot, IsGaloisGroup.fixingSubgroup_bot, Set.exists_seq_iSup_eq_top_iff_countable, BddLat.coe_forget_to_semilatSup, Polynomial.degree_sum_eq_of_disjoint, Fin.rev_zero_eq_top, AlgebraicGeometry.AffineSpace.isoOfIsAffine_hom, sInfHomClass.toInfTopHomClass, AddMonoidAlgebra.supDegree_mul_le, AffineSubspace.instNonemptySubtypeMemTop, Finset.sup_eq_sSup_image, ProbabilityTheory.indep_bot_left, AlgebraicGeometry.affineAnd_apply, IntermediateField.fg_top, instDiscreteMeasurableSpace, Submodule.lTensorOne_symm_apply, Order.isPredPrelimitRecOn_pred, MeasureTheory.OuterMeasure.top_apply', AlgebraicGeometry.AffineSpace.reindex_appTop_coord, AlgebraicGeometry.Spec.algebraMap_stalkIso_inv_assoc, IntermediateField.finInsepDegree_bot, MvPolynomial.supported_empty, Nonneg.coe_toNonneg, IsCyclotomicExtension.iff_adjoin_eq_top, not_supIrred, Order.pred_eq_pred_iff, AlgEquiv.fieldRange_eq_top, LinearOrder.bot_topologicalSpace_eq_generateFrom, MeasureTheory.SimpleFunc.simpleFunc_bot, Field.Emb.Cardinal.iSup_adjoin_eq_top, AlgebraicGeometry.ΓSpec.toSpecΓ_of, affineSpan_eq_bot, AddMonoidAlgebra.sup_support_add_le, ProbabilityTheory.condVar_bot, fixedPoints.lfp_eq_sSup_iterate, Filter.limsup_const_bot, symmDiff_hnot_self, sInf_diff_singleton_top, JacobsonNoether.exists_separable_and_not_isCentral', BooleanAlgebra.top_le_sup_compl, AlgebraicGeometry.exists_appTop_π_eq_of_isLimit, tendsto_atTop_nhds, AlgebraicGeometry.IsAffine.affine, le_kstar, StarSubalgebra.coe_top, AlgebraicGeometry.AffineTargetMorphismProperty.IsLocal.to_basicOpen, AlgebraicGeometry.SheafedSpace.Γ_obj, AddMonoidAlgebra.supDegree_sub_le, Fin.rev_last_eq_bot, Submodule.lTensorOne'_one_tmul, AlgebraicGeometry.Scheme.IdealSheafData.vanishingIdeal_top, AlgebraicGeometry.Proj.basicOpen_zero, Finset.le_sup_dite_neg, IntermediateField.finrank_bot', AlgebraicGeometry.Scheme.mem_basicOpen_top, sdiff_top, ConvexCone.isGenerating_top, Set.unbounded_lt_Ici, Quantale.bot_mul, CategoryTheory.Pretopology.toGrothendieck_bot, EMetric.cauchySeq_iff_NNReal, Partition.bot_lt_of_mem, AlgebraicGeometry.Scheme.Opens.ι_image_basicOpen', AlgebraicGeometry.LocallyRingedSpace.Γevaluation_naturality_assoc, Algebra.eq_top_iff, Filter.liminf_bot, Setoid.mk_eq_bot, AffineSubspace.comap_top, ENNReal.tendsto_atTop_zero, fourierSubalgebra_closure_eq_top, himp_self, IdemSemiring.bot_le, Filter.limsInf_bot, Continuous.partialSups_apply, AlgebraicGeometry.AffineSpace.homOverEquiv_apply, NonUnitalStarAlgebra.range_id, CategoryTheory.isFiltered_of_semilatticeSup_nonempty, Subalgebra.rank_eq_one_iff, sdiff_bot, Multiset.sup_le, DiscreteTopology.eq_bot, Subalgebra.prod_top, pow_le_kstar, CategoryTheory.Sieve.overEquiv_symm_top, TopCat.Sheaf.objSupIsoProdEqLocus_inv_fst, NonUnitalAlgebra.comap_top, MeasureTheory.Measure.toOuterMeasure_top, hnot_sup_self, NonUnitalStarAlgebra.map_top, Finset.sup_le_iff, AlgebraicGeometry.Scheme.comp_appTop, IntermediateField.botEquiv_def, AlgebraicGeometry.IsClosedImmersion.isAffine_surjective_of_isAffine, CategoryTheory.sieve₁'_toPreOneHypercover_eq_top, PseudoMetric.coe_finsetSup, subalgebra_top_finrank_eq_submodule_top_finrank, IntermediateField.adjoin_eq_top_iff, Valuation.Integers.integralClosure, Fin.range_natAdd_eq_Ioi, MeasureTheory.Egorov.measure_notConvergentSeq_tendsto_zero, IntermediateField.finSepDegree_bot', IsCyclotomicExtension.Rat.adjoin_singleton_eq_top, AlgebraicGeometry.Scheme.fromSpecStalk_app, HeytingHom.map_bot', ContinuousOn.partialSups_apply, AlgebraicGeometry.AffineSpace.toSpecMvPolyIntEquiv_comp, Algebra.IsUnramifiedAt.exists_notMem_forall_ne_mem_and_adjoin_eq_top, AlgebraicGeometry.isField_of_universallyClosed, polynomialFunctions.topologicalClosure, Nonneg.toNonneg_coe, sInf_empty, RingCon.range_mkₐ, AlgebraicGeometry.LocallyRingedSpace.Γevaluation_eq_zero_iff_notMem_basicOpen, left_eq_sup, stronglyMeasurable_bot_iff, Finset.sup'_image₂_le, AlgebraicGeometry.Scheme.Spec.algebraMap_residueFieldIso_inv_assoc, compl_top, IntermediateField.eq_bot_of_isSepClosed_of_isSeparable, WellFoundedLT.finite_ne_bot_of_iSupIndep, MeasurableSpace.map_top, iSup_eq_if, ConditionallyCompleteLinearOrderBot.csSup_empty, FirstOrder.Language.Substructure.elementarySkolem₁Reduct.instSmall, Algebra.map_top, CategoryTheory.Subfunctor.top_obj, bot_bihimp, Order.Ideal.mem_sup, Finset.sup_apply, Subalgebra.eq_bot_of_rank_le_one, sup_eq_sup_iff_right, AlgebraicGeometry.Scheme.Hom.smoothLocus_eq_top, CategoryTheory.Sieve.functorPushforward_top, BotHom.coe_sup, NonUnitalStarSubalgebra.center_eq_top, AlgebraicGeometry.IsAffineOpen.fromSpec_top, IntermediateField.bot_eq_top_of_finrank_adjoin_le_one, CategoryTheory.Presieve.isSeparatedFor_top, Submodule.lTensorOne_tmul, AddCon.toSetoid_eq_bot, IntermediateField.relrank_bot_right, le_of_sup_eq', AlgebraicGeometry.Scheme.IdealSheafData.support_top, Subalgebra.comm_trans_lTensorBot, InfiniteGalois.fixedField_bot, CompletelyDistribLattice.himp_bot, Set.Ioi.coe_sup, NonUnitalAlgebra.map_bot, AlgebraicGeometry.Scheme.map_basicOpen_map, CompleteLattice.ωScottContinuous.top, CompleteLattice.sInf_le, StarAlgHom.range_eq_map_top, IsSepClosed.separableClosure_eq_bot_iff, MeasureTheory.OuterMeasure.isCaratheodory_partialSups, Subfield.closure_empty, AlgebraicGeometry.Scheme.Hom.comp_appTop, HeytingAlgebra.himp_bot, NonUnitalStarAlgebra.eq_top_iff, GeneralizedBooleanAlgebra.sup_inf_sdiff, Subalgebra.bot_eq_top_of_finrank_eq_one, AlgebraicGeometry.IsIntegralHom.hasAffineProperty, RingCon.toCon_eq_top, AlgebraicGeometry.Scheme.germ_stalkClosedPointTo_Spec, MeasureTheory.OuterMeasure.map_top_of_surjective, AlgebraicGeometry.Scheme.basicOpen_zero, CategoryTheory.Limits.CompleteLattice.instHasBinaryCoproductsOfOrderBot, iInf_eq_bot, AlgebraicGeometry.instHasAffinePropertyIsomorphismsSchemeAndIsAffineIsIsoCommRingCatAppTop, eq_bot_of_singletons_open, untrop_sum_eq_sInf_image, MvPolynomial.supported_univ, conductor_eq_top_iff_adjoin_eq_top, fixedPoints.gfp_eq_sInf_iterate, Subalgebra.isAlgebraic_bot_iff, TwoSidedIdeal.bot_ringCon, AdjoinRoot.adjoinRoot_eq_top, AlgebraicGeometry.isAffineOpen_bot, AlgebraicGeometry.Scheme.IsLocallyDirected.V_self, List.foldr_sup_eq_sup_toFinset, borel_eq_top_of_countable, CategoryTheory.GrothendieckTopology.top_mem', TopCat.Presheaf.Γgerm_res_apply, IntermediateField.extendScalars_top, iInf₂_eq_bot, ciSup_false, ConditionallyCompleteLinearOrderedField.toIsStrictOrderedRing, SupBotHom.coe_bot, perfectClosure.eq_bot_of_isSeparable, ConvexCone.coe_top, MeasurableSpace.measurableSet_top, CategoryTheory.Presheaf.equalizerSieve_eq_top_iff, ProbabilityTheory.Kernel.indep_bot_left, IntermediateField.fixedField_bot, Order.Frame.MinimalAxioms.inf_sSup_le_iSup_inf, NonUnitalAlgebra.range_eq_top, WithTop.le_of_forall_lt_iff_le, BooleanAlgebra.le_top, MeasureTheory.Egorov.exists_notConvergentSeq_lt, AlgebraicGeometry.LocallyRingedSpace.Γevaluation_ne_zero_iff_mem_basicOpen, AlgebraicGeometry.basicOpen_eq_of_affine, AlgebraicGeometry.LocallyRingedSpace.Γ_map_op, OrdinalApprox.lfp_mem_range_lfpApprox, MeasureTheory.AEEqFun.le_sup_left, FrameHom.toFun_eq_coe, AlgebraicGeometry.Scheme.ΓSpecIso_naturality_assoc, top_himp, AlgebraicGeometry.IsAffineOpen.fromSpec_toSpecΓ_assoc, Complex.adjoin_I, partialSups_bot, SSet.Subcomplex.range_eq_top_iff, Con.toSetoid_top, Partition.coe_removeBot, AlgebraicGeometry.PresheafedSpace.toRestrictTop_base, AlgebraicGeometry.LocallyRingedSpace.isUnit_res_toΓSpecMapBasicOpen, Heyting.isRegular_bot, AlgebraicGeometry.ΓSpec_adjunction_homEquiv_eq, ContinuousMap.elemental_id_eq_top, CompleteLattice.isCompactElement_iff_exists_le_sSup_of_le_sSup, MeasureTheory.OuterMeasure.map_top, Algebra.FiniteType.out, Continuous.partialSups, polynomialFunctions_closure_eq_top', le_partialSups, AffineSubspace.affineSpan_eq_top_iff_vectorSpan_eq_top_of_nontrivial, Projectivization.Subspace.span_univ, AlgebraicGeometry.Scheme.toIso_inv_ι, FirstOrder.Language.Substructure.instIsEmptySubtypeMemBotOfConstants, IntermediateField.insepDegree_bot, Set.Ici_inter_Ici, IsAlgClosed.algebraicClosure_eq_bot_iff, IntermediateField.rank_bot', OpenSubgroup.toOpens_top, Finset.sup_bot, iInf_eq_if, Order.Ideal.mem_sInf, TopologicalSpace.Opens.map_top, CategoryTheory.Functor.imageSieve_map, partialSups_eq_biUnion_range, kstar_eq_self, cauchySeq_iff_tendsto, AlgebraicGeometry.LocallyRingedSpace.toΓSpec_preimage_zeroLocus_eq, AlgebraicGeometry.LocallyRingedSpace.SpecΓIdentity_hom_app, covBy_iff_lt_iff_le_right, CategoryTheory.Sieve.pullback_top, IntermediateField.insepDegree_top, Order.pred_lt_iff, KleeneAlgebra.kstar_mul_le_kstar, ProjectiveSpectrum.basicOpen_one, Filter.blimsup_false, Order.Ideal.coe_inf, AlgebraicGeometry.Scheme.Γevaluation_naturality, MeasureTheory.condExp_bot', Order.Ideal.sup_mem_iff, IsGalois.tfae, Subfield.card_bot, AlgebraicGeometry.basicOpen_eq_bot_iff, RingCon.coe_top, OpenAddSubgroup.toOpens_top, CategoryTheory.Limits.CompleteLattice.finiteColimitCocone_cocone_pt, AlgebraicGeometry.Scheme.IdealSheafData.ker_glueDataObjι_appTop, CategoryTheory.Sieve.uliftFunctorInclusion_top_isIso, AlgebraicGeometry.Spec.germ_stalkMapIso_hom, Finset.sup_univ_eq_iSup, IntermediateField.LinearDisjoint.eq_bot_of_self, NonUnitalStarSubalgebra.prod_top, ProbabilityTheory.Kernel.indep_bot_right, Finset.sup_image₂_le, separableClosure.separableClosure_eq_bot, codisjoint_left_comm, le_sup_right, AlgebraicGeometry.Spec.fromSpecStalk_eq, NonUnitalAlgebra.top_toSubring, ContinuousMapZero.elemental_eq_top, AlgebraicGeometry.AffineSpace.isoOfIsAffine_inv_over, SemilatSupCat_dual_comp_forget_to_partOrd, IntermediateField.fg_top_iff, Finset.subset_Iic_sup_id, AlgebraicGeometry.LocallyRingedSpace.basicOpen_eq_bot_of_isNilpotent, CategoryTheory.GrothendieckTopology.top_covers, CategoryTheory.Presieve.factorsThru_top, NonUnitalAlgebra.mem_bot, AlgebraicGeometry.LocallyRingedSpace.Γevaluation_naturality, AlgebraicGeometry.Proj.iSup_basicOpen_eq_top, AlgebraicGeometry.IsAffineOpen.fromSpec_preimage_basicOpen', CompleteLattice.le_sSup, induced_top, AlgebraicGeometry.Scheme.IdealSheafData.support_bot, SupPrime.le_finset_sup, AlgebraicGeometry.Scheme.Hom.opensRange_of_isIso, AlgebraicGeometry.LocallyRingedSpace.toΓSpecMapBasicOpen_eq, Submodule.lTensorOne_one_tmul, IntermediateField.relfinrank_top_left, Order.Ideal.finsetSup_mem_iff, CompleteLinearOrder.sdiff_le_iff, iSup_of_empty, AlgebraicGeometry.Scheme.Opens.instIsIsoCommRingCatAppLEιTopToScheme, sInf_eq_top, iInf_neg, AlgebraicGeometry.IsAffineOpen.ΓSpecIso_hom_fromSpec_app, CategoryTheory.sheafBotEquivalence_counitIso, Finset.truncatedSup_infs_of_notMem, GroupTopology.toTopologicalSpace_top, Fin.val_top, EMetric.cauchySeq_iff', iInf_lt_top, Con.toSetoid_eq_top, MeasureTheory.OuterMeasure.dirac_caratheodory, LowerAdjoint.closure_sup_closure_le, IntermediateField.finSepDegree_top, SSet.N.iSup_subcomplex_eq_top, IsOpen.affineSpan_eq_top, CategoryTheory.Sieve.id_mem_iff_eq_top, BooleanAlgebra.bot_le, AffineSubspace.not_wOppSide_bot, AlgebraicGeometry.instQuasiCompactToSpecΓOfCompactSpaceCarrierCarrierCommRingCat, IsAdjoinRoot.primitive_element_root, AddMonoidAlgebra.supDegree_withBot_some_comp, AlgebraicGeometry.AffineSpace.comp_homOfVector_assoc, AlgebraicGeometry.Scheme.Opens.ι_image_top, Subfield.extendScalars_self, PseudoMetric.finsetSup_apply, Field.Emb.Cardinal.adjoin_basis_eq_top, NonUnitalAlgebra.top_toSubmodule, iSup_eq_bot, Algebra.TensorProduct.adjoin_tmul_eq_top, AlgebraicGeometry.Scheme.Γ_obj_op, Metric.cauchySeq_iff', ContinuousMap.starSubalgebra_topologicalClosure_eq_top_of_separatesPoints, BiheytingAlgebra.top_sdiff, partialSups_add_one_eq_sup_disjointed, IntermediateField.relrank_bot_left, SSet.Subcomplex.topIso_hom, CompleteBooleanAlgebra.inf_compl_le_bot, Subalgebra.LinearDisjoint.eq_bot_of_commute_of_self, codisjoint_right_comm, CategoryTheory.Sieve.pullback_ofObjects_eq_top, CategoryTheory.isFilteredOrEmpty_of_semilatticeSup, Finset.le_sup', AlgebraicGeometry.Scheme.basicOpen_eq_bot_iff_forall_evaluation_eq_zero, AlgebraicGeometry.HasRingHomProperty.iff_of_source_openCover, MeasureTheory.SimpleFunc.approx_apply, AddSubmonoid.FG.finset_sup, Subalgebra.finrank_bot, Order.pred_lt_iff_eq_or_gt, AlgebraicGeometry.Scheme.Opens.topIso_hom, MeasureTheory.SimpleFunc.finset_sup_apply, MeasureTheory.OuterMeasure.top_apply, Multiset.sup_mono, CategoryTheory.presheafIsGeneratedBy_of_isFinite, ZMod.fieldRange_castHom_eq_bot, CategoryTheory.Limits.CompleteLattice.finiteColimitCocone_isColimit_desc, Subalgebra.restrictScalars_top, isLUB_supClosure, QuotientGroup.leftRel_eq_top, PrimeSpectrum.basicOpen_one, bihimp_hnot_self, AlgebraicGeometry.Scheme.Hom.comp_appTop_assoc, AlgebraicGeometry.IsAffineOpen.fromSpec_app_of_le, AffineSubspace.eq_bot_or_nonempty, MeasureTheory.Measure.top_add, AlgebraicGeometry.AffineSpace.map_appTop_coord, top_symmDiff', AlgebraicGeometry.Scheme.toSpecΓ_preimage_basicOpen, PrimeSpectrum.iSup_basicOpen_eq_top_iff', Filter.bliminf_false, ConditionallyCompleteLinearOrderedField.toMulPosStrictMono, MeasureTheory.hitting_eq_sInf, AlgebraicGeometry.isIso_fromTildeΓ_iff, top_sdiff', Finset.sup_eq_bot_iff, IntermediateField.mem_bot, AlgebraicGeometry.PresheafedSpace.restrictTopIso_inv, Algebra.IsCentral.out, polynomialFunctions_closure_eq_top, AlgebraicGeometry.Scheme.openCoverBasicOpenTop_f, partialSups_le_iff, IsDedekindDomain.integer_univ, Set.unbounded_le_Ici, bihimp_top, PredOrder.prelimitRecOn_pred, PseudoMetric.sup_apply, AlgebraicGeometry.LocallyRingedSpace.toΓSpecSheafedSpace_hom_c_app, IsAdjoinRoot.adjoin_root_eq_top, NonUnitalAlgebra.toNonUnitalSubring_top, SemilatSupCat.coe_forget_to_partOrd, iInf_emptyset, bddAbove_range_partialSups, Set.Icc.coe_sup, Order.Ideal.mem_inf, AlgebraicGeometry.isField_of_isIntegral_of_subsingleton, TopologicalSpace.Opens.not_nonempty_iff_eq_bot, AlgebraicGeometry.ProjectiveSpectrum.Proj.toOpen_toSpec_val_c_app, Finset.sup_id_eq_sSup, CategoryTheory.PreOneHypercover.sieve₀_trivial, Set.Ioc.codisjoint_iff, CategoryTheory.Subfunctor.preimage_eq_top_iff, IntermediateField.fixingSubgroup_bot, CategoryTheory.Subfunctor.Subpresheaf.eq_top_iff_isIso, iSup₂_eq_top, symmDiff_bot, Finset.exists_sup_eq_iSup, CategoryTheory.Presieve.isSheafFor_top, AlgebraicGeometry.IsAffineOpen.fromSpec_toSpecΓ, Subalgebra.bot_eq_top_iff_rank_eq_one, IntermediateField.coe_top, AlgebraicGeometry.AffineSpace.homOfVector_appTop_coord, Monotone.of_map_sup, BiheytingAlgebra.sdiff_le_iff, min_eq_top, isGalois_bot, AlgebraicGeometry.Scheme.IsQuasiAffine.isBasis_basicOpen, Subalgebra.rTensorBot_tmul, Fin.zero_eq_top, AlgebraicGeometry.Scheme.isoSpec_image_zeroLocus, disjointed_partialSups, ClosureOperator.closure_sup_closure_le, iSup_extend_bot, Algebra.range_id, sSupHomClass.toSupBotHomClass, Metric.uniformCauchySeqOn_iff, Polynomial.SplittingField.adjoin_rootSet, AlgebraicGeometry.isCompact_and_isOpen_iff_finite_and_eq_biUnion_basicOpen, isSplittingField_iff_intermediateField, OrderHom.iterate_sup_le_sup_iff, iSup_bot, AlgebraicGeometry.PresheafedSpace.restrict_top_presheaf, isGalois_iff_isGalois_bot, Fin.rev_bot, cauchySeq_of_controlled, TrivSqZeroExt.range_inlAlgHom_sup_adjoin_range_inr, AddMonoidAlgebra.supDegree_prod_le, Monotone.of_left_le_map_sup, MeasureTheory.exists_measure_iInter_lt, Polynomial.adjoin_X, MeasureTheory.SimpleFunc.monotone_approx, AffineSubspace.bot_parallel_iff_eq_bot, bihimp_eq_top, FirstOrder.Language.Substructure.fg_bot, MvPolynomial.weightedTotalDegree_zero, CompleteDistribLattice.MinimalAxioms.inf_sSup_le_iSup_inf, Filter.Tendsto.partialSups, bihimp_bot, TopologicalSpace.Opens.coe_top, partialSups_add_const, CategoryTheory.Subfunctor.epi_iff_range_eq_top, IntermediateField.finrank_adjoin_simple_eq_one_iff, CompleteLattice.ωScottContinuous.bot, Set.Ioc.coe_sup, CategoryTheory.PreOneHypercover.sieve₁_trivial, StarSubalgebra.top_toSubalgebra, Order.Coframe.MinimalAxioms.iInf_sup_le_sup_sInf, mul_kstar_le_kstar, CategoryTheory.Subfunctor.Subpresheaf.range_eq_top, AlgebraicGeometry.LocallyRingedSpace.toΓSpec_preimage_basicOpen_eq, instIndiscreteTopology, SupHom.mk_le_mk, Subalgebra.LinearDisjoint.eq_bot_of_self, Order.Ideal.coe_sInf, NonUnitalAlgebra.toNonUnitalSubsemiring_eq_top, TopologicalSpace.Opens.coe_eq_univ, sInf_eq_bot, Field.primitive_element_iff_algHom_eq_of_eval, inf_compl_eq_bot, AlgebraicGeometry.IsAffineOpen.isoSpec_hom_appTop, separableClosure.eq_bot_iff, Subalgebra.LinearDisjoint.bot_left, Finset.disjiUnion_Iic_disjointed, Subalgebra.rank_bot, AlgebraicGeometry.instIsIsoModulesSpecOfCarrierFromTildeΓFreeOpensCarrierCarrierCommRingCat, CategoryTheory.Subfunctor.range_id, partialSups_disjoint_of_disjoint, trop_sInf_image, Subalgebra.LinearDisjoint.bot_right, IntermediateField.rank_adjoin_simple_eq_one_iff, CategoryTheory.Limits.CompleteLattice.coprod_eq_sup, separableClosure.adjoin_eq_of_isAlgebraic_of_isSeparable, AddCon.toSetoid_eq_top, OrderHom.coe_sup, notMem_iff_exists_ne_and_isConjRoot, ContinuousAt.partialSups_apply, AlgebraicGeometry.instIsAffineHomιBasicOpen, compl_bot, Algebra.adjoin_empty, Subalgebra.fg_bot_toSubmodule, Algebra.botEquiv_symm_apply, MeasurableSpace.generateFrom_singleton_empty, NonUnitalStarAlgebra.toNonUnitalSubalgebra_bot, AffineSubspace.notMem_bot, Set.unbounded_lt_Ioi, not_supPrime_bot, exists_glb_Ioi, lowerBounds_Ioi, DistribLattice.mem_ideal_sup_principal, GeneralizedCoheytingAlgebra.sdiff_le_iff, MeasureTheory.condExp_bot_ae_eq, CategoryTheory.Sieve.generate_of_contains_isSplitEpi, Subalgebra.rank_top, AlgebraicGeometry.HasRingHomProperty.iff_of_isAffine, Subalgebra.bot_eq_top_of_rank_eq_one, RingCon.toCon_bot, sInfHom.top_apply, CategoryTheory.Subfunctor.Subpresheaf.range_toRange, AlgebraicGeometry.SheafedSpace.restrictTopIso_hom, IsGalois.mem_bot_iff_fixed, Pi.partialSups_apply, IdemSemiring.toMulRightMono, Subalgebra.finrank_eq_one_iff, Finset.sup_of_mem, AlgebraicGeometry.ΓSpec.toSpecΓ_unop, MeasureTheory.OuterMeasure.toMeasure_top, IntermediateField.map_bot, subalgebra_top_rank_eq_submodule_top_rank, PrimeSpectrum.basicOpen_eq_bot_iff, AlgebraicGeometry.Scheme.IdealSheafData.vanishingIdeal_bot, AlgebraicGeometry.SheafedSpace.Γ_map_op, AlgebraicGeometry.Scheme.isNilpotent_iff_basicOpen_eq_bot_of_isCompact, IdemSemiring.toIsOrderedAddMonoid, kstar_mul_le_kstar, Finset.le_sup, RingCon.toCon_top, PredOrder.colimitRecOn_pred, isCyclic_tfae, separableClosure.eq_bot_of_isPurelyInseparable, Subalgebra.eq_bot_of_isPurelyInseparable_of_isSeparable, Subalgebra.finite_bot, IntermediateField.finSepDegree_bot, affineSpan_eq_top_iff_nonempty_of_subsingleton, AlgebraicGeometry.SpecMap_ΓSpecIso_inv_toSpecΓ_assoc, kstar_eq_one, CategoryTheory.GrothendieckTopology.top_covering, Lattice.inf_le_right, Filter.limsSup_top, AddMonoidAlgebra.supDegree_sum_le, Fin.succ_top, AlgebraicGeometry.LocallyRingedSpace.Γ_obj, CoheytingAlgebra.top_sdiff, AddGroupTopology.toTopologicalSpace_bot, AlgebraicGeometry.Scheme.Spec_fromSpecStalk, IntermediateField.sepDegree_top, IsGaloisGroup.fixedPoints_eq_bot, MeasureTheory.tendstoUniformlyOn_of_ae_tendsto, SSet.skeleton_zero, AlgebraicGeometry.Scheme.toSpecΓ_base

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
dual_dual 📖	mathematical	—	OrderDual.instSemilatticeSup OrderDual OrderDual.instSemilatticeInf	—	ext
ext 📖	—	Preorder.toLE PartialOrder.toPreorder toPartialOrder	—	—	PartialOrder.ext ext_sup
ext_sup 📖	mathematical	Preorder.toLE PartialOrder.toPreorder toPartialOrder	toMax	—	eq_of_forall_ge_iff sup_le_iff
le_sup_left 📖	mathematical	—	Preorder.toLE PartialOrder.toPreorder toPartialOrder sup	—	—
le_sup_right 📖	mathematical	—	Preorder.toLE PartialOrder.toPreorder toPartialOrder sup	—	—
sup_le 📖	mathematical	Preorder.toLE PartialOrder.toPreorder toPartialOrder	sup	—	—

Subtype

Definitions

Name	Category	Theorems
lattice 📖	CompOp	4 math math: LatticeHom.subtypeVal_coe, LatticeHom.subtypeVal_apply, BoundedLatticeHom.subtypeVal_coe, BoundedLatticeHom.subtypeVal_apply
semilatticeInf 📖	CompOp	7 math math: coe_inf, InfTopHom.subtypeVal_coe, Finset.inf_coe, mk_inf_mk, InfHom.subtypeVal_coe, InfTopHom.subtypeVal_apply, InfHom.subtypeVal_apply
semilatticeSup 📖	CompOp	7 math math: SupHom.subtypeVal_coe, coe_sup, Finset.sup_coe, SupBotHom.subtypeVal_coe, SupBotHom.subtypeVal_apply, SupHom.subtypeVal_apply, mk_sup_mk

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
coe_inf 📖	mathematical	SemilatticeInf.toMin	semilatticeInf	—	—
coe_sup 📖	mathematical	SemilatticeSup.toMax	semilatticeSup	—	—
mk_inf_mk 📖	mathematical	SemilatticeInf.toMin	semilatticeInf	—	—
mk_sup_mk 📖	mathematical	SemilatticeSup.toMax	semilatticeSup	—	—

ULift

Definitions

Name	Category	Theorems
instDistribLattice 📖	CompOp	—
instLattice 📖	CompOp	—
instLinearOrder 📖	CompOp	—
instSemilatticeInf 📖	CompOp	—
instSemilatticeSup 📖	CompOp	—

(root)

Definitions

Name	Category	Theorems
DistribLattice 📖	CompData	—
SemilatticeInf 📖	CompData	—
SemilatticeSup 📖	CompData	—
instDistribLatticeNat 📖	CompOp	38 math math: DFinsupp.toMultiset_sup, Fin.map_valEmbedding_uIcc, Nat.uIcc_eq_range', Multiset.toFinsupp_union, Set.ncard_uIcc_nat, Fin.preimage_val_uIcc_val, Polynomial.natDegree_sum_eq_of_disjoint, Finset.subset_range_sup_succ, Multiset.toFinsupp_inter, Nat.cast_finsetSup', PNat.uIcc_eq_finset_subtype, Polynomial.degree_sum_le, Nat.factorization_lcm, SimpleGraph.extremalNumber_of_fintypeCard_eq, Fin.attachFin_uIcc, DFinsupp.toMultiset_inf, Polynomial.degree_add_le_of_le, PNat.map_subtype_embedding_uIcc, Polynomial.supDegree_eq_degree, Nat.cast_finsetInf', Polynomial.degree_sub_le, Multiset.count_finset_sup, Nat.sup_divisors_id, Nat.cast_finsetSup, Polynomial.degree_sum_eq_of_disjoint, Fin.image_val_uIcc, Polynomial.degree_add_le, Polynomial.degree_update_le, Fin.finsetImage_val_uIcc, Multiset.toDFinsupp_inter, Multiset.toDFinsupp_union, Finsupp.toMultiset_sup, Polynomial.degree_sub_le_of_le, Polynomial.supDegree_eq_natDegree, Polynomial.degree_add_eq_of_leadingCoeff_add_ne_zero, Nat.factorization_gcd, Finsupp.toMultiset_inf, Nat.card_uIcc
instDistribLatticeOfLinearOrder 📖	CompOp	4205 math math: countable_image_lt_image_Ioi_within, max_choice, SuccOrder.hasBasis_nhds_Ioc, max_sub_min_eq_abs', PredOrder.nhdsGT_eq_nhdsNE, HahnSeries.order_lt_iff_exists, Affine.Simplex.sSameSide_affineSpan_faceOpposite_point_left_iff, units_inv_smul, Function.Embedding.encard_le, LinearOrder.isSuccArchimedean_iff_isPredArchimedean, le_iff_forall_lt_one_mul_le, RingCone.nonneg.isMaxCone, Set.finite_diff_iUnion_Ioo, tsub_lt_self_iff, HurwitzZeta.hasSum_int_hurwitzZetaOdd, Multiset.Ico_sub_Ico_right, AddUnits.orderEmbeddingVal_apply, one_le_div_iff, AffineSubspace.sOppSide_iff_exists_right, GenContFract.IntFractPair.nth_stream_fr_nonneg_lt_one, Int.ceil_lt_iff, Mathlib.Meta.NormNum.isNNRat_lt_false, ENat.add_lt_top, HahnSeries.SummableFamily.powerSeriesFamily_add, continuousOn_ceil, PNat.bot_eq_one, Valuation.IsRankOneDiscrete.generator_lt_one, mul_self_nonneg, nhds_basis_one_mabs_lt, sign_intCast, Cardinal.natCast_lt_toENat_iff, hasSum_mellin_pi_mul_sq', Ordinal.toNimber_eq_zero, mul_nonpos_iff_neg_imp_nonneg, IsCompact.bddBelow, Finset.min'_union, Finset.sup_add_sup, Filter.Tendsto.max_left, AddCircle.coe_equivIco_mk_apply, PNat.addLeftMono, WithTop.coe_max, ENat.toENNReal_lt_top, Set.Ioo_subset_Ioo_union_Ico, Valued.isOpen_closedball, emultiplicity_le_emultiplicity_of_dvd_left, DivisibleHull.archimedeanClassMk_mk_eq, continuous_mabs, Set.Iio_union_Ici, Affine.Simplex.wOppSide_affineSpan_faceOpposite_point_left_iff, nsmul_nonneg_iff, abs_sub_abs_le_abs_add, HahnEmbedding.IsPartial.baseEmbedding_le, Rat.intCast_lt_cast, Valuation.IsTrivialOn.valuation_algebraMap_le_one, ArchimedeanClass.FiniteResidueField.mk_ratCast, Irreducible.maximalIdeal_eq_setOf_le_v_coe, IsPreconnected.intermediate_value_Ico, RootPairing.coxeterWeight_nonneg, NNRat.coe_floor, ProbabilityTheory.gaussianReal_map_const_mul, Continuous.strictMono_of_inj_boundedOrder', IsDedekindDomain.HeightOneSpectrum.adicValued.has_uniform_continuous_const_smul', SignType.neg_one_lt_iff, Set.Ici_add_one_eq_Ioi, min_eq_bot, Int.lt_succ_floor, MvPolynomial.isWeightedHomogeneous_zero_iff_weightedTotalDegree_eq_zero, Finsupp.Colex.addLeftStrictMono, Measurable.max, ENat.top_pos, Mathlib.Meta.NormNum.IsNNRat.natFloor, Finset.max_union, strictConvexOn_iff_slope_strict_mono_adjacent, CauSeq.lt_irrefl, closure_interior_Icc, Order.Ioo_succ_right, NNRat.cast_strictMono, Fin.addNatOrderEmb_toEmbedding, LinearOrderedAddCommGroup.wellFoundedOn_setOf_le_lt_iff_nonempty_discrete, Mathlib.Tactic.Order.ToInt.toInt_sup_toInt_eq_toInt, Dense.exists_ge, ValuationSubring.valuation_lt_one_iff, OrderIso.pnatIsoNat_symm_apply, Set.notMem_Ioi, Valuation.FiniteField.algebraMap_le_one, Finset.le_fold_min, LinearOrderedAddCommGroupWithTop.sub_pos, ArchimedeanClass.FiniteElement.instIsStrictOrderedRing, tendsto_inv_atTop_zero, Int.lt_ceil, min_sub_sub_left, Units.min_val, neg_le_self_iff, tendsto_const_mul_pow_nhds_iff', Valuation.HasExtension.val_map_le_iff, Set.compl_ordConnectedSection_ordSeparatingSet_mem_nhdsGE, ENat.lt_add_one_iff', Orientation.ne_iff_eq_neg, Valuation.isEquiv_iff_val_sub_one_lt_one, Summable.abs, HahnSeries.mem_cardSuppLTSubfield, Valuation.one_apply_lt_one_iff, nhds_bot_basis, Finset.exists_mem_eq_inf, dense_iff_exists_between, countable_image_gt_image_Ioi_within, sign_mul_self, Finset.exists_one_lt_of_prod_one_of_exists_ne_one', quasiconcaveOn_iff_min_le, not_isCofinal_iff, AbsoluteValue.isEquiv_trivial_iff_eq_trivial, Set.toENat_cardinalMk_subtype, convexHull_insert, Set.Ioi_subset_Ioo_union_Ici, Set.Infinite.exists_gt, ENat.self_le_mul_left, ValuationSubring.integralClosure_algebraMap_injective, PNat.map_subtype_embedding_Ico, MeasureTheory.aecover_Ioi_of_Ici, Cardinal.toENat_eq_natCast_iff, cocompact_le_atBot, Matrix.abs_det_reindex, tsub_add_min, MeasureTheory.stoppedProcess_stoppedProcess, PowerSeries.heval_C, inv_atBot₀, MonomialOrder.degree_add_of_ne, Polynomial.isEquivalent_atBot_div, ENat.card_le_card_of_injective, tendsto_ceil_right', covBy_iff_le_iff_lt_right, Valuation.mem_maximalIdeal_iff, LinOrd.ofHom_apply, convex_iff_ordConnected, RootPairing.RootPositiveForm.zero_lt_posForm_apply_root, Finset.sup'_add', MeasureTheory.integrable_iff_integrableAtFilter_atBot, convexHull_multiset_sum, FiniteArchimedeanClass.mem_addSubgroup_iff, abs_sub_round, partialSups_succ', WellOrderExtension.wellFoundedLT, Valuation.mem_leSubmodule_iff, isPiSystem_image_Iic, abs_add_eq_add_abs_iff, Multiset.Ico_sub_Ico_left, Left.pow_lt_one_iff', ArchimedeanClass.mk_intCast, ofDual_max, Finset.prod_one_sub_ordered, PredOrder.isOpen_iff, Cardinal.ofENat_lt_ofNat, add_max, ProbabilityTheory.gaussianReal_const_mul, Mathlib.Meta.Positivity.pos_of_isNNRat, Finset.le_fold_max, deriv_abs, Finset.Ioi_disjUnion_Iio, NumberField.FinitePlace.mk_apply, isOpen_lt_prod, NNRat.le_def, CauSeq.sup_inf_distrib_right, IsCompact.exists_isLeast, MeasureTheory.aecover_Ioi_of_Ioi, NNRat.not_cast_lt_zero, Finset.Icc_add_one_left_eq_Ioc, WithTop.continuousOn_untopD, MulArchimedeanClass.subgroup_strictAntiOn, nsmul_neg_iff, concaveOn_iff_slope_anti_adjacent, strictConvex_Iic, sub_le_neg_add_iff, Filter.Tendsto.mabs, min_bot_left, nhdsSet_Ioo, right_lt_lineMap_iff_one_lt, AffineSubspace.setOf_sSameSide_eq_image2, List.sortedLE_mergeSort, Hyperreal.epsilon_lt_of_pos, Finset.Ico_subset_Ico_union_Ico, min_mul_mul_left, OrderEmbedding.mulRight_apply, Nat.succPNat_mono, List.getD_max?_eq_unbotD_maximum, IsNonarchimedean.multiset_powerset_image_add, Set.Ioc_union_Ioc_left, Set.Iio_succ_eq_Iic, Padic.withValUniformEquiv_norm_le_one_iff, Int.cast_one_le_of_pos, Valued.toNormedField.norm_le_one_iff, Rat.padicValuation_cast, nullMeasurableSet_Ioc, Finset.image_orderEmbOfFin_univ, ProbabilityTheory.Kernel.partialTraj_succ_of_le, Int.preimage_Ioc, CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.ofComposableArrows_incl_app, PNat.find_le, Finset.Iio_filter_lt, one_le_pow_mul_abs_eval_div, Set.tsub_encard_le_encard_diff, IsCauSeq.bounded', ConvexCone.canLift, Matrix.eRank_le_card_width, Ordinal.liftOnWellOrder_type, finSumEquivOfFinset_inr, MeasureTheory.ae_le_const_iff_forall_gt_measure_zero, Seminorm.finset_sup_apply, Polynomial.div_tendsto_atTop_leadingCoeff_div_of_degree_eq, AddCircle.card_torsion_le_of_isSMulRegular, min_lt_min_right_iff, Finset.dens_map_le, Order.succ_lt_succ_iff, SuccOrder.limitRecOn_succ, List.maximum_cons, Finset.Colex.toColex_univ, Ordinal.iSup_typein_succ, Affine.Simplex.sign_excenterWeights_singleton_pos, HahnSeries.leadingCoeff_mul, ENat.card_lt_top, Set.range_IciExtend, LinearOrderedCommGroup.tendsto_nhds, Finset.le_sup'_iff, Int.cast_abs, ArchimedeanClass.closedBallAddSubgroup_top, ValuationSubring.valuation_le_iff, List.foldr_max_of_ne_nil, ArchimedeanClass.addSubgroup_antitone, Nat.succPNat_le_succPNat, Finset.min_eq_inf_withTop, Nat.ceil_pos, Set.iUnion_Ioc_eq_Ioi_self_iff, mabs_le, add_right_strictMono_of_ne_top, instCommutativeMax, mapClusterPt_leftLim, le_mabs', abs_dvd, Finset.addConst_le_inv_dens, convex_iff_sum_mem, Finset.card_Ico_mul_right, Finset.fold_min_lt, MvPowerSeries.le_order_mul, OrderRingHom.eq_id, mem_nhdsLT_iff_exists_Ico_subset, Cardinal.ofENat_le_ofNat, Matrix.abs_det_submatrix_equiv_equiv, QuadraticMap.linMulLinSelfPosDef, abs_eq_iff_mul_self_eq, Cardinal.toENat_ofENat, PNat.Icc_eq_finset_subtype, Valuation.IsRankOneDiscrete.exists_generator_lt_one', Function.support_max, signHom_apply, Polynomial.div_tendsto_atBot_leadingCoeff_div_of_degree_eq, Ordinal.toNatOrdinal_eq_one, Set.ncard_le_encard, List.max_prod_le, CategoryTheory.Limits.MultispanIndex.toLinearOrderMultispanIso_inv_app, HahnSeries.instIsStrictOrderedRingLexOfIsDomain, continuousOn_floor, Finset.Icc_min_max, LaurentSeries.LaurentSeriesRingEquiv_def, Field.Emb.Cardinal.directed_filtration, Set.Ioc_union_Ioc_right, abs_smul, AbsoluteValue.map_units_intCast, instIsCountablyGenerated_atBot, tendsto_one_iff_mabs_tendsto_one, Polynomial.eventually_atBot_not_isRoot, Set.OrdConnected.uIcc_subset, HahnEmbedding.Partial.orderTop_eq_archimedeanClassMk, Set.OrdConnected.IicExtend, Finset.uIcc_eq_union, Continuous.upperSemicontinuous, tendsto_smul_comp_nat_floor_of_tendsto_mul, List.minimum_of_length_pos_le_iff, Field.Emb.Cardinal.instInverseSystemWithTopToTypeOrdRankAlgHomSubtypeMemIntermediateFieldCoeOrderEmbeddingFiltrationAlgebraicClosureEmbFunctor, exists_seq_strictMono_tendsto_nhdsWithin, Hyperreal.neg_lt_of_tendsto_zero_of_pos, nhdsWithin_Ioi_isMeasurablyGenerated, HahnSeries.SummableFamily.powers_zero, min_add_distrib', Module.length_of_free, Set.image_const_mul_uIcc, isLocallyClosed_Ioi, PNat.Ioo_eq_finset_subtype, lowerClosure_eq_top_iff, WithZeroTopology.nhds_zero, Set.Icc_succ_left_eq_Ioc, Field.Emb.Cardinal.filtration_succ, Set.unit_eq, ArchimedeanClass.FiniteResidueField.ofArchimedean_apply, Finset.inf_lt_iff, AddCircle.equivIccQuot_comp_mk_eq_toIcoMod, Set.IciExtend_self, Valuation.mem_ltIdeal_iff, CauSeq.abv_pos_of_not_limZero, mabs_pow, Valuation.val_le_one_or_val_inv_lt_one, Mathlib.Tactic.Order.ToInt.toInt_le_toInt, Matrix.eRank_le_card_height, Padic.instCompatibleWithZeroMultiplicativeIntMulValuation, emultiplicity_add_eq_min, Nonneg.nontrivial, Module.End.independent_genEigenspace, NumberField.FinitePlace.norm_def', ENat.card_pos, max_neg_neg, smulPosStrictMono_iff_SMulPosReflectLE, IsCoprime.abs_right_iff, Valuation.leSubmodule_monotone, Int.fract_add_fract_le, sum_div_card_sq_le_sum_sq_div_card, Set.Icc_min_max, PredOrder.isPredLimit_of_mem_frontier, two_mul_le_add_sq, SetTheory.PGame.grundyValue_eq_iff_equiv_nim, interior_Ici, ENat.toENNReal_strictMono, Int.cast_le_neg_one_of_neg, FunctionField.inftyValuation.X_inv, Set.Icc_subset_Ico_union_Icc, LinOrd.hom_id, Set.Ioo_inter_Iio, CategoryTheory.Limits.MultispanIndex.toLinearOrderMultispanIso_hom_app, WithBot.le_of_forall_lt_iff_le, Set.Ioi_diff_Ici, Int.padicValuation_lt_one_iff, HahnSeries.single_zero_ofScientific, Filter.Tendsto.uIcc, Finset.set_encard_biUnion_le, Nat.floor_div_natCast, ENat.one_lt_card_iff_nontrivial, IsDedekindDomain.HeightOneSpectrum.intValuation_if_neg, Set.projIic_surjective, monotone_transfiniteIterate, invOf_pos, PNat.instIsOrderedCancelMonoid, NumberField.FinitePlace.embedding_apply, min_lt_min_left_iff, Ordinal.toNimber_symm_eq, IsDedekindDomain.HeightOneSpectrum.valuation_of_algebraMap, min_mul, nhds_basis_Icc_pos, nullMeasurableSet_Ioo, Valuation.Integers.isPrincipal_iff_exists_isGreatest, Set.encard_preimage_val_le_encard_left, nhds_basis_abs_sub_lt, Finset.one_le_mulConst_self, instWellQuasiOrderedLEOfWellFoundedLT, Set.strictMonoOn_projIic, inv_atTop₀, LinearOrderedCommGroupWithZero.inl_mul_inr_eq_coe_toLex, LaurentSeries.valuation_le_iff_coeff_lt_eq_zero, instIsDiscreteValuationRingSubtypeMemSubringIntegerWithZeroMultiplicativeIntValuation, Finpartition.IsEquipartition.card_biUnion_offDiag_le', OrderIso.isNormal, exists_seq_strictAnti_tendsto, CategoryTheory.Functor.WellOrderInductionData.Extension.map_zero, lowerSemicontinuous_iff_isClosed_preimage, Set.ordConnected_iff_uIcc_subset_left, lt_tsub_iff_right, NatOrdinal.toOrdinal_min, LaurentSeries.valuation_single_zpow, FiniteArchimedeanClass.mk_lt_mk, infPrime_iff_not_isMax, max_add_add_le_max_add_max, tendsto_fract_left', AbsoluteValue.abs_abv_sub_le_abv_sub, CauSeq.sup_idem, monovary_iff_mul_rearrangement, SetTheory.PGame.grundyValue_nim_add_nim, NNRat.instStarOrderedRing, Nimber.succ_def, sbtw_midpoint_of_ne, IsDedekindDomain.HeightOneSpectrum.intValuation_le_one, sameRay_or_ne_zero_and_sameRay_neg_iff_not_linearIndependent, le_iff_forall_rat_lt_imp_le, Affine.Simplex.wSameSide_affineSpan_faceOpposite_iff, smul_nonneg_iff_neg_imp_nonpos, Affine.Simplex.wOppSide_affineSpan_faceOpposite_point_right_iff, WeierstrassCurve.valuation_Δ_aux_eq_of_isIntegral, Nat.preimage_Iio, AEMeasurable.max, Finset.Nonempty.sup_eq_top_iff, MonomialOrder.degree_sub_le, Orientation.eq_or_eq_neg, IsNonarchimedean.apply_sum_le_sup_of_isNonarchimedean, le_of_toZ_le, Finset.inf'_lt_iff, CategoryTheory.TransfiniteCompositionOfShape.fac_assoc, Polynomial.exists_min_root, Hyperreal.infinitesimal_def, isPiSystem_Ioi, ContFract.convs_eq_convs', MeasureTheory.Filtration.rightCont_eq_self, min_mul_min_le_min_mul_mul', ArchimedeanClass.FiniteResidueField.mk_eq_zero, le_zero_iff, Finset.lubell_yamamoto_meshalkin_inequality_sum_card_div_choose, convexJoin_segments, Affine.Simplex.sign_signedInfDist_lineMap_incenter_touchpoint, Finset.Colex.toColex_lt_toColex_iff_max'_mem, Nat.measurable_floor, StieltjesFunction.measure_Ioo, EReal.sign_eq_and_abs_eq_iff_eq, starConvex_iff_ordConnected, Order.pred_injective, AddGroupSeminormClass.toNonnegHomClass, Valuation.Compatible.srel_iff_lt, one_lt_mabs, exists_pos_right_iff_sameRay, Finset.lt_sup'_iff, NNRat.cast_le, Valuation.IsEquiv.valuedCompletion_le_one_iff, antivaryOn_comm, instAssociativeMax, AddMonoidAlgebra.Monic.supDegree_mul_of_ne_zero_right, MvPowerSeries.min_lexOrder_le, NNRat.floor_coe, Order.Ioo_eq_empty_iff_le_succ, mul_self_le_one_iff, Set.Iic_diff_Iio, OrderEmbedding.preimage_uIoc, CategoryTheory.Functor.WellOrderInductionData.surjective, Module.End.genEigenspace_directed, Valuation.isEquiv_iff_val_lt_val, Finset.subConst_le_addConst_sq, le_iff_forall_pos_le_add, lt_emultiplicity_of_lt_multiplicity, ENat.monotone_map_iff, mul_nonpos_iff_pos_imp_nonpos, InnerProductSpace.gramSchmidt_bot, Set.Ioc_subset_uIoc', Submodule.spanRank_toENat_eq_iInf_encard, nhdsWithin_uIcc_isMeasurablyGenerated, Set.neg_uIcc, SimpleGraph.hasse_preconnected_of_pred, max_lt_max_left_iff, variationOnFromTo.antitoneOn, Finset.sortedGT_sort, Finset.mem_uIcc', sign_nonneg_iff, min_abs_abs_le_abs_min, SimpleGraph.regularityReduced_adj, Hyperreal.coe_lt_omega, Finset.card_Ico_add_right, LinOrd.dual_map, nhds_basis_Ioo_one_lt, Pi.instNoMinOrderLexForallOfWellFoundedLTOfNonempty, OrderIso.sumLexIioIci_symm_apply_Ici, Finsupp.Lex.addLeftMono, Ioo_subset_closure_interior, Set.bounded_gt_inter_ge, AbsoluteValue.abs_isEuclidean, Zsqrtd.instIsStrictOrderedRingCastInt, pow_le_pow_iff_left, Finsupp.Lex.single_strictAnti, Valuation.isNontrivial_iff_exists_lt_one, ArchimedeanClass.mk_pow, abs_dvd_abs, ArchimedeanClass.isAddRegular_mk, nullMeasurableSet_Ioi, IsDedekindDomain.HeightOneSpectrum.instIsNontrivialWithZeroMultiplicativeIntValuation, Valuation.Integers.valuation_irreducible_lt_one, Finset.min_union, WithZeroTopology.nhds_zero_of_units, Set.Ico_subset_Icc_union_Ico, AddValuation.map_add', mem_nhdsGT_iff_exists_Ioc_subset, borel_eq_generateFrom_Ici, Topology.RelCWComplex.coe_skeletonLT, Num.cast_le, invOf_nonneg, Filter.tendsto_mabs_atTop_atTop, min_choice, strictConvex_Icc, antivary_iff_smul_rearrangement, Nonneg.mk_nnratCast, Set.Ioo_inter_Ioi, zpow_two_nonneg, GenContFract.succ_nth_fib_le_of_nth_den, Module.End.maxGenEigenspace_eq, one_le_mul_self_iff, List.coe_maximum_of_length_pos, Finset.Colex.le_iff_max'_mem, lt_inv_self_iff, ArchimedeanClass.mk_le_mk, NNRat.lt_def, exists_lub_Iio, Polynomial.div_tendsto_zero_iff_degree_lt, tendsto_floor_right_pure, MeasureTheory.aecover_Iio_of_Iic, Nat.preimage_Ici, upperSemicontinuousAt_iff_frequently, Finsupp.Colex.isStrictOrder, Int.padicValuation_eq_one_iff, smul_nonpos_iff, WithTop.untop₀_min, mabs_div_le, segment_eq_uIcc, Nat.count_le_setENCard, Nat.one_div_le_one_div, IsPreconnected.intermediate_value_Ioo, MvPowerSeries.le_weightedOrder_mul, max_inv_one, Set.unbounded_gt_inter_gt, RootPairing.RootPositiveForm.zero_lt_posForm_iff, MvPolynomial.supDegree_esymmAlgHomMonomial, partialSups_add_one', ofDual_min, LinearOrderedField.lt_inducedMap_iff, Finset.max_sum_le, MvPolynomial.schwartz_zippel_totalDegree, isGLB_Ioi, Finset.max'_le_iff, Right.pow_lt_one_iff, isOpen_lt, PowerSeries.coeff_heval, continuousOn_fract, Cardinal.toENat_eq_zero, Affine.Simplex.sign_touchpointWeights_empty, HahnSeries.ofSuppBddBelow_zero, ProbabilityTheory.HasSubgaussianMGF.const_mul, Tropical.min_eq_add, StieltjesFunction.mono', MvPowerSeries.le_order_prod, CategoryTheory.Functor.WellOrderInductionData.sectionsMk_val_op_bot, BoundedLENhdsClass.of_closedIciTopology, MulArchimedeanClass.top_eq_mk_iff, Ioc_subset_biUnion_Ioc, OrderRingHom.apply_eq_self, Topology.CWComplex.iUnion_openCell_eq_skeletonLT, CategoryTheory.SmallObject.SuccStruct.Iteration.mkOfLimit.inductiveSystem_obj, Hyperreal.InfiniteNeg.lt_zero, Sym2.sortEquiv_apply_coe, Finset.orderIsoOfFin_symm_apply, tsub_pos_iff_lt, emultiplicity_lt_iff_not_dvd, Cardinal.toENat_eq_ofNat, CauSeq.const_lt, CanonicallyOrderedAdd.toOrderedSub, exists_nonneg_left_iff_sameRay, Valuation.Integers.map_le_one, emultiplicity_le_emultiplicity_of_dvd_right, InnerProductSpace.gramSchmidt_def, Orientation.map_eq_neg_iff_det_neg, neg_abs_le_neg, IsDedekindDomain.HeightOneSpectrum.intValuation_le_pow_iff_mem, Finset.mulConst_le_card, Int.preimage_Ioi, MonomialOrder.degree_reduce_lt, IsNonarchimedean.finset_image_add, tendsto_zero_iff_abs_tendsto_zero, Archimedean.embedReal_apply, Order.Ici_pred, Polynomial.abs_div_tendsto_atTop_of_degree_gt, IsDedekindDomain.HeightOneSpectrum.intValuation_singleton, Module.End.maxGenEigenspace_eq_genEigenspace_finrank, Ordinal.toNimber_min, emultiplicity_pos_of_dvd, CategoryTheory.TransfiniteCompositionOfShape.iic_isoBot, HahnEmbedding.Partial.archimedeanClassMk_eq_iff, exists_rat_gt, LinearOrderedCommGroup.Subgroup.genLTOne_lt_one, Module.End.mapsTo_genEigenspace_of_comm, HahnSeries.support_abs, ValuativeRel.ValueGroupWithZero.mk_pos, MonoidWithZeroHom.fst_mono, le_mabs, Odd.pow_nonneg_iff, Topology.IsUpper.isTopologicalBasis_insert_univ_subbasis, IsNonarchimedean.apply_natCast_le_one_of_isNonarchimedean, NNRat.cast_mono, PowerSeries.order_mul_ge, SimpleGraph.farFromTriangleFree_iff, Nat.lt_succ_floor, MonomialOrder.zero_le, Finset.Colex.lt_iff_exists_forall_lt, sbtw_iff_left_ne_and_right_mem_image_Ioi, FunctionField.instIsNontrivialRatFuncWithZeroMultiplicativeIntInftyValuation, MultilinearMap.map_piecewise_sub_map_piecewise, Set.notMem_Iic, ArchimedeanClass.mk_natCast, CategoryTheory.TransfiniteCompositionOfShape.ofArrowIso_isoBot, CategoryTheory.Limits.HasIterationOfShape.hasColimitsOfShape, Nat.ceil_eq_zero, Even.pow_nonneg, zpow_neg_two_nonneg, Int.floor_eq_zero_iff, MeasureTheory.meas_le_ae_eq_meas_lt, Set.uIoo_eq_union, AffineBasis.convexHull_eq_nonneg_coord, Even.zpow_abs, Nat.floor_sub_one, AffineSubspace.sSameSide_iff_exists_left, CauSeq.inf_comm, InitialSeg.isNormal, NNRat.coe_max, pos_add_self_iff, mfderivWithin_projIcc_one, ENat.forall_natCast_le_iff_le, WithBot.lt_add_one_iff, Finset.min'_le, Set.Infinite.exists_lt, Cardinal.ofENat_mono, tendsto_ceil_left_pure_ceil, measurable_lt, Valuation.ltAddSubgroup_monotone, Rat.padicValuation_self, apply_abs_le_mul_of_one_le, hasBasis_nhdsSet_Ici_Ioi, Polynomial.tendsto_atTop_iff_leadingCoeff_nonneg, Polynomial.IsDistinguishedAt.degree_eq_coe_lift_order_map, Set.encard_preimage_val_le_encard_right, apply_abs_le_mul_of_one_le', Set.Iio_inj, MeasureTheory.aecover_Ioo_of_Ioc, max_inv_inv', HahnEmbedding.Seed.baseEmbedding_strictMono, PNat.le_of_dvd, Mathlib.Meta.NormNum.isRat_lt_true, Mathlib.Tactic.Order.ToInt.toInt_nle_toInt, CategoryTheory.TransfiniteCompositionOfShape.ofOrderIso_incl, HasStrictFDerivAt.abs, PowerSeries.le_order_smul, convexHull_toCone_eq_sInf, le_iff_forall_one_lt_lt_mul', max_bot_left, CategoryTheory.TransfiniteCompositionOfShape.isWellOrderContinuous, Valued.isClopen_ball, frontier_Ici, tendsto_ceil_atTop, Finset.max_mono, NonemptyFinLinOrd.epi_iff_surjective, ValuativeRel.ValueGroupWithZero.embed_strictMono, AffineSubspace.wOppSide_iff_exists_wbtw, Valuation.IsEquiv.pos_iff, PNat.card_Icc, Fin.castSuccOrderEmb_toEmbedding, Set.monotone_projIic, List.mem_argmin_iff, exists_lt_mul_self, MonomialOrder.toSyn_strictMono, Function.locallyFinsuppWithin.nsmul_posPart, PowerSeries.order_finite_iff_ne_zero, Finset.Ico_diff_Ico_left, FiniteArchimedeanClass.val_mk, min_sub_sub_right, Int.self_le_zpow_clog, Polynomial.isEquivalent_atTop_lead, Order.IsNormal.monotone, SimpleGraph.posSemidef_lapMatrix, Polynomial.le_trailingDegree_C, Finset.card_div_choose_le_card_shadow_div_choose, max_mul_min, mabs_zpow, MonomialOrder.div_single, LinearOrder.supConvergenceClass, LinOrd.hom_inv_apply, exists_isLocalExtr_Ioo, Polynomial.isLittleO_atTop_of_degree_lt, Set.unbounded_le_inter_le, Nimber.toOrdinal_max, Nonneg.segment_eq_uIcc, mabs_eq_mabs, Finset.Colex.mem_initSeg, abs_eq_max_neg, ArchimedeanClass.mk_add_lt_mk_left_iff, pow_two_nonneg, Tuple.monotone_proj, FiniteArchimedeanClass.mem_ballAddSubgroup_iff, Finset.mem_convexHull', MulArchimedeanClass.mk_eq_mk, MvPowerSeries.le_weightedOrder_prod, closure_uIoo, MeasureTheory.aecover_Ioc_of_Ioo, Set.indicator_le_indicator_nonneg, Finset.orderEmbOfFin_eq_orderEmbOfFin_iff, Hyperreal.infinite_abs_iff, div_neg_iff, Int.cast_min, intermediate_value_Icc', AffineSubspace.sOppSide_iff_exists_left, Tropical.untrop_max, Polynomial.abs_div_tendsto_atBot_atTop_of_degree_gt, Finsupp.disjoint_iff, measurableSet_Ico, Valuation.Integers.le_of_dvd, geom_sum_pos_iff, NumberField.FinitePlace.norm_embedding_eq, OrderRingIso.eq_refl, div_le_one_iff, GenContFract.abs_sub_convergents_le', isClosed_Ioc_iff, abs_sub_le, NNRat.num_pos, partialSups_add_one, AddMonoidAlgebra.supDegree_mem_range, eVariationOn.nonempty_monotone_mem, intermediate_value_Ioo', Polynomial.valuation_of_mk, Mathlib.Tactic.Qify.nnratCast_le, Valuation.leIdeal_map_algebraMap_eq_leSubmodule_min, isOpen_Ioo, Rat.intCast_le_cast, MulArchimedeanClass.mk_left_le_mk_mul_iff, Field.Emb.Cardinal.two_le_deg, RootPairing.exists_ge_zero_eq_rootForm, AbsoluteValue.isEquiv_iff_lt_one_iff, Int.le_ceil, MulArchimedeanClass.mem_subgroup_iff, AddSubmonoid.closure_image_isAddIndecomposable_baseOf, HahnSeries.order_mul, Nat.Prime.emultiplicity_le_emultiplicity_choose_add, tendsto_zpow_atTop_zero, Valuation.val_lt_one_iff, Quaternion.normSq_le_zero, MulArchimedeanClass.subsemigroup_strictAnti, Finset.local_lubell_yamamoto_meshalkin_inequality_div, abs_le, Set.preimage_add_const_uIcc, Odd.zpow_nonpos_iff, Int.fract_pos, Multiset.untrop_sum, GroupSeminormClass.toNonnegHomClass, strictConvex_uIcc, nhds_basis_zero_abs_lt, nhds_eq_iInf_abs_sub, Valuation.val_le_one_or_val_inv_le_one, Fin.natAddOrderEmb_toEmbedding, measurableSet_Iio, WithTop.tendsto_untop, Valuation.map_add_of_distinct_val, RootPairing.RootPositiveForm.posForm_apply_root_root_le_zero_iff, ArchimedeanClass.mk_left_le_mk_sub_iff, CauSeq.not_limZero_of_pos, ENat.map_natCast_strictMono, Nimber.toOrdinal_min, Polynomial.abs_div_tendsto_atTop_atTop_of_degree_gt, leOnePart_lt, Field.Emb.Cardinal.isLeast_leastExt, sub_half_lt_round, ValuativeRel.nonempty_orderIso_withZeroMul_int_iff, Finset.divConst_le_card, Finset.one_le_mulConst, LaurentSeries.inducing_coe, Set.Ioc_disjoint_Ioc, cmp_add_left, exists_isExtrOn_Ioo_of_tendsto, Ordinal.enum_le_enum', Set.Ioo_subset_Ioc_union_Ico, Valuation.map_add, ArchimedeanClass.mk_le_mk_smul, CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.ofComposableArrows_isColimit_desc, MulArchimedeanClass.mk_lt_mk, pred_min, div_le_inv_mul_iff, LaurentSeries.continuous_coe, convexJoin_segment_singleton, Finset.Colex.toColex_le_toColex_iff_max'_mem, min_eq_right_iff, HahnEmbedding.Partial.toOrderAddMonoidHom_apply, monovaryOn_comm, Valuation.HasExtension.val_map_lt_iff, PNat.tendsto_comp_val_iff, Order.IsNormal.ext, openSegment_eq_Ioo', cocompact_le_atTop, MvPowerSeries.lexOrder_def_of_ne_zero, MonomialOrder.degree_add_le, Valued.is_topological_valuation, CategoryTheory.TransfiniteCompositionOfShape.ici_F, HahnEmbedding.Seed.strictMono_coeff, abs_nnqsmul, interior_Iio, min_le_max, one_le_mul_mabs, Nat.floor_div_ofNat, Set.Ioi_diff_Ioi, negPart_pos_iff, isPiSystem_image_Ioi, AddMonoidAlgebra.supDegree_mul, Order.Iio_succ_eq_insert, IsValuativeTopology.isOpen_ball, NatOrdinal.succ_def, continuous_iff_lower_upperSemicontinuous, Topology.RelCWComplex.iUnion_openCell_eq_skeleton, convexJoin_singleton_segment, MvPowerSeries.le_weightedOrder_map, Hyperreal.not_infinite_iff_exist_lt_gt, AffineSubspace.wOppSide_self_iff, le_emultiplicity_map, Dense.Iio_eq_biUnion, CauSeq.coe_sup, Stream'.Seq.length'_le_iff, Hyperreal.archimdeanClassMk_coe, Int.floor_lt, mul_nonneg_iff, IsAbsoluteValue.abs_isAbsoluteValue, Pi.toLex_update_lt_self_iff, Ideal.span_singleton_abs, Order.lt_succ_iff_eq_or_gt, max_div_min_eq_mabs, Field.Emb.Cardinal.succEquiv_coherence, hasDerivWithinAt_abs, NNRat.floor_cast, NNRat.coe_pos, Cardinal.noMaxOrder, abs_sub, Sym2.inf_eq_inf_and_sup_eq_sup, Cardinal.ofENat_lt_aleph0, fn_min_add_fn_max, Hyperreal.tendsto_iff_forall, MvPowerSeries.nat_le_order, Valuation.one_lt_val_iff, Orientation.map_eq_iff_det_pos, smul_nonpos_iff_pos_imp_nonpos, archimedean_iff_nat_le, Mathlib.Meta.NormNum.isNNRat_abs_neg, SuccOrder.nhdsLE_eq_nhds, le_iff_forall_neg_add_le, HahnEmbedding.ArchimedeanStrata.ball_sup_stratum_eq, abs_inv, DFinsupp.lt_of_forall_lt_of_lt, generateFrom_Icc_mem_le_borel, Quaternion.normSq_nonneg, Nat.le_floor_iff', countable_setOf_isolated_right, OrderRingIso.subsingleton_right, Padic.norm_eq_zpow_log_mulValuation, mabs_mul_three, ENat.one_le_card_iff_nonempty, ValuationSubring.valuation_lt_one_or_eq_one, Set.Icc_subset_Icc_union_Ioc, HahnSeries.instIsCancelMulZeroOfIsCancelAdd, Set.unbounded_lt_inter_le, PowerSeries.intValuation_eq_of_coe, Set.Ico_succ_succ_eq_Ioc, LocallyFiniteOrder.orderAddMonoidHom_bijective, HahnSeries.orderTop_mul_of_nonzero, Finset.max_pair, List.minimum_of_length_pos_le_of_mem, Nat.ceil_mono, Tuple.sort_eq_refl_iff_monotone, convexHull_add, Set.Ioo_add_one_right_eq_Ioc, Finset.divConst_le_mulConst_sq, FiniteMulArchimedeanClass.withTopOrderIso_apply_coe, WithTop.instBorelSpace, Finsupp.Lex.isStrictOrder, EReal.abs_mul_sign, Set.Iio_subset_Iic_iff, Finsupp.Colex.addRightMono, PNat.lt_add_right, RootPairing.zero_lt_pairingIn_iff', Nat.preimage_floor_of_ne_zero, Set.Ioc_subset_Ioc_union_Icc, HahnEmbedding.Partial.isWF_support_evalCoeff, Set.projIci_eq_self, Filter.Tendsto.abs, CategoryTheory.OrthogonalReflection.iteration_map_succ, HahnEmbedding.Partial.orderTop_eq_iff, Mathlib.Meta.Positivity.nonneg_of_isNNRat, CauSeq.mul_pos, Polynomial.tendsto_atBot_iff_leadingCoeff_nonpos, List.coe_le_maximum_iff, Mathlib.Tactic.ENatToNat.not_lt_top, Finset.lubell_yamamoto_meshalkin_inequality_sum_inv_choose, PNat.find_mono, Order.pred_le_iff_eq_or_le, Order.lt_succ_iff_eq_or_lt, Continuous.exists_forall_le_of_hasCompactSupport, ArchimedeanClass.top_eq_mk_iff, IsDedekindDomain.HeightOneSpectrum.equivHeightOneSpectrum_symm_apply, LowerSet.total_le, OrderMonoidWithZeroHom.mul_comp, AddValuation.map_add_of_distinct_val, tendsto_ceil_right_pure_add_one, ENat.card_le_one_iff_subsingleton, ArchimedeanClass.instIsOrderedAddMonoid, Hyperreal.isSt_iff_abs_sub_lt_delta, nhds_top_basis_Ici, Cardinal.toENat_lt_natCast_iff, abs_max_sub_max_le_abs, Finsupp.DegLex.single_lt_iff, Set.projIic_surjOn, LaurentSeries.val_le_one_iff_eq_coe, Filter.Tendsto.min_left, ProbabilityTheory.Kernel.HasSubgaussianMGF.const_mul, Polynomial.le_trailingDegree_monomial, Function.Periodic.image_uIcc, ContinuousOn.strictMonoOn_of_injOn_Icc', MonomialOrder.le_degree, Set.Iio_diff_Iio, nhds_basis_Icc_one_lt, Module.Basis.orientation_eq_iff_det_pos, sq_le_sq, List.sum_min_le, LinOrd.inv_hom_apply, max_lt_max_right_iff, ArchimedeanClass.mk_ofNat, mul_nonneg_iff_pos_imp_nonneg, Polynomial.degree_comp, Finset.pluennecke_ruzsa_inequality_nsmul_add, ADEInequality.lt_six, IsDedekindDomain.HeightOneSpectrum.valuation_exists_uniformizer, Finset.abs_sum_le_sum_abs, Finsupp.Colex.addRightStrictMono, Function.locallyFinsuppWithin.posPart_add, frontier_Ioi, Set.Finite.encard_lt_top, invOf_lt_zero, FloorRing.gc_ceil_coe, IsDiscreteValuationRing.isRankOneDiscrete, Set.image_neg_uIcc, instIsStrictOrderedRingNNRat, ENat.card_lt_top_of_finite, ENat.lift_one, apply_abs_le_add_of_nonneg, PredOrder.nhdsGE_eq_nhds, continuousWithinAt_iff_lower_upperSemicontinuousWithinAt, Submodule.inf_genEigenspace, abs_pow_eq_one, Int.ceil_eq_iff, ArchimedeanClass.mk_lt_mk, add_left_strictMono_of_ne_top, abs_neg_one_pow, neg_abs_le, oneLePart_eq_ite_lt, MvPowerSeries.nat_le_weightedOrder, Rat.toNNRat_lt_toNNRat_iff', upperBounds_Iio, Set.encard_union_le, MeasureTheory.aecover_Icc_of_Ioc, ValuativeExtension.mapValueGroupWithZero_strictMono, borel_eq_generateFrom_Icc, Module.End.genEigenspace_top_eq_maxUnifEigenspaceIndex, Set.encard_strictMono, Polynomial.trailingDegree_le_trailingDegree, IsDedekindDomain.HeightOneSpectrum.adicCompletionIntegers.integers, Ordinal.toNatOrdinal_min, exists_wellOrder, unitInterval.symm_projIcc, Rat.preimage_cast_Ioi, cocompact_eq_atTop, ArchimedeanClass.FiniteElement.not_isUnit_iff_mk_pos, exists_lt_add_iff_lt_left, Hyperreal.archimedeanClassMk_neg_of_tendsto_atBot, HahnSeries.order_single_mul_of_isRegular, Polynomial.abs_tendsto_atTop_iff, Finset.min_le, Cardinal.toENat_lift, PNat.Ico_eq_finset_subtype, CategoryTheory.SmallObject.SuccStruct.restrictionLTOfCoconeIso_inv_app, hasDerivAt_iff_tendsto_slope_left_right, MeasureTheory.stoppedProcess_eq_stoppedValue_apply, sign_zero, Function.Lex.wellFoundedLT, min_le_iff, tendsto_floor_right_pure_floor, Finset.Ioc_sub_one_left_eq_Icc, IsOpen.exists_Ioo_subset, CauSeq.bounded', CauSeq.add_pos, convexHull_basis_eq_stdSimplex, Hyperreal.isSt_sSup, Filter.tendsto_const_mul_atBot_iff, Field.Emb.Cardinal.noMaxOrder_rank_toType, Order.Ioo_pred_left, Set.biUnion_Ico_eq_Iio_self_iff, Convex.radon_partition, Finset.Ico_add_one_left_eq_Ioo, Units.orderEmbeddingVal_apply, Continuous.exists_forall_ge_of_hasCompactSupport, HahnSeries.SummableFamily.hsum_powerSeriesFamily_mul, NNRat.one_le_cast, Finset.max'_subset, List.minimum_append, Set.preimage_mul_const_uIcc, max_add_add_left, PosSMulMono.nnrat_of_rat, List.le_maximum_of_length_pos_of_mem, MeasureTheory.aecover_Ioc_of_Icc, OrderMonoidIso.withZeroUnits_symm_apply, ENat.add_one_le_iff, Set.Ioi_inj, ArchimedeanClass.orderHom_zero, Int.preimage_Iio, FunctionField.valuedFqtInfty.def, Polynomial.exists_max_root, Int.floor_le_iff, Rat.preimage_cast_Icc, LinOrd.Iso.mk_hom, Set.Ico_subset_Ico_union_Ico, Finset.prod_sub_ordered, MonoidWithZeroHom.inl_strictMono, PowerSeries.heval_apply, ENat.instOrderTopology, generateFrom_Ico_mem_le_borel, units_smul_eq_self_iff, NormedSpace.normalize_smul, MvPowerSeries.one_le_order_iff_constCoeff_eq_zero, Nonneg.coe_nnratCast, sign_mul_abs, HahnSeries.addVal_le_of_coeff_ne_zero, Set.Icc_pred_right_eq_Ico, SimpleGraph.farFromTriangleFree.le_card_sub_card, min_eq_iff, Set.Ici_subset_Icc_union_Ici, WithBot.ge_of_forall_gt_iff_ge, max_top_right, Affine.Simplex.ExcenterExists.sign_signedInfDist_touchpoint, nhdsGT_basis, MulArchimedeanClass.liftOrderHom_mk, ArchimedeanClass.mem_ball_iff, Finset.max_eq_sup_coe, PNat.sub_coe, SimpleGraph.isUniform_singleton, IsNonarchimedean.multiset_image_add_of_nonempty, Int.floor_le_sub_one_iff, abs_mul, OrderMonoidIso.withZeroUnits_apply, CategoryTheory.TransfiniteCompositionOfShape.ofComposableArrows_F, Cardinal.toENat_le_ofNat, Asymptotics.isEquivalent_nat_ceil, InverseSystem.PEquivOn.nat, units_smul_eq_neg_iff, isPiSystem_Ioc, nonempty_orderEmbedding_of_finite_infinite, abs_one_div, Profinite.NobelingProof.Products.eval_eq, succ_min, ArchimedeanClass.mk_monotoneOn, isCompact_uIcc, WithBot.succ_eq_bot, Int.floor_nonneg, Valuation.IsEquiv.one_lt_iff_one_lt, ArchimedeanClass.mk_sub_lt_mk_right_iff, Polynomial.div_tendsto_atBot_zero_of_degree_lt, Filter.Tendsto.max, Order.pred_top_le_iff, IsDedekindDomain.HeightOneSpectrum.intValuation_le_pow_iff_dvd, Iio_mem_nhdsSet_Iic_iff, Finset.max'_pair, PNat.addLeftReflectLT, max_one_div_max_inv_one_eq_self, abs_sub_le_iff, max_sub_sub_left, abs_div, nhdsWithinLE_sup_nhdsWithinGT, midpoint_le_right, Set.projIic_coe, GenContFract.IntFractPair.nth_stream_fr_lt_one, AddGroupCone.nonneg.hasMemOrNegMem, SMulPosMono.toSMulPosReflectLT, Set.unbounded_inter_ge, covBy_iff_lt_iff_le_left, LipschitzWith.projIcc, min_lt_iff, Set.image_div_const_uIcc, abs_sub_round_div_natCast_eq, MvPowerSeries.le_weightedOrder_pow, Ordinal.toType_noMax_of_succ_lt, RootPairing.zero_lt_pairingIn_iff, IsDedekindDomain.HeightOneSpectrum.valuation_def, le_emultiplicity_of_le_multiplicity, Order.Ioi_pred, Polynomial.abs_tendsto_atTop, MvPolynomial.leadingCoeff_esymmAlgHomMonomial, CategoryTheory.Limits.MultispanIndex.toLinearOrder_fst, MeasureTheory.Measure.pi_prod_map_IocProdIoc, Set.Ioi_subset_Ioc_union_Ioi, Rat.cast_min, lineMap_lt_right_iff_lt_one, tendsto_fract_right', Set.vadd_Icc, ValuationClass.map_add_le_max, Matrix.IsIrreducible.nonneg, closure_uIoc, sign_pos, isPiSystem_Ico_mem, smul_min_of_nonneg, Set.Ioo_min_max, IsCompact.exists_isLUB, ValuationSubring.valuation_le_one, CategoryTheory.Limits.MultispanIndex.toLinearOrder_snd, PNat.natPred_monotone, SuccOrder.nhds_eq_pure, PowerSeries.le_order_map, Affine.Simplex.wSameSide_affineSpan_faceOpposite_point_left_iff, toDual_max, CategoryTheory.Limits.instHasIterationOfShapeElemIic, lineMap_le_lineMap_iff_of_lt', inv_le_self_iff, monovaryOn_iff_forall_smul_nonneg, Finset.dens_le_one, ArchimedeanClass.FiniteElement.mk_intCast, Int.ceil_eq_zero_iff, max_add_min, Finset.le_prod_max_one, CategoryTheory.TransfiniteCompositionOfShape.iic_isColimit, HahnEmbedding.IsPartial.strictMono, MonomialOrder.lex_lt_iff_of_unique, emultiplicity_le_emultiplicity_iff, Finset.le_max_of_eq, max_min_distrib_left, isLocallyClosed_Ico, frontier_lt_subset_eq, add_min, not_bddBelow_iff, Nat.floor_natCast, iUnion_Icc_intCast, Set.coe_projIci, MvPowerSeries.min_weightedOrder_le_add, SignType.neg_one_lt_one, Set.eq_empty_or_encard_eq_top_or_encard_diff_singleton_lt, max_div_min_eq_mabs', Nat.one_le_floor_iff, PNat.ofNat_lt_ofNat, RootPairing.zero_le_rootForm, ZNum.isOrderedAddMonoid, Dense.exists_le', MonomialOrder.degLex_le_iff, fn_max_add_fn_min, Filter.tendsto_zpow_atTop_atTop, Set.Ico_inter_Ico, instMulArchimedeanNNRat, tendsto_PNat_val_atTop_atTop, Tuple.graphEquiv₂_apply, denselyOrdered_units_iff, Nat.measurable_ceil, HahnSeries.cardSuppLTSubfield_carrier, AffineSubspace.wOppSide_iff_exists_left, OrderIso.withZeroUnits_symm_apply, max_zero_add_max_neg_zero_eq_abs_self, Finset.sup'_pow, ENat.eq_top_iff_forall_gt, Finset.coe_orderIsoOfFin_apply, NNRat.coe_lt_coe, Valuation.nonempty_rankOne_iff_mulArchimedean, QuadraticMap.toBilin_apply, MulArchimedeanClass.min_le_mk_mul, atBot_atTop_le_cocompact, tendsto_floor_atTop, MonomialOrder.bot_eq_zero, Function.support_min, Set.ordConnected_iff_disjoint_Ioo_empty, Function.locallyFinsuppWithin.instIsOrderedAddMonoid, ValuativeRel.IsDiscrete.has_maximal_element, Int.floor_mono, ArchimedeanClass.mk_add_lt_mk_right_iff, LinearMap.finrank_genEigenspace_le, FunctionField.InftyValuation.map_add_le_max', MulArchimedeanClass.mem_closedBallSubgroup_iff, FiniteMulArchimedeanClass.mem_ballSubgroup_iff, Finsupp.lt_of_forall_lt_of_lt, WithTop.isOpenEmbedding_coe, inv_mabs_le, MonomialOrder.toSyn_lt_iff_ne_zero, Mathlib.Tactic.Order.ToInt.toInt_inf_toInt_eq_toInt, tendsto_inv_nhdsGT_zero, abs_sub_lt_iff, HasFDerivAt.abs, supPrime_iff_not_isMin, ArchimedeanClass.stdPart_eq_sInf, AffineSubspace.setOf_wOppSide_eq_image2, iUnion_Ioc_add_intCast, LinearOrderedField.cutMap_coe, AbsoluteValue.abs_apply, Finset.sup'_lt_iff, Hyperreal.stdPart_coe, HasFDerivWithinAt.abs, NatOrdinal.toOrdinal_max, Odd.pow_neg_iff, Nonneg.instNontrivialSubtypeLeOfNatOfAddLeftMono, Filter.Tendsto.max_right, Module.End.iSup_genEigenspace_eq, smul_max_of_nonneg, projIcc_eq_one, Hyperreal.infinitePos_iff_infinite_and_pos, Finset.lt_fold_min, strictConvex_Ioo, ArchimedeanClass.ballAddSubgroup_top, LaurentSeries.exists_ratFunc_val_lt, sameRay_smul_left_iff, AffineSubspace.wSameSide_and_wOppSide_iff, min_top_left, List.exists_map_eq_of_sorted_nonempty_iff_sbtw, Int.lt_floor_add_one, Multiset.Ico_filter_lt, LinOrd.id_apply, Module.End.genEigenspace_inf_le_add, interior_Icc, FiniteArchimedeanClass.liftOrderHom_mk, Finset.addConst_le_subConst_sq, Field.Emb.Cardinal.instIsSeparableSubtypeMemIntermediateFieldAdjoinImageToTypeOrdRankCompCoeBasisWellOrderedBasisLeastExtIioSingletonSet, HahnSeries.embDomainOrderEmbedding_apply, ArchimedeanClass.mk_map_nonneg_of_archimedean, LinearOrderedCommMonoidWithZero.toIsOrderedMonoid, ENat.coe_toNat_le_self, Set.IicExtend_apply, Module.End.eigenspace_le_genEigenspace, LocallyFiniteOrder.orderAddMonoidHom_strictMono, Order.isGLB_Ioi_iff_isPredPrelimit, FiniteMulArchimedeanClass.mem_closedBallSubgroup_iff, Valued.hasBasis_nhds_zero, MonomialOrder.degree_le_iff, ArchimedeanClass.FiniteResidueField.ofArchimedean_inj, Affine.Simplex.wOppSide_affineSpan_faceOpposite_iff, Set.indicator_nonpos_le_indicator, abs_sq, Hyperreal.epsilon_lt_pos, abs_lt_iff_mul_self_lt, NonemptyFinLinOrd.hom_comp, Hyperreal.coe_nonneg, Finset.isGreatest_max', GenContFract.zero_le_of_den, Nat.cast_finsetSup', OrderIso.sumLexIioIci_symm_apply_Iio, Finset.fold_max_add, HahnEmbedding.ArchimedeanStrata.disjoint_ball_stratum, lowerSemicontinuous_iff_frequently, comap_mabs_nhds_one, HahnEmbedding.ArchimedeanStrata.archimedeanClassMk_of_mem_stratum, PUnit.isOrderedCancelAddMonoid, WithTop.continuous_coe, smul_min_of_nonpos, Nat.one_div_cast_pos, Set.Ioc_subset_Ioc_union_Ioc, Finset.Ico_inter_Ico, Padic.mulValuation_toFun, Finset.uIcc_subset_uIcc_iff_le, Order.pred_le_pred_iff, zpow_two_pos_of_ne_zero, SimpleGraph.FarFromTriangleFree.nonpos, Finset.inf'_pow, IsDedekindDomain.HeightOneSpectrum.valuation_div_le_one_iff, CategoryTheory.SmallObject.SuccStruct.Iteration.mkOfLimit.inductiveSystem_map, Cardinal.one_le_ofENat, Int.sub_one_lt_floor, Set.projIci_surjective, Ideal.height_le_spanRank_toENat_of_mem_minimal_primes, ArchimedeanClass.stdPart_map_real, Finset.prod_one_add_ordered, Tropical.add_eq_left_iff, instModuleFinite, Hyperreal.infinitePos_iff_infinitesimal_inv_pos, IsValuativeTopology.mem_nhds_iff', HahnEmbedding.IsPartial.truncLT_mem_range, IsDedekindDomain.HeightOneSpectrum.valuation_lt_one_iff_dvd, NNRat.cast_nonneg, SignType.not_one_lt, ContinuousOn.strictMonoOn_of_injOn_Ioo, LinOrd.ofHom_id, WithZero.withZeroUnitsEquiv_symm_strictMono, iUnion_Ico_add_intCast, mapClusterPt_rightLim, Affine.Simplex.wSameSide_affineSpan_faceOpposite_point_right_iff, AffineMap.lineMap_mono, isLUB_Iio, Nat.cast_max, Set.Icc_succ_pred_eq_Ioo, IsDedekindDomain.HeightOneSpectrum.intValuation.map_add_le_max', exists_isLocalExtr_Ioo_of_tendsto, Set.right_mem_uIoc, ENat.epow_right_mono, Finsupp.Colex.wellFoundedLT_of_finite, Rat.cast_lt_natCast, LinearOrderedAddCommGroupWithTop.neg_pos, min_one, WithBot.coe_min, Valuation.isEquiv_iff_val_le_one, Padic.comap_mulValuation_eq_padicValuation, CategoryTheory.SmallObject.SuccStruct.Iteration.obj_bot, Set.exists_min_image, disjointed_add_one, Polynomial.abs_tendsto_atBot_iff, DivisibleHull.instIsStrictOrderedModuleNNRat, Filter.tendsto_const_mul_pow_atTop_iff, Order.pred_lt_iff_eq_or_lt, PowerSeries.le_order_mul, wellQuasiOrderedLE_iff_wellFoundedLT, Set.image_sub_const_uIcc, Mathlib.Meta.NormNum.IsNat.natCeil, NumberField.FinitePlace.norm_lt_one_iff_mem, posSMulStrictMono_iff_PosSMulReflectLE, lowerSemicontinuous_iff_isClosed_epigraph, hasBasis_nhdsSet_Iic_Iic, PNat.find_le_iff, CategoryTheory.instIsCardinalFilteredToTypeOrd, Valuation.Integers.not_denselyOrdered_of_isPrincipalIdealRing, isCompact_Ioo_iff, Module.Basis.orientation_eq_or_eq_neg, tendsto_ceil_right_pure_floor_add_one, Rat.preimage_cast_Ico, Set.Ioc_subset_uIoc, quasiconvexOn_iff_le_max, HahnSeries.order_abs, Set.encard_lt_top_iff, Valuation.HasExtension.val_map_le_one_iff, AddCircle.equivIccQuot_comp_mk_eq_toIocMod, le_iff_forall_pos_lt_add', Valuation.map_sub, Hyperreal.coe_pos, Rat.valuation_le_one_iff_den, supIrred_iff_not_isMin, PosSMulReflectLT.toPosSMulMono, EReal.sign_mul, Hyperreal.archimedeanClassMk_neg_of_tendsto_atTop, MulArchimedeanClass.mk_mul_lt_mk_left_iff, min_mul_distrib', Tropical.trop_min, Nat.floor_div_eq_div, Valuation.mem_valuationSubring_iff, Rat.cast_max, LinearOrderedAddCommGroupWithTop.sub_left_strictMono_of_ne_top, List.argmax_cons, Set.IicExtend_coe, tendsto_ceil_left, continuousWithinAt_iff_continuous_left'_right', ArchimedeanClass.mk_natCast_nonneg, Finset.orderEmbOfFin_zero, WithZero.le_max_iff, Set.encard_le_card, SimpleGraph.hasse_preconnected_of_succ, segment_eq_Icc', Order.PartialIso.exists_across, ProbabilityTheory.Kernel.partialTraj_le_def, NNRat.nonpos_iff_eq_zero, leOnePart_eq_ite_lt, Ioc_subset_closure_interior, Valuation.Integers.isIntegral_iff_v_le_one, partialSups_succ, Set.monotoneOn_or_antitoneOn_iff_uIcc, sbtw_iff_right_ne_and_left_mem_image_Ioi, ArchimedeanClass.mk_right_le_mk_sub_iff, upperSemicontinuous_iff_frequently, tendsto_pow_div_pow_atTop_zero, Multiset.max_sum_le, IsCauSeq.bounded, Valuation.Integers.isPrincipalIdealRing_iff_not_denselyOrdered, isOpen_Iio, WeierstrassCurve.isGoodReduction_iff, max_idem, Rat.toNNRat_lt_toNNRat_iff_of_nonneg, nhds_basis_Ioo_pos, nullMeasurableSet_le, min_div_div_left', NNRat.preimage_cast_Iic, ArchimedeanClass.FiniteResidueField.ofArchimedean_injective, HasProd.abs, lineMap_le_left_iff_nonpos, Finset.exists_max_image, lt_tsub_comm, Set.Finite.encard_lt_encard, EReal.sign_coe, AddCircle.continuous_equivIoc_symm, Ordinal.toNatOrdinal_one, Affine.Simplex.sign_excenterWeights_singleton_neg, NonemptyFinLinOrd.Iso.mk_inv, SSet.stdSimplex.nonDegenerateEquiv_apply_apply, Rat.cast_lt_intCast, Continuous.abs, Valuation.RankOne.strictMono, tendsto_inv_atBot_nhdsLT_zero, Nat.floor_lt', Valuation.Integers.le_iff_dvd, SimpleGraph.IsUniform.pos, CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.instIsIsoAppIncl, Set.uIoc_subset_uIcc, self_dvd_abs, four_mul_le_sq_add, ContinuousOn.surjOn_uIcc, Set.Icc_diff_pi_univ_Ioc_subset, LaurentSeries.exists_Polynomial_intValuation_lt, LinearOrderedAddCommGroupWithTop.top_pos, Hyperreal.infiniteNeg_iff_infinite_and_neg, MonomialOrder.degree_sum_le, tendsto_ceil_atBot, PNat.card_fintype_uIcc, Max.left_comm, Ioc_diff_botSet, round_le, LinearOrderedCommGroup.wellFoundedOn_setOf_ge_gt_iff_nonempty_discrete, LinearOrderedField.inducedOrderRingHom_toFun, ValuationSubring.valuation_le_one_iff, abs_sub_round_eq_min, Field.Emb.Cardinal.strictMono_leastExt, NNRat.natCast_le_cast, ArchimedeanClass.mk_zero, intermediate_value_uIcc, Finset.Ioc_inter_Ioc, Finset.max'_eq_sup', Set.image_mul_const_uIcc, CategoryTheory.TransfiniteCompositionOfShape.map_isoBot, Set.Ioc_diff_Iic, mem_segment_iff_sameRay, Set.exists_max_image, tsub_eq_tsub_min, IsDedekindDomain.HeightOneSpectrum.valuedAdicCompletion_eq_valuation', mem_extremePoints_iff_forall_segment, Nat.preimage_ceil_of_ne_zero, Orientation.map_eq_det_inv_smul, PNat.map_subtype_embedding_Icc, MeasureTheory.integrable_iff_integrableAtFilter_atBot_atTop, HahnSeries.orderTop_le_of_coeff_ne_zero, Finset.Ioi_sub_one_eq_Ici, Order.exists_orderEmbedding_insert, NNRat.coe_ceil, Hyperreal.lt_of_tendsto_atTop, NNRat.preimage_cast_Ioi, Rat.natCast_le_cast, isCompact_Ioc_iff, Finset.nonneg_addConst, Set.exists_lower_bound_image, lowerSemicontinuousOn_iff_isClosed_epigraph, mabs_mem_iff, OrderType.type_eq_type, toIcoDiv_zero_one, concaveOn_iff_div, lt_add_iff_lt_left_or_exists_lt, Dense.exists_ge', Set.uIcc_subset_uIcc_union_uIcc, grade_le_grade_iff, Tropical.add_eq_iff, AEMeasurable.min, ValuationSubring.instIsScalarTowerSubtypeMemValuationSubringWithZeroMultiplicativeInt, continuous_min, max_eq_top, Set.Iic_diff_Ioc, Int.orderedSMul, Valuation.map_add_le_max', minimal_iff_isLeast, add_abs_nonneg, inv_nhdsGT_zero, Rat.cast_lt, Finset.Ioc_sub_one_right_eq_Ioo, Finset.Icc_succ_pred_eq_Ioo, Hyperreal.archimedeanClassMk_pos_of_tendsto, Finsupp.DegLex.single_antitone, PNat.uIcc_eq_finset_subtype, WithTop.pred_eq_top, Finsupp.Lex.single_lt_iff, Nimber.add_nat, RootPairing.posRootForm_posForm_pos_of_ne_zero, tendsto_abs_nhdsNE_zero, monovary_iff_forall_smul_nonneg, exists_isExtrOn_uIoo_of_tendsto, closure_openSegment, Affine.Simplex.ExcenterExists.sign_signedInfDist_lineMap_excenter_touchpoint, min_add_add_right, SimpleGraph.nonuniformWitnesses_spec, Polynomial.isBigO_atBot_of_degree_le, CategoryTheory.TransfiniteCompositionOfShape.fac, Finset.prod_add_ordered, lt_abs, Set.not_monotoneOn_not_antitoneOn_iff_exists_le_le, Finset.dens_strictMono, eventually_nhdsWithin_sign_eq_of_deriv_neg, Rat.preimage_cast_uIcc, OrderRingIso.subsingleton_left, exists_abs_lt, LinearOrderedAddCommGroupWithTop.strictMono_add_left_of_ne_top, borel_eq_generateFrom_Ioc, Valued.isClosed_ball, covBy_iff_le_iff_lt_left, WithZero.exists_ne_zero_and_le_and_le, Tuple.self_comp_sort, max_div_div_left', StieltjesFunction.measurableSet_Ioi, Finset.Ioo_succ_right_eq_Ioc, List.sortedLE_insertionSort, IsCompact.bddAbove, Set.bounded_ge_inter_ge, Even.pow_pos, le_abs, sameRay_smul_left_iff_of_ne, Finset.Colex.ofColex_top, IicProdIoc_def, PNat.ofNat_le_ofNat, Finset.orderEmbOfFin_last, strictConvex_Iio, HahnSeries.order_mul_of_nonzero, List.exists_map_eq_of_sorted_nonempty_iff_wbtw, FiniteMulArchimedeanClass.withTopOrderIso_symm_apply, FiniteArchimedeanClass.mem_closedBallAddSubgroup_iff, OrderHomClass.to_lattice_hom_apply, not_bddAbove_iff_isCofinal, Int.cast_max, Set.Icc_diff_pi_univ_Ioo_subset, PseudoMetric.IsUltra.isTransitiveRel_ball, HahnModule.coeff_smul_order_add_order, Module.Basis.orientation_ne_iff_eq_neg, Valuation.srel_iff_lt, abs_mul_sign, MeasureTheory.Measure.pi_prod_map_IicProdIoc, Set.iUnion_Ico_eq_Iio_self_iff, LinearOrderedAddCommGroup.discrete_iff_not_denselyOrdered, MulArchimedeanOrder.instTotalLe, ENat.natCast_lt_succ, upperSemicontinuousOn_iff_preimage_Iio, FiniteArchimedeanClass.mem_ball_iff, not_isCofinal_iff_bddAbove, PNat.equivNonZeroDivisorsNat_symm_apply_coe, grade_eq_grade_iff, WithZero.exists_ne_zero_and_lt_and_lt, CategoryTheory.TransfiniteCompositionOfShape.map_isColimit, PowerSeries.one_le_order_iff_constCoeff_eq_zero, continuousAt_iff_continuous_left'_right', abs_by_cases, IsCoprime.abs_right, OrderIso.subsingleton_of_wellFoundedGT', Profinite.NobelingProof.Products.eval_πs_image', MulArchimedeanClass.mk_le_mk_iff_lt, Filter.tendsto_mabs_atBot_atTop, OrderIso.sumLexIicIoi_symm_apply_Iic, Nat.succPNat_lt_succPNat, HahnSeries.SummableFamily.powerSeriesFamily_hsum_zero, HahnSeries.archimedeanClassMk_eq_archimedeanClassMk_iff, LinearOrderedAddCommGroupWithTop.add_lt_top, Affine.Simplex.face_points, min_max_distrib_right, Filter.tendsto_abs_atBot_atTop, Finset.range_orderEmbOfFin, tendsto_nat_floor_div_atTop, Units.mem_posSubgroup, FiniteMulArchimedeanClass.liftOrderHom_mk, fn_min_mul_fn_max, Int.abs_fract, tendsto_inv_atTop_nhdsGT_zero, Filter.comap_abs_atTop, Tropical.trop_sup_def, ValuativeRel.ValueGroupWithZero.mk_lt_mk, ENat.toENNRealOrderEmbedding_apply, NNRat.natCast_lt_cast, monovaryOn_iff_exists_monotoneOn, strictConvex_iff_convex, intermediate_value_Ioo, Set.Ioc_pred_right_eq_Ioo, DivisibleHull.mk_le_mk, max_le_iff, one_lt_div_iff, Continuous.bddBelow_range_of_hasCompactSupport, HurwitzZeta.hasSum_int_completedHurwitzZetaOdd, CategoryTheory.SimplicialThickening.functor_map, MonomialOrder.degree_mul_lt_iff_left_lt_of_ne_zero, Field.Emb.Cardinal.equivSucc_coherence, NNRat.cast_le_one, Finset.Iio_add_one_eq_Iic, Finset.sup_eq_top_iff, LinearOrderedCommGroupWithZero.inl_eq_coe_inlₗ, Nat.emultiplicity_two_factorial_lt, convexJoin_assoc, MonomialOrder.degree_smul_le, Rat.comap_cast_atBot, max_eq_left_iff, Finset.Colex.lt_iff_exists_filter_lt, Polynomial.cyclotomic_pos_and_nonneg, max_lt_iff, Set.Ioc_sub_one_right_eq_Ioo, le_emultiplicity_of_pow_dvd, Finset.orderEmbOfFin_singleton, IsDedekindDomain.HeightOneSpectrum.intValuation.le_max_iff_min_le, Tuple.antitone_pair_of_not_sorted, tendsto_inv_atBot_zero, ContinuousOn.upperSemicontinuousOn, MvPolynomial.weightedTotalDegree_eq_zero_iff, nhdsLT_sup_nhdsGE, Multiset.trop_inf, IsNonarchimedean.nmul_le, Finset.inf_eq_bot_iff, right_mem_openSegment_iff, Finset.Icc_sub_one_right_eq_Ico, Order.isSuccLimitRecOn_succ, antivaryOn_iff_exists_monotoneOn_antitoneOn, HahnSeries.leadingCoeff_pos_iff, abs_max_sub_max_le_max, MeasureTheory.stoppedValue_stoppedProcess_apply, countable_image_lt_image_Iio_within, CategoryTheory.Limits.MultispanShape.ofLinearOrder_L, MvPowerSeries.le_weightedOrder_smul, Polynomial.isBigO_of_degree_le, lt_subset_interior_le, Finset.pluennecke_ruzsa_inequality_pow_div_pow_mul, HahnSeries.instNoZeroDivisors, HasCountableSeparatingOn.range_Ioi, IsDedekindDomain.HeightOneSpectrum.valuation_of_mk', HasCountableSeparatingOn.range_Iio, toDual_min, untrop_sum, HahnSeries.leadingCoeff_mul_of_ne_zero, Set.Ioo_subset_uIoo, isLocallyClosed_Ioc, Finset.Ioc_sub_one_sub_one_eq_Ico, not_linearIndependent_iffₒₛ, Multiset.exists_max_image, ArchimedeanClass.mk_abs, ArchimedeanClass.min_le_mk_add, HahnSeries.order_le_of_coeff_ne_zero, Polynomial.le_trailingDegree_mul, Finset.addConst_le_card, div_nonpos_iff, sameRay_of_mem_orbit, Units.inv_pos, Set.Ioi_sub_one_eq_Ici, ArchimedeanClass.mk_le_mk_iff_lt, tendsto_floor_right, Hyperreal.infinitePos_abs_iff_infinite_abs, WithVal.lt_def, Order.isNormal_iff_strictMono_and_continuous, WithTop.ge_of_forall_gt_iff_ge, antivary_iff_exists_monotone_antitone, Set.bounded_gt_inter_gt, HahnSeries.order_ofForallLtEqZero, Set.powersetCard.ofFinEmbEquiv_symm_apply, one_min, IsValuativeTopology.mem_nhds_zero_iff, max_add_add_right, Finset.one_le_divConst, abs_mul_self, HahnSeries.coeff_mul_order_add_order, HahnEmbedding.Partial.eval_smul, fn_max_mul_fn_min, nsmul_le_nsmul_iff_right, min_idem, Order.Ico_succ_right, Int.le_ceil_iff, Finset.Iic_pred_eq_Iio, MulArchimedeanClass.mk_antitoneOn, MulArchimedeanClass.mk_monotoneOn, Nat.ceil_le_floor_add_one, Tropical.untrop_add, MonomialOrder.degree_mul_le, NNRat.preimage_cast_uIcc, Valuation.apply_posSubmonoid_pos, hasStrictDerivAt_abs, one_le_sq_iff_one_le_abs, Valuation.one_srel_iff, Pi.Colex.isStrictOrder, midpoint_le_left, RatFunc.valuation_eq_LaurentSeries_valuation, CategoryTheory.SmallObject.ιFunctorObj_eq, monovary_iff_smul_rearrangement, List.minimum_cons, sum_Ioo_inv_sq_le, negPart_eq_ite, Nat.succPNat_strictMono, Set.compl_Ioi, Ordinal.le_enum_succ, monovary_comm, FiniteArchimedeanClass.subsemigroup_eq_addSubgroup, HahnSeries.orderTop_mul_of_ne_zero, Stream'.Seq.at_least_as_long_as_coind, Finite.exists_max, NNRat.preimage_cast_Icc, exists_Ioo_extr_on_Icc, max_mul_mul_right, continuousOn_iff_lower_upperSemicontinuousOn, toZ_iterate_pred_ge, MeasureTheory.partialTraj_const, monovary_iff_exists_antitone, Set.left_mem_uIoc, Filter.Tendsto.min_right, Module.End.disjoint_genEigenspace, MvPolynomial.supDegree_esymm, Set.mem_Icc_iff_abs_le, ENat.lift_zero, FloorRing.archimedean, Int.gc_coe_floor, ProbabilityTheory.gaussianReal_mul_const, PosSMulStrictMono.toPosSMulReflectLE, ENat.one_le_iff_ne_zero_withTop, add_le_add_iff_left_of_ne_top, Set.image_const_add_uIcc, WithZeroTopology.isClosed_iff, List.minimum_of_length_pos_le_getElem, strictConvex_Ici, Units.max_val, Hyperreal.archimedeanClassMk_nonneg_of_tendsto, mul_pos_iff, Order.not_isMin_succ, Continuous.if_le, Mathlib.Meta.NormNum.IsRat.natFloor, Function.isMinimalFor_argminOn, Nat.choose_lt_pow_div, ArchimedeanClass.mem_addSubgroup_iff, Function.isMinimalFor_argmin, WithZeroTopology.hasBasis_nhds_zero, ArchimedeanClass.addSubgroup_eq_bot, Hyperreal.epsilon_lt_of_neg, Valuation.mem_leAddSubgroup_iff, Submodule.inf_iSup_genEigenspace, tendsto_nat_ceil_atTop, Nat.floor_ofNat, Polynomial.trailingDegree_le_of_ne_zero, MeasureTheory.integrable_iff_integrableAtFilter_atTop, exists_nonneg_right_iff_sameRay, MonomialOrder.le_add_right, FiniteMultiplicity.emultiplicity_le_of_multiplicity_le, AddCircle.coe_image_Icc_eq, Finset.max_le_iff, Polynomial.isEquivalent_atTop_div, isLocallyClosed_Iio, RelHomClass.map_inf, Archimedean.embedReal_injective, IsPreconnected.ordConnected, min_abs_abs_le_abs_max, abs_sub_abs_le_abs_sub, exteriorPower.ιMultiDual_apply_ιMulti, nonemptyFinLinOrd_dual_comp_forget_to_linOrd, Topology.IsLower.tendsto_nhds_iff_lt, List.getD_min?_eq_untopD_minimum, LinearOrderedField.coe_mem_cutMap_iff, Valuation.vle_iff_le, Module.End.genEigenspace_eq_genEigenspace_maxUnifEigenspaceIndex_of_le, Order.Ioi_pred_eq_insert, SimpleGraph.not_isUniform_iff, OrderIso.sumLexIicIoi_symm_apply_Ioi, MonomialOrder.degree_pow_le, Finset.max_eq_sup_withBot, cmp_mul_right', mul_self_pos, ValuationSubring.monotone_mapOfLE, List.exists_map_eq_of_sorted_iff_sbtw, Finset.max'_insert, measurableSet_Ioi, PNat.add_one_le_iff, Int.preimage_Iic, Finset.nsmul_inf', Valued.toNormedField.norm_le_iff, Valuation.map_add', WithTop.untop₀_max, map_pos_of_ne_zero, Orientation.oangle_sign_smul_left, exists_isLocalExtr_uIoo_of_tendsto, iUnion_Icc_add_intCast, Cardinal.ofENat_le_ofENat, ProbabilityTheory.Kernel.partialTraj_succ_self, ENat.toENNReal_lt, MulArchimedeanClass.ballSubgroup_antitone, IsDedekindDomain.HeightOneSpectrum.valuation_lt_one_iff_mem, countable_image_gt_image_Iio_within, Mathlib.Meta.Positivity.nonneg_of_isRat, bot_eq_one', Polynomial.le_trailingDegree_C_mul_X_pow, DivisibleHull.instIsOrderedCancelAddMonoid, Valuation.ltSubmodule_monotone, Pi.lt_toColex_update_self_iff, Cardinal.ofNat_lt_ofENat, MeasureTheory.stoppedValue_stoppedProcess, Cardinal.card_typein_toType_lt, AffineMap.image_uIcc, Finset.dens_biUnion_le, HahnSeries.finiteArchimedeanClassOrderIsoLex_apply_snd, instArchimedeanNNRat, Module.Basis.orientation_comp_linearEquiv_eq_iff_det_pos, PNat.card_Ico, sameRay_neg_smul_left_iff_of_ne, sub_one_lt, continuousAt_iff_continuous_left_right, HahnSeries.cardSupp_div_le, CategoryTheory.SmallObject.instIsIsoRightAppArrowMapToTypeOrdFunctorIterationFunctor, NumberField.RingOfIntegers.HeightOneSpectrum.adicAbv_def, Fin.castLEOrderEmb_toEmbedding, Orientation.oangle_sign_smul_add_smul_smul_add_smul, ValuativeRel.RankLeOneStruct.strictMono, associated_abs_left_iff, IsNonarchimedean.add_eq_max_of_ne, GroupCone.oneLE.hasMemOrInvMem, Finset.Ici_succ_eq_Ioi, MonomialOrder.toSyn_monotone, Valued.integer.mulArchimedean_mrange_of_isCompact_integer, eventually_nhdsWithin_sign_eq_of_deriv_pos, Valuation.Integers.dvdNotUnit_iff_lt, RelHomClass.map_sup, nhds_eq_iInf_mabs_div, exists_le_mul_self, Padic.valuation_p_lt_one, Finset.dens_le_dens_sdiff_add_dens, LaurentSeries.intValuation_le_iff_coeff_lt_eq_zero, Tropical.addLeftMono, min_neg_neg, PointedCone.tmul_subset_maxTensorProduct, MvPowerSeries.weightedOrder_mul_ge, Valuation.IsEquiv.lt_iff_lt, convexJoin_convexJoin_convexJoin_comm, MvPowerSeries.le_order, Nat.ceil_intCast, Finset.dens_lt_dens, Function.argminOn_le, RootPairing.zero_le_posForm, StieltjesFunction.mono, Finset.Iio_succ_eq_Iic, Set.one_le_encard_insert, min_max_distrib_left, PNat.map_subtype_embedding_Ioo, Set.Nonempty.encard_pos, Set.compl_ordConnectedSection_ordSeparatingSet_mem_nhdsLE, convexHull_sum, PowerSeries.le_order_pow_of_constantCoeff_eq_zero, LinearOrderedSemiring.toOrderedSMul, Set.monotone_or_antitone_iff_uIcc, MonomialOrder.degLex_single_le_iff, ArchimedeanClass.mk_mul, strictConcaveOn_iff_slope_strict_anti_adjacent, Continuous.mabs, HahnSeries.addVal_apply_of_ne, tendsto_ratCast_atBot_iff, isLeast_pair, MeasureTheory.aecover_Icc_of_Icc, LinearOrderedCommGroup.wellFoundedOn_setOf_le_lt_iff_nonempty_discrete, posPart_pos_iff, Order.Iio_succ, Nimber.instWellFoundedLT, MvPolynomial.leadingCoeff_toLex_C, AddCircle.coe_image_Ioc_eq, Filter.tendsto_mul_const_atTop_iff, interior_Ioc, ArchimedeanClass.map_mk_eq, max_sub_min_eq_abs, Set.Ioi_pred_eq_Ici, MvPowerSeries.order_le, Multiset.Ico_inter_Ico, Finset.Colex.toColex_lt_toColex_iff_exists_forall_lt, Rat.preimage_cast_Iic, Finset.max'_eq_sorted_last, ENat.toENNReal_min, Finset.min'_subset, LinearLocallyFiniteOrder.instIsPredArchimedeanOfLocallyFiniteOrder, PredOrder.nhds_eq_pure, add_lt_add_iff_left_of_ne_top, hasBasis_nhdsSet_Iic_Iio, NatOrdinal.toOrdinal_natCast, Set.Ioc_pred_left_eq_Icc, Module.End.mem_genEigenspace_top, continuousOn_uIcc_extendFrom_uIoo, Valued.closure_coe_completion_v_lt, List.minimum_eq_coe_iff, Module.Basis.orientation_adjustToOrientation, MulArchimedeanClass.mk_div_lt_mk_left_iff, mul_max, OrderHomClass.toLatticeHomClass, Pi.Lex.wellFoundedLT, sign_mul, grade_lt_grade_iff, countable_setOf_covBy_left, posPart_eq_ite, Polynomial.isEquivalent_atBot_lead, Module.End.injOn_genEigenspace, Finset.mem_convexHull, LinearOrder.infClosed, OrderEmbedding.preimage_uIcc, ZNum.cast_le, max_zero_sub_max_neg_zero_eq_self, IsDiscreteValuationRing.addVal_add, SetTheory.PGame.equiv_nim_grundyValue, Mathlib.Meta.NormNum.isRat_lt_false, Nonneg.coe_nnqsmul, Module.Basis.orientation_comp_linearEquiv_eq_neg_iff_det_neg, mul_neg_iff, Finset.nonneg_addConst_self, Finset.Icc_pred_right_eq_Ico, AbsoluteValue.map_units_int_smul, Module.End.genEigenspace_one, Profinite.NobelingProof.Products.lt_iff_lex_lt, Int.padicValuation_self, mabs_div, Valued.closure_coe_completion_v_mul_v_lt, LinearOrder.isSublattice, Set.encard_iUnion_le_of_finite, mul_self_lt_one_iff, Multipliable.abs, Nat.ceil_one, RootPairing.RootPositiveForm.rootLength_pos, measurable_IicProdIoc, Hyperreal.infinitesimal_neg_iff_infiniteNeg_inv, Set.uIcc_eq_union, mabs_by_cases, HahnSeries.isUnit_iff, Hyperreal.infiniteNeg_def, MulArchimedeanClass.mk_right_le_mk_mul_iff, IsMulIndecomposable.baseOf_subset_one_lt, smul_nonpos_iff_neg_imp_nonneg, Set.Ico_diff_Iio, Set.unbounded_ge_iff_unbounded_inter_ge, isPiSystem_Ico, Valued.cauchy_iff, AffineSubspace.wSameSide_iff_exists_left, Nat.ceil_ofNat, MvPolynomial.schwartz_zippel_sup_sum, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.map_f', Asymptotics.IsEquivalent.tendsto_atBot_iff, Valuation.one_apply_le_one, Cardinal.toENatAux_gc, AddCircle.card_torsion_le_of_isSMulRegular_int, EReal.sign_bot, LinearOrderedAddCommGroup.Subgroup.negGen_neg, HahnSeries.min_order_le_order_add, sbtw_pointReflection_of_ne, PointedCone.minTensorProduct_le_maxTensorProduct, transfiniteIterate_bot, AddMonoidAlgebra.exists_supDegree_mem_support, CategoryTheory.TransfiniteCompositionOfShape.ici_isoBot, Set.compl_Iic, Nat.ceil_sub_natCast, Filter.comap_mabs_atTop, nhdsWithin_Iio_isMeasurablyGenerated, comap_coe_nhdsLT_eq_atTop_iff, Cardinal.toNat_toENat, PNat.Ioc_eq_finset_subtype, ArchimedeanClass.mk_left_le_mk_add_iff, Finset.sort_sorted_lt, Finset.le_card_falling_div_choose, MulArchimedeanClass.mk_one, Finset.Ioc_pred_right_eq_Ioo, exists_pos_left_iff_sameRay, MvPolynomial.monic_esymm, Finset.prod_min_le, Set.Ico_succ_left_eq_Ioo, Int.floor_eq_iff, subsingleton_floorSemiring, ArchimedeanClass.FiniteResidueField.mk_eq_mk, ArchimedeanClass.stdPart_monotoneOn, abs_nonpos_iff, Ordinal.toNimber_one, Convex.min_le_combo, monovaryOn_iff_smul_rearrangement, Odd.strictMono_pow, NNRat.instCanonicallyOrderedAdd, IsDedekindDomain.HeightOneSpectrum.adicValued_apply, Finset.prod_prod_Ioi_mul_eq_prod_prod_off_diag, InnerProductSpace.gramSchmidt_def', closure_Iio, RootPairing.pairingIn_le_zero_iff, CategoryTheory.SmallObject.SuccStruct.extendToSucc.obj_eq, NumberField.FinitePlace.norm_def_int, WithTop.tendsto_untopA, CategoryTheory.TransfiniteCompositionOfShape.iic_F, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.w, Finset.expect_mul_sq_le_sq_mul_sq, NNRat.coe_le_coe, CategoryTheory.SmallObject.SuccStruct.restrictionLTOfCoconeIso_hom_app, tendsto_ceil_left_pure, self_mul_sign, ContinuousWithinAt.lowerSemicontinuousWithinAt, Set.uIcc_subset_uIcc_iff_le, convexHullAddMonoidHom_apply, cocompact_eq_atBot, RingSeminormClass.toNonnegHomClass, vectorSpan_segment, HahnSeries.binomial_power, ENat.toENNReal_mono, OrderTopology.to_orderClosedTopology, Ordinal.cof_eq_cof_toType, RootPairing.pairingIn_lt_zero_iff, LinearLocallyFiniteOrder.succFn_spec, List.argmax_eq_some_iff, MonoidWithZeroHom.inr_mono, IsValuativeTopology.hasBasis_nhds_zero', CauSeq.le_sup_left, Finset.convexHull_eq, Mathlib.Meta.NormNum.isRat_le_false, Set.Infinite.exists_lt_map_eq_of_mapsTo, Set.Iic_sub_one_eq_Iio, isSquare_mabs, Polynomial.div_tendsto_leadingCoeff_div_of_degree_eq, abs_choice, max_mul_mul_left, PNat.find_lt_iff, Filter.not_tendsto_pow_atTop_atBot, Set.Ioc_union_Ioc_symm, le_neg_self_iff, upperSemicontinuousOn_iff_frequently, min_right_comm, Finset.orderEmbOfCardLe_mem, Tropical.trop_max_def, exists_isLocalExtr_uIoo, pow_dvd_iff_le_emultiplicity, ENat.epow_left_mono, Nat.cast_min, Dense.borel_eq_generateFrom_Ico_mem, Mathlib.Meta.NormNum.isNNRat_le_true, PointedCone.tmul_subset_minTensorProduct, Nonneg.coe_inv, Polynomial.eventually_atTop_not_isRoot, Finset.fold_max_le, Order.lt_succ_iff, LinearOrderedField.inducedMap_mono, Polynomial.natTrailingDegree_le_trailingDegree, ValuativeRel.isRankLeOne_iff_mulArchimedean, Valuation.Integers.maximalIdeal_eq_setOf_le_v_algebraMap, nhdsSet_Iic, exteriorPower.pairingDual_apply_apply_eq_one, OrderIso.sumLexIicIoi_apply_inr, ArchimedeanClass.mk_ratCast, Order.isLUB_Iio_iff_isSuccPrelimit, Finset.exists_mem_eq_sup, LinearOrderedAddCommGroup.wellFoundedOn_setOf_ge_gt_iff_nonempty_discrete, pred_max, Set.exists_upper_bound_image, tendsto_floor_left', RootPairing.coxeterWeightIn_le_four, Finset.pluennecke_ruzsa_inequality_pow_div, Order.succ_injective, MulArchimedeanClass.map_mk_eq, ProbabilityTheory.gaussianReal_map_mul_const, MeasureTheory.stoppedProcess_eq'', Nat.orderedSMul, Set.Iic_union_Ioi, MeasureTheory.integrableOn_Ioi_iff_integrableAtFilter_atTop_nhdsWithin, PowerSeries.min_order_le_order_add, CategoryTheory.OrthogonalReflection.iteration_map_succ_assoc, cmp_sub_zero, ValuationSubring.isIntegral_of_mem_ringOfIntegers', max_min_distrib_right, Rat.preimage_cast_Ici, Prime.abs, ArchimedeanClass.ballAddSubgroup_antitone, AddCircle.openPartialHomeomorphCoe_source, sign_apply, HahnSeries.embDomainOrderAddMonoidHom_injective, PosNum.cast_le, sq_lt_one_iff_abs_lt_one, Finite.exists_min, Profinite.NobelingProof.Products.lt_nil_empty, sq_sum_le_card_mul_sum_sq, tendsto_nat_floor_atTop, ValuativeRel.instIsOrderedMonoidValueGroupWithZero, Order.pred_top_lt_iff, Nimber.toOrdinal_eq_one, Tuple.comp_sort_eq_comp_iff_monotone, Set.Ici_diff_Ioi, Finset.Ico_add_one_right_eq_Icc, Sym2.sortEquiv_symm_apply, Ico_mem_nhds_iff, intermediate_value_Ioc', toENat_rank_span_set, Finset.min'_lt_max', GenContFract.of_den_mono, SuccOrder.isOpen_iff, DivisibleHull.qsmul_def, MvPolynomial.supDegree_toLex_C, Finset.mulConst_le_inv_dens, Finset.Ioc_pred_pred_eq_Ico, ArchimedeanClass.out_top, sign_one, ValuativeRel.uniformizer_inv_le_iff, Valuation.one_vlt_iff, neg_lt_self_iff, IsValuativeTopology.isClopen_ball, IsValuativeTopology.hasBasis_nhds, Set.Iic_pred_eq_Iio, Set.encard_mono, abs_cases, Polynomial.tendsto_nhds_iff, Affine.Simplex.sSameSide_affineSpan_faceOpposite_iff, dvd_iff_emultiplicity_pos, AddCircle.measurePreserving_equivIoc, Rat.castOrderEmbedding_apply, ENat.add_lt_add_iff_left, ArchimedeanClass.subsemigroup_strictAnti, Set.encard_singleton_inter, Matrix.IsIrreducible.exists_pos, QuotientAddGroup.btw_coe_iff, Finset.add_sup, Finset.sum_card_slice_div_choose_le_one, IsDedekindDomain.HeightOneSpectrum.intValuation_lt_one_iff_dvd, Filter.Eventually.exists_Ioo_subset, wbtw_iff_right_eq_or_left_mem_image_Ici, Mathlib.Meta.NormNum.isRat_le_true, CauSeq.const_le, FiniteMulArchimedeanClass.mk_le_mk, archimedean_iff_nat_lt, Rat.toNNRat_pos, tendsto_pow_neg_atTop, Asymptotics.IsEquivalent.tendsto_atTop_iff, WithZero.denselyOrdered_set_iff_subsingleton, Set.Iic_subset_Iic_union_Icc, summable_abs_iff, IsConnected.Icc_subset, abs_pos, Set.subsingleton_Icc_iff, Set.bounded_lt_inter_lt, aemeasurable_uIoc_iff, abs_unit_intCast, infIrred_iff_not_isMax, IsDiscreteValuationRing.map_algebraMap_eq_valuationSubring, LinearLocallyFiniteOrder.instIsSuccArchimedeanOfLocallyFiniteOrder, OrderIso.subsingleton_of_wellFoundedLT', Valuation.one_vle_iff, ENat.one_le_epow, lowerSemicontinuousOn_iff_frequently, Filter.tendsto_const_mul_pow_atBot_iff, wbtw_iff_left_eq_or_right_mem_image_Ici, Ioo_subset_openSegment, Set.unbounded_lt_iff, abs_sub_map_le_div, convex_uIcc, convexHull_pi, ArchimedeanClass.ball_top, Cardinal.toENat_strictMonoOn, InnerProductSpace.span_gramSchmidt_Iic, Function.mulSupport_min, HahnSeries.pow_add, Fin.castAddOrderEmb_toEmbedding, Set.Nontrivial.exists_lt, SimpleGraph.FarFromTriangleFree.lt_half, Finset.Nonempty.inf_eq_bot_iff, round_eq_zero_iff, NNRat.preimage_cast_Ici, Finset.min_eq_bot, map_abs, Order.isPredLimitRecOn_pred, FiniteArchimedeanClass.mk_le_mk, CategoryTheory.SmallObject.iterationFunctorMapSuccAppArrowIso_hom_right_right_comp_assoc, HahnSeries.orderTop_mul, Ordinal.ToType.mk_symm_apply_coe, MonomialOrder.wf, ArchimedeanClass.FiniteElement.isUnit_iff_mk_eq_zero, Finset.fold_min_le, Hyperreal.instIsStrictOrderedRing, frontier_Ici_subset, Set.projIic_self, Valued.toNormedField.one_lt_norm_iff, LinOrd.forget_map, Filter.Germ.const_abs, Set.uIoo_subset_uIcc, Finset.max'_union, Field.Emb.Cardinal.filtration_apply, Set.Ioc_pred_pred_eq_Ico, measurableSet_uIcc, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.sq, Finset.Ioo_pred_left_eq_Ioc, Affine.Simplex.ExcenterExists.sign_touchpointWeights, Rat.cast_mono, NNRat.ceil_coe, IsDedekindDomain.HeightOneSpectrum.intValuation_zero_lt, sq_lt_sq, Int.lt_zpow_succ_log_self, add_sq_le, Finset.le_dens_sdiff, strictConvex_Ioc, Finset.min'_lt_max'_of_card, toZ_iterate_succ, IsValuativeTopology.hasBasis_nhds_zero, AffineMap.lineMap_anti, nhdsWithinLT_sup_nhdsWithinGT, IsDedekindDomain.HeightOneSpectrum.valuedAdicCompletion_eq_valuation, posSMulMono_iff_posSMulReflectLT, AddSubmonoid.mem_closure_image_pos_iff, Valuation.IsNontrivial_iff_exists_one_lt, Tropical.trop_add_def, ContinuousOn.abs, Matroid.ExchangeProperty.encard_diff_le_aux, LinOrd.ext_iff, isOpen_Ioi, Affine.Simplex.sign_touchpointWeights_singleton_pos, NonemptyFinLinOrd.hom_hom_id, Padic.toEquiv_withValUniformEquiv_eq_toEquiv_withValRingEquiv, nhdsSet_Ici, instCommutativeMin, isCompact_Ico_iff, AddCircle.eq_coe_Ico, Set.Iio_subset_Iio_iff, Orientation.oangle_sign_smul_right, Finset.min_pair, Odd.zpow_nonneg_iff, Finset.Ioi_pred_eq_Ici, Asymptotics.isEquivalent_nat_floor, Module.End.genEigenspace_eq_iSup_genEigenspace_nat, trop_iInf, Finset.min'_lt_of_mem_erase_min', Valuation.mem_ltAddSubgroup_iff, le_iff_forall_pos_lt_add, mabs_mabs_div_mabs_le_mabs_div, Cardinal.ofNat_le_ofENat, CategoryTheory.TransfiniteCompositionOfShape.ici_isColimit, IsCompact.bddAbove_image, PNat.succ_eq_add_one, Ordinal.enum_succ_eq_top, Set.uIoo_subset_uIcc_self, Nimber.toOrdinal_one, doublyStochastic_eq_convexHull_permMatrix, mul_smul_one_lt_iff, LaurentSeries.valuation_LaurentSeries_equal_extension, cocompact_eq_atBot_atTop, floorDiv_le_ceilDiv, ENat.addLECancellable_coe, max_one_mul_max_inv_one_eq_mabs_self, CauSeq.sup_comm, nhdsLT_basis, Submodule.spanRank_toENat_eq_iInf_finset_card, Finset.min'_insert, PNat.map_subtype_embedding_uIcc, Order.succ_le_succ_iff, LucasLehmer.two_lt_q, HahnSeries.orderTop_nsmul_le_orderTop_pow, variationOnFromTo.sub_self_monotoneOn, min_add_max, Finset.pluennecke_ruzsa_inequality_nsmul_sub_nsmul_sub, CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.instIsIsoMapF, Set.Iio_ssubset_Iio_iff, trichotomy_of_mul_eq_mul, Dense.borel_eq_generateFrom_Ico_mem_aux, RatFunc.v_def, abs_nsmul, DFinsupp.Lex.wellFoundedLT_of_finite, Function.locallyFinsuppWithin.negPart_add, ArchimedeanClass.FiniteResidueField.mk_ne_zero, Nat.one_sub_one_div_cast_nonneg, map_pos_of_ne_one, mul_min, Set.Icc_add_one_left_eq_Ioc, Rat.padicValuation_eq_zero_iff, Set.OrdConnected.IciExtend, NNRat.cast_min, Int.floor_toNat, NonemptyFinLinOrd.dual_map, Finset.nsmul_sup', Set.preimage_const_mul_uIcc, LaurentSeries.LaurentSeries_coe, strictConvex_Ico, MeasureTheory.integrableOn_Iio_iff_integrableAtFilter_atBot_nhdsWithin, PNat.addLeftReflectLE, ENat.pow_lt_top_iff, CategoryTheory.SimplicialThickening.Path.left_le, max_top_left, CategoryTheory.SmallObject.SuccStruct.ofCocone_obj_eq_pt, Finsupp.DegLex.single_le_iff, Finset.centroid_mem_convexHull, IsDedekindDomain.HeightOneSpectrum.intValuation_eq_one_iff, Set.Iio_add_one_eq_Iic, map_mabs, min_top_right, HahnSeries.archimedeanClassOrderIsoWithTop_apply, Finset.untrop_sum, max_eq_bot, Set.OrdConnected.restrict, FiniteMulArchimedeanClass.mem_subgroup_iff, CategoryTheory.TransfiniteCompositionOfShape.ofOrderIso_isoBot, Set.Ico_add_one_left_eq_Ioo, Hyperreal.coe_min, Valuation.Integers.wfDvdMonoid_iff_wellFounded_gt_on_v, Set.encard_le_coe_iff_finite_ncard_le, Rat.preimage_cast_Iio, Finset.Ico_filter_le, Set.unbounded_gt_iff, Rat.cast_nonneg, MvPowerSeries.le_order_smul, NNRat.toNNRat_mono, WithTop.isEmbedding_coe, oneTangentSpaceIcc_def, Set.unit_valuation_eq_one, Set.Ioc_inter_Ioc, Finset.min'_eq_sorted_zero, PowerSeries.le_order_pow, Polynomial.isBoundedUnder_abs_atBot_iff, OrderEmbedding.addRight_apply, negPart_lt, IsNonarchimedean.finset_image_add_of_nonempty, DivisibleHull.coeOrderAddMonoidHom_apply, PosSMulStrictMono.nnrat_of_rat, emultiplicity_prime_le_emultiplicity_image_by_factor_orderIso, stdSimplex.barycenter_apply, mul_nonpos_iff, Nat.floor_le_ceil, Finset.min'_le_max', Int.one_le_ceil_iff, MulArchimedeanClass.mk_mabs, Hyperreal.lt_neg_of_pos_of_infinitesimal, Set.Iio_union_Ioi, abs_mem_iff, Ordinal.iSup_typein_limit, nhdsSet_Iio, IsNonarchimedean.nsmul_le, AbsoluteValue.hasBasis_uniformity, squarefree_iff_emultiplicity_le_one, ArchimedeanClass.mk_le_mk_iff_ratCast, InnerProductSpace.gramSchmidtOrthonormalBasis_inv_blockTriangular, NNRat.one_lt_cast, geom_sum_neg_iff, Set.Ico_disjoint_Ico, Set.image_const_sub_uIcc, ValuativeRel.IsNontrivial.exists_lt_one, Set.unbounded_le_iff, zpowers_mabs, Order.lt_add_one_iff, Rat.toNNRat_add_le, Tuple.eq_sort_iff, MeasureTheory.stoppedProcess_eq_of_mem_finset, sign_neg, Cardinal.continuum_toENat, inv_nhdsLT_zero, OrderIso.sumLexIicIoi_apply_inl, IsPreconnected.intermediate_value_Ioc, SuccOrder.nhdsGT, ValuativeRel.le_uniformizer_iff, LinearOrderedCommGroupWithZero.inr_eq_coe_inrₗ, Ioc_mem_nhds_iff, Finset.Icc_succ_left_eq_Ioc, Field.Emb.Cardinal.deg_lt_aleph0, CategoryTheory.Functor.IsWellOrderContinuous.restriction_setIci, tendsto_const_mul_pow_nhds_iff, isPiSystem_image_Iio, DFinsupp.Lex.isStrictOrder, Mathlib.Meta.NormNum.isNNRat_abs_nonneg, signedDist_smul, max_sub_max_le_max, iUnion_Ico_intCast, GenContFract.le_of_succ_succ_get?_contsAux_b, Finset.max_eq_top, ProbabilityTheory.gaussianPDFReal_inv_mul, nhdsGE_basis_Icc, Valuation.integer.v_irreducible_pos, Set.Ioo_subset_Ioc_union_Ioo, StieltjesFunction.measure_Icc, Finsupp.Lex.addRightStrictMono, Set.Ioi_subset_Ioi_iff, Rat.cast_abs, ConvexCone.isGenerating_iff_isReproducing, CauSeq.inf_le_right, Valuation.leIdeal_mono, Set.Ioc_diff_Ioi, FunctionField.inftyValuation.X_zpow, PNat.card_fintype_Ioo, CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.ofComposableArrows_F, FiniteMulArchimedeanClass.congrOrderIso_symm, Int.ceil_le, Set.strictMonoOn_projIci, Tuple.antitone_pair_of_not_sorted', Polynomial.trailingDegree_lt_wf, le_iff_forall_one_lt_lt_mul, Set.finite_diff_iUnion_Ioo', antivaryOn_iff_smul_rearrangement, sq_eq_sq_iff_abs_eq_abs, mabs_div_pos, Set.Iic_subset_Iic_union_Ioc, Finset.subConst_le_card, NNRat.cast_max, PredOrder.nhdsLT, PNat.Prime.one_lt, Topology.RelCWComplex.iUnion_openCell_eq_skeletonLT, SignType.neg_lt_neg_iff, sq_nonpos_iff, Set.Ioo_pred_left_eq_Ioc, Int.fract_add_le, Finset.trop_inf, HahnSeries.orderTop_add_le_mul, Set.range_projIic, LinOrd.Iso.mk_inv, CategoryTheory.TransfiniteCompositionOfShape.ofArrowIso_incl, Module.End.genEigenspace_le_genEigenspace_maxUnifEigenspaceIndex, HurwitzZeta.hasSum_nat_hurwitzZetaOdd, MeasureTheory.ae_restrict_uIoc_iff, LinearOrderedCommGroupWithZero.fst_comp_inl, upperClosure_eq_bot_iff, ENat.le_coe_iff, IsCompact.exists_isMinOn, abs_pow_sub_pow_le, Int.ceil_lt_add_one, HahnEmbedding.ArchimedeanStrata.isInternal_stratum', Dense.borel_eq_generateFrom_Ioc_mem_aux, Int.image_fract, Multiset.exists_min_image, OrderRingIso.apply_eq_self, Nimber.instZeroLEOneClass, Set.Iic_union_Ici, Fin.succAboveOrderEmb_toEmbedding, PrincipalSeg.isNormal, inv_mabs_le_inv, Positive.coe_inv, Rat.cast_nonpos, Finset.sortedLT_sort, IsCoprime.abs_left_iff, Hyperreal.lt_of_pos_of_infinitesimal, archimedean_iff_rat_le, one_lt_sq_iff_one_lt_abs, ArchimedeanClass.FiniteResidueField.mk_le_mk, OrderIso.subsingleton_of_wellFoundedLT, Filter.tendsto_pow_atTop_iff, Set.encard_le_encard_iff_encard_diff_le_encard_diff, mem_nhdsGE_iff_exists_Ico_subset, Affine.Simplex.sign_touchpointWeights_singleton_neg, PNat.card_uIcc, Set.Ico_add_one_add_one_eq_Ioc, MvPowerSeries.map_iterateFrobenius_expand, Order.succ_eq_succ_iff, Finset.sum_sum_Ioi_add_eq_sum_sum_off_diag, Valuation.IsNontrivial.exists_one_lt, IsDedekindDomain.HeightOneSpectrum.intValuation_def, CategoryTheory.Limits.WalkingMultispan.inclusionOfLinearOrder_obj, OrderIso.pnatIsoNat_apply, LocallyFiniteOrder.orderAddMonoidHom_apply, IsCoprime.abs_left, not_lt_zero', Module.Basis.abs_det_adjustToOrientation, SimpleGraph.le_card_nonuniformWitness, CategoryTheory.SmallObject.SuccStruct.transfiniteCompositionOfShapeιIteration_incl, FunctionField.inftyValuation.X, InnerProductSpace.gramSchmidt_def'', Finset.add_sup', RingCone.nonneg.hasMemOrNegMem, Set.unbounded_ge_inter_gt, StieltjesFunction.length_eq, Nat.cast_finsetInf', mem_nhdsLT_iff_exists_Ioo_subset, FiniteMulArchimedeanClass.min_le_mk_mul, MonomialOrder.degree_prod_le, min_mul_distrib, LinearOrderedSemifield.toPosSMulStrictMono_rat, Module.End.genEigenspace_zero_nat, antivary_iff_mul_rearrangement, MeasureTheory.Filtration.rightCont_eq, Set.infinite_iff_exists_gt, comap_abs_nhds_zero, CauSeq.exists_lt, FiniteMultiplicity.emultiplicity_lt_of_multiplicity_lt, HahnSeries.leadingCoeff_nonneg_iff, WithZeroTopology.isOpen_iff, Order.pred_lt_pred_iff, Measurable.nat_floor, toZ_iterate_pred, CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.ofComposableArrows_isoBot_inv, ENat.lt_add_one_iff, ENat.addLECancellable_of_ne_top, List.prod_min_le, Nimber.instNoMaxOrder, ArchimedeanClass.archimedean_of_mk_eq_mk, Finset.max'_eq_iff, tendsto_nat_ceil_div_atTop, Finsupp.DegLex.isStrictOrder, Cardinal.ofENat_lt_ofENat, Finset.dens_mono, ArchimedeanClass.mk_eq_mk, NNRat.instOrderedSub, EReal.sign_top, Matrix.IsPrimitive.exists_pos_pow, Valuation.srel_one_iff, max_mul_mul_le_max_mul_max', LinearOrder.isSuccArchimedean_of_isPredArchimedean, Continuous.strictMono_of_inj, MonomialOrder.div_set, List.mem_argmax_iff, MulArchimedeanClass.mk_mul_lt_mk_right_iff, MeasureTheory.Lp.coe_posPart, right_le_lineMap_iff_one_le, MonoidWithZeroHom.snd_mono, nullMeasurableSet_lt', Set.inv_uIcc, Module.End.genEigenspace_top, Ordinal.toNatOrdinal_zero, CategoryTheory.SmallObject.iterationFunctorMapSuccAppArrowIso_hom_left, HahnEmbedding.Partial.orderTop_eq_finiteArchimedeanClassMk, Valuation.IsUniformizer.val_pos, Set.Ioi_subset_Ici_iff, Finset.orderEmbOfFin_apply, MeasureTheory.aecover_Ioo_of_Ioo, intermediate_value_Ico', List.exists_map_eq_of_sorted_iff_wbtw, Odd.pow_pos_iff, PointedCone.minTensorProduct_comm, fderiv_norm_smul, abs_add', LinOrd.ofHom_comp, HasFDerivAt.hasFDerivAt_norm_smul, NNRat.cast_pos, borel_eq_generateFrom_Ico, Set.coe_projIic, NatOrdinal.toOrdinal_eq_zero, tendsto_floor_atBot, QuotientAddGroup.btw_coe_iff', Multiset.Ico_filter_le, CategoryTheory.IsGrothendieckAbelian.generatingMonomorphisms.functorToMonoOver_map, List.le_maximum_of_mem', abs_neg_one_zpow, MeasureTheory.aecover_Ioc_of_Ioc, PNat.instWellFoundedLT, Order.isNormal_iff', Cardinal.ofENat_strictMono, Pi.lt_toLex_update_self_iff, Int.preimage_Ioo, mabs_eq_one, OrderType.type_le_type_iff, FunctionField.inftyValuedFqt.def, one_lt_oneLePart_iff, CategoryTheory.SmallObject.πFunctorObj_eq, isPiSystem_Iio, Mathlib.Tactic.Qify.nnratCast_lt, NonemptyFinLinOrd.id_apply, tendsto_ceil_left', hahnEmbedding_isOrderedModule_rat, AddValuation.map_sub, Affine.Simplex.sign_signedInfDist_touchpoint_empty, Finsupp.Lex.addLeftStrictMono, FiniteArchimedeanClass.congrOrderIso_symm, Valuation.RankOne.strictMono', mabs_mul_eq_mul_mabs_iff, mabs_div_mabs_le_mabs_mul, PNat.lt_add_left, SimpContFract.of_isContFract, tendsto_const_mul_zpow_atTop_zero, AffineIndependent.convexHull_inter', Finset.min'_pair, Set.Ioi_inter_Ioo, AffineSubspace.sOppSide_pointReflection, max_eq_right_iff, Set.Ici_subset_Icc_union_Ioi, Finset.le_max', PredOrder.hasBasis_nhds_Ioc, Filter.tendsto_Ioc_uIcc_uIcc, Finset.sup_mem_of_nonempty, GenContFract.of_one_le_get?_partDen, Valuation.vle_one_iff, sign_nonpos_iff, Set.Finite.exists_lt_map_eq_of_forall_mem, smul_nonneg_iff, Cardinal.toENat_le_iff_of_le_aleph0, PNat.sub_le, Finset.intervalGapsWithin_snd_of_lt, Valuation.IsEquiv.val_sub_one_lt_one_iff, Nat.one_div_cast_nonneg, Set.Icc_sub_one_right_eq_Ico, ENat.coe_lt_coe, sign_pow, Set.powersetCard.mem_ofFinEmbEquiv_iff_mem_range, Finset.max_insert, PowerSeries.order_le, measurableSet_Ioo, Valuation.Integers.coe_span_singleton_eq_setOf_le_v_algebraMap, LinearOrderedAddCommGroup.discrete_or_denselyOrdered, MonomialOrder.degLex_lt_iff, IsDedekindDomain.HeightOneSpectrum.adicValued.uniformContinuousConstSMul, IsValuativeTopology.hasBasis_nhds', LinearOrder.infConvergenceClass, ContinuousOn.surjOn_Icc, emultiplicity_lt_top, Finset.Ioo_add_one_right_eq_Ioc, Multiset.max_prod_le, AddMonoidAlgebra.Monic.supDegree_mul_of_ne_zero_left, abs_eq_zero, Set.preimage_const_sub_uIcc, HahnModule.orderTop_vAdd_le_orderTop_smul, strictConvex_iff_ordConnected, NNRat.ofNat_le_cast, Cardinal.toENat_eq_top, sameRay_smul_right_iff_of_ne, extremePoints_doublyStochastic, Valuation.Integers.valuation_pos_iff_ne_zero, hasDerivAt_abs, Valued.isOpen_closedBall, Finset.lt_inf'_iff, lineMap_le_right_iff_le_one, Int.floor_le_neg_one_iff, invOf_nonpos, exists_square_le, Affine.Simplex.sign_excenterWeights_empty, IsPreconnected.mapsTo_Ioi_or_Iio, Finset.intervalGapsWithin_succ_fst_of_lt, Field.Emb.Cardinal.strictMono_filtration, convexHull_eq_union_convexHull_finite_subsets, tendsto_fract_left, Finset.sort_sorted_gt, PNat.card_Ioo, GenContFract.fib_le_of_contsAux_b, Continuous.max, Finset.le_min_iff, ENat.coe_le_coe, OrderHomClass.coe_to_lattice_hom, upperSemicontinuous_iff_isClosed_preimage, AddMonoidAlgebra.Monic.supDegree_pow, Hyperreal.lt_of_tendsto_atBot, max_bot_right, Nat.one_sub_one_div_cast_le_one, MvPowerSeries.weightedOrder_le, Mathlib.Meta.NormNum.IsRat.natCeil, Finset.Ioc_pred_left_eq_Icc, Valuation.IsEquiv.one_le_iff_one_le, Set.Ioo_succ_right_eq_Ioc, Int.ceil_toNat, min_mul_max, SignType.not_lt_neg_one, HahnEmbedding.Seed.truncLT_mem_range_baseEmbedding, NNRat.ceil_cast, Finset.sup'_add, Nat.cast_div_le, Set.Iio_diff_Iic, Positive.isOrderedCancelMonoid, Finset.untrop_sum', Int.floor_pos, Valued.mem_nhds_zero, Odd.zpow_pos_iff, abs_eq_neg_self, sign_eq_zero_iff, sameRay_neg_smul_right_iff_of_ne, associated_abs_right_iff, HahnSeries.orderTop_le_orderTop_smul, PNat.equivNonZeroDivisorsNat_apply_coe, Int.preimage_Ici, PseudoMetric.IsUltra.isTrans_ball, Finset.Colex.lt_iff_max'_mem, Valued.isOpen_ball, ENat.add_one_pos, HahnSeries.orderTop_lt_iff_exists, AddCircle.liftIoc_eq_lift_Icc, Nimber.lt_wf, abs_sub_nonpos, ArchimedeanClass.mk_map_of_archimedean, CategoryTheory.IsGrothendieckAbelian.generatingMonomorphisms.instIsWellOrderContinuousFunctor, CauSeq.le_total, Dense.exists_le, SuccOrder.isOpen_singleton_iff, ValuationSubring.mem_principalUnitGroup_iff, Set.image_add_const_uIcc, LocallyBoundedVariationOn.exists_monotoneOn_sub_monotoneOn, monovary_iff_forall_mul_nonneg, pow_lt_one_iff, ArchimedeanClass.FiniteResidueField.instArchimedean, Valued.mem_nhds, Mathlib.Meta.Positivity.abs_pos_of_ne_zero, Ordinal.lsub_typein, OrderMonoidWithZeroHom.coe_mul, abs_sub_map_le_sub, Set.Ico_inter_Iio, punctured_nhds_eq_nhdsWithin_sup_nhdsWithin, Nat.one_div_pos_of_nat, FiniteArchimedeanClass.withTopOrderIso_symm_apply, Archimedean.exists_orderAddMonoidHom_real_injective, Finset.abs_expect_le, Order.embedding_from_countable_to_dense, HahnEmbedding.Partial.mem_domain, Ordinal.toNatOrdinal_eq_zero, Cardinal.one_lt_ofENat, Even.add_pow_le, intermediate_value_univ, Filter.tendsto_Icc_uIcc_uIcc, Topology.CWComplex.iUnion_openCell_eq_skeleton, Finset.Ioo_filter_lt, sq_pos_iff, abs_sub_sq, Hyperreal.infinite_iff_abs_lt_abs, EReal.le_iff_sign, FloorSemiring.eventually_mul_pow_lt_factorial_sub, WithTop.tendsto_untopD, Finset.nonneg_subConst_self, Pi.Colex.wellFoundedLT, max_cases, Ordinal.enum_zero_eq_bot, Polynomial.isBoundedUnder_abs_atTop_iff, IsDedekindDomain.HeightOneSpectrum.valuationOfNeZero_eq, Finset.min'_eq_iff, LinOrd.coe_id, Nat.ceil_sub_ofNat, Multipliable.abs_tprod, Function.argmin_le, HahnSeries.embDomainOrderAddMonoidHom_apply, Set.Ici_diff_Ici, MulArchimedeanClass.out_top, NNRat.coe_mono, sq_nonneg, MeasureTheory.stoppedProcess_stoppedProcess', convexOn_pow, HahnEmbedding.Seed.mem_domain_baseEmbedding, one_le_pow_iff, MulArchimedeanClass.mk_left_le_mk_div_iff, Finset.isGLB_iff_isLeast, Nat.ceil_sub_one, Finsupp.Lex.single_antitone, Topology.RelCWComplex.skeleton_monotone, sameRay_neg_smul_right_iff, RootPairing.RootPositiveForm.exists_pos_eq, Valued.integer.locallyFiniteOrder_units_mrange_of_isCompact_integer, AffineSubspace.sSameSide_iff_exists_right, NNRat.preimage_cast_Ico, SMulPosReflectLT.toSMulPosMono, FiniteDimensional.exists_relation_sum_zero_pos_coefficient_of_finrank_succ_lt_card, mem_convexHull_iff_exists_fintype, ContinuousWithinAt.mabs, Hyperreal.ofSeq_le_ofSeq, Ico_subset_closure_interior, MeasureTheory.Measure.measure_Ioo_eq_zero, Set.mem_uIoc, Set.Ioc_union_Ioc_union_Ioc_cycle, SuccOrder.isSuccLimit_of_mem_frontier, le_iff_forall_lt_rat_imp_le, toZ_iterate_succ_le, tsub_min, PNat.card_fintype_Ioc, LaurentSeries.instLaurentSeriesComplete, round_le_add_half, Cardinal.ofENat_lt_nat, LinearOrderedCommGroup.to_noMinOrder, Odd.zpow_neg_iff, AbsoluteValue.map_units_int, nullMeasurableSet_Iio, Set.encard_image_le, convexHull_toCone_isLeast, sameRay_or_sameRay_neg_iff_not_linearIndependent, Nat.cast_finsetSup, IsDedekindDomain.HeightOneSpectrum.valuation_surjective, NNRat.cast_nonpos, Set.Ioc_sub_one_sub_one_eq_Ico, Int.le_floor, Hyperreal.omega_pos, Valuation.rel_one_iff, Rat.cast_lt_zero, MvPowerSeries.weightedOrder_add_of_weightedOrder_ne, Int.fract_eq_self, List.minimum_anti, Set.Ico_add_one_right_eq_Icc, lowerSemicontinuousAt_iff_frequently, CategoryTheory.TransfiniteCompositionOfShape.ofComposableArrows_isoBot, Set.projIci_self, Continuous.integrableOn_uIcc, Rat.cast_strictMono, convex_iff_div, HahnSeries.single_div_single, exists_pred_iterate_or, LinearOrderedCommGroupWithZero.wellFoundedOn_setOf_ge_gt_iff_nonempty_discrete_of_ne_zero, Padic.withValUniformEquiv_cast_apply, Module.End.generalized_eigenvec_disjoint_range_ker, NonemptyFinLinOrd.comp_apply, Cardinal.ofENat_le_one, SimpleGraph.right_nonuniformWitnesses_card, Hyperreal.infiniteNeg_iff_infinitesimal_inv_neg, ArchimedeanClass.mk_intCast_nonneg, countable_image_lt_image_Ioi, tendsto_inv_nhdsLT_zero, DFinsupp.Colex.wellFoundedLT_of_finite, convexIndependent_iff_finset, pow_div_pow_eventuallyEq_atTop, Finset.mul_sup', HahnSeries.archimedeanClassMk_le_archimedeanClassMk_iff, LaurentSeries.valuation_coe_ratFunc, DivisibleHull.archimedeanClassOrderIso_apply, Int.fract_lt_one, Hyperreal.archimedeanClassMk_omega_neg, frontier_le_subset_eq, posPart_lt, Valuation.Integers.isPrincipal_iff_exists_eq_setOf_valuation_le, zsmul_lt_zsmul_iff_right, PNat.card_fintype_Ico, Hyperreal.archimedeanClassMk_coe_nonneg, Matrix.mem_glpos, CategoryTheory.TransfiniteCompositionOfShape.iic_incl_app, IsValuativeTopology.isClosed_ball, min_add_min_le_min_add_add, AddCircle.continuous_equivIco_symm, nhdsWithinLE_sup_nhdsWithinGE, HahnSeries.inv_def, intermediate_value_Icc, Cardinal.ofENat_pos, Padic.coe_withValRingEquiv, Valuation.Integer.not_isUnit_iff_valuation_lt_one, CategoryTheory.TransfiniteCompositionOfShape.ofOrderIso_F, CauSeq.le_sup_right, Matrix.IsPrimitive.nonneg, Finset.Ioo_sub_one_left_eq_Ioc, Max.right_comm, Padic.comap_mulValuation_eq_int_padicValuation, Nat.floor_sub_natCast, Finset.one_le_divConst_self, Int.preimage_Icc, MeasureTheory.ae_const_le_iff_forall_lt_measure_zero, AffineSubspace.wSameSide_iff_exists_right, continuousAt_sign_of_neg, Affine.Simplex.sSameSide_affineSpan_faceOpposite_point_right_iff, isPiSystem_Ioc_mem, div_pos_iff, measurableSet_lt, AddCircle.continuousAt_equivIoc, ENat.add_le_add_iff_right, OrderEmbedding.addLeft_apply, Iic_mem_nhdsSet_Iic_iff, Rat.cast_pos_of_pos, Nat.Prime.emultiplicity_factorial_le_div_pred, UniqueFactorizationMonoid.le_emultiplicity_iff_replicate_le_normalizedFactors, LinearOrderedCommGroupWithZero.fst_apply, variationOnFromTo.monotoneOn, Cardinal.toENat_le_natCast_iff, Set.toENat_cardinalMk, NumberField.FinitePlace.norm_eq_one_iff_notMem, MulArchimedeanClass.ballSubgroup_top, grade_injective, Finset.Ico_diff_Ico_right, ArchimedeanClass.mem_closedBall_iff, Polynomial.div_tendsto_atBot_zero_iff_degree_lt, Set.bounded_le_inter_lt, countable_of_isolated_left', Dense.exists_seq_strictAnti_tendsto, Set.range_projIci, Set.Ici_subset_Ico_union_Ici, Valuation.vlt_one_iff, multipliable_mabs_iff, Finset.le_min'_iff, abs_abs_sub_abs_le_abs_sub, extremePoints_convexHull_subset, ENat.mul_left_strictMono, Finset.intervalGapsWithin_fst_of_lt_lt, Module.End.mem_genEigenspace_one, mabs_mul', LaurentSeries.valuation_compare, mem_segment_iff_div, Cardinal.enat_gc, Padic.isUniformInducing_cast_withVal, MeasureTheory.aecover_Ico_of_Ioo, ArchimedeanClass.mk_ratCast_nonneg, Hyperreal.tendsto_atBot_iff, FiniteArchimedeanClass.addSubgroup_strictAnti, Nat.one_le_ceil_iff, PowerSeries.le_order, leOnePart_eq_ite, Orientation.someBasis_orientation, min_div_div_right', Even.zpow_pos_iff, HahnEmbedding.ArchimedeanStrata.archimedean_stratum, exposedPoints_subset_extremePoints, SimpleGraph.nonuniformWitness_spec, Right.nsmul_neg_iff, Set.isPWO_iff_isWF, two_mul_le_add_pow_two, Filter.Germ.const_max, PNat.find_min', Int.ceil_pos, PointedCone.maxTensorProduct_comm, Finset.fold_max_lt, WithTop.tendsto_coe_atTop, Tuple.eq_sort_iff', abs_lt, Set.one_lt_encard_iff, Set.Icc_add_one_sub_one_eq_Ioo, min_zero, MvPowerSeries.order_mul_ge, FiniteMulArchimedeanClass.ballSubgroup_strictAnti, max_mul, HahnSeries.lt_iff, HahnSeries.instIsOrderedAddMonoidLex, instIsCountablyGenerated_atTop, Module.End.IsFinitelySemisimple.genEigenspace_eq_eigenspace, ArchimedeanClass.mk_le_mk_add_of_archimedean, DivisibleHull.mk_lt_mk, Submonoid.closure_image_isMulIndecomposable_baseOf, Rat.toNNRat_le_toNNRat_iff, IsCompact.exists_isGLB, Rat.le_toNNRat_iff_coe_le, Cardinal.toENatAux_le_nat, Finsupp.Colex.addLeftMono, Hyperreal.lt_of_tendsto_zero_of_pos, Finset.Icc_add_one_sub_one_eq_Ioo, Cardinal.toENat_le_nat, Rat.toNNRat_le_iff_le_coe, Rat.cast_le_intCast, Complex.UnitDisc.tendsto_pow_atTop_nhds_zero, Set.encard_pos, mem_nhdsLE_iff_exists_Icc_subset, NNRat.instOrderTopology, Int.preimage_floor_singleton, pow_abs, Int.abs_one_sub_fract, tsub_tsub_eq_min, Finset.map_orderEmbOfFin_univ, closure_Ico, LaurentSeries.tendsto_valuation, abs_max_le_max_abs_abs, ENat.toENNReal_max, HahnSeries.SummableFamily.powers_toFun, Tropical.add_eq_right_iff, nhdsLT_eq_bot_iff, left_le_midpoint, Hyperreal.coe_max, Module.End.genEigenspace_div, Finset.exists_min_image, Set.unbounded_le_inter_lt, List.Perm.maximum_eq, Ordinal.typein_lt_self, LocallyConvexSpace.convex_open_basis_zero, Valuation.IsEquiv.le_one_iff_le_one, Set.encard_le_coe_iff, countable_setOf_isolated_left_within, Set.Iic_diff_Iic, isPiSystem_Icc, Order.isPredPrelimitRecOn_pred, Zsqrtd.instIsOrderedAddMonoidCastInt, PowerSeries.heval_unit, List.maximum_mono, Units.inv_neg, Ioi_mem_nhdsSet_Ici_iff, MeasureTheory.Measure.measure_Ioo_pos, hasBasis_nhdsSet_Ici_Ici, not_bddAbove_iff, pos_invOf_of_invertible_cast, Polynomial.abs_tendsto_atBot, List.foldr_min_of_ne_nil, Set.infinite_iff_exists_lt, Valuation.integer.coe_span_singleton_eq_setOf_le_v_coe, Nat.choose_le_pow_div, dvd_abs, DFinsupp.Colex.total_le, Valuation.Integers.wellFounded_gt_on_v_iff_discrete_mrange, oneLePart_lt, PUnit.canonicallyOrderedAdd, Order.pred_eq_pred_iff, StieltjesFunction.measure_Ioc, Finset.exists_mem_eq_sup', MeasureTheory.AEEqFun.coeFn_posPart, LinearOrder.bot_topologicalSpace_eq_generateFrom, strictConvex_iff_div, PNat.natPred_strictMono, pow_div_pow_eventuallyEq_atBot, ContinuousOn.lowerSemicontinuousOn, LaurentSeries.coe_range_dense, CategoryTheory.Limits.MultispanShape.ofLinearOrder_fst, InnerProductSpace.span_gramSchmidt_Iio, Odd.pow_lt_pow, Field.Emb.Cardinal.iSup_adjoin_eq_top, MeasureTheory.integrableOn_Ici_iff_integrableAtFilter_atTop, toWellOrderExtension_strictMono, Set.notMem_Iio, FiniteArchimedeanClass.coe_congrOrderIso_apply, MeasureTheory.integrableOn_Iic_iff_integrableAtFilter_atBot, Nat.nth_eq_orderEmbOfFin, zero_le', MvPowerSeries.le_weightedOrder, Module.End.genEigenspace_eq_genEigenspace_finrank_of_le, NonemptyFinLinOrd.hom_hom_comp, nhdsLE_basis_Icc, tendsto_floor_left_pure_ceil_sub_one, Set.compl_Iio, SimpleGraph.FarFromTriangleFree.lt_one, abs_mul_abs_self, Ordinal.toNatOrdinal_natCast, HahnSeries.orderTop_self_sub_one_pos_iff, min_cases, SimpleGraph.left_nonuniformWitnesses_card, AbsoluteValue.map_prod, Finset.lt_min'_iff, PowerSeries.intValuation_X, mabs_eq_inv_self, IsSumSq.nonneg, pow_two_pos_of_ne_zero, Set.Ioc_subset_Ioo_union_Icc, AddCircle.continuousAt_equivIco, isCofinal_setOf_imp_lt, SimplexCategory.toCat_obj, Finset.lt_sup_iff, Set.projIci_surjOn, Finpartition.mk_mem_sparsePairs, continuousAt_sign_of_pos, Int.floor_lt_self_iff, NatOrdinal.toOrdinal_symm_eq, CategoryTheory.SmallObject.SuccStruct.iterationCocone_pt, Polynomial.div_tendsto_atTop_zero_of_degree_lt, LocallyFiniteOrder.denselyOrdered_iff_subsingleton, toIcoMod_zero_one, IsDedekindDomain.HeightOneSpectrum.adicValued_apply', Hyperreal.stdPart_of_tendsto, ContinuousWithinAt.abs, OrderRingHom.subsingleton, MulArchimedeanClass.mem_ballSubgroup_iff, PredOrder.nhdsLE, Finset.min_le_of_eq, midpoint_mem_segment, Set.encard_lt_encard_iff_encard_diff_lt_encard_diff, isLocallyClosed_Ioo, strictConcaveOn_iff_div, Int.gc_ceil_coe, LocallyFiniteOrder.orderAddMonoidHom_toAddMonoidHom, trichotomy_of_add_eq_add, ArchimedeanClass.mk_eq_top_iff, NatOrdinal.toOrdinal_one, ArchimedeanClass.mk_le_add_mk_of_archimedean, Pi.instNoMaxOrderColexForallOfWellFoundedGTOfNonempty, Order.isNormal_iff, Finset.inf'_le_iff, PowerSeries.IsWeierstrassFactorization.degree_eq_coe_lift_order_map, isGreatest_pair, OrderIso.subsingleton_of_wellFoundedGT, ArchimedeanClass.mk_right_le_mk_add_iff, Rat.cast_le_natCast, mabs_max_le_max_mabs_mabs, archimedean_iff_int_lt, Set.Ico_succ_right_eq_Icc, ArchimedeanClass.FiniteResidueField.mk_lt_mk, Function.mulSupport_max, Finset.min_insert, stdSimplex.barycenter_eq_centerMass, NNRat.Nonneg.coe_ofScientific, tendsto_const_mul_zpow_atTop_nhds_iff, HahnSeries.min_orderTop_le_orderTop_sub, Ordinal.toNimber_zero, CategoryTheory.SmallObject.iterationFunctorObjObjRightIso_ιIteration_app_right, Polynomial.div_tendsto_zero_of_degree_lt, cocompact_le_atBot_atTop, nhdsGT_eq_bot_iff, IsPreconnected.Icc_subset, Finsupp.DegLex.instIsOrderedCancelAddMonoidDegLexNat, cmp_mul_left', Mathlib.Meta.Positivity.pos_of_isRat, min_lt_max, NatOrdinal.toOrdinal_toNatOrdinal, FiniteMulArchimedeanClass.subgroup_eq_bot, interior_Ico, SMulPosStrictMono.toSMulPosReflectLE, RootPairing.rootForm_pos_of_ne_zero, Finset.sup_eq_zero, Set.ordConnected_iff_uIcc_subset_right, OrderIso.withZeroUnits_apply, Function.locallyFinsuppWithin.nsmul_negPart, LinOrd.hom_comp, AffineSpace.asymptoticNhds_eq_smul, smul_max_of_nonpos, exteriorPower.pairingDual_apply_apply_eq_one_zero, exists_seq_strictMono_tendsto, IsRealClosed.nonneg_iff_isSquare, MulArchimedeanClass.subgroup_antitone, WithZeroTopology.Iio_mem_nhds_zero, AddCircle.openPartialHomeomorphCoe_symm_apply, lt_mabs, GenContFract.IntFractPair.succ_nth_stream_b_le_nth_stream_fr_inv, SignType.pos_iff, SuccOrder.prelimitRecOn_succ, frontier_Iic, Finset.subConst_le_inv_dens, upperSemicontinuous_iff_IsClosed_hypograph, NatOrdinal.instWellFoundedLT, Nat.preimage_floor_zero, Module.End.genEigenspace_nat, Affine.Simplex.ExcenterExists.signedInfDist_excenter, Icc_mem_nhds_iff, antivaryOn_iff_forall_mul_nonpos, IsSquare.nonneg, Padic.coe_withValRingEquiv_symm, MulArchimedeanClass.closedBallSubgroup_top, Dense.exists_lt, SuccOrder.nhdsGE, HahnSeries.leadingCoeff_mul_of_nonzero, Mathlib.Tactic.Order.ToInt.toInt_nlt_toInt, LinearOrder.supClosed, Int.abs_sub_lt_one_of_floor_eq_floor, frontier_Iic_subset, archimedean_iff_rat_lt, mabs_min_le_max_mabs_mabs, Valuation.HasExtension.mk_smul_mk, Nat.floor_eq_zero, WithTop.denselyOrdered_set_iff_subsingleton, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.w_assoc, ValuationSubring.mem_nonunits_iff, min_mul_mul_right, Cardinal.toENat_comp_ofENat, one_lt_leOnePart_iff, Real.Angle.sign_toReal, IsAbsoluteValue.abs_abv_sub_le_abv_sub, Valued.toNormedField.norm_lt_iff, MeasureTheory.aecover_Ioc_of_Ico, PseudoMetric.coe_finsetSup, NNRat.preimage_cast_Ioo, Int.floor_le, PowerSeries.IsWeierstrassFactorizationAt.degree_eq_coe_lift_order_map_of_ne_top, Valuation.rel_iff_le, sq_le_one_iff_abs_le_one, Polynomial.abs_isBoundedUnder_iff, HahnSeries.order_pow, MulArchimedeanClass.mk_le_mk, StieltjesFunction.iInf_Ioi_eq, segment_subset_uIcc, Set.Ici_succ_eq_Ioi, quasilinearOn_iff_mem_uIcc, lt_add_iff_lt_right_or_exists_lt, sign_eq_sign_or_eq_neg, Hyperreal.lt_of_st_lt, MulArchimedeanClass.mk_eq_top_iff, Pi.instNoMaxOrderLexForallOfWellFoundedLTOfNonempty, LocallyFiniteOrder.orderMonoidHom_strictMono, Rat.toNNRat_lt_iff_lt_coe, Set.Ico_subset_Icc_union_Ioo, Asymptotics.superpolynomialDecay_iff_superpolynomialDecay_abs, countable_image_gt_image_Ioi, ENat.strictMono_map_iff, MonomialOrder.lex_lt_iff, Nat.lt_ceil, FloorRing.gc_coe_floor, CategoryTheory.TransfiniteCompositionOfShape.ofArrowIso_isColimit, Hyperreal.coe_abs, MonomialOrder.eq_zero_iff, mabs_choice, PNat.natPred_lt_natPred, Filter.tendsto_div_const_atBot_iff, ENat.one_lt_top, Valuation.Integers.valuation_irreducible_pos, Module.End.genEigenspace_le_maximal, nhdsLE_sup_nhdsGT, LaurentSeries.comparePkg_eq_extension, NumberField.toNNReal_valued_eq_adicAbv, HahnSeries.finiteArchimedeanClassOrderIsoLex_apply_fst, Valuation.vlt_iff_lt, Cardinal.toENat_le_iff_of_lt_aleph0, lowerSemicontinuousOn_iff_preimage_Iic, MonoidWithZeroHom.inr_strictMono, nullMeasurableSet_Ico, convexJoin_left_comm, FiniteArchimedeanClass.ballAddSubgroup_strictAnti, min_add_add_left, one_lt_pow_iff, CategoryTheory.HasLiftingProperty.transfiniteComposition.sqFunctor_obj, Nat.sub_one_lt_floor, Order.iso_of_countable_dense, disjoint_disjointed, Rat.preimage_cast_Ioo, DivisibleHull.archimedeanClassOrderIso_symm_apply, Ordinal.ToType.mk_apply, even_abs, Nonneg.coe_div, borel_eq_generateFrom_Ioc_le, iInter_Iic_eq_empty_iff, Valued.hasBasis_uniformity, LinearOrderedField.coe_lt_inducedMap_iff, Set.exists_lt_mem_inter_of_not_pairwiseDisjoint, ArchimedeanClass.addSubgroup_strictAntiOn, Nat.floor_mono, ArchimedeanClass.FiniteResidueField.ordConnected_preimage_mk, Valuation.mem_ltSubmodule_iff, nhds_basis_Ioo, MeasureTheory.stoppedValue_stoppedProcess_ae_eq, one_lt_mul_self_iff, StieltjesFunction.outer_Ioc, Module.End.mem_genEigenspace_nat, IsPreconnected.intermediate_value, Set.Iio_inter_Iio, List.minimum_le_of_mem', Nat.le_ceil, ContinuousAt.abs, PNat.instNoMaxOrder, isPiSystem_Ici, Set.preimage_sub_const_uIcc, FiniteArchimedeanClass.submodule_strictAnti, MeasureTheory.aecover_Ioo_of_Ico, PNat.lt_add_one_iff, ArchimedeanClass.mk_one, HahnSeries.orderTop_abs, Set.compl_Ici, NNRat.cast_lt_one, abs_dvd_self, Field.Emb.Cardinal.adjoin_image_leastExt, div_nonneg_iff, mul_nonneg_iff_neg_imp_nonpos, borel_eq_generateFrom_Ioi, LaurentSeries.valuation_def, OrderIso.sumLexIioIci_apply_inl, zero_lt_iff, Set.projIci_coe, Mathlib.Tactic.Order.ToInt.exists_translation, HahnSeries.le_order_iff_forall, Valuation.integer.v_irreducible_lt_one, Cardinal.ofENat_toENat_le, sum_Ioc_inv_sq_le_sub, EReal.sign_mul_inv_abs, Left.pow_lt_one_iff, Nat.ceil_zero, Ordinal.typein_one_toType, MeasureTheory.aecover_Iio_of_Iio, mabs_eq_max_inv, NNRat.floor_def, PNat.card_Ioc, ArchimedeanClass.mem_ballAddSubgroup_iff, HahnSeries.forallLTEqZero_supp_BddBelow, Convex.combo_le_max, convexHull_prod, Set.bounded_le_inter_le, Filter.isBoundedUnder_le_abs, PNat.natPred_le_natPred, LinearOrderedCommMonoidWithZero.toMulPosStrictMono, zero_min, Rat.cast_pos, MvPowerSeries.order_add_of_order_ne, Set.encard_insert_le, Nat.pow_le_choose, FunctionField.inftyValuation.C, EisensteinSeries.tendsto_tsum_one_div_linear_sub_succ_eq, OrderTopology.of_discreteTopology, NNRat.preimage_cast_Ioc, Valuation.IsNontrivial.exists_lt_one, HahnSeries.instIsOrderedRingLexOfNoZeroDivisors, Even.zpow_nonneg, mem_nhds_iff_exists_Ioo_subset, Set.encard_le_one_iff, Ordinal.toNimber_toOrdinal, Cardinal.toENat_le_one, interior_Ioo, Field.Emb.Cardinal.instFiniteDimensionalSubtypeMemIntermediateFieldAdjoinImageToTypeOrdRankCompCoeBasisWellOrderedBasisLeastExtIioSingletonSet, neg_one_lt_zero, Affine.Simplex.sign_signedInfDist_incenter, Affine.Simplex.ExcenterExists.sign_signedInfDist_excenter, LinearOrderedAddCommGroup.to_noMaxOrder, Finsupp.Colex.single_le_iff, MeasureTheory.aecover_Icc_of_Ioo, Ordinal.cof_type_lt, Nat.ceil_natCast, LinearOrderedAddCommGroup.isAddCyclic_iff_not_denselyOrdered, round_eq_iff, PNat.lt_find_iff, FiniteMulArchimedeanClass.subsemigroup_eq_subgroup, Set.Iio_subset_Iio_union_Ico, Finset.pluennecke_ruzsa_inequality_pow_div_pow_div, Ordinal.toNimber_max, mem_segment_add_sub, OrderTopology.of_linearLocallyFinite, Filter.tendsto_div_const_atTop_iff, isClosed_Ico_iff, MeasureTheory.countable_meas_le_ne_meas_lt, Set.encard_le_encard_of_injOn, min_eq_left_iff, ArchimedeanOrder.instTotalLe, Set.Iio_subset_Iic_union_Ico, frontier_Iio, IsCoprime.abs_abs_iff, Hyperreal.IsSt.lt, denselyOrdered_set_iff_subsingleton, NNRat.cast_lt, Set.encard_tsub_one_le_encard_diff_singleton, pow_pos_iff, ENat.mul_le_mul_right_iff, HomotopicalAlgebra.RelativeCellComplex.Cells.hj, convexHull_eq_union, Set.preimage_div_const_uIcc, EReal.sign_mul_abs, Order.Ioo_eq_empty_iff_pred_le, Cardinal.toENat_injOn, ArchimedeanClass.min_le_mk_sub, PredOrder.isOpen_singleton_iff, untrop_sum_eq_sInf_image, LinearIndepOn.encard_le_toENat_rank, Ordinal.sup_typein_limit, Int.preimage_ceil_singleton, antivary_iff_forall_mul_nonpos, pow_le_one_iff, Rat.HeightOneSpectrum.valuation_equiv_padicValuation, DivisibleHull.instIsStrictOrderedModuleRat, le_inv_self_iff, LaurentSeries.valuation_le_iff_coeff_lt_log_eq_zero, convexHull_eq, GenContFract.le_of_succ_get?_den, RootPairing.RootPositiveForm.zero_lt_apply_root_root_iff, Cardinal.toENat_eq_nat, exists_seq_strictAnti_tendsto_nhdsWithin, Pi.instNoMinOrderColexForallOfWellFoundedGTOfNonempty, convexJoin_assoc_aux, isPiSystem_Ioo, Orientation.oangle_sign_smul_add_smul_right, MeasureTheory.aecover_Ico_of_Ioc, borel_eq_generateFrom_Iio, Rat.lt_toNNRat_iff_coe_lt, div_le_div_flip, CategoryTheory.HasLiftingProperty.transfiniteComposition.sqFunctor_map, Set.one_lt_encard_iff_nontrivial, LaurentSeries.uniformContinuous_coeff, CategoryTheory.MorphismProperty.IsCardinalForSmallObjectArgument.preservesColimit, GenContFract.zero_le_of_contsAux_b, Mathlib.Meta.NormNum.IsInt.natCeil, Finsupp.DegLex.wellFoundedLT, WithBot.coe_max, LinearOrderedAddCommGroup.Subgroup.exists_neg_generator, AddSubgroup.isLeast_of_closure_iff_eq_abs, ArchimedeanClass.eq_zero_or_top_of_archimedean, tendsto_pow_div_pow_atTop_atTop, mabs_lt, LinearLocallyFiniteOrder.le_succFn, CategoryTheory.IsGrothendieckAbelian.generatingMonomorphisms.functorToMonoOver_obj, HasStrictFDerivAt.hasStrictFDerivAt_norm_smul, min_le_emultiplicity_add, Polynomial.signVariations_eq_eraseLead_add_ite, List.sortedGE_mergeSort, Ordinal.toNimber_eq_one, Filter.Germ.const_min, Valuation.mem_leIdeal_iff, WithZeroTopology.tendsto_zero, LinearOrderedAddCommGroupWithTop.sub_le_sub_iff_left_of_ne_top, IsNonarchimedean.multiset_image_add, apply_abs_le_add_of_nonneg', Padic.norm_rat_le_one_iff_padicValuation_le_one, emultiplicity_pos_iff, LinearOrderedSemiring.toLocallyConvexSpace, Finset.exists_pos_of_sum_zero_of_exists_nonzero, Nonneg.Icc_subset_segment, Set.nontrivial_iff_exists_lt, Set.bounded_ge_inter_gt, Set.notMem_Ici, Valued.isClosed_closedBall, SignType.lt_one_iff, ENat.succ_def, mem_nhdsGT_iff_exists_Ioo_subset, Cardinal.nat_le_ofENat, Set.smul_Icc, Finset.Ico_succ_left_eq_Ioo, Set.integer_valuation_le_one, grade_covBy_grade_iff, sq_abs, CategoryTheory.SmallObject.SuccStruct.instIsWellOrderContinuousIterationFunctor, interior_Iic, Filter.Tendsto.min, Valuation.coe_ltAddSubgroup, Cardinal.ofENat_toENat_eq_self, AddCircle.coe_image_Ico_eq, Finset.sum_sym2_filter_not_isDiag, Finset.Iic_sub_one_eq_Iio, Order.le_succ_bot_iff, IsDedekindDomain.HeightOneSpectrum.coe_smul_adicCompletion, List.max_sum_le, Finsupp.DegLex.le_iff, Rat.surjective_padicValuation, interior_Ioi, WithTop.le_of_forall_lt_iff_le, Real.smoothTransition.projIcc, Set.Finite.convexHull_eq_image, MonoidWithZeroHom.inl_mono, convexJoin_right_comm, nhdsWithinLT_sup_nhdsWithinGE, Affine.Simplex.sOppSide_affineSpan_faceOpposite_point_right_iff, antivaryOn_iff_exists_antitoneOn_monotoneOn, Matrix.isIrreducible_iff, MvPolynomial.schwartz_zippel_sum_degreeOf, Mathlib.Meta.NormNum.IsInt.natFloor, FiniteMulArchimedeanClass.val_mk, Set.range_injOn_strictMono, FiniteArchimedeanClass.ball_strictAnti, right_le_midpoint, Int.ceil_mono, CategoryTheory.TransfiniteCompositionOfShape.ofComposableArrows_incl_app, Continuous.exists_forall_le_of_hasCompactMulSupport, ArchimedeanClass.orderHom_top, ENat.exists_nat_gt, Topology.IsLower.isTopologicalBasis_insert_univ_subbasis, mem_openSegment_iff_div, MeasureTheory.AEEqFun.posPart_mk, HahnEmbedding.Partial.eval_zero, CauSeq.lt_total, Finset.sup_add, max_neg_zero, nhdsGE_basis, measurable_IocProdIoc, Cardinal.ofENat_toENat, Ordinal.typein_le_typein', StieltjesFunction.measure_Ico, Hyperreal.abs_omega, Left.nsmul_neg_iff, IsNonarchimedean.apply_intCast_le_one_of_isNonarchimedean, Set.ordConnected_iff_uIcc_subset, NNRat.cast_le_natCast, antivaryOn_iff_forall_smul_nonpos, List.minimum_concat, tendsto_floor_left, CategoryTheory.Limits.MultispanIndex.toLinearOrder_left, Multiset.sum_min_le, OrderEmbedding.isEmbedding_of_ordConnected, LinearOrderedCommGroup.to_noMaxOrder, convexHull_rangle_single_eq_stdSimplex, Hyperreal.InfinitePos.pos, Function.Injective.encard_range, Set.biUnion_Ioc_eq_Ioi_self_iff, instAssociativeMin, Set.encard_le_one_iff_eq, sameRay_smul_right_iff, HahnSeries.finiteArchimedeanClassOrderIso_apply, LaurentSeries.ratfuncAdicComplRingEquiv_apply, LinearOrderedAddCommGroupWithTop.strictMono_add_right_of_ne_top, WithTop.tendsto_nhds_top_iff, Polynomial.isLittleO_atBot_of_degree_lt, min_mabs_mabs_le_mabs_max, AffineSpace.asymptoticNhds_eq_smul_vadd, MonomialOrder.div, Finset.pluennecke_ruzsa_inequality_pow_mul, Nimber.toOrdinal_symm_eq, convexHull_union, sq_pos_of_ne_zero, convexHull_sub, Hyperreal.infinitePos_def, Associated.abs_right, Topology.RelCWComplex.skeletonLT_I, Cardinal.aleph_toENat, maximal_iff_isGreatest, cmp_div_one', WithZeroTopology.orderClosedTopology, Finsupp.support_sup, Int.cast_le_neg_one_or_one_le_cast_of_ne_zero, Irreducible.maximalIdeal_pow_eq_setOf_le_v_coe_pow, Finset.lt_fold_max, tendsto_ceil_right, PowerSeries.coeff_heval_zero, Subgroup.HasDetPlusMinusOne.abs_det, MeasureTheory.Measure.measure_Ioi_pos, smul_nonneg_iff_pos_imp_nonneg, MonomialOrder.lex_le_iff, exists_pos_left_iff_sameRay_and_ne_zero, HahnSeries.instIsDomainOfIsCancelAdd, abs_add_three, sameRay_neg_smul_left_iff, Nat.floor_zero, CategoryTheory.SmallObject.prop_iterationFunctor_map_succ, Rat.cast_le, Order.not_isMax_pred, zsmul_le_zsmul_iff_right, antivary_iff_forall_smul_nonpos, Finset.Ico_filter_lt, FiniteArchimedeanClass.min_le_mk_add, Finset.min_mono, IsDedekindDomain.HeightOneSpectrum.intValuation_exists_uniformizer, Continuous.bddBelow_range_of_hasCompactMulSupport, antivaryOn_iff_mul_rearrangement, Set.Ioo_sub_one_left_eq_Ioc, Nat.inv_pos_of_nat, HahnSeries.min_le_min_add, convexHull_list_sum, Set.not_monotoneOn_not_antitoneOn_iff_exists_lt_lt, Nat.floor_one, gauge_smul_left, Nat.floor_sub_ofNat, exists_Icc_mem_subset_of_mem_nhds, measurableSet_Ioc, MonomialOrder.degree_sPolynomial_le, OrderEmbedding.range_inj, AffineSubspace.wOppSide_iff_exists_right, EReal.sign_neg, LinearOrderedField.cutMap_self, add_self_nonpos_iff, GroupCone.oneLE.isMaxMulCone, WithVal.le_def, HasCountableSeparatingOn.range_Ici, Finset.pluennecke_ruzsa_inequality_nsmul_sub, Hyperreal.stdPart_omega, Set.Ioc_inter_Ioi, Nat.floor_eq_iff', List.argmin_eq_some_iff, IsDiscreteValuationRing.addVal_le_iff_dvd, Mathlib.Meta.NormNum.isNNRat_le_false, isPiSystem_Icc_mem, ArchimedeanClass.liftOrderHom_mk, Valuation.HasExtension.val_map_lt_one_iff, abs_one, LinearOrderedAddCommGroupWithTop.sub_self_nonneg, LinearOrderedField.cutMap_bddAbove, CategoryTheory.TransfiniteCompositionOfShape.map_incl, ArchimedeanClass.orderHom_mk, zmultiples_abs, covBy_iff_lt_iff_le_right, WithBot.denselyOrdered_set_iff_subsingleton, Set.Ici.subtype_functor_final, Set.ordConnectedProj_eq, Metric.isBounded_of_abs_le, Set.Iic_subset_Iio_union_Icc, IicProdIoc_comp_restrict₂, CategoryTheory.SimplicialThickening.Path.le_right, StieltjesFunction.length_Ioc, Order.lt_succ_bot_iff, Continuous.lowerSemicontinuous, Order.pred_lt_iff, MvPolynomial.IsSymmetric.antitone_supDegree, Set.encard_le_encard, ENat.toENNReal_le, Valuation.one_le_val_iff, Cardinal.toENat_eq_iff_of_le_aleph0, FiniteMulArchimedeanClass.mk_lt_mk, Submonoid.closure_image_one_lt_and_isMulIndecomposable, WithTop.coe_min, Set.Ioo_disjoint_Ioo, MulArchimedeanClass.mk_right_le_mk_div_iff, IsCompact.bddBelow_image, four_mul_le_pow_two_add, Valuation.Compatible.vle_iff_le, Mathlib.Tactic.PNatToNat.coe_le_coe, SetTheory.PGame.nim_grundyValue, Iotop_subset_Ioc, PNat.le_one_iff, atTop_le_cocompact, WithZeroTopology.isOpen_Iio, NNRat.floor_natCast_div_natCast, Finsupp.Lex.addRightMono, max_zero_sub_eq_self, Int.fract_nonneg, MonomialOrder.degree_sub_leadingTerm_lt_degree, CauSeq.exists_gt, projIcc_eq_zero, nhds_bot_basis_Iic, Set.integer_eq, mabs_div_lt_iff, measurableSet_lt', Ici_mem_nhdsSet_Ici_iff, Positive.coe_zpow, WithTop.continuousOn_untopA, nhds_top_basis, Hyperreal.abs_lt_real_iff_infinitesimal, Int.preimage_fract, zpow_le_zpow_iff_left, inv_lt_self_iff, instLawfulOrderSup_mathlib, AffineIndependent.not_wbtw_of_injective, Hyperreal.infinitesimal_pos_iff_infinitePos_inv, Multiset.abs_sum_le_sum_abs, AddGroupCone.nonneg.isMaxCone, oneLePart_eq_ite, PowerSeries.order_add_of_order_ne, Module.End.hasGenEigenvector_iff, MulArchimedeanClass.orderHom_mk, Module.Basis.orientation_neg_single, IsCompact.exists_isGreatest, MvPolynomial.leadingCoeff_toLex, Measurable.min, LinearOrder.isPredArchimedean_of_isSuccArchimedean, Ico_subset_biUnion_Ico, ArchimedeanClass.mk_div, abs_le_one_iff_mul_self_le_one, nullMeasurableSet_lt, odd_abs, Set.range_IicExtend, CategoryTheory.TransfiniteCompositionOfShape.map_F, antivary_comm, HahnSeries.leadingCoeff_neg_iff, CategoryTheory.SimplicialThickening.Path.le, ENat.tendsto_nhds_top_iff_natCast_lt, Filter.Germ.min_def, Order.IsNormal.strictMono, iUnion_Ioc_intCast, convexOn_iff_div, Nonneg.coe_zpow, left_mem_openSegment_iff, MonomialOrder.degree_monomial_le, CategoryTheory.SimplicialThickening.functor_id, HahnSeries.order_mul_of_ne_zero, Units.zero_lt, Set.range_injOn_strictAnti, OrderMonoidWithZeroHom.comp_mul, AffineSubspace.setOf_sOppSide_eq_image2, AddValuation.map_add, Module.End.mem_genEigenspace_zero, Finset.Ioc_disjoint_Ioc, Valuation.ltIdeal_mono, Valuation.IsEquiv.lt_one_iff_lt_one, Set.encard_iUnion_le_of_fintype, ProbabilityTheory.gaussianPDFReal_mul, Even.convexOn_pow, abs_sub_pos, Set.one_le_encard_iff_nonempty, Int.sign_eq_sign, Ideal.height_le_spanRank_toENat, Archimedean.embedReal_one, borel_eq_generateFrom_Iic, MonomialOrder.degLex_single_lt_iff, CategoryTheory.OrthogonalReflection.iteration_map_succ_surjectivity, Set.unbounded_ge_iff, strictConvexOn_iff_div, CauSeq.trichotomy, nhdsLE_sup_nhdsGE, ContinuousAt.mabs, NNRat.bddAbove_coe, CategoryTheory.Limits.WalkingMultispan.inclusionOfLinearOrder_map, PointedCone.mem_maxTensorProduct, MeasureTheory.aecover_Ico_of_Icc, List.getElem_le_maximum_of_length_pos, lineMap_lt_lineMap_iff_of_lt', Int.padicValuation_le_one, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.w₁, Finsupp.support_inf, max_left_commutative, ArchimedeanClass.addValuation_apply, MeasureTheory.aecover_Ico_of_Ico, Valuation.isEquiv_iff_val_lt_one, Cardinal.natCast_eq_toENat_iff, le_max_iff, IsDedekindDomain.HeightOneSpectrum.embedding_mul_absNorm, nsmul_pos_iff, Set.not_equitableOn, AffineSubspace.not_sOppSide_self, HahnSeries.inv_single, Valuation.IsUniformizer.val_lt_one, ENat.eq_top_iff_forall_ge, MultilinearMap.map_sub_map_piecewise, Cardinal.ofENat_le_nat, Finsupp.Colex.single_lt_iff, ContinuousAt.lowerSemicontinuousAt, segment_subset_closure_openSegment, CategoryTheory.SmallObject.iterationFunctorMapSuccAppArrowIso_hom_right_right_comp, IsNonarchimedean.finset_powerset_image_add, ringHom_monotone, SMulPosReflectLE.toSMulPosStrictMono, Mathlib.Tactic.PNatToNat.coe_lt_coe, monovaryOn_iff_exists_antitoneOn, MonomialOrder.degree_sub_LTerm_lt, HahnModule.instIsTorsionFree, wbtw_pointReflection, NNRat.cast_lt_natCast, linOrd_dual_comp_forget_to_Lat, continuous_abs, instNonemptySeedRatReal, abs_min_sub_min_le_max, countable_setOf_isolated_left, Finset.pluennecke_ruzsa_inequality_nsmul_sub_nsmul_add, Hyperreal.coe_le_coe, MulArchimedeanClass.min_le_mk_div, CategoryTheory.TransfiniteCompositionOfShape.ofComposableArrows_isColimit, LocallyFiniteOrder.orderMonoidWithZeroHom_strictMono, Nimber.toOrdinal_zero, monovaryOn_iff_mul_rearrangement, ENat.mul_le_mul_left_iff, AffineSubspace.setOf_wSameSide_eq_image2, NatOrdinal.toOrdinal_zero, mul_nonneg_of_three, Module.End.genEigenspace_le_genEigenspace_finrank, MonomialOrder.sPolynomial_lt_of_degree_ne_zero_of_degree_eq, mabs_div_mabs_le_mabs_div, NumberField.FinitePlace.norm_le_one, min_mabs_mabs_le_mabs_min, CategoryTheory.Limits.MultispanShape.ofLinearOrder_snd, Order.Iic_succ, PseudoMetric.finsetSup_apply, add_self_neg_iff, Dense.exists_seq_strictMono_tendsto, Module.End.mem_genEigenspace, Collinear.wbtw_or_wbtw_or_wbtw, Valuation.mem_integer_iff, Nat.cast_mul_floor_div_cancel, Units.mulArchimedean_iff, Nat.mul_cast_floor_div_cancel, Set.powersetCard.mem_range_ofFinEmbEquiv_symm_iff_mem, nsmul_nonpos_iff, Finsupp.DegLex.monotone_degree, le_emultiplicity_iff_replicate_subperm_primeFactorsList, ArchimedeanClass.mk_antitoneOn, partialSups_add_one_eq_sup_disjointed, Rat.toNNRat_lt_toNNRat_iff, isPiSystem_Iic, Affine.Simplex.face_points', nhdsGT_sup_nhdsWithin_singleton, abs_eq_abs, HahnSeries.addVal_apply, tendsto_fract_right, Cardinal.toENat_nat, tendsto_floor_left_pure_sub_one, Hyperreal.coe_lt_coe, LinearOrderedCommGroup.Subgroup.exists_generator_lt_one, Tropical.trop_inf, HahnEmbedding.Partial.exists_domain_eq_top, cmp_add_right, Topology.RelCWComplex.skeletonLT_monotone, div_lt_one_iff, FiniteMulArchimedeanClass.subgroup_strictAnti, PowerSeries.nat_le_order, WeierstrassCurve.IsGoodReduction.goodReduction, LinearOrderedCommGroupWithZero.discrete_iff_not_denselyOrdered, NNRat.coe_min, Order.pred_lt_iff_eq_or_gt, LinearOrderedCommGroup.discrete_or_denselyOrdered, Finset.dens_union_le, Polynomial.roots_countP_pos_le_signVariations, Valued.isClopen_closedBall, ArchimedeanClass.mk_eq_zero_of_archimedean, PNat.map_subtype_embedding_Ioc, SimplexCategory.toCat_map, Dense.Ioi_eq_biUnion, upperSemicontinuousOn_iff_isClosed_hypograph, Nimber.toOrdinal_toNimber, HahnSeries.cardSupp_hsum_powers_le, min_inv_inv', abs_eq_self, NonemptyFinLinOrd.mono_iff_injective, lt_neg_self_iff, Finset.sup'_mul, nhdsLT_sup_nhdsGT, Rat.preimage_cast_Ioc, iUnion_Iio_eq_univ_iff, LinearOrderedCommGroupWithZero.inl_apply, Set.bounded_lt_inter_le, nhdsLT_neBot, ArchimedeanClass.mk_sub_lt_mk_left_iff, WithTop.continuous_untop, CategoryTheory.SmallObject.preservesColimit, Filter.tendsto_abs_atTop_atTop, Orientation.eq_or_eq_neg_of_isEmpty, Valuation.leAddSubgroup_monotone, LinearOrderedCommGroupWithZero.inr_apply, Finsupp.Lex.single_le_iff, isPiSystem_Ioo_mem, Orientation.oangle_sign_smul_add_smul_left, Dense.exists_gt, convexOn_zpow, RootPairing.posRootForm_rootFormIn_posDef, abs_zsmul, Module.End.genEigenspace_zero, not_linearIndepOn_finset_iffₒₛ, Polynomial.le_trailingDegree_X_pow, continuousWithinAt_iff_continuous_left_right, Matroid.toENat_cRank_eq, List.minimum_le_coe_iff, measurableSet_bddBelow_range, ValuationSubring.algebraMap_injective, Hyperreal.st_eq_sSup, Nonneg.toNonneg_lt, PosSMulMono.toPosSMulReflectLT, abs_min_le_max_abs_abs, Finset.orderEmbOfFin_mem, Ordinal.toNatOrdinal_toOrdinal, Set.Finite.encard_biUnion_le, Finset.max_prod_le, Hyperreal.infinitePos_abs_iff_infinite, ContinuousWithinAt.upperSemicontinuousWithinAt, MvPowerSeries.le_order_pow, MeasureTheory.aecover_Icc_of_Ico, Set.projIic_eq_self, continuousAt_sign_of_ne_zero, AffineSubspace.wOppSide_pointReflection, tendsto_floor_right', IsValuativeTopology.mem_nhds_iff, PowerSeries.heval_mul, Int.lt_floor_iff, lowerSemicontinuousWithinAt_iff_frequently, MulArchimedeanClass.subgroup_eq_bot, nhds_basis_mabs_div_lt, Valuation.pos_iff, LinearOrderedCommGroup.discrete_iff_not_denselyOrdered, Valued.norm_pos_iff_valuation_pos, wbtw_midpoint, Nat.ceil_eq_iff, exists_zero_lt, List.maximum_eq_coe_iff, Rat.natCast_lt_cast, HahnSeries.SummableFamily.support_powerSeriesFamily_subset, PredOrder.prelimitRecOn_pred, Ordinal.enum_zero_le', HahnSeries.zero_ofSuppBddBelow, smulPosMono_iff_smulPosReflectLT, MeasureTheory.IsSetSemiring.Ioc, List.sortedGE_insertionSort, tsub_add_eq_max, LocallyFiniteOrder.orderAddMonoidEquiv_apply, Right.sign_neg, List.le_maximum_of_length_pos_iff, Set.compl_Ioc, AffineIndependent.convexHull_inter, List.coe_minimum_of_length_pos, CauSeq.sup_inf_distrib_left, exists_le_add_iff_le_right, LinOrd.comp_apply, NatOrdinal.toOrdinal_eq_one, Finset.Ici_add_one_eq_Ioi, abs_zpow, isPiSystem_image_Ici, ArchimedeanClass.FiniteElement.mk_natCast, Odd.geom_sum_pos, LinOrd.coe_comp, IsDedekindDomain.HeightOneSpectrum.valuation_le_one, ENat.one_lt_card, ENat.self_le_mul_right, ENat.add_le_add_iff_left, PosSMulMono.toPosSMulReflectLE, tendsto_pow_atTop_nhds_zero_iff, Set.Ioi_inter_Ioi, Dense.borel_eq_generateFrom_Ioc_mem, ENat.mul_right_strictMono, CategoryTheory.SmallObject.iterationFunctorObjObjRightIso_ιIteration_app_right_assoc, instIsPrincipalIdealRingSubtypeMemSubringIntegerWithZeroMultiplicativeIntValuation, Finset.max'_lt_iff, comap_coe_nhdsGT_eq_atBot_iff, MeasureTheory.uIoc_ae_eq_interval, Finset.listMap_orderEmbOfFin_finRange, strictConvex_Ioi, Ordinal.familyOfBFamily_enum, Polynomial.div_tendsto_atTop_zero_iff_degree_lt, Valued.toNormedField.norm_lt_one_iff, le_min_iff, CauSeq.inf_idem, CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.ofComposableArrows_isoBot_hom, UpperSet.total_le, instLawfulOrderInf_mathlib, Nat.add_one_le_ceil_iff, HahnSeries.mem_orderTopSubOnePos_iff, Continuous.exists_forall_ge_of_hasCompactMulSupport, denselyOrdered_iff_denselyOrdered_units_and_nontrivial_units, Measurable.nat_ceil, Continuous.min, SuccOrder.nhdsLT_eq_nhdsNE, CategoryTheory.TransfiniteCompositionOfShape.ici_incl, IsDedekindDomain.HeightOneSpectrum.valuationOfNeZeroToFun_eq, Finset.uIcc_subset_uIcc_union_uIcc, Order.sub_one_lt_iff, ZSpan.mem_fundamentalDomain, exists_succ_iterate_or, MeasureTheory.aecover_Ioo_of_Icc, Set.Iio_subset_Iic_union_Ioo, Set.Ici_eq_singleton_iff_isTop, Real.log_of_ne_zero, ArchimedeanClass.mk_map_of_archimedean', Filter.tendsto_uIcc_of_Icc, Module.End.genEigenspace_le_smul, CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.mem_map, Order.lt_one_iff_nonpos, Subgroup.isLeast_of_closure_iff_eq_mabs, MvPowerSeries.min_order_le_add, Nonneg.orderedSub, AddCircle.liftIco_eq_lift_Icc, PNat.card_fintype_Icc, MeasureTheory.ae_restrict_uIoc_eq, Finset.Nonempty.dens_pos, succ_max, FiniteArchimedeanClass.addSubgroup_eq_bot, WithZero.min_le_iff, mabs_div_le_iff, WithZeroTopology.nhds_eq_update, ValuativeRel.uniformizer_lt_one, nhdsGT_neBot, continuous_max, archimedean_iff_int_le, min_eq_top, Finset.add_sup'', countable_setOf_covBy_right, PowerSeries.le_order_prod, ValuativeRel.uniformizer_pos, HahnEmbedding.Partial.exists_isMax, Archimedean.mkRat_mem_ratLt, CauSeq.bounded, NNRat.cast_le_ofNat, exists_uIoo_isExtrOn_uIcc, Ordinal.type_toType, le_add_iff_lt_right_or_exists_le, LinearOrderedAddCommGroup.isAddCyclic_iff_nonempty_equiv_int, HahnSeries.orderTop_embDomain, Valuation.IsRankOneDiscrete.exists_generator_lt_one, SignType.neg_iff, Ordinal.nmul_eq_mul, PowerSeries.order_add_of_order_eq, Set.preimage_const_add_uIcc, Set.Finite.convexHull_eq, BoundedGENhdsClass.of_closedIicTopology, Archimedean.embedRealFun_strictMono, HahnSeries.cardSupp_inv_le, MeasureTheory.Measure.measure_Iio_pos, Hyperreal.stdPart_epsilon, min_add, Set.IsPWO.of_linearOrder, Profinite.NobelingProof.Products.instWellFoundedLT, mabs_div_le_one, ZNum.isStrictOrderedRing, MulArchimedeanClass.mk_div_lt_mk_right_iff, Matrix.eRank_submatrix_le, Finset.dens_le_dens, DFinsupp.Lex.total_le, Complex.sum_div_factorial_le, Hyperreal.ofSeq_lt_ofSeq, Module.End.genEigenspace_restrict, ContinuousAt.upperSemicontinuousAt, orderTopology_of_ordConnected, finSumEquivOfFinset_inl, exists_one_lt', CategoryTheory.TransfiniteCompositionOfShape.ofOrderIso_isColimit, exists_rat_lt, CategoryTheory.SimplicialThickening.functor_obj_as, Set.Ioo_subset_uIoo', Set.Ioc_sub_one_left_eq_Icc, Archimedean.of_locallyFiniteOrder, LinearOrder.topologicalLattice, FunctionField.inftyValuation_apply, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.w₂, IsCompact.exists_isMaxOn, MulArchimedeanClass.mulArchimedean_of_mk_eq_mk, Order.Ioc_pred_left, isClosed_Ioo_iff, Fintype.not_linearIndependent_iffₒₛ, min_add_distrib, nonneg_add_self_iff, zpow_lt_zpow_iff_left, sub_le_sub_flip, Odd.pow_nonpos_iff, Polynomial.cyclotomic_pos, Dense.borel_eq_generateFrom_Icc_mem, Finset.Iic_diff_Ioc, ValuativeRel.instMulArchimedeanValueGroupWithZeroOfIsRankLeOne, ArchimedeanClass.ball_antitone, Set.Ioo_inter_Ioo, Finset.Ico_succ_succ_eq_Ioc, starConvex_iff_div, nhdsSet_Ioi, Finset.sup'_eq_zero, Mathlib.Meta.NormNum.IsNat.natFloor, Left.sign_neg, Affine.Simplex.sOppSide_affineSpan_faceOpposite_iff, measurableSet_bddAbove_range, Finset.le_max, HahnSeries.min_orderTop_le_orderTop_add, Profinite.NobelingProof.Products.eval_πs_image, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.w₁_assoc, PNat.one_le_find, Valuation.val_le_one_iff, max_sub_sub_right, Filter.tendsto_mul_const_atBot_iff, HahnSeries.leadingCoeff_nonpos_iff, StieltjesFunction.right_continuous, Odd.pow_le_pow, Set.instOrdConnectedOrdConnectedComponent, Filter.Germ.max_def, LaurentSeries.exists_ratFunc_eq_v, HahnSeries.SummableFamily.powerSeriesFamily_smul, Cardinal.natCast_le_toENat_iff, Polynomial.trailingDegree_one_le, Set.Ioi_subset_Ioc_union_Ici, min_bot_right, Valued.toNormedField.one_le_norm_iff, Pi.Lex.isStrictOrder, Even.pow_abs, EReal.sign_mul_inv_abs', countable_image_gt_image_Iio, Stream'.Seq.lt_length'_iff, Set.Finite.encard_strictMonoOn, le_iff_forall_one_lt_le_mul, Set.mem_ordConnectedComponent, ENat.add_lt_add_iff_right, wellFoundedLT_toType, one_lt_ltOnePart_iff, openSegment_subset_union, Nat.cast_inv_le_one, Finset.divConst_le_inv_dens, multiplicity_le_emultiplicity, Hyperreal.gt_of_neg_of_infinitesimal, LinearOrderedCommGroupWithZero.wellFoundedOn_setOf_le_lt_iff_nonempty_discrete_of_ne_zero, Int.add_one_le_ceil_iff, Nat.lt_floor_add_one, Finsupp.Lex.wellFoundedLT_of_finite, OrderIso.sumLexIioIci_apply_inr, Rat.comap_cast_atTop, MonomialOrder.degree_sPolynomial_lt_sup_degree, Padic.isDenseInducing_cast_withVal, left_lt_lineMap_iff_pos, add_lt_add_iff_right_of_ne_top, Set.encard_le_one_iff_subsingleton, HahnEmbedding.Seed.domain_baseEmbedding, NNRat.cast_lt_ofNat, Nat.one_div_lt_one_div, abs_le_iff_mul_self_le, Finset.abs_prod, PNat.mod_le, Continuous.bddAbove_range_of_hasCompactSupport, ArchimedeanClass.mem_closedBallAddSubgroup_iff, Finset.disjiUnion_Iic_disjointed, sign_eq_neg_one_iff, FiniteArchimedeanClass.withTopOrderIso_apply_coe, CategoryTheory.SimplicialThickening.functor_comp, LinearOrderedField.mem_cutMap_iff, Module.End.pos_finrank_genEigenspace_of_hasEigenvalue, Set.Iio_injective, Finset.orderEmbOfFin_compl_singleton_apply, ENat.lt_coe_add_one_iff, Dense.borel_eq_generateFrom_Icc_mem_aux, Dense.topology_eq_generateFrom, Asymptotics.isLittleO_pow_pow_atTop_of_lt, DFinsupp.Colex.isStrictOrder, Metric.isBounded_of_abs_lt, Finset.mulConst_le_divConst_sq, ENat.card_le_one, trop_sInf_image, negPart_eq_ite_lt, Polynomial.le_trailingDegree_X, Module.length_eq_rank, WithTop.nhds_coe, min_left_commutative, FiniteMulArchimedeanClass.coe_congrOrderIso_apply, SetTheory.PGame.nim_add_nim_equiv, intermediate_value_Ioc, CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.w₂_assoc, NNRat.preimage_cast_Iio, CauSeq.const_pos, PseudoMetric.nonneg, Ioo_subset_Iotop, intermediate_value_Ico, Tropical.untrop_sup, MonomialOrder.degree_sub_leadingTerm_lt_iff, NNRat.ofNat_lt_cast, sign_eq_one_iff, exists_le_add_iff_le_left, Set.Ioi_injective, Set.unbounded_lt_inter_lt, Subfield.toIsStrictOrderedRing, ArchimedeanClass.FiniteResidueField.instIsOrderedRing, Cardinal.toENat_lt_top, MonomialOrder.degree_sub_leadingTerm_le, Valuation.exists_div_eq_of_surjective, le_abs', Valuation.Integers.maximalIdeal_pow_eq_setOf_le_v_algebraMap_pow, Submonoid.mem_closure_image_one_lt_iff, Finset.mul_sup₀, IsDedekindDomain.HeightOneSpectrum.intValuation_apply, IsCoprime.abs_abs, Finset.min'_eq_inf', nhdsLE_basis, Cardinal.lift_min, Int.preimage_Ico, Filter.Germ.abs_def, le_add_iff_lt_left_or_exists_le, HahnSeries.le_orderTop_iff_forall, MvPowerSeries.le_order_pow_of_constantCoeff_eq_zero, ArchimedeanClass.mk_inv, Valuation.Integers.isPrincipalIdealRing_iff_not_denselyOrdered_mrange, Asymptotics.superpolynomialDecay_iff_abs_tendsto_zero, Finsupp.DegLex.single_strictAnti, List.trop_minimum, Set.Icc_subset_Icc_union_Icc, Finset.lt_max'_of_mem_erase_max', Ordinal.toNatOrdinal_max, upperSemicontinuousWithinAt_iff_frequently, Set.IciExtend_apply, Set.uIoc_eq_union, Set.IicExtend_self, convexHull_range_eq_exists_affineCombination, mabs_le_one, Matrix.isPrimitive_iff, Real.arcsin_projIcc, wbtw_iff_sameRay_vsub, NonemptyFinLinOrd.Iso.mk_hom, LaurentSeries.valuation_X_pow, exists_glb_Ioi, Set.ordConnected_uIoc, Order.le_succ_iff_eq_or_le, Nimber.toOrdinal_eq_zero, lowerBounds_Ioi, countable_setOf_isolated_right_within, tendsto_mabs_nhdsNE_one, Tropical.inf_eq_add, lt_max_iff, abs_pow, HahnSeries.le_order_smul, Finset.sum_mul_sq_le_sq_mul_sq, Finset.exists_mem_eq_inf', IsDedekindDomain.HeightOneSpectrum.intValuation_lt_one_iff_mem, Set.monotone_projIci, Int.padicValuation_eq_zero_iff, Valuation.Integers.dvd_iff_le, List.maximum_concat, Cardinal.toENat_congr, CategoryTheory.Limits.instIsWellOrderContinuousCompOfPreservesWellOrderContinuousOfShape, OrderMonoidWithZeroHom.mul_apply, ENat.range_natCast, Finset.sum_min_le, Polynomial.eventually_no_roots, NumberField.FinitePlace.norm_def, CauSeq.coe_inf, lt_min_iff, FiniteArchimedeanClass.mem_closedBall_iff, antivary_iff_exists_antitone_monotone, Even.pow_pos_iff, Finset.sup_mul₀, discreteTopology_iff_orderTopology_of_pred_succ, toZ_le_iff, AddUnits.min_val, Valuation.one_rel_iff, MulArchimedeanClass.orderHom_top, Valuation.le_one_of_subsingleton, NonnegSpectrumClass.iff_spectrum_nonneg, mabs_cases, Nat.preimage_Ico, GenContFract.abs_sub_convs_le, CategoryTheory.Functor.WellOrderInductionData.Extension.zero_val, NNRat.castOrderEmbedding_apply, continuousAt_iff_lower_upperSemicontinuousAt, AddMonoidAlgebra.supDegree_mem_support, ArchimedeanClass.closedBall_top, PosSMulStrictMono.toPosSMulReflectLT, ENat.one_le_iff_ne_zero, Finsupp.Colex.single_strictMono, NonarchimedeanHomClass.map_add_le_max, PNat.addLeftStrictMono, countable_image_lt_image_Iio, Cardinal.lift_max, mem_segment_sub_add, monovary_iff_exists_monotone, Pi.toColex_update_lt_self_iff, Subgroup.hasDetPlusMinusOne_iff_abs_det, WithZero.withZeroUnitsEquiv_strictMono, LinearOrderedAddCommGroupWithTop.sub_lt_sub_iff_left_of_ne_top, hahnEmbedding_isOrderedAddMonoid, List.maximum_append, ENat.lt_one_iff_eq_zero, Matroid.toENat_cRk_eq, HasCountableSeparatingOn.range_Iic, CauSeq.inf_le_left, exists_lt_mem_inter_of_not_pairwise_disjoint, LinearOrderedCommGroupWithZero.discrete_or_denselyOrdered, GenContFract.IntFractPair.nth_stream_fr_nonneg, Finset.isLeast_min', List.argmin_cons, Tuple.monotone_sort, Set.Ioi_ssubset_Ioi_iff, Set.encard_le_encard_diff_add_encard, ProbabilityTheory.Kernel.partialTraj_eq_prod, Set.image_subtype_val_uIcc, ContinuousOn.mabs, Icc_subset_segment, LinearOrderedAddCommGroup.to_noMinOrder, Filter.tendsto_const_mul_atTop_iff, PNat.le_find_iff, contMDiffOn_projIcc, Mathlib.Meta.NormNum.isNNRat_lt_true, Cardinal.toENat_eq_one, Order.isSuccPrelimitRecOn_succ, Ordinal.toNatOrdinal_symm_eq, NonemptyFinLinOrd.hom_id, Associated.abs_left, MonomialOrder.iocam, posPart_eq_ite_lt, Finset.max_abv_sum_one_le, mem_nhdsLE_iff_exists_Ioc_subset, ENat.not_lt_zero, MonomialOrder.degree_sub_LTerm_le, Rat.padicValuation_le_one_iff, Finset.Ico_succ_right_eq_Icc, HahnSeries.leadingCoeff_abs, left_le_lineMap_iff_nonneg, exists_lt_add_iff_lt_right, MonomialOrder.lex_le_iff_of_unique, max_add, lineMap_lt_left_iff_neg, LinearOrderedCommGroup.isCyclic_iff_nonempty_equiv_int, max_div_div_right', Measurable.lt, tendsto_ratCast_atTop_iff, PredOrder.colimitRecOn_pred, ArchimedeanClass.stdPart_eq_sSup, OrderEmbedding.mulLeft_apply, max_eq_iff, bot_eq_zero', tendsto_smul_comp_nat_floor_of_tendsto_nsmul, Hyperreal.gt_of_tendsto_zero_of_neg, Cardinal.mk_Iio_ord_toType, Hyperreal.epsilon_pos, PosSMulReflectLE.toPosSMulStrictMono, Multiset.prod_min_le, Set.IciExtend_coe, LinearOrderedCommGroup.isCyclic_iff_not_denselyOrdered, instDenselyOrderedUnits, upperSemicontinuousOn_iff_preimage_Ici, Hyperreal.archimedeanClassMk_epsilon_pos, Finset.dens_pos, Set.mem_uIcc, Profinite.NobelingProof.Products.head_lt_ord_of_isGood, Finset.nonneg_subConst, NNRat.cast_lt_zero, CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape.mem_incl_app, Ordinal.sup_typein_succ, exists_pos_right_iff_sameRay_and_ne_zero, Hyperreal.tendsto_atTop_iff, IsAddIndecomposable.baseOf_subset_pos, Set.powersetCard.ofFinEmbEquiv_apply, LinearOrderedCommMonoidWithZero.toZeroLeOneClass, Set.notMem_uIoc, Topology.IsUpper.tendsto_nhds_iff_lt, Mathlib.Tactic.Order.ToInt.toInt_lt_toInt, LinearOrderedField.toPosSMulStrictMono_rat, ENat.coe_lt_top, MonomialOrder.degree_sPolynomial, Polynomial.isBigO_atTop_of_degree_le, Nat.preimage_ceil_zero, nhdsGE_basis_Ico, Ordinal.nadd_eq_add, AddMonoidAlgebra.apply_supDegree_add_supDegree, HahnSeries.BddBelow_zero, Continuous.bddAbove_range_of_hasCompactMulSupport, Cardinal.nat_lt_ofENat, polynomialFunctions.comap_compRightAlgHom_iccHomeoI, Polynomial.valuation_X_eq_neg_one, hahnEmbedding_isOrderedModule, Ordinal.one_toType_eq, List.Perm.minimum_eq, LinearOrderedAddCommGroup.tendsto_nhds, Nat.ceil_add_le, AbsoluteValue.eq_trivial_of_isEquiv_trivial, closure_Ioc, Finset.Ico_add_one_add_one_eq_Ioc, Set.Iio_inter_Ioo, restrict₂_comp_IicProdIoc, Finset.isLUB_iff_isGreatest, ProbabilityTheory.Kernel.traj_eq_prod, MonomialOrder.degree_X_le_single, NatOrdinal.lt_wf, PNat.lt_succ_self, WithBot.add_one_le_iff, tendsto_zero_geometric_tsum_pnat, AddUnits.max_val, IsNonarchimedean.add_pow_le, MeasureTheory.stoppedProcess_eq_stoppedValue, Int.fract_eq_iff, closure_Ioi, abs_two, convexOn_iff_slope_mono_adjacent, ArchimedeanClass.mk_zpow, lt_tsub_iff_left, add_tsub_eq_max, Set.ordConnected_uIcc, mem_nhdsGE_iff_exists_Icc_subset, Affine.Simplex.sOppSide_affineSpan_faceOpposite_point_left_iff, mabs_eq_self, MeasureTheory.AEStronglyMeasurable.aestronglyMeasurable_uIoc_iff, add_le_add_iff_right_of_ne_top, closure_Ioo, MvPowerSeries.le_order_map, atBot_le_cocompact, MulArchimedean.of_locallyFiniteOrder, Hyperreal.coeRingHom_toFun, Even.zpow_pos, Nat.floor_pos, StieltjesFunction.right_continuous', HahnEmbedding.Partial.toOrderAddMonoidHom_injective, monovaryOn_iff_forall_mul_nonneg
instLatticeInt 📖	CompOp	368 math math: RatFunc.instFaithfulSMulPolynomialLaurentSeries, ValueDistribution.logCounting_zero, instPosSMulStrictMonoIntOfIsOrderedAddMonoid, sign_intCast, Int.emod_lt_abs, mapClusterPt_atTop_pow_tfae, zpow_right_strictAnti, LinearOrderedAddCommGroup.wellFoundedOn_setOf_le_lt_iff_nonempty_discrete, Int.abs_le_sqrt, Polynomial.cardPowDegree_zero, Int.negOnePow_abs, norm_jacobiTheta₂_term_le, Nat.Ioc_filter_modEq_cast, norm_jacobiTheta₂_term_fderiv_ge, Int.preimage_Ioc, Int.instIsStrictOrderedRing, Int.cast_abs, Polynomial.exists_partition_polynomial, LaurentSeries.LaurentSeriesRingEquiv_def, Zsqrtd.abs_norm, Int.strictAntiOn_natAbs, RootPairing.Base.cartanMatrix_map_abs, IsDedekindDomain.HeightOneSpectrum.mem_adicCompletionIntegers, Finset.Icc_succ_succ, Finset.prod_Icc_eq_prod_Ico_mul, EisensteinSeries.abs_le_right_of_norm, VertexOperator.of_coeff_apply_coeff, meromorphicOrderAt_add_of_ne, LaurentSeries.valuation_le_iff_coeff_lt_eq_zero, Int.card_Ioo, LaurentSeries.valuation_single_zpow, Finset.sum_Ico_le_sum, Int.abs_sub_lt_of_lt_lt, IsDedekindDomain.HeightOneSpectrum.intValuation_le_one, WeierstrassCurve.valuation_Δ_aux_eq_of_isIntegral, Finset.sum_Ico_int_sub, NumberField.abs_discr_ge', FractionalIdeal.absNorm_eq', NumberField.abs_discr_ge, LieModule.genWeightSpaceChain_def', Polynomial.exists_partition_polynomial_aux, Nat.ceil_int, IsStrictOrderedRing.int_mem_Icc_of_mul_mem_Ioo, PowerSeries.coe_add, Nat.image_cast_int_Icc, Nat.image_cast_int_Iic, IsDedekindDomain.HeightOneSpectrum.intValuation_le_pow_iff_mem, Int.preimage_Ioi, LaurentSeries.ofPowerSeries_powerSeriesPart, LaurentSeries.single_order_mul_powerSeriesPart, Int.comap_cast_atTop, RatFunc.coe_X, PowerSeries.coeff_coe, tendsto_ceil_atTop, AbsoluteValue.exists_partition_int, NumberField.house_intCast, ValueDistribution.logCounting_top, mabs_zpow, LaurentSeries.coe_algebraMap, Nat.image_cast_int_Ioc, RatFunc.coe_coe, toIocDiv_wcovBy_toIcoDiv, Polynomial.cardPowDegree_isEuclidean, LaurentSeries.inducing_coe, PowerSeries.coe_smul, LaurentSeries.continuous_coe, LaurentSeries.algebraMap_C_mem_adicCompletionIntegers, Rat.num_abs_eq_abs_num, mapClusterPt_atTop_nsmul_tfae, Nat.image_cast_int_Ici, LocallyFiniteOrder.orderAddMonoidHom_bijective, meromorphicOrderAt_add, LaurentSeries.val_le_one_iff_eq_coe, zpow_right_strictMono, Order.krullDim_int, FloorRing.gc_ceil_coe, ZMod.valMinAbs_mem_Ioc, CategoryTheory.Triangulated.TStructure.le_monotone, PowerSeries.coe_mul, Int.instIsSuccArchimedean, WithZero.lt_mul_exp_iff_le, Int.card_Ioc, Int.preimage_Iio, mapClusterPt_atTop_zsmul_iff_nsmul, PowerSeries.coe_sub, WithZeroMulInt.toNNReal_lt_one_iff, Int.cast_natAbs, LaurentSeries.algebraMap_apply, IsDedekindDomain.HeightOneSpectrum.intValuation_le_pow_iff_dvd, Equiv.Perm.sign_abs, Int.cast_strictMono, Int.card_fintype_Ioo_of_lt, Int.card_box, LaurentSeries.derivative_iterate_coeff, tendsto_floor_atTop, Int.floor_mono, FunctionField.InftyValuation.map_add_le_max', Int.one_le_abs, WeierstrassCurve.IsMinimal.val_Δ_maximal, Nat.floor_int, Int.dist_eq', LaurentSeries.exists_ratFunc_val_lt, Int.Ioo_eq_finset_map, Finset.prod_Ico_int_div, Int.abs_le_sqrt_iff_sq_le, LocallyFiniteOrder.orderAddMonoidHom_strictMono, Int.card_Ico_of_le, Nat.cast_natAbs, IsDedekindDomain.HeightOneSpectrum.valuation_div_le_one_iff, IsDedekindDomain.HeightOneSpectrum.valuation_lt_one_iff_dvd, IsDedekindDomain.HeightOneSpectrum.intValuation.map_add_le_max', LaurentSeries.derivative_apply, VertexOperator.ncoeff_apply, FixedDetMatrices.reps_entries_le_m', Rat.valuation_le_one_iff_den, NumberField.abs_discr_gt_two, LaurentSeries.powerSeriesPart_coeff, HurwitzZeta.hasSum_int_cosZeta, norm_abs_zsmul, MeromorphicOn.negPart_divisor_add_of_analyticNhdOn_right, LaurentSeries.exists_Polynomial_intValuation_lt, NumberField.hermiteTheorem.finite_of_discr_bdd_of_isComplex, tendsto_ceil_atBot, LinearOrderedCommGroup.wellFoundedOn_setOf_ge_gt_iff_nonempty_discrete, Int.injOn_natAbs_Iic, Padic.AddValuation.map_add, norm_zpow_abs, Int.orderedSMul, Int.Ioc_filter_modEq_card, ZMod.intCast_abs_mod_two, Finset.sum_Icc_eq_sum_Ico_add, Int.card_Ico, Int.card_Ioc_of_le, LinearOrderedAddCommGroup.discrete_iff_not_denselyOrdered, Finset.Ioc_succ_succ, MeromorphicOn.negPart_divisor_add_of_analyticNhdOn_left, Int.image_Ico_emod, Order.coheight_int, WithZeroMulInt.toNNReal_le_one_iff, Int.card_fintype_Icc_of_le, LaurentSeries.of_powerSeries_localization, Int.abs_le_one_iff, RatFunc.valuation_eq_LaurentSeries_valuation, norm_intCast_abs, Int.gc_coe_floor, CharP.intCast_injOn_Ico, mapClusterPt_atTop_zpow_iff_pow, Int.preimage_Iic, Int.Icc_eq_finset_map, IsDedekindDomain.HeightOneSpectrum.valuation_lt_one_iff_mem, LaurentSeries.coe_X_compare, Int.card_fintype_Ioc_of_le, LaurentSeries.hasseDeriv_comp_coeff, LaurentSeries.intValuation_le_iff_coeff_lt_eq_zero, RatFunc.algebraMap_apply_div, Int.Ico_filter_dvd_card, LinearOrderedCommGroup.wellFoundedOn_setOf_le_lt_iff_nonempty_discrete, Finset.Ico_succ_succ, nnnorm_intCast_abs, PowerSeries.coe_zero, FractionalIdeal.absNorm_eq, nnnorm_zpow_abs, Int.natAbs_abs, Int.Ioc_eq_finset_map, Int.instIsPredArchimedean, zpow_abs_eq_one, LaurentSeries.exists_powerSeries_of_memIntegers, Polynomial.cardPowDegree_apply, Int.card_uIcc, Int.card_Icc_of_le, Nat.Ico_filter_modEq_cast, PowerSeries.coe_C, tendsto_intCast_atTop_iff, PowerSeries.coe_neg, LinearOrderedAddCommGroup.wellFoundedOn_setOf_ge_gt_iff_nonempty_discrete, zsmul_left_strictMono, LaurentSeries.hasseDeriv_coeff, Polynomial.exists_approx_polynomial, Int.comap_cast_atBot, AbsoluteValue.IsAdmissible.exists_approx, Int.abs_negOnePow, Int.isUnit_iff_abs_eq, Int.instStarOrderedRing, IsDedekindDomain.HeightOneSpectrum.intValuation_lt_one_iff_dvd, Int.abs_sign_of_ne_zero, Int.sign_eq_abs_ediv, ZLattice.exists_forall_abs_repr_le_norm, Nat.image_cast_int_Ioi, IsDedekindDomain.HeightOneSpectrum.intValuation_zero_lt, LaurentSeries.LaurentSeriesRingEquiv_mem_valuationSubring, Int.uIcc_eq_finset_map, LaurentSeries.valuation_LaurentSeries_equal_extension, LaurentSeries.hasseDeriv_single_add, NumberField.finite_of_discr_bdd, WeierstrassCurve.isMinimal_iff, zsmul_left_strictAnti, LaurentSeries.LaurentSeries_coe, Int.existsUnique_mem_box, AbsoluteValue.IsAdmissible.exists_partition, LaurentSeries.powerSeries_ext_subring, VertexOperator.ext_iff, CategoryTheory.Triangulated.TStructure.ge_antitone, Nat.range_cast_int, LieModule.genWeightSpaceChain_def, LaurentSeries.hasseDeriv_comp, LaurentSeries.powerSeriesRingEquiv_coe_apply, AbsoluteValue.IsAdmissible.exists_partition', LaurentSeries.powerSeriesEquivSubring_apply, LocallyFiniteOrder.orderAddMonoidHom_apply, Int.emod_abs, tendsto_intCast_atBot_iff, Int.abs_eq_normalize, ArithmeticFunction.abs_moebius_eq_one_of_squarefree, Int.Icc_eq_pair, tendsto_floor_atBot, CFC.abs_intCast, Int.preimage_Ioo, LTSeries.head_add_length_le_int, Int.addSubmonoid_closure_range_pow, ZLattice.abs_repr_lt_of_norm_lt, Int.sign_mul_self_eq_abs, norm_jacobiTheta₂'_term_le, LinearOrderedAddCommGroup.discrete_or_denselyOrdered, Int.card_Icc, Int.cast_mono, Int.preimage_Ici, LaurentSeries.powerSeriesEquivSubring_coe_apply, Finset.sum_Icc_of_even_eq_range, PowerSeries.coe_X, LaurentSeries.instLaurentSeriesComplete, ModularGroup.abs_c_le_one, LinearOrderedCommGroupWithZero.wellFoundedOn_setOf_ge_gt_iff_nonempty_discrete_of_ne_zero, LaurentSeries.valuation_coe_ratFunc, Function.locallyFinsuppWithin.restrict_posPart, Int.Ico_filter_modEq_card, Int.pred_eq_pred, Int.abs_sign_of_nonzero, Nat.image_cast_int_Ioo, Int.Ioc_filter_dvd_eq, Int.preimage_Icc, MeromorphicOn.negPart_divisor_add_le_max, LaurentSeries.valuation_compare, Int.sign_eq_ediv_abs', LieAlgebra.IsKilling.rootSpace_zsmul_add_ne_bot_iff_mem, AbsoluteValue.IsAdmissible.toIsEuclidean, WithZeroMulInt.toNNReal_strictMono, RatFunc.single_one_eq_pow, Finset.Ioo_succ_succ, NumberField.abs_discr_ge_of_isTotallyComplex, Int.mem_box, Valuation.Integers.wellFounded_gt_on_v_iff_discrete_mrange, zpow_right_mono, LaurentSeries.coe_range_dense, ENNReal.monotone_zpow, Int.abs_le_floor_nnreal_iff, Int.Ico_eq_finset_map, instSMulPosStrictMonoIntOfIsOrderedAddMonoid, Polynomial.cardPowDegree_nonzero, EisensteinSeries.abs_le_left_of_norm, Int.gc_ceil_coe, LocallyFiniteOrder.orderAddMonoidHom_toAddMonoidHom, RootPairing.GeckConstruction.lie_e_lie_f_apply, ZMod.abs_valMinAbs_eq_abs_valMinAbs, norm_intCast_eq_abs_mul_norm_one, Int.modEq_abs, AbsoluteValue.IsAdmissible.exists_approx_aux, Order.height_int, HurwitzZeta.hasSum_int_sinZeta, Int.abs_ediv_le_abs, Finset.prod_Icc_succ_eq_mul_endpoints, LocallyFiniteOrder.orderMonoidHom_strictMono, FloorRing.gc_coe_floor, VertexOperator.ncoeff_of_coeff, LaurentSeries.comparePkg_eq_extension, instArchimedeanInt, FractionalIdeal.absNorm_div_norm_eq_absNorm_div_norm, RatFunc.single_zpow, LaurentSeries.valuation_def, Int.abs_lt_one_iff, Int.natCast_strictMono, LaurentSeries.derivative_iterate, Nat.map_cast_int_atTop, Int.le_abs_of_dvd, ZLattice.normBound_spec, NumberField.abs_discr_rpow_ge_of_isTotallyComplex, LaurentSeries.valuation_le_iff_coeff_lt_log_eq_zero, MeromorphicOn.negPart_divisor_add_le_add, LaurentSeries.uniformContinuous_coeff, nnnorm_abs_zsmul, PowerSeries.coe_one, summable_pow_mul_jacobiTheta₂_term_bound, Int.card_fintype_Ico_of_le, LaurentSeries.hasseDeriv_zero, Set.integer_valuation_le_one, Int.ediv_emod_unique'', Int.ceil_mono, not_denselyOrdered_withZero_int, LaurentSeries.ratfuncAdicComplRingEquiv_apply, instIsLocalizationIntPosRat, Int.strictMonoOn_natAbs, Filter.Eventually.intCast_atBot, Finset.prod_Icc_of_even_eq_range, ArithmeticFunction.abs_moebius_le_one, Int.Ico_filter_modEq_eq, Int.injOn_natAbs_Ici, Int.Ioc_filter_modEq_eq, Int.addSubmonoid_closure_range_mul_self, Int.sign_eq_sign, HurwitzZeta.hasSum_int_completedCosZeta, LocallyFiniteOrder.orderMonoidWithZeroHom_strictMono, PowerSeries.coe_pow, Int.succ_eq_succ, Function.locallyFinsuppWithin.restrict_negPart, LaurentSeries.mem_integers_of_powerSeries, LinearOrderedCommGroupWithZero.discrete_iff_not_denselyOrdered, LaurentSeries.instIsFractionRingPowerSeries, LinearOrderedCommGroup.discrete_or_denselyOrdered, RootPairing.Base.abs_cartanMatrix_apply, tendsto_intCast_atTop_atTop, ValueDistribution.logCounting_coe, abs_zsmul, HurwitzZeta.hasSum_int_completedSinZeta, RatFunc.single_inv, LinearOrderedCommGroup.discrete_iff_not_denselyOrdered, LocallyFiniteOrder.orderAddMonoidEquiv_apply, IsDedekindDomain.HeightOneSpectrum.valuation_le_one, LaurentPolynomial.degree_T_le, LaurentSeries.coeff_coe_powerSeries, LinearOrderedAddCommGroup.isAddCyclic_iff_nonempty_equiv_int, VertexOperator.coeff_eq_ncoeff, Int.Ico_filter_dvd_eq, Int.hasSolidNorm, instWellFoundedGTWithZeroMultiplicativeIntLeOne, LaurentSeries.powerSeriesPart_zero, Finset.sum_Icc_succ_eq_add_endpoints, Finset.sum_le_sum_Ioc, LaurentSeries.exists_ratFunc_eq_v, Int.card_Ioo_of_lt, abs_zsmul_eq_zero, ZMod.valMinAbs_spec, LinearOrderedCommGroupWithZero.wellFoundedOn_setOf_le_lt_iff_nonempty_discrete_of_ne_zero, Int.sign_mul_abs, zsmul_left_mono, Nat.image_cast_int_Ico, Int.preimage_Ico, LaurentSeries.valuation_X_pow, LaurentPolynomial.degree_C_le, IsDedekindDomain.HeightOneSpectrum.intValuation_lt_one_iff_mem, LaurentSeries.hasseDeriv_single, Int.Ioc_filter_dvd_card, RootPairing.GeckConstruction.e_lie_u, Filter.Eventually.intCast_atTop, Polynomial.abs_leadingCoeff_eq_one_of_mahlerMeasure_eq_one, Int.abs_natCast, Int.abs_eq_natAbs, LinearOrderedCommGroupWithZero.discrete_or_denselyOrdered, Rat.abs_def', LinearOrderedCommGroup.isCyclic_iff_nonempty_equiv_int, IsDedekindDomain.HeightOneSpectrum.notMem_adicCompletionIntegers, LaurentPolynomial.degree_C_mul_T_le, ZLattice.abs_repr_le, norm_jacobiTheta₂_term_fderiv_le, LaurentSeries.powerSeriesPart_eq_zero, Int.natCast_natAbs, NumberField.hermiteTheorem.finite_of_discr_bdd_of_isReal, ArithmeticFunction.abs_moebius, Nat.image_cast_int_Iio, Int.instIsOrderedAddMonoid

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
eq_of_inf_eq_sup_eq 📖	—	SemilatticeInf.toMin Lattice.toSemilatticeInf DistribLattice.toLattice SemilatticeSup.toMax Lattice.toSemilatticeSup	—	—	le_antisymm le_of_inf_le_sup_le le_of_eq
exists_and_iff_of_antitone 📖	—	Antitone PartialOrder.toPreorder SemilatticeInf.toPartialOrder Prop.partialOrder	—	—	inf_le_left inf_le_right
exists_and_iff_of_monotone 📖	—	Monotone PartialOrder.toPreorder SemilatticeSup.toPartialOrder Prop.partialOrder	—	—	le_sup_left le_sup_right
exists_ge_and_iff_exists 📖	mathematical	Monotone PartialOrder.toPreorder SemilatticeSup.toPartialOrder Prop.partialOrder	Preorder.toLE	—	le_sup_right le_sup_left
exists_le_and_iff_exists 📖	mathematical	Antitone PartialOrder.toPreorder SemilatticeInf.toPartialOrder Prop.partialOrder	Preorder.toLE	—	exists_ge_and_iff_exists Antitone.dual_left
inf_assoc 📖	mathematical	—	SemilatticeInf.toMin	—	eq_of_forall_le_iff le_inf_iff
inf_comm 📖	mathematical	—	SemilatticeInf.toMin	—	ge_antisymm le_inf_iff inf_le_right inf_le_left
inf_congr_left 📖	—	Preorder.toLE PartialOrder.toPreorder SemilatticeInf.toPartialOrder SemilatticeInf.toMin	—	—	LE.le.antisymm' le_inf inf_le_left
inf_congr_right 📖	—	Preorder.toLE PartialOrder.toPreorder SemilatticeInf.toPartialOrder SemilatticeInf.toMin	—	—	LE.le.antisymm' le_inf inf_le_right
inf_eq_and_sup_eq_iff 📖	mathematical	—	SemilatticeInf.toMin Lattice.toSemilatticeInf SemilatticeSup.toMax Lattice.toSemilatticeSup	—	inf_of_le_left sup_of_le_left sup_eq_inf inf_idem sup_idem
inf_eq_iff_sup_eq 📖	mathematical	—	SemilatticeInf.toMin Lattice.toSemilatticeInf SemilatticeSup.toMax Lattice.toSemilatticeSup	—	inf_eq_right sup_eq_left
inf_eq_inf_iff_left 📖	mathematical	—	SemilatticeInf.toMin Preorder.toLE PartialOrder.toPreorder SemilatticeInf.toPartialOrder	—	inf_le_right inf_congr_left
inf_eq_inf_iff_right 📖	mathematical	—	SemilatticeInf.toMin Preorder.toLE PartialOrder.toPreorder SemilatticeInf.toPartialOrder	—	inf_le_left inf_congr_right
inf_eq_left 📖	mathematical	—	SemilatticeInf.toMin Preorder.toLE PartialOrder.toPreorder SemilatticeInf.toPartialOrder	—	ge_antisymm_iff le_inf_iff le_refl inf_le_left
inf_eq_minDefault 📖	mathematical	—	SemilatticeInf.toMin minDefault Preorder.toLE PartialOrder.toPreorder SemilatticeInf.toPartialOrder	—	inf_of_le_left inf_of_le_right total_of
inf_eq_right 📖	mathematical	—	SemilatticeInf.toMin Preorder.toLE PartialOrder.toPreorder SemilatticeInf.toPartialOrder	—	ge_antisymm_iff le_inf_iff le_refl inf_le_right
inf_eq_sup 📖	mathematical	—	SemilatticeInf.toMin Lattice.toSemilatticeInf SemilatticeSup.toMax Lattice.toSemilatticeSup	—	LE.le.ge_iff_eq inf_le_sup sup_le_inf
inf_idem 📖	mathematical	—	SemilatticeInf.toMin	—	inf_of_le_left le_refl
inf_ind 📖	mathematical	—	SemilatticeInf.toMin Lattice.toSemilatticeInf LinearOrder.toLattice	—	LE.total' inf_eq_right inf_eq_left
inf_inf_distrib_left 📖	mathematical	—	SemilatticeInf.toMin	—	inf_inf_inf_comm inf_idem
inf_inf_distrib_right 📖	mathematical	—	SemilatticeInf.toMin	—	inf_inf_inf_comm inf_idem
inf_inf_inf_comm 📖	mathematical	—	SemilatticeInf.toMin	—	inf_assoc inf_left_comm
inf_le_iff 📖	mathematical	—	Preorder.toLE PartialOrder.toPreorder SemilatticeSup.toPartialOrder Lattice.toSemilatticeSup LinearOrder.toLattice SemilatticeInf.toMin Lattice.toSemilatticeInf	—	—
inf_le_inf 📖	mathematical	Preorder.toLE PartialOrder.toPreorder SemilatticeInf.toPartialOrder	SemilatticeInf.toMin	—	le_inf inf_le_of_left_le inf_le_of_right_le
inf_le_inf_left 📖	mathematical	Preorder.toLE PartialOrder.toPreorder SemilatticeInf.toPartialOrder	SemilatticeInf.toMin	—	inf_le_inf le_rfl
inf_le_inf_right 📖	mathematical	Preorder.toLE PartialOrder.toPreorder SemilatticeInf.toPartialOrder	SemilatticeInf.toMin	—	inf_le_inf le_rfl
inf_le_ite 📖	mathematical	—	Preorder.toLE PartialOrder.toPreorder SemilatticeInf.toPartialOrder SemilatticeInf.toMin	—	Eq.trans_ge inf_le_left inf_le_right
inf_le_left 📖	mathematical	—	Preorder.toLE PartialOrder.toPreorder SemilatticeInf.toPartialOrder SemilatticeInf.toMin	—	SemilatticeInf.inf_le_left
inf_le_of_left_le 📖	mathematical	Preorder.toLE PartialOrder.toPreorder SemilatticeInf.toPartialOrder	SemilatticeInf.toMin	—	ge_trans inf_le_left
inf_le_of_right_le 📖	mathematical	Preorder.toLE PartialOrder.toPreorder SemilatticeInf.toPartialOrder	SemilatticeInf.toMin	—	ge_trans inf_le_right
inf_le_right 📖	mathematical	—	Preorder.toLE PartialOrder.toPreorder SemilatticeInf.toPartialOrder SemilatticeInf.toMin	—	SemilatticeInf.inf_le_right
inf_le_sup 📖	mathematical	—	Preorder.toLE PartialOrder.toPreorder SemilatticeInf.toPartialOrder Lattice.toSemilatticeInf SemilatticeInf.toMin SemilatticeSup.toMax Lattice.toSemilatticeSup	—	LE.le.trans inf_le_left le_sup_left
inf_left_comm 📖	mathematical	—	SemilatticeInf.toMin	—	inf_assoc inf_comm
inf_left_idem 📖	mathematical	—	SemilatticeInf.toMin	—	inf_of_le_right inf_le_left
inf_left_le_sup_left 📖	mathematical	—	Preorder.toLE PartialOrder.toPreorder SemilatticeInf.toPartialOrder Lattice.toSemilatticeInf SemilatticeInf.toMin SemilatticeSup.toMax Lattice.toSemilatticeSup	—	le_trans inf_le_right le_sup_right
inf_left_le_sup_right 📖	mathematical	—	Preorder.toLE PartialOrder.toPreorder SemilatticeInf.toPartialOrder Lattice.toSemilatticeInf SemilatticeInf.toMin SemilatticeSup.toMax Lattice.toSemilatticeSup	—	le_trans inf_le_right le_sup_left
inf_left_right_swap 📖	mathematical	—	SemilatticeInf.toMin	—	inf_comm inf_assoc
inf_lt_iff 📖	mathematical	—	Preorder.toLT PartialOrder.toPreorder SemilatticeSup.toPartialOrder Lattice.toSemilatticeSup LinearOrder.toLattice SemilatticeInf.toMin Lattice.toSemilatticeInf	—	—
inf_lt_left 📖	mathematical	—	Preorder.toLT PartialOrder.toPreorder SemilatticeInf.toPartialOrder SemilatticeInf.toMin Preorder.toLE	—	LE.le.lt_iff_ne' inf_le_left left_eq_inf
inf_lt_left_or_right 📖	mathematical	—	Preorder.toLT PartialOrder.toPreorder SemilatticeInf.toPartialOrder SemilatticeInf.toMin	—	inf_lt_left inf_lt_right Ne.not_ge_or_not_le
inf_lt_of_left_lt 📖	mathematical	Preorder.toLT PartialOrder.toPreorder SemilatticeInf.toPartialOrder	SemilatticeInf.toMin	—	LT.lt.trans_le' inf_le_left
inf_lt_of_right_lt 📖	mathematical	Preorder.toLT PartialOrder.toPreorder SemilatticeInf.toPartialOrder	SemilatticeInf.toMin	—	LT.lt.trans_le' inf_le_right
inf_lt_right 📖	mathematical	—	Preorder.toLT PartialOrder.toPreorder SemilatticeInf.toPartialOrder SemilatticeInf.toMin Preorder.toLE	—	LE.le.lt_iff_ne' inf_le_right right_eq_inf
inf_lt_sup 📖	mathematical	—	Preorder.toLT PartialOrder.toPreorder SemilatticeInf.toPartialOrder Lattice.toSemilatticeInf SemilatticeInf.toMin SemilatticeSup.toMax Lattice.toSemilatticeSup	—	LE.le.lt_iff_ne inf_le_sup inf_eq_sup
inf_of_le_left 📖	mathematical	Preorder.toLE PartialOrder.toPreorder SemilatticeInf.toPartialOrder	SemilatticeInf.toMin	—	inf_eq_left
inf_of_le_right 📖	mathematical	Preorder.toLE PartialOrder.toPreorder SemilatticeInf.toPartialOrder	SemilatticeInf.toMin	—	inf_eq_right
inf_right_comm 📖	mathematical	—	SemilatticeInf.toMin	—	inf_assoc inf_comm
inf_right_idem 📖	mathematical	—	SemilatticeInf.toMin	—	inf_of_le_left inf_le_right
inf_right_le_sup_left 📖	mathematical	—	Preorder.toLE PartialOrder.toPreorder SemilatticeSup.toPartialOrder Lattice.toSemilatticeSup SemilatticeInf.toMin Lattice.toSemilatticeInf SemilatticeSup.toMax	—	ge_trans le_sup_right inf_le_left
inf_right_le_sup_right 📖	mathematical	—	Preorder.toLE PartialOrder.toPreorder SemilatticeInf.toPartialOrder Lattice.toSemilatticeInf SemilatticeInf.toMin SemilatticeSup.toMax Lattice.toSemilatticeSup	—	le_trans inf_le_left le_sup_left
inf_sup_le 📖	mathematical	—	Preorder.toLE PartialOrder.toPreorder SemilatticeInf.toPartialOrder Lattice.toSemilatticeInf DistribLattice.toLattice SemilatticeInf.toMin SemilatticeSup.toMax Lattice.toSemilatticeSup	—	inf_sup_left le_refl
inf_sup_left 📖	mathematical	—	SemilatticeInf.toMin Lattice.toSemilatticeInf DistribLattice.toLattice SemilatticeSup.toMax Lattice.toSemilatticeSup	—	inf_sup_self inf_assoc sup_inf_right sup_inf_self sup_comm sup_inf_left
inf_sup_right 📖	mathematical	—	SemilatticeInf.toMin Lattice.toSemilatticeInf DistribLattice.toLattice SemilatticeSup.toMax Lattice.toSemilatticeSup	—	inf_comm inf_sup_left
inf_sup_self 📖	mathematical	—	SemilatticeInf.toMin Lattice.toSemilatticeInf SemilatticeSup.toMax Lattice.toSemilatticeSup	—	inf_of_le_left
instAssociativeMax_mathlib 📖	mathematical	—	SemilatticeSup.toMax	—	sup_assoc
instAssociativeMin_mathlib 📖	mathematical	—	SemilatticeInf.toMin	—	inf_assoc
instCommutativeMax_mathlib 📖	mathematical	—	SemilatticeSup.toMax	—	sup_comm
instCommutativeMin_mathlib 📖	mathematical	—	SemilatticeInf.toMin	—	inf_comm
instIdempotentOpMax_mathlib 📖	mathematical	—	SemilatticeSup.toMax	—	sup_idem
instIdempotentOpMin_mathlib 📖	mathematical	—	SemilatticeInf.toMin	—	inf_idem
ite_le_sup 📖	mathematical	—	Preorder.toLE PartialOrder.toPreorder SemilatticeSup.toPartialOrder SemilatticeSup.toMax	—	Eq.trans_le le_sup_left le_sup_right
le_iff_exists_inf 📖	mathematical	—	Preorder.toLE PartialOrder.toPreorder SemilatticeInf.toPartialOrder SemilatticeInf.toMin	—	inf_eq_right inf_le_left
le_iff_exists_sup 📖	mathematical	—	Preorder.toLE PartialOrder.toPreorder SemilatticeSup.toPartialOrder SemilatticeSup.toMax	—	sup_eq_right le_sup_left
le_inf 📖	mathematical	Preorder.toLE PartialOrder.toPreorder SemilatticeInf.toPartialOrder	SemilatticeInf.toMin	—	SemilatticeInf.le_inf
le_inf_iff 📖	mathematical	—	Preorder.toLE PartialOrder.toPreorder SemilatticeInf.toPartialOrder SemilatticeInf.toMin	—	ge_trans inf_le_left inf_le_right le_inf
le_inf_sup 📖	mathematical	—	Preorder.toLE PartialOrder.toPreorder SemilatticeSup.toPartialOrder Lattice.toSemilatticeSup SemilatticeSup.toMax SemilatticeInf.toMin Lattice.toSemilatticeInf	—	sup_le inf_le_inf_left le_sup_left le_sup_right
le_of_inf_eq 📖	mathematical	SemilatticeInf.toMin	Preorder.toLE PartialOrder.toPreorder SemilatticeInf.toPartialOrder	—	inf_eq_left
le_of_inf_eq' 📖	mathematical	SemilatticeInf.toMin	Preorder.toLE PartialOrder.toPreorder SemilatticeInf.toPartialOrder	—	inf_eq_right
le_of_inf_le_sup_le 📖	—	Preorder.toLE PartialOrder.toPreorder SemilatticeInf.toPartialOrder Lattice.toSemilatticeInf DistribLattice.toLattice SemilatticeInf.toMin SemilatticeSup.toMax Lattice.toSemilatticeSup	—	—	le_sup_right sup_inf_right sup_comm inf_le_inf_left sup_inf_left sup_le_sup_left sup_le le_refl inf_le_left
le_of_sup_eq 📖	mathematical	SemilatticeSup.toMax	Preorder.toLE PartialOrder.toPreorder SemilatticeSup.toPartialOrder	—	sup_eq_right
le_of_sup_eq' 📖	mathematical	SemilatticeSup.toMax	Preorder.toLE PartialOrder.toPreorder SemilatticeSup.toPartialOrder	—	sup_eq_left
le_sup_iff 📖	mathematical	—	Preorder.toLE PartialOrder.toPreorder SemilatticeInf.toPartialOrder Lattice.toSemilatticeInf LinearOrder.toLattice SemilatticeSup.toMax Lattice.toSemilatticeSup	—	—
le_sup_inf 📖	mathematical	—	Preorder.toLE PartialOrder.toPreorder SemilatticeInf.toPartialOrder Lattice.toSemilatticeInf DistribLattice.toLattice SemilatticeInf.toMin SemilatticeSup.toMax Lattice.toSemilatticeSup	—	DistribLattice.le_sup_inf
le_sup_left 📖	mathematical	—	Preorder.toLE PartialOrder.toPreorder SemilatticeSup.toPartialOrder SemilatticeSup.toMax	—	SemilatticeSup.le_sup_left
le_sup_of_le_left 📖	mathematical	Preorder.toLE PartialOrder.toPreorder SemilatticeSup.toPartialOrder	SemilatticeSup.toMax	—	le_trans le_sup_left
le_sup_of_le_right 📖	mathematical	Preorder.toLE PartialOrder.toPreorder SemilatticeSup.toPartialOrder	SemilatticeSup.toMax	—	le_trans le_sup_right
le_sup_right 📖	mathematical	—	Preorder.toLE PartialOrder.toPreorder SemilatticeSup.toPartialOrder SemilatticeSup.toMax	—	SemilatticeSup.le_sup_right
left_eq_inf 📖	mathematical	—	SemilatticeInf.toMin Preorder.toLE PartialOrder.toPreorder SemilatticeInf.toPartialOrder	—	inf_eq_left
left_eq_sup 📖	mathematical	—	SemilatticeSup.toMax Preorder.toLE PartialOrder.toPreorder SemilatticeSup.toPartialOrder	—	sup_eq_left
left_lt_sup 📖	mathematical	—	Preorder.toLT PartialOrder.toPreorder SemilatticeSup.toPartialOrder SemilatticeSup.toMax Preorder.toLE	—	LE.le.lt_iff_ne le_sup_left left_eq_sup
left_or_right_lt_sup 📖	mathematical	—	Preorder.toLT PartialOrder.toPreorder SemilatticeSup.toPartialOrder SemilatticeSup.toMax	—	left_lt_sup right_lt_sup Ne.not_le_or_not_ge
lt_inf_iff 📖	mathematical	—	Preorder.toLT PartialOrder.toPreorder SemilatticeSup.toPartialOrder Lattice.toSemilatticeSup LinearOrder.toLattice SemilatticeInf.toMin Lattice.toSemilatticeInf	—	LE.le.trans_lt' inf_le_left inf_le_right inf_ind
lt_sup_iff 📖	mathematical	—	Preorder.toLT PartialOrder.toPreorder SemilatticeInf.toPartialOrder Lattice.toSemilatticeInf LinearOrder.toLattice SemilatticeSup.toMax Lattice.toSemilatticeSup	—	—
lt_sup_of_lt_left 📖	mathematical	Preorder.toLT PartialOrder.toPreorder SemilatticeSup.toPartialOrder	SemilatticeSup.toMax	—	LT.lt.trans_le le_sup_left
lt_sup_of_lt_right 📖	mathematical	Preorder.toLT PartialOrder.toPreorder SemilatticeSup.toPartialOrder	SemilatticeSup.toMax	—	LT.lt.trans_le le_sup_right
max_max_max_comm 📖	mathematical	—	SemilatticeSup.toMax Lattice.toSemilatticeSup LinearOrder.toLattice	—	sup_sup_sup_comm
min_min_min_comm 📖	mathematical	—	SemilatticeInf.toMin Lattice.toSemilatticeInf LinearOrder.toLattice	—	inf_inf_inf_comm
ofDual_inf 📖	mathematical	—	DFunLike.coe Equiv OrderDual EquivLike.toFunLike Equiv.instEquivLike OrderDual.ofDual OrderDual.instInf	—	—
ofDual_max 📖	mathematical	—	DFunLike.coe Equiv OrderDual EquivLike.toFunLike Equiv.instEquivLike OrderDual.ofDual OrderDual.instSup SemilatticeInf.toMin Lattice.toSemilatticeInf DistribLattice.toLattice instDistribLatticeOfLinearOrder	—	—
ofDual_min 📖	mathematical	—	DFunLike.coe Equiv OrderDual EquivLike.toFunLike Equiv.instEquivLike OrderDual.ofDual OrderDual.instInf SemilatticeSup.toMax Lattice.toSemilatticeSup DistribLattice.toLattice instDistribLatticeOfLinearOrder	—	—
ofDual_sup 📖	mathematical	—	DFunLike.coe Equiv OrderDual EquivLike.toFunLike Equiv.instEquivLike OrderDual.ofDual OrderDual.instSup	—	—
pairwise_iff_gt 📖	mathematical	Symmetric	Pairwise	—	—
pairwise_iff_lt 📖	mathematical	Symmetric	Pairwise	—	—
right_eq_inf 📖	mathematical	—	SemilatticeInf.toMin Preorder.toLE PartialOrder.toPreorder SemilatticeInf.toPartialOrder	—	inf_eq_right
right_eq_sup 📖	mathematical	—	SemilatticeSup.toMax Preorder.toLE PartialOrder.toPreorder SemilatticeSup.toPartialOrder	—	sup_eq_right
right_lt_sup 📖	mathematical	—	Preorder.toLT PartialOrder.toPreorder SemilatticeSup.toPartialOrder SemilatticeSup.toMax Preorder.toLE	—	LE.le.lt_iff_ne le_sup_right right_eq_sup
semilatticeSup_mk'_partialOrder_eq_semilatticeInf_mk'_partialOrder 📖	mathematical	—	SemilatticeSup.toPartialOrder SemilatticeSup.mk' SemilatticeInf.toPartialOrder SemilatticeInf.mk'	—	PartialOrder.ext
sup_assoc 📖	mathematical	—	SemilatticeSup.toMax	—	eq_of_forall_ge_iff
sup_comm 📖	mathematical	—	SemilatticeSup.toMax	—	le_antisymm
sup_congr_left 📖	—	Preorder.toLE PartialOrder.toPreorder SemilatticeSup.toPartialOrder SemilatticeSup.toMax	—	—	LE.le.antisymm sup_le le_sup_left
sup_congr_right 📖	—	Preorder.toLE PartialOrder.toPreorder SemilatticeSup.toPartialOrder SemilatticeSup.toMax	—	—	LE.le.antisymm sup_le le_sup_right
sup_eq_and_inf_eq_iff 📖	mathematical	—	SemilatticeSup.toMax Lattice.toSemilatticeSup SemilatticeInf.toMin Lattice.toSemilatticeInf	—	sup_of_le_left le_refl inf_of_le_left inf_eq_sup sup_idem inf_idem
sup_eq_iff_inf_eq 📖	mathematical	—	SemilatticeSup.toMax Lattice.toSemilatticeSup SemilatticeInf.toMin Lattice.toSemilatticeInf	—	sup_eq_right inf_eq_left
sup_eq_inf 📖	mathematical	—	SemilatticeSup.toMax Lattice.toSemilatticeSup SemilatticeInf.toMin Lattice.toSemilatticeInf	—	LE.le.ge_iff_eq' inf_le_sup sup_le_inf
sup_eq_left 📖	mathematical	—	SemilatticeSup.toMax Preorder.toLE PartialOrder.toPreorder SemilatticeSup.toPartialOrder	—	le_antisymm_iff
sup_eq_maxDefault 📖	mathematical	—	SemilatticeSup.toMax maxDefault Preorder.toLE PartialOrder.toPreorder SemilatticeSup.toPartialOrder	—	sup_of_le_right sup_of_le_left total_of
sup_eq_right 📖	mathematical	—	SemilatticeSup.toMax Preorder.toLE PartialOrder.toPreorder SemilatticeSup.toPartialOrder	—	le_antisymm_iff
sup_eq_sup_iff_left 📖	mathematical	—	SemilatticeSup.toMax Preorder.toLE PartialOrder.toPreorder SemilatticeSup.toPartialOrder	—	le_sup_right sup_congr_left
sup_eq_sup_iff_right 📖	mathematical	—	SemilatticeSup.toMax Preorder.toLE PartialOrder.toPreorder SemilatticeSup.toPartialOrder	—	le_sup_left sup_congr_right
sup_idem 📖	mathematical	—	SemilatticeSup.toMax	—	sup_of_le_left
sup_ind 📖	mathematical	—	SemilatticeSup.toMax Lattice.toSemilatticeSup LinearOrder.toLattice	—	LE.total sup_eq_right sup_eq_left
sup_inf_le 📖	mathematical	—	Preorder.toLE PartialOrder.toPreorder SemilatticeInf.toPartialOrder Lattice.toSemilatticeInf SemilatticeSup.toMax Lattice.toSemilatticeSup SemilatticeInf.toMin	—	le_inf sup_le_sup_left inf_le_left inf_le_right
sup_inf_left 📖	mathematical	—	SemilatticeSup.toMax Lattice.toSemilatticeSup DistribLattice.toLattice SemilatticeInf.toMin Lattice.toSemilatticeInf	—	le_antisymm sup_inf_le le_sup_inf
sup_inf_right 📖	mathematical	—	SemilatticeSup.toMax Lattice.toSemilatticeSup DistribLattice.toLattice SemilatticeInf.toMin Lattice.toSemilatticeInf	—	sup_comm sup_inf_left
sup_inf_self 📖	mathematical	—	SemilatticeSup.toMax Lattice.toSemilatticeSup SemilatticeInf.toMin Lattice.toSemilatticeInf	—	sup_of_le_left inf_le_left
sup_le 📖	mathematical	Preorder.toLE PartialOrder.toPreorder SemilatticeSup.toPartialOrder	SemilatticeSup.toMax	—	SemilatticeSup.sup_le
sup_le_iff 📖	mathematical	—	Preorder.toLE PartialOrder.toPreorder SemilatticeSup.toPartialOrder SemilatticeSup.toMax	—	le_trans le_sup_left le_sup_right sup_le
sup_le_inf 📖	mathematical	—	Preorder.toLE PartialOrder.toPreorder SemilatticeInf.toPartialOrder Lattice.toSemilatticeInf SemilatticeSup.toMax Lattice.toSemilatticeSup SemilatticeInf.toMin	—	—
sup_le_sup 📖	mathematical	Preorder.toLE PartialOrder.toPreorder SemilatticeSup.toPartialOrder	SemilatticeSup.toMax	—	sup_le le_sup_of_le_left le_sup_of_le_right
sup_le_sup_left 📖	mathematical	Preorder.toLE PartialOrder.toPreorder SemilatticeSup.toPartialOrder	SemilatticeSup.toMax	—	sup_le_sup le_rfl
sup_le_sup_right 📖	mathematical	Preorder.toLE PartialOrder.toPreorder SemilatticeSup.toPartialOrder	SemilatticeSup.toMax	—	sup_le_sup le_rfl
sup_left_comm 📖	mathematical	—	SemilatticeSup.toMax	—	sup_assoc sup_comm
sup_left_idem 📖	mathematical	—	SemilatticeSup.toMax	—	sup_of_le_right
sup_left_right_swap 📖	mathematical	—	SemilatticeSup.toMax	—	sup_comm sup_assoc
sup_lt_iff 📖	mathematical	—	Preorder.toLT PartialOrder.toPreorder SemilatticeInf.toPartialOrder Lattice.toSemilatticeInf LinearOrder.toLattice SemilatticeSup.toMax Lattice.toSemilatticeSup	—	LE.le.trans_lt le_sup_left le_sup_right sup_ind
sup_of_le_left 📖	mathematical	Preorder.toLE PartialOrder.toPreorder SemilatticeSup.toPartialOrder	SemilatticeSup.toMax	—	sup_eq_left
sup_of_le_right 📖	mathematical	Preorder.toLE PartialOrder.toPreorder SemilatticeSup.toPartialOrder	SemilatticeSup.toMax	—	sup_eq_right
sup_right_comm 📖	mathematical	—	SemilatticeSup.toMax	—	sup_assoc sup_comm
sup_right_idem 📖	mathematical	—	SemilatticeSup.toMax	—	sup_of_le_left
sup_sup_distrib_left 📖	mathematical	—	SemilatticeSup.toMax	—	sup_sup_sup_comm sup_idem
sup_sup_distrib_right 📖	mathematical	—	SemilatticeSup.toMax	—	sup_sup_sup_comm sup_idem
sup_sup_sup_comm 📖	mathematical	—	SemilatticeSup.toMax	—	sup_assoc sup_left_comm
toDual_inf 📖	mathematical	—	DFunLike.coe Equiv OrderDual EquivLike.toFunLike Equiv.instEquivLike OrderDual.toDual OrderDual.instSup	—	—
toDual_max 📖	mathematical	—	DFunLike.coe Equiv OrderDual EquivLike.toFunLike Equiv.instEquivLike OrderDual.toDual SemilatticeSup.toMax Lattice.toSemilatticeSup DistribLattice.toLattice instDistribLatticeOfLinearOrder OrderDual.instInf	—	—
toDual_min 📖	mathematical	—	DFunLike.coe Equiv OrderDual EquivLike.toFunLike Equiv.instEquivLike OrderDual.toDual SemilatticeInf.toMin Lattice.toSemilatticeInf DistribLattice.toLattice instDistribLatticeOfLinearOrder OrderDual.instSup	—	—
toDual_sup 📖	mathematical	—	DFunLike.coe Equiv OrderDual EquivLike.toFunLike Equiv.instEquivLike OrderDual.toDual OrderDual.instInf	—	—

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