Defs

📁 Source: Mathlib/Topology/MetricSpace/Pseudo/Defs.lean

Statistics

Metric	Count
Definitions ofDist, dist, evalDist, ball, closedBall, sphere, NNDist, nndist, toPseudoMetricSpace, toPseudoMetricSpaceOfDist, PseudoMetricSpace, edist, ofDistTopology, replaceBornology, replaceTopology, replaceUniformity, toBornology, toDist, toEDist, toNNDist, toPseudoEMetricSpace, toUniformSpace, pseudoMetricSpace, ofDist, instPseudoMetricSpaceAdditive, instPseudoMetricSpaceMultiplicative, instPseudoMetricSpaceOrderDual	27
Theorems exists_dist_lt, exists_dist_lt, of_forall_le_dist, ext, ext_iff, congr_dist, ball_disjoint_ball, ball_disjoint_closedBall, ball_eq_ball, ball_eq_ball', ball_eq_empty, ball_eq_singleton_of_subsingleton, ball_half_subset, ball_mem_nhds, ball_subset, ball_subset_ball, ball_subset_ball', ball_subset_closedBall, ball_subset_interior_closedBall, ball_union_sphere, ball_zero, boundedSpace_iff, boundedSpace_iff_edist, boundedSpace_iff_nndist, closedBall_diff_ball, closedBall_diff_sphere, closedBall_disjoint_ball, closedBall_disjoint_closedBall, closedBall_eq_bInter_ball, closedBall_eq_empty, closedBall_eq_singleton_of_subsingleton, closedBall_eq_sphere_of_nonpos, closedBall_mem_nhds, closedBall_mem_nhds_of_mem, closedBall_of_neg, closedBall_subset_ball, closedBall_subset_ball', closedBall_subset_closedBall, closedBall_subset_closedBall', closedEBall_coe, closedEBall_ofReal, continuousAt_iff, continuousAt_iff', continuousOn_iff, continuousOn_iff', continuousWithinAt_iff, continuousWithinAt_iff', continuous_iff, continuous_iff', denseRange_iff, dense_iff, dense_iff_iUnion_ball, dist_le_add_of_nonempty_closedBall_inter_closedBall, dist_lt_add_of_nonempty_ball_inter_ball, dist_lt_add_of_nonempty_ball_inter_closedBall, dist_lt_add_of_nonempty_closedBall_inter_ball, dist_mem_uniformity, eball_coe, eball_ofReal, eball_top, eball_top_eq_univ, emetric_ball, emetric_ball_nnreal, emetric_ball_top, emetric_closedBall, emetric_closedBall_nnreal, eventually_nhds_iff, eventually_nhds_iff_ball, eventually_nhds_prod_iff, eventually_prod_nhds_iff, exists_ball_subset_ball, exists_lt_mem_ball_of_mem_ball, forall_of_forall_mem_ball, forall_of_forall_mem_closedBall, iUnion_ball_nat, iUnion_ball_nat_succ, iUnion_closedBall_nat, iUnion_inter_closedBall_nat, isBounded_iff, isBounded_iff_eventually, isBounded_iff_exists_ge, isBounded_iff_nndist, isOpen_ball, isOpen_iff, isOpen_singleton_iff, mem_ball, mem_ball', mem_ball_comm, mem_ball_self, mem_closedBall, mem_closedBall', mem_closedBall_comm, mem_closedBall_self, mem_closure_iff, mem_closure_range_iff, mem_closure_range_iff_nat, mem_nhdsWithin_iff, mem_nhds_iff, mem_of_closed', mem_sphere, mem_sphere', mem_sphere_comm, mem_uniformity_dist, mk_uniformity_basis, mk_uniformity_basis_le, ne_of_mem_sphere, nhdsWithin_basis_ball, nhds_basis_ball, nhds_basis_ball_inv_nat_pos, nhds_basis_ball_inv_nat_succ, nhds_basis_ball_pow, nhds_basis_closedBall, nhds_basis_closedBall_pow, nonempty_ball, nonempty_closedBall, nonneg_of_mem_sphere, pos_of_mem_ball, sphere_disjoint_ball, sphere_eq_empty_of_neg, sphere_eq_empty_of_subsingleton, sphere_isEmpty_of_subsingleton, sphere_subset_ball, sphere_subset_closedBall, sphere_union_ball, tendsto_atTop, tendsto_atTop', tendsto_nhds, tendsto_nhdsWithin_nhds, tendsto_nhdsWithin_nhdsWithin, tendsto_nhds_nhds, toUniformSpace_eq, uniformContinuousOn_iff, uniformContinuousOn_iff_le, uniformContinuous_iff, uniformContinuous_iff_le, uniformSpace_eq_bot, uniformity_basis_dist, uniformity_basis_dist_inv_nat_pos, uniformity_basis_dist_inv_nat_succ, uniformity_basis_dist_le, uniformity_basis_dist_le_pow, uniformity_basis_dist_lt, uniformity_basis_dist_pow, uniformity_basis_dist_rat, uniformity_edist, uniformity_edist_aux, uniformity_eq_comap_nhds_zero, cobounded_sets, dist_comm, dist_eq_of_dist_zero, dist_self, dist_triangle, edist_dist, ext, ext_iff, replaceBornology_eq, replaceTopology_eq, replaceUniformity_eq, uniformity_dist, Icc_eq_closedBall, Ioo_eq_ball, ball_eq_Ioo, ball_zero_eq_Ioo, closedBall_eq_Icc, closedBall_zero_eq_Icc, dist_0_eq_abs, dist_eq, nndist_eq, nndist_eq', sub_le_dist, ofDist_aux, abs_dist, abs_dist_sub_le, coe_nndist, coe_nnreal_ennreal_nndist, dist_comm, dist_dist_dist_le, dist_dist_dist_le_left, dist_dist_dist_le_right, dist_edist, dist_le_coe, dist_lt_coe, dist_nndist, dist_nonneg, dist_self, dist_triangle, dist_triangle4, dist_triangle4_left, dist_triangle4_right, dist_triangle8, dist_triangle_left, dist_triangle_right, edist_dist, edist_le_coe, edist_le_ofReal, edist_lt_coe, edist_lt_ofReal, edist_lt_top, edist_ne_top, edist_nndist, nhds_comap_dist, nndist_comm, nndist_dist, nndist_edist, nndist_ofAdd, nndist_ofDual, nndist_ofMul, nndist_self, nndist_toAdd, nndist_toDual, nndist_toMul, nndist_triangle, nndist_triangle_left, nndist_triangle_right, swap_dist, tendsto_iff_dist_tendsto_zero, tendsto_iff_of_dist, tendsto_of_tendsto_of_dist, tendsto_uniformity_iff_dist_tendsto_zero	219
Total	246

Bornology

Definitions

Name	Category	Theorems
ofDist 📖	CompOp	—

Dense

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
exists_dist_lt 📖	mathematical	Dense UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace Real Real.instLT Real.instZero	Set Set.instMembership Dist.dist PseudoMetricSpace.toDist	—	exists_mem_open Metric.isOpen_ball

DenseRange

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
exists_dist_lt 📖	mathematical	DenseRange UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace Real Real.instLT Real.instZero	Dist.dist PseudoMetricSpace.toDist	—	Set.exists_range_iff Dense.exists_dist_lt

DiscreteTopology

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
of_forall_le_dist 📖	mathematical	Real Real.instLT Real.instZero Pairwise Real.instLE Dist.dist PseudoMetricSpace.toDist	DiscreteTopology UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace	—	Metric.uniformSpace_eq_bot UniformSpace.toTopologicalSpace_bot

Dist

Definitions

Name	Category	Theorems
dist 📖	CompOp	837 math math: EuclideanGeometry.Sphere.mul_dist_eq_abs_power, comap_dist_left_atTop_eq_cocompact, BoundedContinuousFunction.tietze_extension_step, Affine.Triangle.equilateral_iff_dist_01_eq_02_and_dist_01_eq_12, EuclideanGeometry.dist_smul_vadd_sq, dist_le_range_sum_dist, dist_triangle, Metric.cauchySeq_iff, EuclideanGeometry.sin_oangle_right_mul_dist_of_oangle_eq_pi_div_two, BoundedContinuousMapClass.map_bounded, BoundedContinuousFunction.dist_eq_iSup, segment_subset_closedBall_right, dist_midpoint_right, EuclideanGeometry.Sphere.isExtTangent_iff_dist_center, EuclideanGeometry.sin_oangle_right_of_oangle_eq_pi_div_two, MeasureTheory.MeasuredSets.real_sub_real_le_dist, ContractingWith.dist_fixedPoint_le, dist_vadd, ContinuousMap.dist_lt_iff, Metric.uniformContinuous_iff_le, Metric.continuousWithinAt_iff', EuclideanGeometry.dist_inversion_inversion, NormedAddGroup.dist_eq, Real.dist_mulExpNegMulSq_le_two_mul_sqrt, EuclideanGeometry.dist_eq_of_angle_eq_angle_of_angle_ne_pi, Wbtw.dist_add_dist, dist_smul_le, Metric.infDist_le_dist_of_mem, UpperHalfPlane.im_div_exp_dist_le, dist_sq_lineMap_lineMap_of_inner_eq_zero, EuclideanGeometry.law_sin, dist_partial_sum, LipschitzWith.dist_le_mul, Metric.diam_triple, MeasureTheory.LevyProkhorov.dist_probabilityMeasure_def, Nat.dist_cast_real, dist_triangle4_right, EuclideanGeometry.dist_div_tan_oangle_right_of_oangle_eq_pi_div_two, PseudoMetricSpace.dist_self, Affine.Simplex.dist_point_faceOppositeCentroid, Metric.equicontinuousAt_iff_pair, EuclideanGeometry.Sphere.secondInter_dist, EuclideanGeometry.Sphere.IsExtTangent.dist_center, dist_div_eq_dist_mul_left, dist_toDual, Metric.tendsto_atTop, dist_left_midpoint, dist_iteratedFDerivWithin_one, EuclideanGeometry.preimage_inversion_perpBisector_inversion, BoundedContinuousFunction.dist_le, UpperHalfPlane.dist_le_iff_dist_coe_center_le, ContinuousMap.dist_le_two_norm, IsCompact.exists_infDist_eq_dist, Tactic.ComputeAsymptotics.Seq.dist_cons_nil, dist_mul_self_left, PiCountable.min_dist_le_dist_pi, MeasureTheory.Lp.dist_def, Metric.comap_dist_left_atTop, Continuous.exists_contDiff_dist_le_of_forall_mem_ball_dist_le, cauchySeq_iff_tendsto_dist_atTop_0, dist_eq_norm, TopologicalSpace.Opens.CompleteCopy.dist_eq, Affine.Triangle.dist_point_faceOppositeCentroid, ContinuousMap.dist_le, NNRat.dist_eq, EuclideanGeometry.inversion_dist_center, EuclideanGeometry.dist_orthogonalProjection_eq_iff_oangle_eq, NNReal.tendsto_dist_agmSequences_atTop_zero, EuclideanGeometry.dist_eq_add_dist_iff_angle_eq_pi, Besicovitch.SatelliteConfig.hlast, Affine.Triangle.prod_dist_div_dist_eq_one_of_mem_line_of_mem_line, PNat.dist_eq, EuclideanGeometry.angle_eq_arctan_of_angle_eq_pi_div_two, Metric.dist_lt_add_of_nonempty_ball_inter_ball, EuclideanGeometry.Sphere.IsDiameter.dist_left_right, dist_le_norm_add_norm, CircleDeg1Lift.dist_map_zero_translationNumber_le, AntilipschitzWith.mul_le_dist, dist_eq_norm_sub, Rat.dist_eq, Metric.tendsto_nhds_nhds, exists_dist_slope_lt_pairwiseDisjoint_hasSum, dist_birkhoffSum_birkhoffSum_le, dist_sub_right, BoundedContinuousFunction.dist_toContinuousMap, EuclideanGeometry.dist_eq_abs_sub_dist_of_angle_eq_zero, EuclideanGeometry.inversion_mem_perpBisector_inversion_iff', coe_nndist, Similar.exists_pos_dist_eq, Besicovitch.SatelliteConfig.h, EuclideanGeometry.dist_eq_iff_eq_smul_rotation_pi_div_two_vadd_midpoint, dist_inv_inv₀, UniformSpace.Completion.uniformContinuous_dist, Metric.equicontinuousAt_iff, Continuous.exists_contDiff_approx_and_eqOn, convexOn_univ_dist, dist_sub_sub_le, BoxIntegral.Integrable.dist_integralSum_le_of_memBaseSet, Metric.tendsto_nhds, PiNat.dist_triangle_nonarch, ODE.FunSpace.dist_next_next, antilipschitzWith_iff_le_mul_dist, Metric.inseparable_iff, Unitization.dist_inr, Rat.dist_cast, LipschitzWith.le_add_mul, EuclideanGeometry.Sphere.dist_div_sin_oangle_div_two_eq_radius, PiLp.dist_eq_card, EuclideanGeometry.angle_le_iff_dist_le, WithLp.prod_dist_eq_of_L2, EuclideanGeometry.tan_oangle_right_of_oangle_eq_pi_div_two, EuclideanGeometry.dist_orthogonalProjection_eq_of_oangle_eq, Metric.uniformity_basis_dist_lt, signedDist_le_dist, EuclideanGeometry.dist_lt_of_sbtw_of_inner_eq_zero, AntilipschitzWith.le_mul_dist, EuclideanGeometry.inversion_vsub_center, EuclideanGeometry.dist_orthogonalProjection_eq_iff_angle_eq, similar_iff_exists_dist_eq, Affine.Triangle.dist_div_sin_angle_eq_two_mul_circumradius, EuclideanGeometry.oangle_right_eq_arcsin_of_oangle_eq_pi_div_two, NNReal.dist_agmSequences_fst_snd, Metric.comap_dist_right_atTop, dist_left_pointReflection, Metric.uniformEquicontinuous_iff, Metric.tendsto_atTop', UpperHalfPlane.dist_eq_iff_eq_sinh, EuclideanGeometry.oangle_right_eq_arctan_of_oangle_eq_pi_div_two, Congruent.pairwise_dist_eq, NormedAddCommGroup.dist_eq, MeasureTheory.Lp.dist_edist, dist_pair_smul, dist_ofDual, AffineIsometryEquiv.dist_pointReflection_fixed, Metric.PiNatEmbed.dist_def, MeasureTheory.L1.dist_eq_integral_dist, dist_eq_norm_div', UpperHalfPlane.dist_log_im_le, EuclideanGeometry.dist_of_mem_subset_sphere, uniformContinuous_dist, ContinuousMap.dist_apply_le_dist, Set.Finite.infsep_of_nontrivial, Metric.continuous_iff, DifferentiableWithinAt.dist, exists_dist_eq, IsUltrametricDist.dist_triangle_max, EuclideanGeometry.tan_oangle_left_mul_dist_of_oangle_eq_pi_div_two, UpperHalfPlane.im_le_im_mul_exp_dist, dist_div_div_le, CircleDeg1Lift.dist_map_map_zero_lt, Affine.Simplex.ExcenterExists.dist_excenter, EuclideanSpace.dist_single_same, dist_left_midpoint_eq_dist_right_midpoint, Metric.mem_thickening_iff, dist_triangle4, EuclideanGeometry.mul_dist_eq_mul_dist_of_cospherical, dist_vsub_cancel_left, UpperHalfPlane.dist_eq_iff_eq_sq_sinh, Finset.coe_infsep_of_offDiag_nonempty, ZeroAtInftyContinuousMap.dist_toBCF_eq_dist, Set.Nontrivial.infsep_of_fintype, PseudoMetricSpace.le_two_mul_dist_ofPreNNDist, Metric.infDist_inter_closedBall_of_mem, MeasureTheory.AEStronglyMeasurable.dist, edist_le_ofReal, convexOn_dist, dist_self_sub_right, LipschitzWith.dist_left, MeasureTheory.tendstoInMeasure_iff_measureReal_dist, EuclideanGeometry.dist_orthogonalProjection_eq_of_two_zsmul_oangle_eq, zero_eq_dist, Set.Finite.infsep, dist_nonneg, ContractingWith.aposteriori_dist_iterate_fixedPoint_le, Affine.Simplex.dist_sq_eq_dist_orthogonalProjection_sq_add_dist_orthogonalProjection_sq, Similar.exists_dist_eq, EuclideanGeometry.dist_sq_eq_dist_sq_add_dist_sq_sub_two_mul_dist_mul_dist_mul_cos_angle, AddOpposite.dist_unop, EuclideanGeometry.Sphere.power_pos_iff_radius_lt_dist_center, continuous_dist, Complex.dist_self_conj, ODE.FunSpace.dist_iterate_iterate_next_le_of_lipschitzWith, EuclideanGeometry.mul_dist_eq_mul_dist_of_cospherical_of_angle_eq_zero, GromovHausdorff.dist_ghDist, edist_lt_ofReal, Affine.Triangle.dist_circumcenter_reflection_orthocenter, dist_ofAdd, NormedDivisionRing.dist_eq, SeminormedAddCommGroup.dist_eq, Metric.ball_eq_ball, ContinuousLinearMap.exists_approx_preimage_norm_le, dist_vadd_cancel_right, UpperHalfPlane.dist_triangle, Affine.Simplex.ExcenterExists.dist_excenter_eq_dist_excenter, abs_dist_sub_le, dist_birkhoffAverage_apply_birkhoffAverage, BoundedContinuousFunction.dist_eq, Metric.tendsto_nhdsWithin_nhds, Real.dist_right_le_of_mem_uIcc, UpperHalfPlane.dist_of_re_eq, dist_eq_norm', dist_le_zero, Set.Nontrivial.infsep_eq_iInf, dist_lineMap_left, PseudoMetricSpace.dist_ofPreNNDist, Tactic.ComputeAsymptotics.Seq.dist_cons_cons_eq_one, EuclideanGeometry.preimage_inversion_perpBisector, dist_le_coe, abs_dist_sub_le_dist_mul_mul, ULift.dist_eq, dist_midpoint_midpoint_le, Metric.toUniformSpace_eq, EuclideanGeometry.dist_div_tan_angle_of_angle_eq_pi_div_two, BoxIntegral.Integrable.dist_integralSum_integral_le_of_memBaseSet, EuclideanGeometry.dist_eq_add_dist_of_angle_eq_pi, MeasureTheory.tendstoInMeasure_iff_dist, Inseparable.dist_eq_zero, ContractingWith.apriori_dist_iterate_fixedPoint_le, Metric.uniformity_basis_dist, UpperHalfPlane.cosh_dist, Wbtw.dist_le_max_dist, Tactic.ComputeAsymptotics.Seq.dist_eq_one_of_head, Continuous.dist, UniformSpace.Completion.dist_eq, PseudoMetricSpace.dist_triangle, NonUnitalSeminormedRing.dist_eq, Continuous.exists_contMDiff_approx, PiNat.dist_triangle, EuclideanGeometry.Sphere.dist_sq_eq_mul_dist_of_tangent_and_secant, EuclideanGeometry.Sphere.IsTangentAt.power_eq_dist_sq, Metric.uniformity_basis_dist_rat, convexHull_exists_dist_ge, UpperHalfPlane.dist_coe_center, NormedCommGroup.dist_eq, Int.dist_eq', EuclideanGeometry.Sphere.dist_div_sin_oangle_eq_two_mul_radius, PiLp.dist_eq_of_L1, dist_right_midpoint, CircleDeg1Lift.transnumAuxSeq_dist_lt, dist_center_homothety, dist_toAdd, Metric.uniformity_basis_dist_inv_nat_succ, BoxIntegral.Integrable.dist_integralSum_sum_integral_le_of_memBaseSet, Metric.isUniformInducing_iff, Metric.dist_le_infDist_add_diam, Prod.dist_eq, MeasureTheory.Lp.dist_eq_norm, Metric.boundedSpace_iff, Metric.tendsto_dist_left_atTop_iff, EuclideanGeometry.image_inversion_perpBisector, Set.infsep_eq_iInf, lipschitz_with_lipschitz_const_mul, Complex.dist_le_mul_div_pow_of_mapsTo_ball_of_isLittleO, ContinuousMap.dist_lt_iff_of_nonempty, PiLp.dist_pseudoMetricSpaceToPi, dist_eq_norm_vsub', UpperHalfPlane.lt_dist_iff_lt_dist_coe_center, WithLp.dist_snd_le, PseudoMetricSpace.dist_ofPreNNDist_le, dist_mul_left, dist_triangle_right, Complex.dist_le_dist_of_mapsTo_ball, PiLp.dist_eq_iSup, Metric.tendsto_dist_left_cobounded_atTop, Int.dist_cast_rat, Set.infsep_pair, EuclideanGeometry.Sphere.IsTangentAt.radius_lt_dist_center, similar_iff_exists_pairwise_dist_eq, dist_birkhoffAverage_birkhoffAverage, EuclideanGeometry.angle_lt_iff_dist_lt, TopologicalSpace.Opens.CompleteCopy.dist_val_le_dist, Affine.Triangle.circumsphere_eq_of_dist_of_oangle, AffineIsometryEquiv.dist_pointReflection_self, BoxIntegral.Box.dist_le_distortion_mul, AffineIsometryEquiv.dist_pointReflection_self_real, UpperHalfPlane.dist_lt_iff_dist_coe_center_lt, Nat.dist_eq, PiNat.lipschitz_with_one_iff_forall_dist_image_le_of_mem_cylinder, EuclideanGeometry.image_inversion_sphere_dist_center, EuclideanGeometry.dist_div_sin_oangle_left_of_oangle_eq_pi_div_two, BoundedContinuousFunction.dist_lt_iff_of_nonempty_compact, Set.le_edist_of_le_infsep, dist_right_pointReflection, WithLp.prod_dist_eq_sup, Metric.uniformContinuousOn_iff, PiNat.mem_cylinder_iff_dist_le, Set.Nontrivial.infsep_lt_iff, ContractingWith.dist_le_mul, Metric.tendsto_dist_right_cobounded_atTop, Tactic.ComputeAsymptotics.Seq.dist_cons_cons, UpperHalfPlane.dist_self_center, LinearIsometry.dist_map, dist_lineMap_right, CircleDeg1Lift.dist_map_zero_lt_of_semiconj, EuclideanGeometry.dist_center_eq_dist_center_of_mem_sphere', dist_iteratedFDerivWithin_zero, dist_triangle_left, LipschitzWith.dist_iterate_succ_le_geometric, Metric.isBounded_iff, dist_inv_inv, EuclideanGeometry.preimage_inversion_sphere_dist_center, Set.infsep_of_fintype, Metric.mem_closure_iff, PiCountable.dist_summable, Affine.Triangle.dist_orthocenter_reflection_circumcenter, dist_add_self_left, Subtype.dist_eq, EuclideanGeometry.cospherical_def, Besicovitch.SatelliteConfig.inter', PseudoMetricSpace.dist_comm, SeminormedRing.dist_eq, EuclideanGeometry.cos_oangle_left_mul_dist_of_oangle_eq_pi_div_two, dist_comm, Metric.tendsto_nhdsWithin_nhdsWithin, LinearIsometryEquiv.dist_map, PNat.dist_coe, dist_pi_le_iff, dist_nndist, Affine.Triangle.dist_div_sin_oangle_eq_two_mul_circumradius, EuclideanGeometry.dist_orthogonalProjection_eq_dist_iff_eq_of_mem, dist_triangle_max, NormedField.dist_eq, Filter.Tendsto.dist, Real.dist_le_of_mem_Icc, AffineSubspace.abs_signedInfDist_eq_dist_of_mem_affineSpan_insert, EuclideanGeometry.Sphere.dist_div_cos_oangle_center_div_two_eq_radius, EuclideanGeometry.dist_eq_abs_sub_dist_iff_angle_eq_zero, SimpleGraph.UnitDistEmbedding.unit_dist, Complex.dist_le_dist_of_mapsTo_ball_self, EuclideanGeometry.sin_angle_div_dist_eq_sin_angle_div_dist, EuclideanGeometry.Sphere.power_neg_iff_dist_center_lt_radius, Metric.dist_lt_add_of_nonempty_closedBall_inter_ball, Tactic.ComputeAsymptotics.Seq.dist_eq_two_inv_pow, Tactic.ComputeAsymptotics.Seq.Stream'.dist_le_one, Metric.continuous_iff', Set.Finite.infsep_exists_of_nontrivial, dist_self_div_right, dist_homothety_self, BoundedContinuousFunction.dist_coe_le_dist, Complex.dist_le_div_mul_dist_of_mapsTo_ball, ContDiffWithinAt.dist, Complex.dist_of_im_eq, Affine.Simplex.dist_incenter_eq_dist_incenter, Affine.Triangle.prod_dist_eq_prod_dist_of_mem_line_of_mem_line, UpperHalfPlane.dist_eq, dist_prod_same_left, nhds_comap_dist, Tactic.ComputeAsymptotics.Seq.dist_nil_cons, SeminormedGroup.dist_eq, Affine.Simplex.exists_forall_dist_eq_iff_exists_excenterExists_and_eq_excenter, WithLp.dist_toLp_snd, isometry_iff_dist_eq, dist_single_single, dist_self_homothety, Real.dist_le_of_mem_uIcc, Metric.le_infDist, MulOpposite.dist_unop, EuclideanGeometry.dist_div_sin_angle_of_angle_eq_pi_div_two, Isometry.preimage_setOf_dist, dist_mulIndicator, dist_pi_lt_iff, inner_vsub_vsub_right_eq_dist_sq_left_iff, Affine.Simplex.dist_point_centroid, Finset.coe_infsep, dist_vsub_cancel_right, dist_prod_same_right, dist_self_mul_left, Nat.pairwise_one_le_dist, dist_mono_left_pi, MeasureTheory.LevyProkhorov.dist_def, dist_vadd_left, Nat.dist_cast_rat, Metric.infDist_singleton, UpperHalfPlane.dist_eq_iff_dist_coe_center_eq, dist_self_mul_right, Metric.mem_closedBall', UniformFun.dist_le, Metric.mem_closure_range_iff, dist_add_add_le, Metric.mem_ball, EuclideanGeometry.cos_oangle_left_of_oangle_eq_pi_div_two, EuclideanGeometry.dist_sq_eq_dist_orthogonalProjection_sq_add_dist_orthogonalProjection_sq, PseudoMetricSpace.uniformity_dist, Metric.continuousAt_iff', MulOpposite.dist_op, dist_one, CircleDeg1Lift.dist_pow_map_zero_mul_translationNumber_le, PiLp.dist_apply_le, UpperHalfPlane.cmp_dist_eq_cmp_dist_coe_center, WithLp.prod_dist_eq_add, Metric.exists_subseq_bounded_of_cauchySeq, EuclideanGeometry.dist_le_of_wbtw_of_mem_perpBisector, EuclideanGeometry.oangle_left_eq_arccos_of_oangle_eq_pi_div_two, EuclideanGeometry.dist_lt_of_sbtw_of_mem_perpBisector, segment_subset_closedBall_left, Complex.dist_eq, tendsto_uniformity_iff_dist_tendsto_zero, Affine.Simplex.dist_circumcenter_eq_circumradius, dist_self, EuclideanGeometry.cos_angle_of_angle_eq_pi_div_two, DenseRange.exists_dist_lt, Metric.mem_sphere, dist_vadd_right, EuclideanGeometry.sin_angle_of_angle_eq_pi_div_two, Metric.continuousWithinAt_iff, dist_add_dist_eq_iff, Metric.uniformity_basis_dist_le, UpperHalfPlane.le_dist_coe, Metric.mk_uniformity_basis_le, EuclideanGeometry.inversion_def, EuclideanGeometry.oangle_left_eq_arcsin_of_oangle_eq_pi_div_two, GromovHausdorff.ghDist_le_nonemptyCompacts_dist, Metric.diam_pair, dist_pi_eq_iff, BoundedContinuousFunction.dist_zero_of_empty, dist_neg, Affine.Simplex.dist_circumcenter_eq_circumradius', Metric.mem_of_closed', LipschitzOnWith.le_add_mul, EuclideanGeometry.exists_dist_eq_circumradius_of_subset_insert_orthocenter, Metric.isBounded_image_iff, IsBoundedSMul.dist_pair_smul', Metric.exists_dist_lt_of_hausdorffDist_lt, dist_homothety_center, EuclideanGeometry.sin_angle_mul_dist_eq_sin_angle_mul_dist, EuclideanGeometry.oangle_left_eq_arctan_of_oangle_eq_pi_div_two, abs_signedDist_eq_dist_iff_vsub_mem_span, EuclideanGeometry.dist_div_tan_oangle_left_of_oangle_eq_pi_div_two, WithLp.prod_dist_eq_of_L1, WithLp.prod_dist_eq_card, tendsto_dist_left_cocompact_atTop, EuclideanGeometry.tan_angle_of_angle_eq_pi_div_two, disjoint_ball_closedBall_iff, UpperHalfPlane.le_dist_iff_le_dist_coe_center, EuclideanGeometry.Sphere.dist_div_cos_oangle_center_eq_two_mul_radius, Int.dist_cast_real, cauchySeq_iff_le_tendsto_0, Delone.DeloneSet.packingRadius_lt_dist_of_mem_ne, LipschitzWith.dist_right, dist_zero_left, DomMulAct.dist_smul_Lp, PiNat.dist_eq_of_ne, EuclideanGeometry.mul_dist_add_mul_dist_eq_mul_dist_of_cospherical, ODE.FunSpace.exists_forall_closedBall_funSpace_dist_le_mul, dist_sub_eq_dist_add_left, Metric.dist_le_diam_of_mem, ContractingWith.dist_inequality, AffineIsometryEquiv.dist_map, isProperMap_dist, EuclideanGeometry.dist_eq_dist_mul_sin_angle_div_sin_angle, PiLp.dist_toLp_single_same, EuclideanGeometry.dist_reflection_eq_of_mem, signedDist_vsub_self_rev, EuclideanGeometry.Sphere.dist_orthogonalProjection_eq_radius_iff_isTangent, BoundedContinuousFunction.dist_le_iff_of_nonempty, EuclideanGeometry.mem_sphere, EuclideanGeometry.angle_eq_arccos_of_angle_eq_pi_div_two, UpperHalfPlane.dist_comm, UpperHalfPlane.dist_center_dist, EuclideanGeometry.dist_reflection, dist_eq_norm_sub', dist_birkhoffSum_apply_birkhoffSum, EuclideanGeometry.mul_dist_le_mul_dist_add_mul_dist, dist_sq_of_inner_eq_zero, Metric.uniformity_basis_dist_pow, dist_one_left, MeasureTheory.L1.dist_def, BoundedContinuousFunction.norm_def, IsometryClass.dist_eq, EuclideanGeometry.tan_oangle_right_mul_dist_of_oangle_eq_pi_div_two, edist_dist, UpperHalfPlane.dist_le_dist_coe_div_sqrt, PiLp.dist_sq_eq_of_L2, Set.Nontrivial.infsep_exists_of_finite, signedDist_vsub_self, EuclideanGeometry.dist_eq_iff_dist_orthogonalProjection_eq, EuclideanGeometry.Sphere.power_nonneg_iff_radius_le_dist_center, LipschitzOnWith.iff_le_add_mul, Int.dist_eq, lipschitzWith_iff_dist_le_mul, dist_partial_sum_le_of_le_geometric, AffineSubspace.mem_perpBisector_iff_dist_eq', EuclideanGeometry.cos_angle_mul_dist_of_angle_eq_pi_div_two, dist_lt_coe, dist_toMul, EuclideanGeometry.Sphere.power_nonpos_iff_dist_center_le_radius, Metric.infDist_lt_iff, EuclideanGeometry.dist_orthogonalProjection_eq_infDist, dist_pointReflection_right, EuclideanGeometry.tan_angle_mul_dist_of_angle_eq_pi_div_two, EuclideanGeometry.mem_sphere', Real.dist_eq, Set.infsep_triple, dist_sub_left, EuclideanGeometry.sin_angle_mul_dist_of_angle_eq_pi_div_two, Metric.cauchy_iff, Continuous.exists_contMDiff_approx_and_eqOn, dist_pos, EuclideanGeometry.inner_weightedVSub, dist_smul, CantorScheme.VanishingDiam.dist_lt, EuclideanGeometry.dist_eq_of_two_zsmul_oangle_eq, dist_triangle4_left, disjoint_closedBall_closedBall_iff, ContractingWith.dist_le_of_fixedPoint, EuclideanGeometry.cospherical_iff_exists_mem_of_complete, Set.infsep_le_dist_of_mem, ODE.FunSpace.dist_iterate_next_le, Real.dist_le_of_mem_Icc_01, EuclideanGeometry.dist_orthogonalProjection_eq_zero_iff, EuclideanGeometry.dist_sq_smul_orthogonal_vadd_smul_orthogonal_vadd, BoxIntegral.integrable_iff_cauchy_basis, EuclideanGeometry.Sphere.isDiameter_iff_mem_and_mem_and_dist, EuclideanGeometry.exists_dist_eq_iff_exists_dist_orthogonalProjection_eq, Complex.dist_conj_conj, UniformSpace.Completion.uniformity_dist, Real.dist_0_eq_abs, BoundedVariationOn.dist_le, dist_eq_norm_div, dist_le_dist_of_le_pi, EuclideanGeometry.angle_eq_arcsin_of_angle_eq_pi_div_two, dist_mul_mul_le, Affine.Triangle.dist_circumcenter_reflection_orthocenter_finset, dist_vadd_cancel_left, abs_dist, MeasureTheory.LocallyIntegrable.exists_contDiff_dist_le_of_forall_mem_ball_dist_le, ODE.FunSpace.dist_iterate_next_iterate_next_le, UpperHalfPlane.cosh_half_dist, EuclideanGeometry.Sphere.mul_dist_eq_zero_of_mem_sphere, dist_vsub_vsub_le, LipschitzWith.iff_le_add_mul, dist_self_sub_left, LipschitzOnWith.dist_le_mul, IsometryEquiv.dist_eq, Real.dist_le_of_mem_pi_Icc, EuclideanGeometry.triangle_congruent_iff_dist_eq, inner_vsub_vsub_left_eq_dist_sq_right_iff, Differentiable.dist, Affine.Simplex.Equilateral.dist_eq, UpperHalfPlane.exp_half_dist, ContDiffAt.dist, TensorProduct.dist_tmul_le, EuclideanGeometry.dist_div_cos_oangle_right_of_oangle_eq_pi_div_two, dist_div_eq_dist_mul_right, MeasureTheory.MeasuredSets.dist_def, IsBoundedSMul.dist_smul_pair', Metric.Sum.dist_eq, NonUnitalNormedRing.dist_eq, EuclideanGeometry.dist_le_of_wbtw_of_inner_eq_zero, dist_left_lineMap, Isometry.dist_eq, Metric.infDist_le_infDist_add_dist, Dense.exists_dist_lt, WithLp.dist_pseudoMetricSpaceToProd, Measurable.dist, dist_indicator, ContDiff.dist, EuclideanGeometry.hasFDerivAt_inversion, dist_div_norm_sq_smul, lipschitzOnWith_iff_dist_le_mul, EuclideanGeometry.dist_div_cos_oangle_left_of_oangle_eq_pi_div_two, EuclideanGeometry.inversion_mem_perpBisector_inversion_iff, Metric.mem_closure_range_iff_nat, EuclideanGeometry.dist_div_cos_angle_of_angle_eq_pi_div_two, BoundedContinuousFunction.dist_extend_extend, dist_partial_sum', EuclideanGeometry.dist_of_mem_subset_mk_sphere, disjoint_ball_ball_iff, abs_dist_sub_le_dist_add_add, UniformSpace.Completion.dist_comm, BoundedContinuousFunction.dist_set_exists, dist_neg_neg, dist_pi_def, ext_iff, PiNat.dist_nonneg, EuclideanGeometry.Sphere.IsTangentAt.dist_sq_eq_of_mem, UpperHalfPlane.sinh_half_dist_add_dist, Metric.denseRange_iff, AffineSubspace.mem_perpBisector_iff_dist_eq, Similar.exists_pairwise_dist_eq, Metric.inductiveLimitDist_eq_dist, dist_eq_zero, UniformContinuous.dist, Complex.dist_mk, EuclideanGeometry.mul_dist_eq_mul_dist_of_cospherical_of_angle_eq_pi, Metric.Sigma.one_le_dist_of_ne, Continuous.exists_contDiff_approx, tendsto_dist_right_cocompact_atTop, dist_add_right, BoundedContinuousFunction.bounded, dist_norm_norm_le', dist_anti_right_pi, DifferentiableOn.dist, dist_dist_dist_le, dist_smul₀, EuclideanSpace.dist_eq, Metric.uniformity_eq_comap_nhds_zero, BoundedContinuousFunction.abs_diff_coe_le_dist, Affine.Simplex.abs_signedInfDist_eq_dist_of_mem_affineSpan_range, EuclideanGeometry.sin_oangle_left_of_oangle_eq_pi_div_two, convexHull_exists_dist_ge2, ZeroAtInftyContinuousMap.bounded, dist_div_left, Metric.uniformContinuousOn_iff_le, absolutelyContinuousOnInterval_iff, Nat.dist_coe_int, dist_le_norm_add_norm', Real.sub_le_dist, Metric.exists_subseq_summable_dist_of_cauchySeq, ULift.dist_up_up, dist_add_left, EuclideanGeometry.Sphere.isIntTangent_iff_dist_center, SeminormedCommGroup.dist_eq, dist_lt_dist_add_dist_iff, EuclideanGeometry.dist_lt_of_angle_lt, IsClosed.exists_infDist_eq_dist, dist_prod_prod_le, EuclideanGeometry.Sphere.mem_coe', PiLp.dist_eq_of_L2, nndist_dist, dist_sub_eq_dist_add_right, dist_pi_const, Complex.dist_conj_comm, Metric.controlled_of_isUniformEmbedding, dist_pi_const_le, cauchySeq_bdd, EuclideanGeometry.oangle_right_eq_arccos_of_oangle_eq_pi_div_two, Metric.isUniformEmbedding_iff, dist_pointReflection_left, Affine.Triangle.dist_div_sin_angle_div_two_eq_circumradius, dist_eq_norm_vsub, Hamming.dist_eq_hammingDist, Sbtw.dist_lt_max_dist, Metric.tendstoUniformlyOnFilter_iff, Metric.mem_closedBall, EuclideanGeometry.Sphere.isTangentAt_iff_dist_sq_eq_power, KuratowskiEmbedding.embeddingOfSubset_dist_le, EuclideanSpace.dist_sq_eq, EuclideanGeometry.law_cos, EuclideanGeometry.sin_oangle_left_mul_dist_of_oangle_eq_pi_div_two, Fin.dist_insertNth_insertNth, IsUltrametricDist.dist_eq_max_of_dist_ne_dist, UpperHalfPlane.dist_coe_le, Tactic.ComputeAsymptotics.Seq.FriendlyOperation.dist_le, EuclideanGeometry.dist_affineCombination, similar_iff_exists_pos_pairwise_dist_eq, signedDist_eq_dist_iff_vsub_mem_span, IsCompact.exists_mem_frontier_infDist_compl_eq_dist, HolderOnWith.dist_le, EuclideanGeometry.dist_smul_vadd_eq_dist, dist_birkhoffAverage_birkhoffAverage_le, ConvexBody.hausdorffDist_coe, Metric.Snowflaking.dist_ofSnowflaking_ofSnowflaking, AffineSubspace.mem_perpBisector_iff_inner_eq, SeparationQuotient.dist_mk, HasCompactSupport.exists_simpleFunc_approx_of_prod, UniformContinuous.exists_contDiff_dist_le, Tactic.ComputeAsymptotics.Seq.dist_eq_half_of_head, dist_self_add_right, EuclideanGeometry.dist_sq_mul_dist_add_dist_sq_mul_dist, Metric.continuousAt_iff, Metric.mem_sphere', NormedRing.dist_eq, dist_midpoint_midpoint_le', dist_algebraMap, UpperHalfPlane.sinh_half_dist, dist_self_div_left, EuclideanGeometry.cos_oangle_right_mul_dist_of_oangle_eq_pi_div_two, NNReal.dist_eq, UpperHalfPlane.dist_le_iff_le_sinh, AddOpposite.dist_op, Dilation.dist_eq, dist_mono_right_pi, UniformSpace.Completion.dist_triangle, dist_dist_dist_le_left, dist_right_lineMap, Metric.hausdorffDist_singleton, EuclideanGeometry.dist_inversion_mul_dist_center_eq, BoundedContinuousFunction.coe_le_coe_add_dist, EuclideanGeometry.dist_div_sin_oangle_right_of_oangle_eq_pi_div_two, EuclideanGeometry.Sphere.IsTangentAt.dist_eq_of_mem_of_mem, Metric.continuousOn_iff', UpperHalfPlane.dist_coe_center_sq, Metric.dist_le_diam_of_mem', Tactic.ComputeAsymptotics.Seq.dist_le_one, dist_self_add_left, Metric.exists_mem_closure_infDist_eq_dist, hofer, Similar.exists_pos_pairwise_dist_eq, dist_div_right, congruent_iff_dist_eq, HolderWith.dist_le, PiCountable.dist_eq_tsum, dist_ofMul, BoundedContinuousFunction.map_bounded', UpperHalfPlane.cosh_dist', EuclideanGeometry.dist_center_inversion, dist_edist, Besicovitch.SatelliteConfig.inter, EuclideanGeometry.dist_sq_add_dist_sq_eq_two_mul_dist_midpoint_sq_add_half_dist_sq, EuclideanGeometry.cospherical_iff_exists_mem_of_finiteDimensional, Metric.Sigma.dist_triangle, Metric.isBounded_iff_exists_ge, EuclideanGeometry.Sphere.IsIntTangent.dist_center, KuratowskiEmbedding.embeddingOfSubset_coe, Metric.infDist_eq_iInf, Metric.isGLB_infDist, inner_vsub_vsub_left_eq_dist_sq_left_iff, BoxIntegral.hasIntegral_iff, UpperHalfPlane.tanh_half_dist, abs_signedDist_le_dist, EuclideanGeometry.tan_oangle_left_of_oangle_eq_pi_div_two, dist_midpoint_left, Metric.continuousOn_iff, Metric.cauchySeq_iff', dist_add_self_right, EuclideanGeometry.Sphere.IsTangent.radius_le_dist_center, Affine.Triangle.dist_div_sin_oangle_div_two_eq_circumradius, dist_zero_right, EuclideanGeometry.dist_inversion_center, dist_algebraMap', dist_dist_dist_le_right, Affine.Simplex.dist_incenter, EuclideanGeometry.inversion_dist_center', DomAddAct.dist_vadd_Lp, dist_le_pi_dist, ContinuousMap.uniform_continuity, dist_inf_sup_pi, UniformFun.dist_def, dist_add_dist_of_mem_segment, Metric.uniformity_basis_dist_le_pow, AbsoluteValue.Completion.extensionEmbedding_dist_eq_of_comp, dist_smul_add_one_sub_smul_le, SeminormedAddGroup.dist_eq, Metric.uniformContinuous_iff, dist_sum_sum_le, dist_norm_norm_le, Real.dist_mulExpNegMulSq_le_dist, tendsto_nhds_unique_dist, tendsto_iff_dist_tendsto_zero, uniformity_basis_dist_pow_of_lt_one, BoundedContinuousFunction.dist_le_two_norm, MeasureTheory.StronglyMeasurable.dist, PiNat.dist_self, dist_zero, ContinuousLinearMap.dist_le_opNorm, EuclideanGeometry.inversion_eq_lineMap, Metric.dist_lt_add_of_nonempty_ball_inter_closedBall, dist_pi_le_iff', swap_dist, Complex.dist_of_re_eq, MeasureTheory.Lp.edist_dist, Affine.Triangle.dist_orthocenter_reflection_circumcenter_finset, Congruent.dist_eq, dist_sq_lineMap_of_inner_eq_zero, Metric.diam_union, BoundedContinuousFunction.dist_mkOfCompact, Metric.uniformCauchySeqOn_iff, EuclideanGeometry.dist_orthogonalProjection_line_eq_iff_two_zsmul_oangle_eq, dist_le_Ico_sum_dist, EuclideanGeometry.cos_oangle_right_of_oangle_eq_pi_div_two, EuclideanGeometry.dist_orthogonalProjection_line_eq_of_two_zsmul_oangle_eq, properSpace_iff_isProperMap_dist, ContinuousMap.dist_le_iff_of_nonempty, CircleDeg1Lift.dist_map_zero_lt_of_semiconjBy, PseudoMetricSpace.edist_dist, dist_inv, Metric.uniformSpace_eq_bot, Int.pairwise_one_le_dist, NNReal.dist_gm_am_le, BoundedContinuousFunction.dist_lt_iff_of_compact, dist_smul_pair, AffineIsometryEquiv.dist_pointReflection_self', WithLp.dist_toLp_fst, dist_vadd_vadd_le, PiNat.dist_le_one, PiNat.dist_comm, Metric.Snowflaking.dist_toSnowflaking_toSnowflaking, congruent_iff_pairwise_dist_eq, ODE.FunSpace.dist_iterate_next_apply_le, dist_triangle8, AEMeasurable.dist, Set.Nontrivial.le_infsep_iff, disjoint_closedBall_ball_iff, UniformSpace.Completion.uniformity_dist', EuclideanGeometry.Sphere.dist_orthogonalProjection_eq_radius_iff_isTangentAt, EuclideanGeometry.dist_sq_eq_dist_sq_add_dist_sq_iff_angle_eq_pi_div_two, Metric.tendsto_dist_right_atTop_iff, MeasureTheory.dist_indicatorConstLp_eq_norm, dist_one_right, Complex.dist_conj_self, UniformSpace.Completion.dist_self, BoundedContinuousFunction.dist_le_two_norm', similar_iff_exists_pos_dist_eq, EuclideanGeometry.dist_set_eq_iff_dist_orthogonalProjection_eq, Metric.uniformity_basis_dist_inv_nat_pos, Metric.isBounded_range_iff, DifferentiableAt.dist, BoxIntegral.Integrable.dist_integralSum_sum_integral_le_of_memBaseSet_of_iUnion_eq, NormedGroup.dist_eq, AffineIsometry.dist_map, Metric.ball_eq_ball', isClosedMap_dist, inner_vsub_vsub_right_eq_dist_sq_right_iff, PiLp.dist_eq_sum, MeasureTheory.LevyProkhorov.dist_finiteMeasure_def, ContDiffOn.dist, dist_mul_right, Real.dist_left_le_of_mem_uIcc, EuclideanGeometry.Sphere.IsDiameter.dist_left_right_div_two, dist_lineMap_lineMap, lipschitz_with_lipschitz_const_add, Affine.Triangle.dist_point_centroid, NormedAddTorsor.dist_eq_norm', Delone.DeloneSet.exists_dist_le_coveringRadius, dist_mul_self_right, dist_anti_left_pi, ContinuousMap.dist_eq_iSup, UniformSpace.Completion.continuous_dist, Metric.NonemptyCompacts.dist_eq, LipschitzWith.dist, Metric.dist_le_add_of_nonempty_closedBall_inter_closedBall, AbsolutelyContinuousOnInterval.hasBasis_totalLengthFilter, Affine.Triangle.equilateral_iff_dist_eq_and_dist_eq, Complex.dist_eq_re_im, Metric.mem_ball', Metric.Sigma.dist_ne, Metric.isUniformEmbedding_iff', WithLp.dist_fst_le, Metric.mk_uniformity_basis, continuous_iff_continuous_dist, EuclideanGeometry.dist_center_eq_dist_center_of_mem_sphere, Metric.exists_dist_lt_of_hausdorffDist_lt', Metric.Sigma.dist_same, Metric.dist_mem_uniformity, exists_mem_frontier_infDist_compl_eq_dist, measurable_dist

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
ext 📖	—	dist	—	—	—
ext_iff 📖	mathematical	—	dist	—	ext

Filter.Tendsto

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
congr_dist 📖	—	Filter.Tendsto nhds UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace Real Dist.dist PseudoMetricSpace.toDist Real.pseudoMetricSpace Real.instZero	—	—	congr_uniformity tendsto_uniformity_iff_dist_tendsto_zero

Mathlib.Meta.Positivity

Definitions

Name	Category	Theorems
evalDist 📖	CompOp	—

Metric

Definitions

Name	Category	Theorems
ball 📖	CompOp	352 math math: Isometry.preimage_ball, Unitary.openPartialHomeomorph_source, MeasureTheory.exists_pos_preimage_ball, continuousSMul_sphere_ball, ball_sub, isPreconnected_ball, thickening_eq_biUnion_ball, isBounded_ball, ball_disjoint_ball, disjoint_ball_infDist, mul_ball, smul_ball, isBounded_iff_subset_ball, ExistsContDiffBumpBase.u_support, SmoothBumpFunction.support_eq_symm_image, ContinuousLinearMap.sSup_unit_ball_eq_norm, lebesgue_number_lemma_of_metric_sUnion, closedBall_eq_bInter_ball, hasAntitoneBasis_cobounded_compl_ball, contractibleSpace_ball, ball_subset_closedBall, MeasureTheory.aecover_ball, singleton_sub_ball, exists_isLocalMin_mem_ball, Seminorm.ball_smul_closedBall, ContDiffBump.support_normed_eq, NormedSpace.isBounded_iff_subset_smul_ball, Real.Ioo_eq_ball, ball_mul_singleton, Unitary.continuousOn_argSelfAdjoint, OpenPartialHomeomorph.continuousOn_univBall_symm, Set.instTietzeExtensionUnitBall, closedBall_sub_ball, eball_ofReal, egauge_ball_le_of_one_lt_norm, IsUltrametricDist.ball_subset_trichotomy, mem_ball_iff_norm'', combo_mem_ball_of_ne, mem_ball_one_iff, balanced_ball_zero, Topology.RelCWComplex.pairwiseDisjoint', instContinuousNegElemBallOfNat, CStarAlgebra.span_nonneg_inter_unitBall, ball_div_one, MeasureTheory.Measure.toSphere_real_apply_univ, unitBall.instContinuousMul, emetric_ball, centerMass_mem_ball_of_strictConvexSpace, NormedSpace.isVonNBounded_ball, Besicovitch.exist_disjoint_covering_families, MeasureTheory.Measure.addHaar_ball_of_pos, interior_closedBall, Homeomorph.contDiff_unitBall, IsUltrametricDist.mem_ball_iff, Real.ball_eq_Ioo, Real.volume_pi_ball, DifferentiableOn.diffContOnCl_ball, ball_zero_eq, isPathConnected_ball, iUnion_ball_nat_succ, neg_ball, closedBall_diff_sphere, Topology.RelCWComplex.source_eq, ball_infDist_compl_subset, ball_eq_singleton_of_subsingleton, ball_mul_one, MeasureTheory.Measure.addHaar_ball_mul, SmoothBumpFunction.exists_r_pos_lt_subset_ball, ball_subset_thickening, isCompactOperator_iff_isCompact_closure_image_ball, ball_subset_interior_closedBall, IsCompact.finite_cover_balls, biInter_gt_ball, MeasureTheory.Measure.addHaar_unitClosedBall_eq_addHaar_unitBall, ball_infDist_subset_compl, mem_approxOrderOf_iff, smul_ball'', add_mem_ball_iff_norm, Real.totallyBounded_ball, preimage_vadd_ball, dense_iff_iUnion_ball, UpperHalfPlane.image_coe_ball, mem_nhdsWithin_iff, ball_add_ball, ball_mul, Homeomorph.coe_unitBall_apply_zero, closedBall_add_ball, LipschitzWith.mapsTo_ball, Seminorm.ball_zero_eq_preimage_ball, ball_eq_ball, vadd_ball, openSegment_subset_ball_of_ne, Subtype.preimage_ball, lebesgue_number_lemma_of_metric, Real.volume_ball, ball_eq, ball_zero_add_singleton, SmoothBumpFunction.support_eq_inter_preimage, exists_homeomorph_image_interior_closure_frontier_eq_unitBall, Ioo_smul_sphere_zero, Real.dimH_ball_pi, MeasureTheory.Measure.addHaar_ball_center, MeasureTheory.Measure.toSphere_apply_univ, iUnion_ball_nat, ball_add_zero, Int.ball_eq_Ioo, Snowflaking.image_ofSnowflaking_ball, continuousSMul_closedBall_ball, ball_one_eq, ContDiffBumpBase.support, MeasureTheory.Measure.pi_ball, NormedSpace.polar_ball_subset_closedBall_div, ball_normSeminorm, closedBall_subset_ball, LinearIsometryEquiv.preimage_ball, Real.ball_eq_openSegment, mem_ball_self, div_ball, AnalyticAt.exists_ball_analyticOnNhd, ball_add_closedBall, gauge_ball, nonempty_ball, ExistsContDiffBumpBase.w_support, exists_locallyFinite_iUnion_eq_ball_radius_lt, ball_sub_zero, ball_zero, affinity_unitBall, SmoothBumpFunction.ball_subset, InnerProductSpace.volume_ball, add_ball_zero, circleMap_notMem_ball, ExistsContDiffBumpBase.u_exists, unitBall.coe_eq_zero, ContDiffBump.support_eq, mem_approx_add_orderOf_iff, vadd_ball_zero, exists_ball_inter_eq_singleton_of_mem_discrete, LinearIsometryEquiv.image_ball, isScalarTower_closedBall_ball_ball, OpenPartialHomeomorph.univUnitBall_target, diam_ball, Bornology.IsBounded.subset_ball_lt, emetric_ball_nnreal, ball_div, hasBasis_cobounded_compl_ball, mul_mem_ball_mul_iff, OpenPartialHomeomorph.contDiffOn_univUnitBall_symm, singleton_div_ball_one, InnerProductSpace.volume_ball_of_dim_odd, Topology.CWComplex.source_eq, Topology.CWComplex.pairwiseDisjoint', frontier_ball_subset_sphere, preimage_mul_left_ball, smul_unitBall_of_pos, mem_ball_iff_norm, ball_pi, LinearIsometry.preimage_ball, dense_iff, HasFPowerSeriesOnBall.tendstoUniformlyOn, preimage_add_left_ball, nonunits.subset_compl_ball, thickening_closedBall, LatticeOrderedAddCommGroup.isSolid_ball, OpenPartialHomeomorph.unitBallBall_target, MeasureTheory.exists_pos_ball, Real.ball_zero_eq_Ioo, IsUltrametricDist.ball_eq_or_disjoint, unitBall.instIsLeftCancelMulZero, Homeomorph.unitBall_apply_coe, ball_eq', ball_disjoint_closedBall, mem_ball, convex_ball, ball_union_sphere, ball_one_div_singleton, MeasureTheory.integral_fun_norm_addHaar, preimage_mul_right_ball, Unitary.openPartialHomeomorph_target, sum_mem_ball_of_strictConvexSpace, singleton_div_ball, closure_ball_subset_closedBall, ball_one_mul_singleton, ball_prod_same, thickening_ball, HasFPowerSeriesOnBall.tendstoUniformlyOn', isScalarTower_sphere_sphere_ball, diam_ball_eq, ball_mem_nhds, egauge_ball_one_le_of_one_lt_norm, Dilation.mapsTo_ball, finite_cover_balls_of_compact, ContinuousLinearMap.sSup_unit_ball_eq_nnnorm, disjoint_ball_closedBall_iff, EuclideanSpace.volume_ball_fin_three, isScalarTower_sphere_closedBall_ball, sphere_subset_ball, Snowflaking.preimage_ofSnowflaking_ball, Complex.ball_one_subset_slitPlane, isOpen_ball, gauge_unit_ball, eventually_ball_subset, isOpen_iff, ball_div_singleton, smul_unitBall, NNReal.ball_zero_eq_Ico', singleton_sub_ball_zero, MeasureTheory.Measure.toSphereBallBound_mul_measureReal_unitBall_le_toSphere_ball, mem_nhds_iff, Seminorm.ball_smul_ball, Bornology.IsBounded.subset_ball, mem_ball_iff_norm', thickening_singleton, MeasureTheory.volume_pi_ball, ball_add, Snowflaking.preimage_toSnowflaking_ball, EuclideanSpace.ball_zero_eq, closedBall_disjoint_ball, EuclideanSpace.volume_ball_fin_two, NormedSpace.polar_ball, add_ball, Euclidean.ball_eq_preimage, absorbent_ball, MeasureTheory.Measure.addHaar_real_ball_center, EuclideanSpace.volume_ball, ball_subset_ball, Real.dimH_ball_pi_fin, Unitary.isPathConnected_ball, OpenPartialHomeomorph.unitBallBall_source, ball_add_singleton, mem_ball_iff_norm''', CPolynomialAt.exists_ball_cpolynomialOn, measurableSet_ball, MeasureTheory.Measure.addHaar_ball_mul_of_pos, instSMulCommClass_sphere_ball_ball, HasFPowerSeriesWithinOnBall.tendstoUniformlyOn, div_ball_one, unitBall.coe_mul, Real.volume_real_ball, totallyBounded_iff, unitBall.instIsRightCancelMulZero, mul_ball_one, disjoint_ball_ball_iff, isCompactOperator_iff_image_ball_subset_compact, singleton_mul_ball_one, Topology.RelCWComplex.disjointBase', frontier_ball, preimage_add_right_ball, isConnected_ball, exists_locallyFinite_subset_iUnion_ball_radius_lt, Nat.preimage_ball, biUnion_lt_closedBall, MeasureTheory.measure_ball_lt_top, IsCompactOperator.image_ball_subset_compact, smul_ball, HasFPowerSeriesWithinOnBall.tendstoUniformlyOn', CStarAlgebra.directedOn_nonneg_ball, ball_subset_range_iff_surjective, ExistsContDiffBumpBase.y_support, biUnion_lt_ball, IsUltrametricDist.frontier_ball_eq_empty, ball_eq_empty, OpenPartialHomeomorph.contDiffOn_univBall_symm, div_le_egauge_ball, Complex.volume_ball, sphere_union_ball, instSMulCommClass_closedBall_closedBall_ball, ball_zero_sub_singleton, NNReal.ball_zero_eq_Ico, closedBall_diff_ball, isScalarTower_sphere_ball_ball, MeasureTheory.Measure.addHaar_closedBall, nhds_basis_ball_inv_nat_succ, setOf_liouville_eq_iInter_iUnion, exists_finite_cover_balls_of_isCompact_closure, ball_subset, Int.preimage_ball, Seminorm.preimage_metric_ball, isMIntegralCurveAt_iff', nhds_basis_ball, closedBall_subset_ball', closure_ball, interior_closedBall', preimage_smul_ball, le_egauge_ball_one, sub_ball_zero, ModularFormClass.differentiableOn_cuspFunction_ball, preimage_add_ball, MeasureTheory.Measure.addHaar_real_closedBall_eq_addHaar_real_ball, IsometryEquiv.image_ball, MeasureTheory.Measure.toSphereBallBound_mul_measure_unitBall_le_toSphere_ball, DilationEquiv.smulTorsor_preimage_ball, singleton_add_ball_zero, eball_coe, cthickening_ball, OpenPartialHomeomorph.ball_subset_univBall_target, unitary.isPathConnected_ball, setOf_liouville_eq_irrational_inter_iInter_iUnion, MeasureTheory.Measure.addHaar_ball, sphere_disjoint_ball, unitBall.instIsCancelMulZero, AddCircle.closedBall_ae_eq_ball, CStarAlgebra.span_nonneg_inter_ball, instSMulCommClass_sphere_closedBall_ball, IsCompactOperator.isCompact_closure_image_ball, isScalarTower_closedBall_closedBall_ball, preimage_mul_ball, thickening_ball, singleton_add_ball, inv_ball, smul_ball_one, coe_neg_ball, measure_ball_pos, Snowflaking.image_toSnowflaking_ball, ball_sub_ball, finite_approx_of_totallyBounded, nhdsWithin_basis_ball, OpenPartialHomeomorph.univBall_target, instTietzeExtensionBall, nhds_basis_ball_inv_nat_pos, vadd_ball'', MeasureTheory.measure_unitBall_eq_integral_div_gamma, ball_subset_ball', ball_sub_singleton, absorbent_ball_zero, mul_mem_ball_iff_norm, Isometry.mapsTo_ball, sub_ball, unitBall.coe_zero, IsometryEquiv.preimage_ball, instSMulCommClass_sphere_sphere_ball, InnerProductSpace.volume_ball_of_dim_even, mem_ball_comm, disjoint_closedBall_ball_iff, mem_ball_zero_iff, ball_sub_closedBall, IsUltrametricDist.isClosed_ball, nhds_basis_ball_pow, ball_eq_ball', MeasureTheory.Measure.toSphere_apply_univ', Subtype.image_ball, ball_pi', MeasureTheory.Measure.addHaar_closedBall_eq_addHaar_ball, IsUltrametricDist.isClopen_ball, singleton_mul_ball, add_mem_ball_add_iff, MeasureTheory.Measure.addHaar_real_closedBall, mem_ball', ball_zero_subset_range_iff_surjective, Homeomorph.unitBall_symm_apply, ball_contractible, unitary.continuousOn_argSelfAdjoint, SmoothBumpFunction.ball_inter_range_eq_ball_inter_target
closedBall 📖	CompOp	393 math math: singleton_sub_closedBall_zero, CStarAlgebra.preimage_inr_Icc_zero_one, hasBasis_cobounded_compl_closedBall, instCompactSpaceElemClosedBallOfProperSpace, vadd_closedBall, Complex.norm_circleTransformBoundingFunction_le, segment_subset_closedBall_right, InnerProductSpace.volume_closedBall_of_dim_even, isBounded_closedBall, Function.locallyFinsuppWithin.toClosedBall_support_subset_closedBall, singleton_div_closedBall, EuclideanSpace.closedBall_zero_eq, ContinuousLinearMap.sSup_unitClosedBall_eq_nnnorm, spectrum.subset_closedBall_norm_mul, closedBall_eq_bInter_ball, ball_subset_closedBall, mem_cocompact_iff_closedBall_compl_subset, frontier_closedBall_subset_sphere, AddCircle.coe_real_preimage_closedBall_eq_iUnion, Snowflaking.preimage_ofSnowflaking_closedBall, nhds_basis_closedBall_pow, closedBall_sub_singleton, Topology.CWComplex.continuousOn, IsCompact.closedBall_mul, Complex.UnitDisc.instSMulCommClass_closedBall_circle, Complex.UnitDisc.instSMulCommClass_closedBall_left, closedBall_sub_ball, IsCompact.mul_closedBall_one, Besicovitch.ae_tendsto_measure_inter_div_of_measurableSet, ODE.FunSpace.range_toContinuousMap, closedBall_mem_nhds, Bornology.IsCobounded.closedBall_compl_subset, IsUnifLocDoublingMeasure.eventually_measure_mul_le_scalingConstantOf_mul, emetric_closedBall, coe_neg_closedBall, IsLowerSet.exists_subset_ball, sphere_prod, smul_unitClosedBall, Real.volume_closedBall, Besicovitch.exists_closedBall_covering_tsum_measure_le, contractibleSpace_closedBall, mem_closedBall_iff_norm'', Besicovitch.exist_disjoint_covering_families, interior_closedBall, smul_unitClosedBall_of_nonneg, Seminorm.closedBall_smul_ball, exists_continuous_nnreal_forall_closedBall_subset, closedBall_add_closedBall, NormedSpace.isBounded_iff_subset_smul_closedBall, IsCompact.closedBall_zero_add, IsUltrametricDist.mem_closedBall_iff, closedBall_diff_sphere, preimage_add_right_closedBall, LinearIsometry.preimage_closedBall, isScalarTower_closedBall_closedBall_closedBall, Topology.RelCWComplex.continuousOn, Euclidean.closedBall_eq_image, isScalarTower_sphere_closedBall_closedBall, closedEBall_ofReal, stdSimplex_subset_closedBall, Topology.RelCWComplex.union', Real.closedBall_eq_Icc, ContDiffBump.measure_closedBall_div_le_integral, ball_subset_interior_closedBall, smul_closedBall', mem_closedBall_iff_norm', singleton_mul_closedBall_one, EuclideanSpace.volume_closedBall_fin_three, biInter_gt_ball, measure_closedBall_pos_iff, ContinuousLinearMap.isCompact_image_coe_closedBall, ContinuousLinearMap.isClosed_image_coe_closedBall, Nat.closedBall_eq_Icc, isClosed_closedBall, MeasureTheory.Measure.addHaar_unitClosedBall_eq_addHaar_unitBall, closure_closedBall, Seminorm.closedBall_zero_eq_preimage_closedBall, NormedSpace.isVonNBounded_closedBall, affinity_unitClosedBall, ContDiffBump.normed_le_div_measure_closedBall_rOut, preimage_add_left_closedBall, sphere_pi, diam_closedBall_eq, Nat.preimage_closedBall, closedBall_mem_nhds_of_mem, infDist_inter_closedBall_of_mem, VitaliFamily.filterAt_basis_closedBall, smul_closedBall_one, strictConvex_closedBall, closedBall_pi', BoxIntegral.TaggedPrepartition.isSubordinate_single, NumberField.canonicalEmbedding.integerLattice.inter_ball_finite, mem_closedBall_iff_norm, NNReal.closedBall_zero_eq_Icc, IsCompact.div_closedBall, closedBall_add_ball, Besicovitch.ae_tendsto_rnDeriv, exists_smooth_forall_closedBall_subset, exists_homeomorph_image_interior_closure_frontier_eq_unitBall, Ioo_smul_sphere_zero, singleton_div_closedBall_one, SmoothBumpFunction.tsupport_subset_symm_image_closedBall, UpperHalfPlane.image_coe_closedBall, MeasureTheory.aecover_closedBall, EuclideanSpace.volume_closedBall_fin_two, WeakDual.isCompact_closedBall, continuousSMul_closedBall_ball, IsPicardLindelof.lipschitzOnWith, IsCompact.cthickening_eq_biUnion_closedBall, CStarAlgebra.span_nonneg_inter_unitClosedBall, closedBall_compl_subset_of_mem_cocompact, Besicovitch.exist_finset_disjoint_balls_large_measure, NormedSpace.polar_ball_subset_closedBall_div, Dilation.mapsTo_closedBall, closedBall_subset_ball, inv_norm_smul_mem_unitClosedBall, Real.volume_real_closedBall, Besicovitch.exists_disjoint_closedBall_covering_ae_of_finiteMeasure_aux, Complex.UnitDisc.coe_closedBall_smul, unitClosedBall.coe_mul, ball_add_closedBall, Complex.continuousOn_norm_circleTransformBoundingFunction, AddCircle.volume_closedBall, instSMulCommClass_sphere_closedBall_closedBall, IsUnifLocDoublingMeasure.measure_mul_le_scalingConstantOf_mul, IsCompact.mul_closedBall, Snowflaking.preimage_toSnowflaking_closedBall, DiffContOnCl.continuousOn_ball, continuousSMul_sphere_closedBall, strictConvexSpace_iff, Function.locallyFinsuppWithin.toClosedBall_divisor, IsCompact.closedBall_one_mul, Topology.CWComplex.union', closedBall_zero_sub_singleton, isScalarTower_closedBall_ball_ball, WeakDual.isSeqCompact_closedBall, IsPicardLindelof.continuousOn_uncurry, IsCompact.closedBall_div, IsUnifLocDoublingMeasure.closedBall_mem_vitaliFamily_of_dist_le_mul, MeasureTheory.Measure.addHaar_real_closedBall', hasAntitoneBasis_cobounded_compl_closedBall, diam_closedBall, Seminorm.preimage_metric_closedBall, exists_continuous_real_forall_closedBall_subset, cthickening_eq_biUnion_closedBall, closedBall_subset_range_iff_surjective, isCompactOperator_iff_image_closedBall_subset_compact, closedBall_div_singleton, ProbabilityTheory.Fernique.lintegral_closedBall_diff_exp_logRatio_mul_sq_le, closedBall_one_div_singleton, mem_closedBall_iff_norm''', preimage_add_closedBall, Vitali.exists_disjoint_subfamily_covering_enlargement_closedBall, closedBall_prod_same, closedBall_zero, Isometry.preimage_closedBall, vadd_closedBall'', add_mem_closedBall_iff_norm, IsClosed.cthickening_eq_biUnion_closedBall, Complex.eqOn_closedBall_of_isMaxOn_norm, preimage_smul_closedBall, StrictConvexSpace.strictConvex_closedBall, Real.closedBall_zero_eq_Icc, preimage_vadd_closedBall, thickening_closedBall, closedBall_of_neg, Topology.CWComplex.mapsTo', exists_contMDiffMap_forall_closedBall_subset, mem_closedBall', ContDiffBump.measure_closedBall_le_integral, convexHull_sphere_eq_closedBall, ball_disjoint_closedBall, Subtype.preimage_closedBall, cthickening_singleton, ball_union_sphere, circleMap_mem_closedBall, Real.closedBall_eq_segment, NumberField.Units.dirichletUnitTheorem.unitLattice_inter_ball_finite, isScalarTower_sphere_sphere_closedBall, Complex.UnitDisc.instSMulCommClass_closedBall_right, closedBall_zero', segment_subset_closedBall_left, SmoothBumpFunction.isClosed_symm_image_closedBall, IsCompact.sub_closedBall_zero, closure_ball_subset_closedBall, WeakDual.isClosed_closedBall, Besicovitch.ae_tendsto_measure_inter_div, Complex.UnitDisc.instIsScalarTower_closedBall, IsUltrametricDist.isOpen_closedBall, cthickening_closedBall, instContinuousNegElemClosedBallOfNat, iUnion_inter_closedBall_nat, nonempty_closedBall, smul_closedBall'', Valued.integer.coe_span_singleton_eq_closedBall, closedBall_pi, exists_isCompact_closedBall, AddCircle.closedBall_eq_univ_of_half_period_le, MeasureTheory.Measure.addHaar_real_closedBall_center, isConnected_closedBall, disjoint_ball_closedBall_iff, isScalarTower_sphere_closedBall_ball, closedBall_eq_singleton_of_subsingleton, Complex.volume_closedBall, NormedDivisionRing.unitClosedBall_eq_univ_of_discrete, singleton_mul_closedBall, Bornology.IsBounded.subset_closedBall, singleton_add_closedBall_zero, MeasureTheory.Measure.pi_closedBall, Subtype.image_closedBall, Complex.continuousOn_prod_circle_transform_function, IsUltrametricDist.frontier_closedBall_eq_empty, closedBall_eq_empty, Complex.UnitDisc.coe_smul_closedBall, ODE.FunSpace.mem_closedBall, unitClosedBall.coe_eq_zero, IsPicardLindelof.exists_forall_mem_closedBall_eq_hasDerivWithinAt_continuousOn, mul_mem_closedBall_mul_iff, disjoint_closedBall_of_lt_infDist, Euclidean.closedBall_eq_preimage, isCompactOperator_iff_isCompact_closure_image_closedBall, mem_closedBall_one_iff, smul_closedBall, closedBall_add_singleton, LinearMap.polar_eq_biInter_preimage, IsCompact.closedBall_one_div, Bornology.IsBounded.subset_closedBall_lt, Besicovitch.exists_disjoint_closedBall_covering_ae, NormedField.completeSpace_iff_isComplete_closedBall, spectrum.differentiableOn_inverse_one_sub_smul, ContDiffBump.integral_le_measure_closedBall, frontier_closedBall, disjoint_closedBall_closedBall_iff, IsCompact.sub_closedBall, add_mem_closedBall_add_iff, eigenvalue_mem_ball, Set.instTietzeExtensionUnitClosedBall, isPathConnected_closedBall, CStarAlgebra.span_nonneg_inter_closedBall, IsometryEquiv.image_closedBall, closedBall_disjoint_ball, MeasureTheory.Measure.addHaar_closedBall_mul_of_pos, frontier_closedBall', AddCircle.coe_real_preimage_closedBall_period_zero, ContDiffBump.tsupport_eq, NormedSpace.polar_ball, VitaliFamily.tendsto_filterAt_iff, preimage_mul_left_closedBall, closedBall_normSeminorm, measure_closedBall_pos, emetric_closedBall_nnreal, tendsto_closedBall_smallSets, MeasureTheory.volume_pi_closedBall, IsCompact.closedBall_zero_sub, Topology.RelCWComplex.mapsTo, VitaliFamily.frequently_filterAt_iff, balanced_closedBall_zero, NormedSpace.sInter_polar_eq_closedBall, circleAverage_log_norm_factorizedRational, Int.closedBall_eq_Icc, IsCompactOperator.image_closedBall_subset_compact, unitClosedBall.coe_one, isCobounded_iff_closedBall_compl_subset, vadd_closedBall_zero, Snowflaking.image_toSnowflaking_closedBall, biUnion_lt_closedBall, IsUltrametricDist.closedBall_subset_trichotomy, continuousSMul_closedBall_closedBall, IsUpperSet.exists_subset_ball, Irreducible.maximalIdeal_eq_closedBall, eventually_closedBall_subset, closedBall_mul_singleton, Complex.norm_eqOn_closedBall_of_isMaxOn, sphere_union_ball, IsCover.subset_iUnion_closedBall, instSMulCommClass_closedBall_closedBall_ball, Complex.UnitDisc.instSMulCommClass_circle_closedBall, Besicovitch.tendsto_filterAt, closedBall_diff_ball, closedBall_rpow_sub_one_eq_empty_aux, MeasureTheory.Measure.addHaar_closedBall, neg_closedBall, mem_closedBall_comm, NormedSpace.closedBall_inv_subset_polar_closedBall, ODE.FunSpace.mem_closedBall₀, ContDiffBump.normed_le_div_measure_closedBall_rIn, mem_closedBall, mul_mem_closedBall_iff_norm, MeasureTheory.tendsto_measure_compl_closedBall_of_isTightMeasureSet, closedBall_subset_ball', closure_ball, interior_closedBall', Valued.toNormedField.setOf_mem_integer_eq_closedBall, isCover_iff_subset_iUnion_closedBall, closedBall_infDist_compl_subset_closure, ProperSpace.isCompact_closedBall, unitClosedBall.coe_pow, InnerProductSpace.volume_closedBall, IsUltrametricDist.isClopen_closedBall, inv_closedBall, unitClosedBall.instIsCancelMulZero, div_le_egauge_closedBall, nhds_basis_closedBall, Snowflaking.image_ofSnowflaking_closedBall, MeasureTheory.Measure.addHaar_real_closedBall_eq_addHaar_real_ball, sphere_subset_closedBall, IsCompact.closedBall_add, InnerProductSpace.volume_closedBall_of_dim_odd, unitClosedBall.instContinuousMul, Irreducible.maximalIdeal_pow_eq_closedBall_pow, unitClosedBall.coe_eq_one, MeasureTheory.Measure.addHaar_closedBall_mul, VitaliFamily.nontrivial, cthickening_ball, closedBall_subset_closedBall, DiffContOnCl.ball_subset_image_closedBall, measurableSet_closedBall, unitInterval.eq_closedBall, NNReal.closedBall_zero_eq_Icc', mem_closedBall_zero_iff, closedBall_eq_sphere_of_nonpos, ContinuousLinearMap.sSup_unitClosedBall_eq_norm, IsPicardLindelof.exists_forall_mem_closedBall_eq_hasDerivWithinAt_lipschitzOnWith, ContDiffBump.tsupport_normed_eq, Besicovitch.exists_disjoint_closedBall_covering_ae_aux, AddCircle.closedBall_ae_eq_ball, LipschitzWith.mapsTo_closedBall, instSMulCommClass_sphere_closedBall_ball, ODE.FunSpace.compProj_mem_closedBall, IsCompact.div_closedBall_one, NormedSpace.polar_closedBall, isScalarTower_closedBall_closedBall_ball, closedEBall_coe, MeasureTheory.Measure.addHaar_closedBall_center, closedBall_subset_closedBall', Topology.CWComplex.mapsTo, instTietzeExtensionClosedBall, isBounded_iff_subset_closedBall, closedBall_sub_closedBall, smul_closedBall, Real.Icc_eq_closedBall, unitClosedBall.coe_zero, SmoothBumpFunction.nhdsWithin_range_basis, isPreconnected_closedBall, CStarAlgebra.hasBasis_approximateUnit, closedBall_subset_cthickening_singleton, instSMulCommClass_sphere_sphere_closedBall, MeasureTheory.isTightMeasureSet_iff_tendsto_measure_compl_closedBall, biInter_gt_closedBall, IsCompact.add_closedBall_zero, closedBall_one_mul_singleton, VitaliFamily.eventually_filterAt_subset_closedBall, exists_closedBall_inter_eq_singleton_of_discrete, gauge_closedBall, iUnion_closedBall_nat, Real.volume_pi_closedBall, instSMulCommClass_closedBall_closedBall_closedBall, eventually_isCompact_closedBall, singleton_sub_closedBall, IsometryEquiv.preimage_closedBall, singleton_add_closedBall, mem_closedBall_self, spectrum.subset_closedBall_norm, cthickening_subset_iUnion_closedBall_of_lt, MeasureTheory.measure_closedBall_lt_top, closedBall_zero_add_singleton, EuclideanSpace.volume_closedBall, le_egauge_closedBall_one, subsingleton_closedBall, balanced_iff_closedBall_smul, convex_closedBall, disjoint_closedBall_ball_iff, Complex.UnitDisc.instIsScalarTower_closedBall_closedBall, closedBall_subset_cthickening, IsCompact.add_closedBall, ball_sub_closedBall, Int.preimage_closedBall, preimage_mul_closedBall, preimage_mul_right_closedBall, MeasureTheory.Measure.addHaar_closedBall_eq_addHaar_ball, Isometry.mapsTo_closedBall, IsUltrametricDist.closedBall_eq_or_disjoint, IsCompactOperator.isCompact_closure_image_closedBall, MeasureTheory.Measure.addHaar_closedBall', LinearIsometryEquiv.image_closedBall, SmoothBumpFunction.image_eq_inter_preimage_of_subset_support, Seminorm.closedBall_smul_closedBall, SmoothBumpFunction.closedBall_subset, MeasureTheory.Measure.addHaar_real_closedBall, SmoothBumpFunction.isCompact_symm_image_closedBall, closedBall_disjoint_closedBall, IsCompact.closedBall_sub, LinearIsometryEquiv.preimage_closedBall
sphere 📖	CompOp	175 math math: norm_eq_of_mem_sphere, continuousSMul_sphere_ball, IsometryEquiv.image_sphere, EuclideanGeometry.subset_sphere, instIsManifoldRealEuclideanSpaceFinModelWithCornersSelfTopWithTopENatElemHAddNatOfNatSphere, MeasureTheory.Measure.addHaar_sphere, IsometryEquiv.preimage_sphere, unitSphere.coe_one, continuousSMul_sphere_sphere, mem_sphere_iff_norm', UpperHalfPlane.image_coe_sphere, range_circleMap, frontier_closedBall_subset_sphere, ContinuousLinearMap.iSup_rayleigh_eq_iSup_rayleigh_sphere, AffineSpace.cobounded_eq_iSup_sphere_asymptoticNhds, MeasureTheory.Measure.toSphere_apply_aux, EuclideanGeometry.preimage_inversion_perpBisector_inversion, NormedSpace.sphere_nonempty_rclike, ContinuousLinearMap.image_rayleigh_eq_image_rayleigh_sphere, sphere_zero, contMDiff_neg_sphere, instSMulCommClass_sphere_sphere_sphere, Behrend.sphere_subset_preimage_metric_sphere, Dilation.mapsTo_sphere, sphere_prod, MeasureTheory.Measure.toSphere_real_apply_univ, threeAPFree_sphere, sphere_isEmpty_of_subsingleton, stereographic'_source, sphere_subset_range_iff_surjective, MeasureTheory.Measure.addHaar_sphere_of_ne_zero, closedBall_diff_sphere, ContinuousLinearMap.sSup_sphere_eq_nnnorm, image_circleMap_Ioc, isScalarTower_sphere_closedBall_closedBall, sphere_eq_empty_of_neg, isConnected_sphere, set_smul_sphere_zero, EuclideanGeometry.Sphere.nonempty_iff, preimage_add_sphere, unitSphere.coe_mul, ContinuousLinearMap.iInf_rayleigh_eq_iInf_rayleigh_sphere, coe_neg_sphere, contMDiff_coe_sphere, stereographic_apply_neg, sphere_pi, isOpenEmbedding_stereographic_symm, closure_sphere, stereo_left_inv, unitSphereToUnits_apply_coe, exists_homeomorph_image_interior_closure_frontier_eq_unitBall, EuclideanGeometry.preimage_inversion_perpBisector, Ioo_smul_sphere_zero, smul_sphere', stereoInvFun_apply, MeasureTheory.Measure.toSphere_apply_univ, unitSphereToUnits_injective, stereographic'_target, LinearIsometryEquiv.image_sphere, isScalarTower_sphere_sphere_sphere, EuclideanSpace.instIsManifoldSphere, MeasureTheory.Measure.instIsFiniteMeasureElemSphereOfNatRealToSphere, EuclideanGeometry.image_inversion_perpBisector, isPreconnected_sphere, instSMulCommClass_sphere_closedBall_closedBall, EuclideanGeometry.image_inversion_sphere_dist_center, vadd_sphere, preimage_vadd_sphere, EuclideanSpace.sphere_zero_eq, continuousSMul_sphere_closedBall, sphere.compactSpace, smul_sphere, Affine.Simplex.circumsphere_unique_dist_eq, EuclideanGeometry.preimage_inversion_sphere_dist_center, mfderiv_coe_sphere_injective, IsUltrametricDist.isOpen_sphere, subsingleton_sphere, Isometry.preimage_sphere, preimage_smul_sphere, instContinuousNegElemSphereOfNat, frontier_ball_subset_sphere, smul_sphere, unitary.spectrum_subset_circle, ContinuousLinearMap.sSup_sphere_eq_norm, mem_sphere_zero_iff_norm, homeomorphUnitSphereProd_symm_apply_coe, Topology.CWComplex.mapsTo', convexHull_sphere_eq_closedBall, circleMap_mem_sphere, circleMap_preimage_codiscrete, ball_union_sphere, stereographic_neg_apply, EuclideanGeometry.Sphere.cospherical, isScalarTower_sphere_sphere_closedBall, mem_sphere_one_iff_norm, mem_sphere, Submonoid.coe_unitSphere, sphere.instContinuousMul, homeomorphSphereProd_symm_apply_coe, isScalarTower_sphere_sphere_ball, MeasureTheory.Measure.measurePreserving_homeomorphUnitSphereProd, homeomorphUnitSphereProd_apply_fst_coe, unitSphere.coe_inv, LinearIsometry.preimage_sphere, frontier_sphere', mem_sphere_comm, isScalarTower_sphere_closedBall_ball, sphere_subset_ball, isCompact_sphere, interior_sphere, unitSphere.coe_zpow, stereographic_target, MeasureTheory.Measure.toSphereBallBound_mul_measureReal_unitBall_le_toSphere_ball, mem_sphere_iff_norm, isClosed_sphere, EuclideanGeometry.Sphere.mem_coe, frontier_closedBall, stereoInvFunAux_mem, range_mfderiv_coe_sphere, Complex.norm_sub_one_sq_eqOn_sphere, stereographic_source, frontier_closedBall', circleIntegrable_sub_zpow_iff, isPathConnected_sphere, diam_sphere_eq, isBounded_sphere, Topology.RelCWComplex.mapsTo, EuclideanGeometry.Sphere.coe_mk, instSMulCommClass_sphere_ball_ball, unitSphere.coe_pow, preimage_mul_sphere, Isometry.mapsTo_sphere, frontier_ball, NormedSpace.sphere_nonempty, circleIntegrable_sub_inv_iff, unitSphere.coe_div, stereo_right_inv, stereographic_apply, homeomorphSphereProd_apply_snd_coe, sphere_union_ball, closedBall_diff_ball, isScalarTower_sphere_ball_ball, IsUltrametricDist.isClopen_sphere, sphere_ext_iff, frontier_sphere, homeomorphUnitSphereProd_apply_snd_coe, stereographic'_symm_apply, homeomorphSphereProd_apply_fst_coe, mem_sphere', sphere_subset_closedBall, MeasureTheory.Measure.toSphereBallBound_mul_measure_unitBall_le_toSphere_ball, sphere_disjoint_ball, closedBall_eq_sphere_of_nonpos, instSMulCommClass_sphere_closedBall_ball, MeasureTheory.Measure.toSphere_eq_zero_iff_finrank, AffineIndependent.existsUnique_dist_eq, Complex.image_exp_Ioc_eq_sphere, interior_sphere', Topology.CWComplex.mapsTo, sphere_eq_empty_of_subsingleton, instSMulCommClass_sphere_sphere_closedBall, continuous_stereoInvFun, EuclideanGeometry.cospherical_iff_exists_sphere, Complex.range_exp_mul_I, spectrum.subset_circle_of_unitary, instSMulCommClass_sphere_sphere_ball, MeasureTheory.Measure.toSphere.instIsOpenPosMeasure, circleMap_mem_sphere', Unitary.spectrum_subset_circle, MeasureTheory.Measure.toSphere_apply_univ', surjective_stereographic, norm_eq_of_mem_sphere', LinearIsometryEquiv.preimage_sphere, MeasureTheory.Measure.toSphere_eq_zero_iff, sphere.instIsTopologicalGroup

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
ball_disjoint_ball 📖	mathematical	Real Real.instLE Real.instAdd Dist.dist PseudoMetricSpace.toDist	Disjoint Set ConditionallyCompletePartialOrderSup.toPartialOrder ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup ConditionallyCompleteLattice.toConditionallyCompletePartialOrder CompleteLattice.toConditionallyCompleteLattice CompleteBooleanAlgebra.toCompleteLattice CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra Set.instCompleteAtomicBooleanAlgebra HeytingAlgebra.toOrderBot Order.Frame.toHeytingAlgebra CompleteDistribLattice.toFrame CompleteBooleanAlgebra.toCompleteDistribLattice ball	—	Disjoint.mono_left ball_subset_closedBall closedBall_disjoint_ball
ball_disjoint_closedBall 📖	mathematical	Real Real.instLE Real.instAdd Dist.dist PseudoMetricSpace.toDist	Disjoint Set ConditionallyCompletePartialOrderSup.toPartialOrder ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup ConditionallyCompleteLattice.toConditionallyCompletePartialOrder CompleteLattice.toConditionallyCompleteLattice CompleteBooleanAlgebra.toCompleteLattice CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra Set.instCompleteAtomicBooleanAlgebra HeytingAlgebra.toOrderBot Order.Frame.toHeytingAlgebra CompleteDistribLattice.toFrame CompleteBooleanAlgebra.toCompleteDistribLattice ball closedBall	—	Disjoint.symm closedBall_disjoint_ball add_comm dist_comm
ball_eq_ball 📖	mathematical	—	UniformSpace.ball setOf Real Real.instLT Dist.dist PseudoMetricSpace.toDist ball	—	—
ball_eq_ball' 📖	mathematical	—	UniformSpace.ball setOf Real Real.instLT Dist.dist PseudoMetricSpace.toDist ball	—	Set.ext dist_comm
ball_eq_empty 📖	mathematical	—	ball Set Set.instEmptyCollection Real Real.instLE Real.instZero	—	Set.not_nonempty_iff_eq_empty nonempty_ball not_lt
ball_eq_singleton_of_subsingleton 📖	mathematical	Real Real.instLT Real.instZero	ball Set Set.instSingletonSet	—	Set.ext dist_self
ball_half_subset 📖	mathematical	Set Set.instMembership ball Real DivInvMonoid.toDiv Real.instDivInvMonoid instOfNatAtLeastTwo Real.instNatCast Nat.instAtLeastTwoHAddOfNat	Set.instHasSubset	—	Nat.instAtLeastTwoHAddOfNat ball_subset sub_self_div_two Real.instIsStrictOrderedRing le_of_lt
ball_mem_nhds 📖	mathematical	Real Real.instLT Real.instZero	Set Filter Filter.instMembership nhds UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace ball	—	IsOpen.mem_nhds isOpen_ball mem_ball_self
ball_subset 📖	mathematical	Real Real.instLE Dist.dist PseudoMetricSpace.toDist Real.instSub	Set Set.instHasSubset ball	—	add_sub_cancel lt_of_le_of_lt dist_triangle add_lt_add_of_lt_of_le IsOrderedAddMonoid.toAddLeftMono Real.instIsOrderedAddMonoid IsRightCancelAdd.addRightStrictMono_of_addRightMono AddRightCancelSemigroup.toIsRightCancelAdd covariant_swap_add_of_covariant_add
ball_subset_ball 📖	mathematical	Real Real.instLE	Set Set.instHasSubset ball	—	lt_of_lt_of_le mem_ball
ball_subset_ball' 📖	mathematical	Real Real.instLE Real.instAdd Dist.dist PseudoMetricSpace.toDist	Set Set.instHasSubset ball	—	dist_triangle add_lt_add_left IsRightCancelAdd.addRightStrictMono_of_addRightMono AddRightCancelSemigroup.toIsRightCancelAdd covariant_swap_add_of_covariant_add IsOrderedAddMonoid.toAddLeftMono Real.instIsOrderedAddMonoid
ball_subset_closedBall 📖	mathematical	—	Set Set.instHasSubset ball closedBall	—	mem_closedBall le_of_lt
ball_subset_interior_closedBall 📖	mathematical	—	Set Set.instHasSubset ball interior UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace closedBall	—	interior_maximal ball_subset_closedBall isOpen_ball
ball_union_sphere 📖	mathematical	—	Set Set.instUnion ball sphere closedBall	—	Set.ext le_iff_lt_or_eq
ball_zero 📖	mathematical	—	ball Real Real.instZero Set Set.instEmptyCollection	—	ball_eq_empty le_refl
boundedSpace_iff 📖	mathematical	—	BoundedSpace PseudoMetricSpace.toBornology Real Real.instLE Dist.dist PseudoMetricSpace.toDist	—	Bornology.isBounded_univ isBounded_iff
boundedSpace_iff_edist 📖	mathematical	—	BoundedSpace PseudoMetricSpace.toBornology ENNReal Preorder.toLE PartialOrder.toPreorder ENNReal.instPartialOrder EDist.edist PseudoMetricSpace.toEDist ENNReal.ofNNReal	—	—
boundedSpace_iff_nndist 📖	mathematical	—	BoundedSpace PseudoMetricSpace.toBornology NNReal Preorder.toLE PartialOrder.toPreorder instPartialOrderNNReal NNDist.nndist PseudoMetricSpace.toNNDist	—	Bornology.isBounded_univ isBounded_iff_nndist
closedBall_diff_ball 📖	mathematical	—	Set Set.instSDiff closedBall ball sphere	—	ball_union_sphere Set.union_diff_cancel_left Disjoint.le_bot Disjoint.symm sphere_disjoint_ball
closedBall_diff_sphere 📖	mathematical	—	Set Set.instSDiff closedBall sphere ball	—	ball_union_sphere Set.union_diff_cancel_right Disjoint.le_bot Disjoint.symm sphere_disjoint_ball
closedBall_disjoint_ball 📖	mathematical	Real Real.instLE Real.instAdd Dist.dist PseudoMetricSpace.toDist	Disjoint Set ConditionallyCompletePartialOrderSup.toPartialOrder ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup ConditionallyCompleteLattice.toConditionallyCompletePartialOrder CompleteLattice.toConditionallyCompleteLattice CompleteBooleanAlgebra.toCompleteLattice CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra Set.instCompleteAtomicBooleanAlgebra HeytingAlgebra.toOrderBot Order.Frame.toHeytingAlgebra CompleteDistribLattice.toFrame CompleteBooleanAlgebra.toCompleteDistribLattice closedBall ball	—	Set.disjoint_left LE.le.not_gt LE.le.trans dist_triangle_left add_lt_add_of_le_of_lt IsLeftCancelAdd.addLeftStrictMono_of_addLeftMono AddLeftCancelSemigroup.toIsLeftCancelAdd IsOrderedAddMonoid.toAddLeftMono Real.instIsOrderedAddMonoid covariant_swap_add_of_covariant_add
closedBall_disjoint_closedBall 📖	mathematical	Real Real.instLT Real.instAdd Dist.dist PseudoMetricSpace.toDist	Disjoint Set ConditionallyCompletePartialOrderSup.toPartialOrder ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup ConditionallyCompleteLattice.toConditionallyCompletePartialOrder CompleteLattice.toConditionallyCompleteLattice CompleteBooleanAlgebra.toCompleteLattice CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra Set.instCompleteAtomicBooleanAlgebra HeytingAlgebra.toOrderBot Order.Frame.toHeytingAlgebra CompleteDistribLattice.toFrame CompleteBooleanAlgebra.toCompleteDistribLattice closedBall	—	Set.disjoint_left LT.lt.not_ge LE.le.trans dist_triangle_left add_le_add IsOrderedAddMonoid.toAddLeftMono Real.instIsOrderedAddMonoid covariant_swap_add_of_covariant_add
closedBall_eq_bInter_ball 📖	mathematical	—	closedBall Set.iInter Real Real.instLT ball	—	Set.ext mem_closedBall forall_gt_iff_le Set.mem_iInter₂
closedBall_eq_empty 📖	mathematical	—	closedBall Set Set.instEmptyCollection Real Real.instLT Real.instZero	—	Set.not_nonempty_iff_eq_empty nonempty_closedBall not_le
closedBall_eq_singleton_of_subsingleton 📖	mathematical	Real Real.instLE Real.instZero	closedBall Set Set.instSingletonSet	—	Set.ext dist_self
closedBall_eq_sphere_of_nonpos 📖	mathematical	Real Real.instLE Real.instZero	closedBall sphere	—	Set.ext LE.le.ge_iff_eq' LE.le.trans dist_nonneg
closedBall_mem_nhds 📖	mathematical	Real Real.instLT Real.instZero	Set Filter Filter.instMembership nhds UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace closedBall	—	Filter.mem_of_superset ball_mem_nhds ball_subset_closedBall
closedBall_mem_nhds_of_mem 📖	mathematical	Set Set.instMembership ball	Filter Filter.instMembership nhds UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace closedBall	—	Filter.mem_of_superset IsOpen.mem_nhds isOpen_ball ball_subset_closedBall
closedBall_of_neg 📖	mathematical	Real Real.instLT Real.instZero	closedBall Set Set.instEmptyCollection	—	closedBall_eq_empty
closedBall_subset_ball 📖	mathematical	Real Real.instLT	Set Set.instHasSubset closedBall ball	—	lt_of_le_of_lt
closedBall_subset_ball' 📖	mathematical	Real Real.instLT Real.instAdd Dist.dist PseudoMetricSpace.toDist	Set Set.instHasSubset closedBall ball	—	dist_triangle add_le_add_left covariant_swap_add_of_covariant_add IsOrderedAddMonoid.toAddLeftMono Real.instIsOrderedAddMonoid
closedBall_subset_closedBall 📖	mathematical	Real Real.instLE	Set Set.instHasSubset closedBall	—	le_trans
closedBall_subset_closedBall' 📖	mathematical	Real Real.instLE Real.instAdd Dist.dist PseudoMetricSpace.toDist	Set Set.instHasSubset closedBall	—	dist_triangle add_le_add_left covariant_swap_add_of_covariant_add IsOrderedAddMonoid.toAddLeftMono Real.instIsOrderedAddMonoid
closedEBall_coe 📖	mathematical	—	closedEBall PseudoMetricSpace.toPseudoEMetricSpace ENNReal.ofNNReal closedBall NNReal.toReal	—	closedEBall_ofReal NNReal.coe_nonneg ENNReal.ofReal_coe_nnreal
closedEBall_ofReal 📖	mathematical	Real Real.instLE Real.instZero	closedEBall PseudoMetricSpace.toPseudoEMetricSpace ENNReal.ofReal closedBall	—	Set.ext edist_le_ofReal
continuousAt_iff 📖	mathematical	—	ContinuousAt UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace Real Real.instLT Real.instZero Dist.dist PseudoMetricSpace.toDist	—	ContinuousAt.eq_1 tendsto_nhds_nhds
continuousAt_iff' 📖	mathematical	—	ContinuousAt UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace Filter.Eventually Real Real.instLT Dist.dist PseudoMetricSpace.toDist nhds	—	ContinuousAt.eq_1 tendsto_nhds
continuousOn_iff 📖	mathematical	—	ContinuousOn UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace Real Real.instLT Real.instZero Dist.dist PseudoMetricSpace.toDist	—	—
continuousOn_iff' 📖	mathematical	—	ContinuousOn UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace Filter.Eventually Real Real.instLT Dist.dist PseudoMetricSpace.toDist nhdsWithin	—	—
continuousWithinAt_iff 📖	mathematical	—	ContinuousWithinAt UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace Real Real.instLT Real.instZero Dist.dist PseudoMetricSpace.toDist	—	ContinuousWithinAt.eq_1 tendsto_nhdsWithin_nhds
continuousWithinAt_iff' 📖	mathematical	—	ContinuousWithinAt UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace Filter.Eventually Real Real.instLT Dist.dist PseudoMetricSpace.toDist nhdsWithin	—	ContinuousWithinAt.eq_1 tendsto_nhds
continuous_iff 📖	mathematical	—	Continuous UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace Real Real.instLT Real.instZero Dist.dist PseudoMetricSpace.toDist	—	continuous_iff_continuousAt tendsto_nhds_nhds
continuous_iff' 📖	mathematical	—	Continuous UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace Filter.Eventually Real Real.instLT Dist.dist PseudoMetricSpace.toDist nhds	—	continuous_iff_continuousAt tendsto_nhds
denseRange_iff 📖	mathematical	—	DenseRange UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace Real Real.instLT Dist.dist PseudoMetricSpace.toDist	—	—
dense_iff 📖	mathematical	—	Dense UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace Set.Nonempty Set Set.instInter ball	—	—
dense_iff_iUnion_ball 📖	mathematical	—	Dense UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace Set.iUnion Set Set.instMembership ball Set.univ	—	—
dist_le_add_of_nonempty_closedBall_inter_closedBall 📖	mathematical	Set.Nonempty Set Set.instInter closedBall	Real Real.instLE Dist.dist PseudoMetricSpace.toDist Real.instAdd	—	dist_triangle_left add_le_add IsOrderedAddMonoid.toAddLeftMono Real.instIsOrderedAddMonoid covariant_swap_add_of_covariant_add
dist_lt_add_of_nonempty_ball_inter_ball 📖	mathematical	Set.Nonempty Set Set.instInter ball	Real Real.instLT Dist.dist PseudoMetricSpace.toDist Real.instAdd	—	dist_lt_add_of_nonempty_closedBall_inter_ball Set.Nonempty.mono Set.inter_subset_inter ball_subset_closedBall Set.Subset.rfl
dist_lt_add_of_nonempty_ball_inter_closedBall 📖	mathematical	Set.Nonempty Set Set.instInter ball closedBall	Real Real.instLT Dist.dist PseudoMetricSpace.toDist Real.instAdd	—	add_comm dist_comm dist_lt_add_of_nonempty_closedBall_inter_ball Set.inter_comm
dist_lt_add_of_nonempty_closedBall_inter_ball 📖	mathematical	Set.Nonempty Set Set.instInter closedBall ball	Real Real.instLT Dist.dist PseudoMetricSpace.toDist Real.instAdd	—	dist_triangle_left add_lt_add_of_le_of_lt IsLeftCancelAdd.addLeftStrictMono_of_addLeftMono AddLeftCancelSemigroup.toIsLeftCancelAdd IsOrderedAddMonoid.toAddLeftMono Real.instIsOrderedAddMonoid covariant_swap_add_of_covariant_add
dist_mem_uniformity 📖	mathematical	Real Real.instLT Real.instZero	Set Filter Filter.instMembership uniformity PseudoMetricSpace.toUniformSpace setOf Dist.dist PseudoMetricSpace.toDist	—	mem_uniformity_dist
eball_coe 📖	mathematical	—	eball PseudoMetricSpace.toPseudoEMetricSpace ENNReal.ofNNReal ball NNReal.toReal	—	eball_ofReal ENNReal.ofReal_coe_nnreal
eball_ofReal 📖	mathematical	—	eball PseudoMetricSpace.toPseudoEMetricSpace ENNReal.ofReal ball	—	Set.ext edist_dist ENNReal.ofReal_lt_ofReal_iff_of_nonneg dist_nonneg
eball_top 📖	mathematical	—	eball PseudoMetricSpace.toPseudoEMetricSpace Top.top ENNReal instTopENNReal Set.univ	—	Set.eq_univ_of_forall edist_lt_top
eball_top_eq_univ 📖	mathematical	—	eball PseudoMetricSpace.toPseudoEMetricSpace Top.top ENNReal instTopENNReal Set.univ	—	Set.eq_univ_iff_forall edist_lt_top
emetric_ball 📖	mathematical	—	eball PseudoMetricSpace.toPseudoEMetricSpace ENNReal.ofReal ball	—	eball_ofReal
emetric_ball_nnreal 📖	mathematical	—	eball PseudoMetricSpace.toPseudoEMetricSpace ENNReal.ofNNReal ball NNReal.toReal	—	eball_coe
emetric_ball_top 📖	mathematical	—	eball PseudoMetricSpace.toPseudoEMetricSpace Top.top ENNReal instTopENNReal Set.univ	—	eball_top
emetric_closedBall 📖	mathematical	Real Real.instLE Real.instZero	closedEBall PseudoMetricSpace.toPseudoEMetricSpace ENNReal.ofReal closedBall	—	closedEBall_ofReal
emetric_closedBall_nnreal 📖	mathematical	—	closedEBall PseudoMetricSpace.toPseudoEMetricSpace ENNReal.ofNNReal closedBall NNReal.toReal	—	closedEBall_coe
eventually_nhds_iff 📖	mathematical	—	Filter.Eventually nhds UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace Real Real.instLT Real.instZero	—	mem_nhds_iff
eventually_nhds_iff_ball 📖	mathematical	—	Filter.Eventually nhds UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace Real Real.instLT Real.instZero	—	mem_nhds_iff
eventually_nhds_prod_iff 📖	mathematical	—	Filter.Eventually SProd.sprod Filter Filter.instSProd nhds UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace Real Real.instLT Real.instZero	—	Filter.HasBasis.eventually_iff Filter.HasBasis.prod nhds_basis_ball Filter.basis_sets
eventually_prod_nhds_iff 📖	mathematical	—	Filter.Eventually SProd.sprod Filter Filter.instSProd nhds UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace Real Real.instLT Real.instZero	—	Filter.eventually_swap_iff eventually_nhds_prod_iff
exists_ball_subset_ball 📖	mathematical	Set Set.instMembership ball	Real Real.instLT Real.instZero Set.instHasSubset	—	sub_pos IsRightCancelAdd.addRightStrictMono_of_addRightMono AddRightCancelSemigroup.toIsRightCancelAdd covariant_swap_add_of_covariant_add IsOrderedAddMonoid.toAddLeftMono Real.instIsOrderedAddMonoid ball_subset sub_sub_self le_refl
exists_lt_mem_ball_of_mem_ball 📖	mathematical	Set Set.instMembership ball	Real Real.instLT	—	exists_between' LinearOrderedSemiField.toDenselyOrdered PosMulReflectLE.toPosMulReflectLT PosMulStrictMono.toPosMulReflectLE IsStrictOrderedRing.toPosMulStrictMono Real.instIsStrictOrderedRing
forall_of_forall_mem_ball 📖	—	Filter.Frequently Real Filter.atTop Real.instPreorder	—	—	Filter.frequently_iff Filter.Ioi_mem_atTop instNoTopOrderOfNoMaxOrder instNoMaxOrderOfNontrivial Real.instIsOrderedRing Real.instNontrivial
forall_of_forall_mem_closedBall 📖	—	Filter.Frequently Real Filter.atTop Real.instPreorder	—	—	Filter.frequently_iff Filter.Ici_mem_atTop
iUnion_ball_nat 📖	mathematical	—	Set.iUnion ball Real Real.instNatCast Set.univ	—	Set.iUnion_eq_univ_iff exists_nat_gt Real.instIsStrictOrderedRing Real.instArchimedean
iUnion_ball_nat_succ 📖	mathematical	—	Set.iUnion ball Real Real.instAdd Real.instNatCast Real.instOne Set.univ	—	Set.iUnion_eq_univ_iff LT.lt.trans lt_add_one Real.instZeroLEOneClass NeZero.charZero_one IsStrictOrderedRing.toCharZero Real.instIsStrictOrderedRing IsLeftCancelAdd.addLeftStrictMono_of_addLeftMono AddLeftCancelSemigroup.toIsLeftCancelAdd IsOrderedAddMonoid.toAddLeftMono Real.instIsOrderedAddMonoid exists_nat_gt Real.instArchimedean
iUnion_closedBall_nat 📖	mathematical	—	Set.iUnion closedBall Real Real.instNatCast Set.univ	—	Set.iUnion_eq_univ_iff exists_nat_ge Real.instIsOrderedRing Real.instArchimedean
iUnion_inter_closedBall_nat 📖	mathematical	—	Set.iUnion Set Set.instInter closedBall Real Real.instNatCast	—	Set.inter_iUnion iUnion_closedBall_nat Set.inter_univ
isBounded_iff 📖	mathematical	—	Bornology.IsBounded PseudoMetricSpace.toBornology Real Real.instLE Dist.dist PseudoMetricSpace.toDist	—	Bornology.isBounded_def Filter.mem_sets PseudoMetricSpace.cobounded_sets Set.mem_setOf_eq compl_compl
isBounded_iff_eventually 📖	mathematical	—	Bornology.IsBounded PseudoMetricSpace.toBornology Filter.Eventually Real Filter.atTop Real.instPreorder	—	isBounded_iff Filter.eventually_atTop instIsDirectedOrder Real.instIsOrderedRing Real.instArchimedean LE.le.trans Filter.Eventually.exists Filter.atTop_neBot
isBounded_iff_exists_ge 📖	mathematical	—	Bornology.IsBounded PseudoMetricSpace.toBornology Real Real.instLE Dist.dist PseudoMetricSpace.toDist	—	Filter.Eventually.exists Filter.atTop_neBot instIsDirectedOrder Real.instIsOrderedRing Real.instArchimedean Filter.Eventually.and Filter.eventually_ge_atTop isBounded_iff_eventually isBounded_iff
isBounded_iff_nndist 📖	mathematical	—	Bornology.IsBounded PseudoMetricSpace.toBornology NNReal Preorder.toLE PartialOrder.toPreorder instPartialOrderNNReal NNDist.nndist PseudoMetricSpace.toNNDist	—	isBounded_iff_exists_ge
isOpen_ball 📖	mathematical	—	IsOpen UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace ball	—	isOpen_iff exists_ball_subset_ball
isOpen_iff 📖	mathematical	—	IsOpen UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace Real Real.instLT Real.instZero Set Set.instHasSubset ball	—	—
isOpen_singleton_iff 📖	mathematical	—	IsOpen UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace Set Set.instSingletonSet Real Real.instLT Real.instZero	—	—
mem_ball 📖	mathematical	—	Set Set.instMembership ball Real Real.instLT Dist.dist PseudoMetricSpace.toDist	—	—
mem_ball' 📖	mathematical	—	Set Set.instMembership ball Real Real.instLT Dist.dist PseudoMetricSpace.toDist	—	dist_comm mem_ball
mem_ball_comm 📖	mathematical	—	Set Set.instMembership ball	—	mem_ball' mem_ball
mem_ball_self 📖	mathematical	Real Real.instLT Real.instZero	Set Set.instMembership ball	—	mem_ball dist_self
mem_closedBall 📖	mathematical	—	Set Set.instMembership closedBall Real Real.instLE Dist.dist PseudoMetricSpace.toDist	—	—
mem_closedBall' 📖	mathematical	—	Set Set.instMembership closedBall Real Real.instLE Dist.dist PseudoMetricSpace.toDist	—	dist_comm mem_closedBall
mem_closedBall_comm 📖	mathematical	—	Set Set.instMembership closedBall	—	mem_closedBall' mem_closedBall
mem_closedBall_self 📖	mathematical	Real Real.instLE Real.instZero	Set Set.instMembership closedBall	—	mem_closedBall dist_self
mem_closure_iff 📖	mathematical	—	Set Set.instMembership closure UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace Real Real.instLT Dist.dist PseudoMetricSpace.toDist	—	mem_closure_iff_nhds_basis nhds_basis_ball dist_comm
mem_closure_range_iff 📖	mathematical	—	Set Set.instMembership closure UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace Set.range Real Real.instLT Dist.dist PseudoMetricSpace.toDist	—	—
mem_closure_range_iff_nat 📖	mathematical	—	Set Set.instMembership closure UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace Set.range Real Real.instLT Dist.dist PseudoMetricSpace.toDist DivInvMonoid.toDiv Real.instDivInvMonoid Real.instOne Real.instAdd Real.instNatCast	—	mem_closure_iff_nhds_basis nhds_basis_ball_inv_nat_succ dist_comm
mem_nhdsWithin_iff 📖	mathematical	—	Set Filter Filter.instMembership nhdsWithin UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace Real Real.instLT Real.instZero Set.instHasSubset Set.instInter ball	—	Filter.HasBasis.mem_iff nhdsWithin_basis_ball
mem_nhds_iff 📖	mathematical	—	Set Filter Filter.instMembership nhds UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace Real Real.instLT Real.instZero Set.instHasSubset ball	—	Filter.HasBasis.mem_iff nhds_basis_ball
mem_of_closed' 📖	mathematical	—	Set Set.instMembership Real Real.instLT Dist.dist PseudoMetricSpace.toDist	—	IsClosed.closure_eq mem_closure_iff
mem_sphere 📖	mathematical	—	Set Set.instMembership sphere Dist.dist PseudoMetricSpace.toDist	—	—
mem_sphere' 📖	mathematical	—	Set Set.instMembership sphere Dist.dist PseudoMetricSpace.toDist	—	dist_comm mem_sphere
mem_sphere_comm 📖	mathematical	—	Set Set.instMembership sphere	—	mem_sphere' mem_sphere
mem_uniformity_dist 📖	mathematical	—	Set Filter Filter.instMembership uniformity PseudoMetricSpace.toUniformSpace Real Real.instLT Real.instZero Set.instMembership	—	Filter.HasBasis.mem_uniformity_iff uniformity_basis_dist
mk_uniformity_basis 📖	mathematical	Real Real.instLT Real.instZero Real.instLE	Filter.HasBasis uniformity PseudoMetricSpace.toUniformSpace setOf Dist.dist PseudoMetricSpace.toDist	—	Filter.HasBasis.mem_iff uniformity_basis_dist lt_of_lt_of_le
mk_uniformity_basis_le 📖	mathematical	Real Real.instLT Real.instZero Real.instLE	Filter.HasBasis uniformity PseudoMetricSpace.toUniformSpace setOf Dist.dist PseudoMetricSpace.toDist	—	Filter.HasBasis.mem_iff uniformity_basis_dist exists_between LinearOrderedSemiField.toDenselyOrdered PosMulReflectLE.toPosMulReflectLT PosMulStrictMono.toPosMulReflectLE IsStrictOrderedRing.toPosMulStrictMono Real.instIsStrictOrderedRing lt_of_le_of_lt le_trans Set.mem_setOf LT.lt.le
ne_of_mem_sphere 📖	—	Set Set.instMembership sphere	—	—	dist_self
nhdsWithin_basis_ball 📖	mathematical	—	Filter.HasBasis Real nhdsWithin UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace Real.instLT Real.instZero Set Set.instInter ball	—	nhdsWithin_hasBasis nhds_basis_ball
nhds_basis_ball 📖	mathematical	—	Filter.HasBasis Real nhds UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace Real.instLT Real.instZero ball	—	nhds_basis_uniformity uniformity_basis_dist
nhds_basis_ball_inv_nat_pos 📖	mathematical	—	Filter.HasBasis nhds UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace ball Real DivInvMonoid.toDiv Real.instDivInvMonoid Real.instOne Real.instNatCast	—	nhds_basis_uniformity uniformity_basis_dist_inv_nat_pos
nhds_basis_ball_inv_nat_succ 📖	mathematical	—	Filter.HasBasis nhds UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace ball Real DivInvMonoid.toDiv Real.instDivInvMonoid Real.instOne Real.instAdd Real.instNatCast	—	nhds_basis_uniformity uniformity_basis_dist_inv_nat_succ
nhds_basis_ball_pow 📖	mathematical	Real Real.instLT Real.instZero Real.instOne	Filter.HasBasis nhds UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace ball Monoid.toNatPow Real.instMonoid	—	nhds_basis_uniformity uniformity_basis_dist_pow
nhds_basis_closedBall 📖	mathematical	—	Filter.HasBasis Real nhds UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace Real.instLT Real.instZero closedBall	—	nhds_basis_uniformity uniformity_basis_dist_le
nhds_basis_closedBall_pow 📖	mathematical	Real Real.instLT Real.instZero Real.instOne	Filter.HasBasis nhds UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace closedBall Monoid.toNatPow Real.instMonoid	—	nhds_basis_uniformity uniformity_basis_dist_le_pow
nonempty_ball 📖	mathematical	—	Set.Nonempty ball Real Real.instLT Real.instZero	—	pos_of_mem_ball mem_ball_self
nonempty_closedBall 📖	mathematical	—	Set.Nonempty closedBall Real Real.instLE Real.instZero	—	LE.le.trans dist_nonneg mem_closedBall_self
nonneg_of_mem_sphere 📖	mathematical	Set Set.instMembership sphere	Real Real.instLE Real.instZero	—	LE.le.trans_eq dist_nonneg
pos_of_mem_ball 📖	mathematical	Set Set.instMembership ball	Real Real.instLT Real.instZero	—	LE.le.trans_lt dist_nonneg
sphere_disjoint_ball 📖	mathematical	—	Disjoint Set ConditionallyCompletePartialOrderSup.toPartialOrder ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup ConditionallyCompleteLattice.toConditionallyCompletePartialOrder CompleteLattice.toConditionallyCompleteLattice CompleteBooleanAlgebra.toCompleteLattice CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra Set.instCompleteAtomicBooleanAlgebra HeytingAlgebra.toOrderBot Order.Frame.toHeytingAlgebra CompleteDistribLattice.toFrame CompleteBooleanAlgebra.toCompleteDistribLattice sphere ball	—	Set.disjoint_left ne_of_lt
sphere_eq_empty_of_neg 📖	mathematical	Real Real.instLT Real.instZero	sphere Set Set.instEmptyCollection	—	Set.eq_empty_iff_forall_notMem LE.le.not_gt nonneg_of_mem_sphere
sphere_eq_empty_of_subsingleton 📖	mathematical	—	sphere Set Set.instEmptyCollection	—	Set.eq_empty_iff_forall_notMem ne_of_mem_sphere
sphere_isEmpty_of_subsingleton 📖	mathematical	—	IsEmpty Set.Elem sphere	—	sphere_eq_empty_of_subsingleton Set.instIsEmptyElemEmptyCollection
sphere_subset_ball 📖	mathematical	Real Real.instLT	Set Set.instHasSubset sphere ball	—	Eq.trans_lt mem_sphere
sphere_subset_closedBall 📖	mathematical	—	Set Set.instHasSubset sphere closedBall	—	le_of_eq
sphere_union_ball 📖	mathematical	—	Set Set.instUnion sphere ball closedBall	—	Set.union_comm ball_union_sphere
tendsto_atTop 📖	mathematical	—	Filter.Tendsto Filter.atTop PartialOrder.toPreorder SemilatticeSup.toPartialOrder nhds UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace Real Real.instLT Dist.dist PseudoMetricSpace.toDist	—	Filter.HasBasis.tendsto_iff Filter.atTop_basis SemilatticeSup.instIsDirectedOrder nhds_basis_ball
tendsto_atTop' 📖	mathematical	—	Filter.Tendsto Filter.atTop PartialOrder.toPreorder SemilatticeSup.toPartialOrder nhds UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace Real Real.instLT Dist.dist PseudoMetricSpace.toDist	—	Filter.HasBasis.tendsto_iff Filter.atTop_basis_Ioi SemilatticeSup.instIsDirectedOrder nhds_basis_ball
tendsto_nhds 📖	mathematical	—	Filter.Tendsto nhds UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace Filter.Eventually Real Real.instLT Dist.dist PseudoMetricSpace.toDist	—	Filter.HasBasis.tendsto_right_iff nhds_basis_ball
tendsto_nhdsWithin_nhds 📖	mathematical	—	Filter.Tendsto nhdsWithin UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace nhds Real Real.instLT Real.instZero Dist.dist PseudoMetricSpace.toDist	—	nhdsWithin_univ tendsto_nhdsWithin_nhdsWithin
tendsto_nhdsWithin_nhdsWithin 📖	mathematical	—	Filter.Tendsto nhdsWithin UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace Real Real.instLT Real.instZero Set Set.instMembership Dist.dist PseudoMetricSpace.toDist	—	Filter.HasBasis.tendsto_iff nhdsWithin_basis_ball Set.inter_comm
tendsto_nhds_nhds 📖	mathematical	—	Filter.Tendsto nhds UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace Real Real.instLT Real.instZero Dist.dist PseudoMetricSpace.toDist	—	Filter.HasBasis.tendsto_iff nhds_basis_ball
toUniformSpace_eq 📖	mathematical	—	PseudoMetricSpace.toUniformSpace UniformSpace.ofDist Dist.dist PseudoMetricSpace.toDist dist_self dist_comm dist_triangle	—	UniformSpace.ext dist_self dist_comm dist_triangle PseudoMetricSpace.uniformity_dist
uniformContinuousOn_iff 📖	mathematical	—	UniformContinuousOn PseudoMetricSpace.toUniformSpace Real Real.instLT Real.instZero Dist.dist PseudoMetricSpace.toDist	—	Filter.HasBasis.uniformContinuousOn_iff uniformity_basis_dist
uniformContinuousOn_iff_le 📖	mathematical	—	UniformContinuousOn PseudoMetricSpace.toUniformSpace Real Real.instLT Real.instZero Real.instLE Dist.dist PseudoMetricSpace.toDist	—	Filter.HasBasis.uniformContinuousOn_iff uniformity_basis_dist_le
uniformContinuous_iff 📖	mathematical	—	UniformContinuous PseudoMetricSpace.toUniformSpace Real Real.instLT Real.instZero Dist.dist PseudoMetricSpace.toDist	—	Filter.HasBasis.uniformContinuous_iff uniformity_basis_dist
uniformContinuous_iff_le 📖	mathematical	—	UniformContinuous PseudoMetricSpace.toUniformSpace Real Real.instLT Real.instZero Real.instLE Dist.dist PseudoMetricSpace.toDist	—	Filter.HasBasis.uniformContinuous_iff uniformity_basis_dist_le
uniformSpace_eq_bot 📖	mathematical	—	PseudoMetricSpace.toUniformSpace Bot.bot UniformSpace instBotUniformSpace Real Real.instLT Real.instZero Pairwise Real.instLE Dist.dist PseudoMetricSpace.toDist	—	Filter.HasBasis.uniformSpace_eq_bot uniformity_basis_dist
uniformity_basis_dist 📖	mathematical	—	Filter.HasBasis Real uniformity PseudoMetricSpace.toUniformSpace Real.instLT Real.instZero setOf Dist.dist PseudoMetricSpace.toDist	—	dist_self dist_comm dist_triangle toUniformSpace_eq UniformSpace.hasBasis_ofFun NoMaxOrder.exists_gt instNoMaxOrderOfNontrivial Real.instIsOrderedRing Real.instNontrivial UniformSpace.ofDist_aux
uniformity_basis_dist_inv_nat_pos 📖	mathematical	—	Filter.HasBasis uniformity PseudoMetricSpace.toUniformSpace setOf Real Real.instLT Dist.dist PseudoMetricSpace.toDist DivInvMonoid.toDiv Real.instDivInvMonoid Real.instOne Real.instNatCast	—	mk_uniformity_basis div_pos PosMulReflectLE.toPosMulReflectLT PosMulStrictMono.toPosMulReflectLE IsStrictOrderedRing.toPosMulStrictMono Real.instIsStrictOrderedRing zero_lt_one Real.instZeroLEOneClass NeZero.charZero_one IsStrictOrderedRing.toCharZero Nat.cast_pos Real.instIsOrderedRing Real.instNontrivial exists_nat_one_div_lt Real.instArchimedean Nat.cast_one LT.lt.le
uniformity_basis_dist_inv_nat_succ 📖	mathematical	—	Filter.HasBasis uniformity PseudoMetricSpace.toUniformSpace setOf Real Real.instLT Dist.dist PseudoMetricSpace.toDist DivInvMonoid.toDiv Real.instDivInvMonoid Real.instOne Real.instAdd Real.instNatCast	—	mk_uniformity_basis div_pos PosMulReflectLE.toPosMulReflectLT PosMulStrictMono.toPosMulReflectLE IsStrictOrderedRing.toPosMulStrictMono Real.instIsStrictOrderedRing zero_lt_one Real.instZeroLEOneClass NeZero.charZero_one IsStrictOrderedRing.toCharZero Nat.cast_add_one_pos IsOrderedAddMonoid.toAddLeftMono Real.instIsOrderedAddMonoid le_of_lt exists_nat_one_div_lt Real.instArchimedean
uniformity_basis_dist_le 📖	mathematical	—	Filter.HasBasis Real uniformity PseudoMetricSpace.toUniformSpace Real.instLT Real.instZero setOf Real.instLE Dist.dist PseudoMetricSpace.toDist	—	mk_uniformity_basis_le le_refl
uniformity_basis_dist_le_pow 📖	mathematical	Real Real.instLT Real.instZero Real.instOne	Filter.HasBasis uniformity PseudoMetricSpace.toUniformSpace setOf Real.instLE Dist.dist PseudoMetricSpace.toDist Monoid.toNatPow Real.instMonoid	—	mk_uniformity_basis_le pow_pos IsStrictOrderedRing.toPosMulStrictMono Real.instIsStrictOrderedRing Real.instZeroLEOneClass exists_pow_lt_of_lt_one Real.instArchimedean AddGroup.existsAddOfLE LT.lt.le
uniformity_basis_dist_lt 📖	mathematical	Real Real.instLT Real.instZero	Filter.HasBasis uniformity PseudoMetricSpace.toUniformSpace setOf Dist.dist PseudoMetricSpace.toDist	—	mk_uniformity_basis Nat.instAtLeastTwoHAddOfNat lt_min half_pos PosMulReflectLE.toPosMulReflectLT PosMulStrictMono.toPosMulReflectLE IsStrictOrderedRing.toPosMulStrictMono Real.instIsStrictOrderedRing min_lt_iff half_lt_self min_le_left
uniformity_basis_dist_pow 📖	mathematical	Real Real.instLT Real.instZero Real.instOne	Filter.HasBasis uniformity PseudoMetricSpace.toUniformSpace setOf Dist.dist PseudoMetricSpace.toDist Monoid.toNatPow Real.instMonoid	—	mk_uniformity_basis pow_pos IsStrictOrderedRing.toPosMulStrictMono Real.instIsStrictOrderedRing Real.instZeroLEOneClass exists_pow_lt_of_lt_one Real.instArchimedean AddGroup.existsAddOfLE LT.lt.le
uniformity_basis_dist_rat 📖	mathematical	—	Filter.HasBasis uniformity PseudoMetricSpace.toUniformSpace setOf Real Real.instLT Dist.dist PseudoMetricSpace.toDist Real.instRatCast	—	mk_uniformity_basis Rat.cast_pos Real.instIsStrictOrderedRing exists_rat_btwn Real.instArchimedean LT.lt.le
uniformity_edist 📖	mathematical	—	uniformity PseudoMetricSpace.toUniformSpace iInf Filter ENNReal Filter.instInfSet Preorder.toLT PartialOrder.toPreorder ENNReal.instPartialOrder instZeroENNReal Filter.principal setOf EDist.edist PseudoMetricSpace.toEDist	—	PseudoMetricSpace.uniformity_dist iInf_congr_Prop uniformity_edist_aux edist_nndist
uniformity_edist_aux 📖	mathematical	—	iInf Filter Real Filter.instInfSet Real.instLT Real.instZero Filter.principal setOf NNReal.toReal ENNReal Preorder.toLT PartialOrder.toPreorder ENNReal.instPartialOrder instZeroENNReal ENNReal.ofNNReal	—	ENNReal.lt_iff_exists_nnreal_btwn Filter.mem_iInf_of_mem ENNReal.coe_pos lt_trans ENNReal.coe_lt_coe CanLift.prf NNReal.canLift le_of_lt
uniformity_eq_comap_nhds_zero 📖	mathematical	—	uniformity PseudoMetricSpace.toUniformSpace Filter.comap Real Dist.dist PseudoMetricSpace.toDist nhds UniformSpace.toTopologicalSpace Real.pseudoMetricSpace Real.instZero	—	Filter.ext Filter.HasBasis.mem_iff Filter.HasBasis.comap nhds_basis_ball Real.dist_0_eq_abs abs_dist

NNDist

Definitions

Name	Category	Theorems
nndist 📖	CompOp	175 math math: nndist_ofMul, PiLp.nndist_eq_sum, nndist_ofAdd, WithLp.prod_nndist_eq_of_L2, nndist_inv_inv, AntilipschitzWith.mul_le_nndist, nndist_self, Fin.nndist_insertNth_insertNth, nndist_pi_le_iff, AffineIsometry.nndist_map, nndist_edist, Complex.nndist_self_conj, nndist_eq_zero, nndist_mul_left, nndist_midpoint_right, nndist_smul₀, nndist_mul_right, EuclideanSpace.nndist_eq, coe_nndist, nndist_eq_nnnorm_div, nndist_right_lineMap, Similar.exists_nndist_eq, WithLp.nndist_fst_le, nndist_toMul, nndist_add_add_le, Complex.nndist_of_im_eq, nndist_left_lineMap, nndist_toDual, ULift.nndist_up_up, MeasureTheory.nndist_integral_add_measure_le_lintegral, nndist_vadd_cancel_right, WithLp.prod_nndist_eq_of_L1, Hamming.nndist_eq_hammingDist, similar_iff_exists_nndist_eq, nndist_smul_le, nndist_inv_inv₀, BoxIntegral.Box.nndist_le_distortion_mul, AddOpposite.nndist_op, PiLp.nndist_toLp_single_same, BoundedContinuousFunction.nnnorm_def, Dilation.nndist_eq, nndist_le_pi_nndist, Congruent.nndist_eq, PiLp.nndist_apply_le, BoundedContinuousFunction.nndist_set_exists, dist_le_coe, Isometry.nndist_eq, antilipschitzWith_iff_le_mul_nndist, nndist_triangle_right, nndist_vadd_left, nndist_comm, uniformContinuous_nndist, nndist_single_single, nndist_pi_const, coe_nnreal_ennreal_nndist, nndist_div_left, nndist_left_midpoint, nndist_one_left, ULift.nndist_eq, nndist_sub_right, isClosedMap_nndist, MulOpposite.nndist_op, NNReal.le_add_nndist, MeasureTheory.hausdorffMeasure_lineMap_image, nndist_midpoint_left, dist_nndist, Filter.Tendsto.nndist, nndist_midpoint_midpoint_le', nndist_center_homothety, nndist_vsub_vsub_le, WithLp.prod_nndist_eq_add, Complex.nndist_of_re_eq, WithLp.nndist_toLp_snd, nndist_mul_mul_le, nndist_triangle, AntilipschitzWith.le_mul_nndist, nndist_div_right, nndist_neg_neg, congruent_iff_pairwise_nndist_eq, nndist_lineMap_right, nndist_triangle_left, nndist_eq_nnnorm_sub, edist_lt_coe, BoundedContinuousFunction.nndist_coe_le_nndist, nndist_mulIndicator, nndist_pi_const_le, Congruent.pairwise_nndist_eq, BoundedContinuousFunction.nndist_eq_iSup, nndist_pi_def, NNReal.nndist_eq, EuclideanGeometry.dist_orthogonalProjection_eq_infNndist, nndist_vadd_right, nndist_eq_nnnorm_vsub, nndist_add_left, Real.nndist_eq, dist_lt_coe, nndist_nnnorm_nnnorm_le', nndist_zero_right, Subtype.nndist_eq, edist_le_coe, nndist_midpoint_midpoint_le, WithLp.prod_nndist_eq_sup, IsometryClass.nndist_eq, similar_iff_exists_pairwise_nndist_eq, Complex.nndist_conj_self, ContinuousLinearMap.nndist_le_opNNNorm, LipschitzWith.nndist_le, Metric.isBounded_iff_nndist, ContinuousMap.nndist_eq_iSup, nndist_vsub_cancel_left, Continuous.nndist, NNRat.nndist_eq, dist_pi_def, zero_eq_nndist, Complex.nndist_conj_comm, Complex.nndist_conj_conj, Metric.boundedSpace_iff_nndist, nndist_lineMap_lineMap, BoundedContinuousFunction.nndist_eq, nndist_vsub_cancel_right, nndist_sub_left, Unitization.nndist_inr, nndist_dist, nndist_vadd, nndist_indicator, Inseparable.nndist_eq_zero, Metric.inseparable_iff_nndist, measurable_nndist, nndist_eq_nnnorm, nndist_pi_lt_iff, nndist_homothety_center, UniformContinuous.nndist, HolderOnWith.nndist_le, nndist_nnnorm_nnnorm_le, nndist_zero_left, edist_nndist, NNReal.nndist_zero_eq_val', TensorProduct.nndist_tmul_le, IsometryEquiv.nndist_eq, isometry_iff_nndist_eq, nndist_vadd_cancel_left, AddOpposite.nndist_unop, lipschitzWith_lineMap, MeasureTheory.FiniteMeasure.testAgainstNN_lipschitz_estimate, congruent_iff_nndist_eq, nndist_right_midpoint, Measurable.nndist, MulOpposite.nndist_unop, antilipschitzWith_lineMap, Real.nndist_eq', nndist_vadd_vadd_le, EuclideanSpace.nndist_single_same, WithLp.nndist_toLp_fst, continuous_nndist, nndist_smul, nndist_self_homothety, NNReal.nndist_zero_eq_val, nndist_toAdd, HolderWith.nndist_le, nndist_homothety_self, BoundedContinuousFunction.apply_le_nndist_zero, nndist_add_right, BoundedContinuousFunction.nndist_le_two_nnnorm, BoundedContinuousFunction.NNReal.upper_bound, PiLp.nndist_eq_of_L2, nndist_eq_nnnorm_vsub', Similar.exists_pairwise_nndist_eq, WithLp.nndist_snd_le, nndist_lineMap_left, nndist_one_right, nndist_pi_eq_iff, PiLp.nndist_eq_iSup, isProperMap_nndist, PiLp.nndist_eq_of_L1, nndist_ofDual

PseudoEMetricSpace

Definitions

Name	Category	Theorems
toPseudoMetricSpace 📖	CompOp	—
toPseudoMetricSpaceOfDist 📖	CompOp	—

PseudoMetricSpace

Definitions

Name	Category	Theorems
edist 📖	CompOp	1 math math: edist_dist
ofDistTopology 📖	CompOp	—
replaceBornology 📖	CompOp	1 math math: replaceBornology_eq
replaceTopology 📖	CompOp	1 math math: replaceTopology_eq
replaceUniformity 📖	CompOp	1 math math: replaceUniformity_eq
toBornology 📖	CompOp	189 math math: absorbent_iff_eventually_nhdsNE_zero, Metric.hasBasis_cobounded_compl_closedBall, Metric.isBounded_ball, NormedSpace.isBounded_polar_of_mem_nhds_zero, MonoidHom.exists_nhds_isBounded, Seminorm.absorbent_closedBall_zero, tendsto_const_sub_cobounded, Metric.isCompact_iff_isClosed_bounded, Metric.isBounded_closedBall, Metric.isBounded_iff_subset_ball, tendsto_const_add_cobounded, Filter.hasBasis_cobounded_norm', Complex.comap_exp_cobounded, Metric.hasAntitoneBasis_cobounded_compl_ball, UniformOnFun.instBoundedSpace, tendsto_cobounded_iff_meromorphicOrderAt_neg, Filter.inv_nhdsWithin_ne_zero, Metric.isBounded_range_of_tendsto_cofinite, isBounded_iff_forall_norm_le', AffineSpace.cobounded_eq_iSup_sphere_asymptoticNhds, tendsto_zpow_nhdsNE_zero_cobounded, not_bounded_iff_exists_ne_zero_mem_asymptoticCone, eventually_cobounded_le_norm, NormedSpace.isBounded_iff_subset_smul_ball, NormedSpace.isVonNBounded_iff, BoxIntegral.Box.isBounded, Metric.isBounded_range_of_tendsto, Metric.comap_dist_left_atTop, DilationEquiv.map_cobounded, MeasureTheory.SeparableSpace.exists_measurable_partition_diam_le, Filter.map_mul_left_cobounded, comap_norm_atTop', Tactic.ComputeAsymptotics.Seq.instBoundedSpaceSeq, AntilipschitzWith.tendsto_cobounded, Filter.map_mul_right_cobounded, Metric.isBounded_of_bddAbove_of_bddBelow, Filter.inv_nhdsNE_zero, IsCompact.isBounded, TotallyBounded.isBounded, NormedSpace.isBounded_iff_subset_smul_closedBall, RealNormedSpace.cobounded_neBot, Metric.disjoint_cobounded_nhdsSet, Metric.ediam_eq_top_iff_unbounded, Metric.comap_dist_right_atTop, boundedSub_of_lipschitzWith_sub, Bornology.isVonNBounded_iff_absorbing_le, bornology_eq_of_bilipschitz, tendsto_cobounded_of_meromorphicOrderAt_neg, Complex.tendsto_exp_comap_re_atTop, Metric.disjoint_nhds_cobounded, Metric.isBounded_iff_eventually, Filter.inv_cobounded₀, Metric.isBounded_Ioo, tendsto_sub_const_cobounded, BoundedContinuousFunction.isBounded_range, Asymptotics.isLittleO_const_id_cobounded, Complex.map_exp_comap_re_atTop, Filter.tendsto_inv₀_cobounded, tendsto_intCast_atBot_sup_atTop_cobounded, Unitization.cobounded_eq_aux, absorbs_iff_eventually_nhdsNE_zero, Metric.cobounded_le_cocompact, instBoundedAddOfLipschitzAdd, Metric.isBounded_iff_ediam_ne_top, spectrum.eventually_isUnit_resolvent, instBoundedMul, Bornology.isVonNBounded_iff, absorbent_nhds_zero, Filter.tendsto_inv_cobounded, Metric.boundedSpace_iff, Metric.tendsto_dist_left_atTop_iff, isBounded_iff_asymptoticCone_subset_singleton, Metric.tendsto_dist_left_cobounded_atTop, Real.instIsOrderBornology, Filter.HasBasis.cobounded_of_norm', Filter.hasBasis_cobounded_norm, Metric.tendsto_dist_right_cobounded_atTop, PiNat.boundedSpace, Metric.isBounded_iff, Metric.hasBasis_cobounded_compl_ball, NNReal.instIsOrderBornology, Metric.exists_isOpen_isBounded_image_of_isCompact_of_continuousOn, instBoundedMulOfLipschitzMul, Metric.hasAntitoneBasis_cobounded_compl_closedBall, Metric.exists_isBounded_image_of_tendsto, ZeroAtInftyContinuousMap.isBounded_image, UniformFun.instBoundedSpace, isBounded_iff_of_bilipschitz, bounded_stdSimplex, RCLike.tendsto_ofReal_cobounded_cobounded, LipschitzWith.comap_cobounded_le, ConvexBody.isBounded, IsOrderBornology.of_isCompactIcc, NontriviallyNormedField.cobounded_neBot, eventually_cobounded_le_norm', spectrum.isBounded, isBounded_convexHull, Nat.instIsOrderBornology, BoxIntegral.Box.isBounded_Icc, Filter.tendsto_inv₀_nhdsWithin_ne_zero, Subalgebra.spectrum_isBounded_connectedComponentIn, cobounded_sets, comap_norm_atTop, isBounded_iff_forall_norm_le, absorbs_iff_norm, NormedSpace.vonNBornology_eq, Metric.isBounded_of_compactSpace, Metric.isBounded_image_iff, Balanced.absorbs_self, Seminorm.ball_zero_absorbs_ball_zero, NormedSpace.unbounded_univ, LipschitzWith.coe_toLocallyBoundedMap, Filter.HasBasis.cobounded_of_norm, Dilation.comap_cobounded, Metric.isBounded_Ico, Dilation.tendsto_cobounded, Seminorm.absorbent_ball_zero, Metric.isBounded_closure_iff, Tactic.ComputeAsymptotics.Seq.instBoundedSpaceStream', absorbent_ball, CauchySeq.isBounded_range, Metric.isBounded_range_of_cauchy_map_cofinite, Metric.cobounded_eq_cocompact, Metric.disjoint_cobounded_nhds, Metric.isBounded_sphere, tendsto_norm_atTop_iff_cobounded', Metric.isBounded_iff_nndist, AffineSpace.asymptoticNhds_le_cobounded, BoundedContinuousFunction.isBounded_range_integral, ZSpan.fundamentalDomain_isBounded, Filter.neg_cobounded, Metric.isCobounded_iff_closedBall_compl_subset, Metric.compactSpace_iff_isBounded_univ, Metric.isBounded_range_of_tendsto_cofinite_uniformity, tendsto_norm_cobounded_atTop', instBoundedSubNNReal, Filter.tendsto_mul_left_cobounded, Filter.HasBasis.isVonNBounded_iff, tendsto_norm_cobounded_atTop, Real.cobounded_eq, Metric.boundedSpace_iff_nndist, Metric.exists_isOpen_isBounded_image_of_isCompact_of_forall_continuousAt, NumberField.mixedEmbedding.fundamentalCone.isBounded_normLeOne, NumberField.mixedEmbedding.convexBodySum_isBounded, Filter.comap_mul_left_cobounded, Function.Periodic.isBounded_of_continuous, Metric.isBounded_Ioc, spectrum.resolvent_tendsto_cobounded, Seminorm.absorbent_closedBall, tendsto_norm_atTop_iff_cobounded, absorbs_iff_eventually_nhds_zero, Absorbs.of_norm, ZeroAtInftyContinuousMap.isBounded_range, AddMonoidHom.exists_nhds_isBounded, instBoundedSub, tendsto_add_const_cobounded, NormedSpace.cobounded_neBot, Metric.exists_isOpen_isBounded_image_inter_of_isCompact_of_continuousOn, Metric.isBounded_of_abs_le, Filter.comap_mul_right_cobounded, tendsto_intCast_atTop_cobounded, Metric.isBounded_iff_exists_ge, Filter.tendsto_mul_right_cobounded, instBoundedMulNNReal, Filter.tendsto_inv₀_nhdsNE_zero, Metric.isBounded_iff_subset_closedBall, RCLike.tendsto_ofReal_atBot_cobounded, Metric.disjoint_nhdsSet_cobounded, Int.instIsOrderBornology, tendsto_pow_cobounded_cobounded, Metric.isBounded_Icc, tendsto_algebraMap_cobounded, Seminorm.absorbent_ball, spectrum.resolvent_isBigO_inv, Filter.tendsto_neg_cobounded, tendsto_intCast_atBot_cobounded, Metric.exists_isOpen_isBounded_image_inter_of_isCompact_of_forall_continuousWithinAt, absorbent_ball_zero, algebraMap_cobounded_le_cobounded, Metric.isBounded_of_abs_lt, Metric.tendsto_dist_right_atTop_iff, BoundedContinuousFunction.isBounded_image, RCLike.tendsto_ofReal_atTop_cobounded, Metric.isBounded_range_iff, Filter.tendsto_inv₀_cobounded', Metric.boundedSpace_iff_edist, Int.cobounded_eq, Filter.inv_cobounded, tendsto_natCast_atTop_cobounded
toDist 📖	CompOp	802 math math: EuclideanGeometry.Sphere.mul_dist_eq_abs_power, comap_dist_left_atTop_eq_cocompact, Affine.Triangle.equilateral_iff_dist_01_eq_02_and_dist_01_eq_12, EuclideanGeometry.dist_smul_vadd_sq, dist_le_range_sum_dist, Valued.instIsUltrametricDist, dist_triangle, Metric.cauchySeq_iff, EuclideanGeometry.sin_oangle_right_mul_dist_of_oangle_eq_pi_div_two, BoundedContinuousMapClass.map_bounded, BoundedContinuousFunction.dist_eq_iSup, segment_subset_closedBall_right, dist_midpoint_right, EuclideanGeometry.Sphere.isExtTangent_iff_dist_center, IsUltrametricDist.isUltrametricDist_of_forall_norm_add_le_max_norm, EuclideanGeometry.sin_oangle_right_of_oangle_eq_pi_div_two, MeasureTheory.MeasuredSets.real_sub_real_le_dist, ContractingWith.dist_fixedPoint_le, dist_vadd, ContinuousMap.dist_lt_iff, Metric.uniformContinuous_iff_le, Metric.continuousWithinAt_iff', EuclideanGeometry.dist_inversion_inversion, NormedAddGroup.dist_eq, Real.dist_mulExpNegMulSq_le_two_mul_sqrt, EuclideanGeometry.dist_eq_of_angle_eq_angle_of_angle_ne_pi, Wbtw.dist_add_dist, dist_smul_le, Metric.infDist_le_dist_of_mem, dist_sq_lineMap_lineMap_of_inner_eq_zero, EuclideanGeometry.law_sin, dist_partial_sum, LipschitzWith.dist_le_mul, Metric.diam_triple, MeasureTheory.LevyProkhorov.dist_probabilityMeasure_def, Nat.dist_cast_real, dist_triangle4_right, EuclideanGeometry.dist_div_tan_oangle_right_of_oangle_eq_pi_div_two, dist_self, Affine.Simplex.dist_point_faceOppositeCentroid, Metric.equicontinuousAt_iff_pair, EuclideanGeometry.Sphere.secondInter_dist, EuclideanGeometry.Sphere.IsExtTangent.dist_center, dist_div_eq_dist_mul_left, Metric.tendsto_atTop, dist_left_midpoint, dist_iteratedFDerivWithin_one, EuclideanGeometry.preimage_inversion_perpBisector_inversion, BoundedContinuousFunction.dist_le, UpperHalfPlane.dist_le_iff_dist_coe_center_le, ContinuousMap.dist_le_two_norm, IsCompact.exists_infDist_eq_dist, Tactic.ComputeAsymptotics.Seq.dist_cons_nil, ContinuousMap.isUltrametricDist, dist_mul_self_left, PiCountable.min_dist_le_dist_pi, Metric.comap_dist_left_atTop, Continuous.exists_contDiff_dist_le_of_forall_mem_ball_dist_le, cauchySeq_iff_tendsto_dist_atTop_0, dist_eq_norm, TopologicalSpace.Opens.CompleteCopy.dist_eq, Affine.Triangle.dist_point_faceOppositeCentroid, ContinuousMap.dist_le, isUltrametricDist_iff_forall_norm_natCast_le_one, NNRat.dist_eq, EuclideanGeometry.inversion_dist_center, EuclideanGeometry.dist_orthogonalProjection_eq_iff_oangle_eq, NNReal.tendsto_dist_agmSequences_atTop_zero, EuclideanGeometry.dist_eq_add_dist_iff_angle_eq_pi, Besicovitch.SatelliteConfig.hlast, Affine.Triangle.prod_dist_div_dist_eq_one_of_mem_line_of_mem_line, PNat.dist_eq, EuclideanGeometry.angle_eq_arctan_of_angle_eq_pi_div_two, Metric.dist_lt_add_of_nonempty_ball_inter_ball, EuclideanGeometry.Sphere.IsDiameter.dist_left_right, dist_le_norm_add_norm, IsUltrametricDist.of_normedAlgebra', CircleDeg1Lift.dist_map_zero_translationNumber_le, AntilipschitzWith.mul_le_dist, dist_eq_norm_sub, Rat.dist_eq, Metric.tendsto_nhds_nhds, exists_dist_slope_lt_pairwiseDisjoint_hasSum, dist_birkhoffSum_birkhoffSum_le, dist_sub_right, BoundedContinuousFunction.dist_toContinuousMap, EuclideanGeometry.dist_eq_abs_sub_dist_of_angle_eq_zero, ext_iff, EuclideanGeometry.inversion_mem_perpBisector_inversion_iff', coe_nndist, Similar.exists_pos_dist_eq, Besicovitch.SatelliteConfig.h, EuclideanGeometry.dist_eq_iff_eq_smul_rotation_pi_div_two_vadd_midpoint, dist_inv_inv₀, Metric.equicontinuousAt_iff, Continuous.exists_contDiff_approx_and_eqOn, convexOn_univ_dist, dist_sub_sub_le, BoxIntegral.Integrable.dist_integralSum_le_of_memBaseSet, Metric.tendsto_nhds, ODE.FunSpace.dist_next_next, antilipschitzWith_iff_le_mul_dist, Metric.inseparable_iff, Unitization.dist_inr, Rat.dist_cast, LipschitzWith.le_add_mul, EuclideanGeometry.Sphere.dist_div_sin_oangle_div_two_eq_radius, EuclideanGeometry.angle_le_iff_dist_le, WithLp.prod_dist_eq_of_L2, EuclideanGeometry.tan_oangle_right_of_oangle_eq_pi_div_two, EuclideanGeometry.dist_orthogonalProjection_eq_of_oangle_eq, Metric.uniformity_basis_dist_lt, signedDist_le_dist, EuclideanGeometry.dist_lt_of_sbtw_of_inner_eq_zero, AntilipschitzWith.le_mul_dist, EuclideanGeometry.inversion_vsub_center, EuclideanGeometry.dist_orthogonalProjection_eq_iff_angle_eq, similar_iff_exists_dist_eq, Affine.Triangle.dist_div_sin_angle_eq_two_mul_circumradius, EuclideanGeometry.oangle_right_eq_arcsin_of_oangle_eq_pi_div_two, NNReal.dist_agmSequences_fst_snd, Metric.comap_dist_right_atTop, dist_left_pointReflection, Metric.uniformEquicontinuous_iff, Metric.tendsto_atTop', UpperHalfPlane.dist_eq_iff_eq_sinh, IsUltrametricDist.isUltrametricDist_iff_isNonarchimedean_norm, EuclideanGeometry.oangle_right_eq_arctan_of_oangle_eq_pi_div_two, Congruent.pairwise_dist_eq, NormedAddCommGroup.dist_eq, dist_pair_smul, AffineIsometryEquiv.dist_pointReflection_fixed, Metric.PiNatEmbed.dist_def, MeasureTheory.L1.dist_eq_integral_dist, dist_eq_norm_div', UpperHalfPlane.dist_log_im_le, EuclideanGeometry.dist_of_mem_subset_sphere, uniformContinuous_dist, ContinuousMap.dist_apply_le_dist, Set.Finite.infsep_of_nontrivial, Metric.continuous_iff, DifferentiableWithinAt.dist, exists_dist_eq, EuclideanGeometry.tan_oangle_left_mul_dist_of_oangle_eq_pi_div_two, dist_div_div_le, CircleDeg1Lift.dist_map_map_zero_lt, Affine.Simplex.ExcenterExists.dist_excenter, EuclideanSpace.dist_single_same, MetricSpace.ext_iff, dist_left_midpoint_eq_dist_right_midpoint, Metric.mem_thickening_iff, dist_triangle4, EuclideanGeometry.mul_dist_eq_mul_dist_of_cospherical, dist_vsub_cancel_left, UpperHalfPlane.dist_eq_iff_eq_sq_sinh, Finset.coe_infsep_of_offDiag_nonempty, ZeroAtInftyContinuousMap.dist_toBCF_eq_dist, Set.Nontrivial.infsep_of_fintype, le_two_mul_dist_ofPreNNDist, Metric.infDist_inter_closedBall_of_mem, MeasureTheory.AEStronglyMeasurable.dist, IsUltrametricDist.isUltrametricDist_of_forall_norm_sub_one_of_norm_le_one, edist_le_ofReal, convexOn_dist, dist_self_sub_right, LipschitzWith.dist_left, MeasureTheory.tendstoInMeasure_iff_measureReal_dist, EuclideanGeometry.dist_orthogonalProjection_eq_of_two_zsmul_oangle_eq, zero_eq_dist, Set.Finite.infsep, dist_nonneg, ContractingWith.aposteriori_dist_iterate_fixedPoint_le, Affine.Simplex.dist_sq_eq_dist_orthogonalProjection_sq_add_dist_orthogonalProjection_sq, Similar.exists_dist_eq, EuclideanGeometry.dist_sq_eq_dist_sq_add_dist_sq_sub_two_mul_dist_mul_dist_mul_cos_angle, AddOpposite.dist_unop, EuclideanGeometry.Sphere.power_pos_iff_radius_lt_dist_center, continuous_dist, Complex.dist_self_conj, ODE.FunSpace.dist_iterate_iterate_next_le_of_lipschitzWith, EuclideanGeometry.mul_dist_eq_mul_dist_of_cospherical_of_angle_eq_zero, edist_lt_ofReal, Affine.Triangle.dist_circumcenter_reflection_orthocenter, NormedDivisionRing.dist_eq, SeminormedAddCommGroup.dist_eq, Metric.ball_eq_ball, ContinuousLinearMap.exists_approx_preimage_norm_le, IsUltrametricDist.isUltrametricDist_of_forall_pow_norm_le_nsmul_pow_max_one_norm, dist_vadd_cancel_right, Affine.Simplex.ExcenterExists.dist_excenter_eq_dist_excenter, IsUltrametricDist.isUltrametricDist_of_forall_norm_add_one_le_max_norm_one, abs_dist_sub_le, dist_birkhoffAverage_apply_birkhoffAverage, Metric.tendsto_nhdsWithin_nhds, Real.dist_right_le_of_mem_uIcc, UpperHalfPlane.dist_of_re_eq, dist_eq_norm', dist_le_zero, Set.Nontrivial.infsep_eq_iInf, dist_lineMap_left, dist_ofPreNNDist, Tactic.ComputeAsymptotics.Seq.dist_cons_cons_eq_one, EuclideanGeometry.preimage_inversion_perpBisector, dist_le_coe, abs_dist_sub_le_dist_mul_mul, ULift.dist_eq, dist_midpoint_midpoint_le, Metric.toUniformSpace_eq, EuclideanGeometry.dist_div_tan_angle_of_angle_eq_pi_div_two, BoxIntegral.Integrable.dist_integralSum_integral_le_of_memBaseSet, EuclideanGeometry.dist_eq_add_dist_of_angle_eq_pi, MeasureTheory.tendstoInMeasure_iff_dist, Inseparable.dist_eq_zero, ContractingWith.apriori_dist_iterate_fixedPoint_le, Metric.uniformity_basis_dist, UpperHalfPlane.cosh_dist, Wbtw.dist_le_max_dist, Tactic.ComputeAsymptotics.Seq.dist_eq_one_of_head, Continuous.dist, UniformSpace.Completion.dist_eq, dist_triangle, NonUnitalSeminormedRing.dist_eq, Continuous.exists_contMDiff_approx, EuclideanGeometry.Sphere.dist_sq_eq_mul_dist_of_tangent_and_secant, EuclideanGeometry.Sphere.IsTangentAt.power_eq_dist_sq, Metric.uniformity_basis_dist_rat, convexHull_exists_dist_ge, UpperHalfPlane.dist_coe_center, NormedCommGroup.dist_eq, EuclideanGeometry.Sphere.dist_div_sin_oangle_eq_two_mul_radius, PiLp.dist_eq_of_L1, dist_right_midpoint, CircleDeg1Lift.transnumAuxSeq_dist_lt, dist_center_homothety, Metric.uniformity_basis_dist_inv_nat_succ, BoxIntegral.Integrable.dist_integralSum_sum_integral_le_of_memBaseSet, Metric.isUniformInducing_iff, Metric.dist_le_infDist_add_diam, Prod.dist_eq, Metric.boundedSpace_iff, Metric.tendsto_dist_left_atTop_iff, EuclideanGeometry.image_inversion_perpBisector, Set.infsep_eq_iInf, lipschitz_with_lipschitz_const_mul, Complex.dist_le_mul_div_pow_of_mapsTo_ball_of_isLittleO, ContinuousMap.dist_lt_iff_of_nonempty, PiLp.dist_pseudoMetricSpaceToPi, dist_eq_norm_vsub', UpperHalfPlane.lt_dist_iff_lt_dist_coe_center, WithLp.dist_snd_le, dist_ofPreNNDist_le, dist_mul_left, dist_triangle_right, Complex.dist_le_dist_of_mapsTo_ball, Metric.tendsto_dist_left_cobounded_atTop, Int.dist_cast_rat, Set.infsep_pair, EuclideanGeometry.Sphere.IsTangentAt.radius_lt_dist_center, IsUltrametricDist.isUltrametricDist_of_forall_nnnorm_add_le_max_nnnorm, similar_iff_exists_pairwise_dist_eq, dist_birkhoffAverage_birkhoffAverage, EuclideanGeometry.angle_lt_iff_dist_lt, TopologicalSpace.Opens.CompleteCopy.dist_val_le_dist, IsUltrametricDist.subtype, IsUltrametricDist.of_normedAlgebra, Affine.Triangle.circumsphere_eq_of_dist_of_oangle, AffineIsometryEquiv.dist_pointReflection_self, BoxIntegral.Box.dist_le_distortion_mul, AffineIsometryEquiv.dist_pointReflection_self_real, UpperHalfPlane.dist_lt_iff_dist_coe_center_lt, PiNat.lipschitz_with_one_iff_forall_dist_image_le_of_mem_cylinder, EuclideanGeometry.image_inversion_sphere_dist_center, EuclideanGeometry.dist_div_sin_oangle_left_of_oangle_eq_pi_div_two, BoundedContinuousFunction.dist_lt_iff_of_nonempty_compact, Set.le_edist_of_le_infsep, dist_right_pointReflection, Metric.uniformContinuousOn_iff, Set.Nontrivial.infsep_lt_iff, ContractingWith.dist_le_mul, Metric.tendsto_dist_right_cobounded_atTop, Tactic.ComputeAsymptotics.Seq.dist_cons_cons, UpperHalfPlane.dist_self_center, LinearIsometry.dist_map, dist_lineMap_right, CircleDeg1Lift.dist_map_zero_lt_of_semiconj, EuclideanGeometry.dist_center_eq_dist_center_of_mem_sphere', dist_iteratedFDerivWithin_zero, dist_triangle_left, LipschitzWith.dist_iterate_succ_le_geometric, Metric.isBounded_iff, dist_inv_inv, EuclideanGeometry.preimage_inversion_sphere_dist_center, Set.infsep_of_fintype, Metric.mem_closure_iff, PiCountable.dist_summable, Affine.Triangle.dist_orthocenter_reflection_circumcenter, dist_add_self_left, Subtype.dist_eq, EuclideanGeometry.cospherical_def, Besicovitch.SatelliteConfig.inter', dist_comm, SeminormedRing.dist_eq, EuclideanGeometry.cos_oangle_left_mul_dist_of_oangle_eq_pi_div_two, dist_comm, Metric.tendsto_nhdsWithin_nhdsWithin, LinearIsometryEquiv.dist_map, PNat.dist_coe, dist_pi_le_iff, dist_nndist, Affine.Triangle.dist_div_sin_oangle_eq_two_mul_circumradius, EuclideanGeometry.dist_orthogonalProjection_eq_dist_iff_eq_of_mem, dist_triangle_max, NormedField.dist_eq, Filter.Tendsto.dist, Real.dist_le_of_mem_Icc, AffineSubspace.abs_signedInfDist_eq_dist_of_mem_affineSpan_insert, EuclideanGeometry.Sphere.dist_div_cos_oangle_center_div_two_eq_radius, EuclideanGeometry.dist_eq_abs_sub_dist_iff_angle_eq_zero, SimpleGraph.UnitDistEmbedding.unit_dist, Complex.dist_le_dist_of_mapsTo_ball_self, EuclideanGeometry.sin_angle_div_dist_eq_sin_angle_div_dist, EuclideanGeometry.Sphere.power_neg_iff_dist_center_lt_radius, Metric.dist_lt_add_of_nonempty_closedBall_inter_ball, Tactic.ComputeAsymptotics.Seq.dist_eq_two_inv_pow, Tactic.ComputeAsymptotics.Seq.Stream'.dist_le_one, Metric.continuous_iff', Set.Finite.infsep_exists_of_nontrivial, dist_self_div_right, dist_homothety_self, BoundedContinuousFunction.dist_coe_le_dist, Complex.dist_le_div_mul_dist_of_mapsTo_ball, ContDiffWithinAt.dist, Complex.dist_of_im_eq, Affine.Simplex.dist_incenter_eq_dist_incenter, Affine.Triangle.prod_dist_eq_prod_dist_of_mem_line_of_mem_line, UpperHalfPlane.dist_eq, dist_prod_same_left, nhds_comap_dist, Tactic.ComputeAsymptotics.Seq.dist_nil_cons, SeminormedGroup.dist_eq, Affine.Simplex.exists_forall_dist_eq_iff_exists_excenterExists_and_eq_excenter, WithLp.dist_toLp_snd, isometry_iff_dist_eq, dist_single_single, dist_self_homothety, Real.dist_le_of_mem_uIcc, Metric.le_infDist, MulOpposite.dist_unop, EuclideanGeometry.dist_div_sin_angle_of_angle_eq_pi_div_two, Isometry.preimage_setOf_dist, dist_mulIndicator, dist_pi_lt_iff, inner_vsub_vsub_right_eq_dist_sq_left_iff, Affine.Simplex.dist_point_centroid, Finset.coe_infsep, dist_vsub_cancel_right, dist_prod_same_right, dist_self_mul_left, dist_mono_left_pi, MeasureTheory.LevyProkhorov.dist_def, dist_vadd_left, Nat.dist_cast_rat, Metric.infDist_singleton, UpperHalfPlane.dist_eq_iff_dist_coe_center_eq, dist_self_mul_right, Metric.mem_closedBall', UniformFun.dist_le, Metric.mem_closure_range_iff, PiCountable.dist_le_dist_pi_of_dist_lt, dist_add_add_le, Metric.mem_ball, EuclideanGeometry.cos_oangle_left_of_oangle_eq_pi_div_two, EuclideanGeometry.dist_sq_eq_dist_orthogonalProjection_sq_add_dist_orthogonalProjection_sq, uniformity_dist, Metric.continuousAt_iff', MulOpposite.dist_op, dist_one, CircleDeg1Lift.dist_pow_map_zero_mul_translationNumber_le, PiLp.dist_apply_le, UpperHalfPlane.cmp_dist_eq_cmp_dist_coe_center, Metric.exists_subseq_bounded_of_cauchySeq, EuclideanGeometry.dist_le_of_wbtw_of_mem_perpBisector, EuclideanGeometry.oangle_left_eq_arccos_of_oangle_eq_pi_div_two, EuclideanGeometry.dist_lt_of_sbtw_of_mem_perpBisector, segment_subset_closedBall_left, Complex.dist_eq, tendsto_uniformity_iff_dist_tendsto_zero, Affine.Simplex.dist_circumcenter_eq_circumradius, dist_self, EuclideanGeometry.cos_angle_of_angle_eq_pi_div_two, DenseRange.exists_dist_lt, Metric.mem_sphere, dist_vadd_right, EuclideanGeometry.sin_angle_of_angle_eq_pi_div_two, Metric.continuousWithinAt_iff, dist_add_dist_eq_iff, Metric.uniformity_basis_dist_le, UpperHalfPlane.le_dist_coe, Metric.mk_uniformity_basis_le, EuclideanGeometry.inversion_def, EuclideanGeometry.oangle_left_eq_arcsin_of_oangle_eq_pi_div_two, GromovHausdorff.ghDist_le_nonemptyCompacts_dist, Metric.diam_pair, dist_pi_eq_iff, dist_neg, Affine.Simplex.dist_circumcenter_eq_circumradius', Metric.mem_of_closed', LipschitzOnWith.le_add_mul, EuclideanGeometry.exists_dist_eq_circumradius_of_subset_insert_orthocenter, Metric.isBounded_image_iff, IsBoundedSMul.dist_pair_smul', Metric.exists_dist_lt_of_hausdorffDist_lt, dist_homothety_center, EuclideanGeometry.sin_angle_mul_dist_eq_sin_angle_mul_dist, EuclideanGeometry.oangle_left_eq_arctan_of_oangle_eq_pi_div_two, abs_signedDist_eq_dist_iff_vsub_mem_span, EuclideanGeometry.dist_div_tan_oangle_left_of_oangle_eq_pi_div_two, WithLp.prod_dist_eq_of_L1, tendsto_dist_left_cocompact_atTop, EuclideanGeometry.tan_angle_of_angle_eq_pi_div_two, disjoint_ball_closedBall_iff, UpperHalfPlane.le_dist_iff_le_dist_coe_center, EuclideanGeometry.Sphere.dist_div_cos_oangle_center_eq_two_mul_radius, PadicInt.instIsUltrametricDist, Int.dist_cast_real, cauchySeq_iff_le_tendsto_0, Delone.DeloneSet.packingRadius_lt_dist_of_mem_ne, LipschitzWith.dist_right, dist_zero_left, EuclideanGeometry.mul_dist_add_mul_dist_eq_mul_dist_of_cospherical, ODE.FunSpace.exists_forall_closedBall_funSpace_dist_le_mul, dist_sub_eq_dist_add_left, Metric.dist_le_diam_of_mem, ContractingWith.dist_inequality, AffineIsometryEquiv.dist_map, isProperMap_dist, EuclideanGeometry.dist_eq_dist_mul_sin_angle_div_sin_angle, PiLp.dist_toLp_single_same, EuclideanGeometry.dist_reflection_eq_of_mem, signedDist_vsub_self_rev, EuclideanGeometry.Sphere.dist_orthogonalProjection_eq_radius_iff_isTangent, BoundedContinuousFunction.dist_le_iff_of_nonempty, EuclideanGeometry.mem_sphere, EuclideanGeometry.angle_eq_arccos_of_angle_eq_pi_div_two, UpperHalfPlane.dist_center_dist, EuclideanGeometry.dist_reflection, dist_eq_norm_sub', dist_birkhoffSum_apply_birkhoffSum, EuclideanGeometry.mul_dist_le_mul_dist_add_mul_dist, dist_sq_of_inner_eq_zero, Metric.uniformity_basis_dist_pow, dist_one_left, IsometryClass.dist_eq, EuclideanGeometry.tan_oangle_right_mul_dist_of_oangle_eq_pi_div_two, edist_dist, UpperHalfPlane.dist_le_dist_coe_div_sqrt, PiLp.dist_sq_eq_of_L2, Set.Nontrivial.infsep_exists_of_finite, signedDist_vsub_self, IsUltrametricDist.isUltrametricDist_of_forall_norm_add_one_of_norm_le_one, EuclideanGeometry.dist_eq_iff_dist_orthogonalProjection_eq, EuclideanGeometry.Sphere.power_nonneg_iff_radius_le_dist_center, LipschitzOnWith.iff_le_add_mul, lipschitzWith_iff_dist_le_mul, dist_partial_sum_le_of_le_geometric, AffineSubspace.mem_perpBisector_iff_dist_eq', EuclideanGeometry.cos_angle_mul_dist_of_angle_eq_pi_div_two, dist_lt_coe, EuclideanGeometry.Sphere.power_nonpos_iff_dist_center_le_radius, Metric.infDist_lt_iff, EuclideanGeometry.dist_orthogonalProjection_eq_infDist, dist_pointReflection_right, EuclideanGeometry.tan_angle_mul_dist_of_angle_eq_pi_div_two, EuclideanGeometry.mem_sphere', Real.dist_eq, Set.infsep_triple, dist_sub_left, EuclideanGeometry.sin_angle_mul_dist_of_angle_eq_pi_div_two, Metric.cauchy_iff, Continuous.exists_contMDiff_approx_and_eqOn, dist_pos, EuclideanGeometry.inner_weightedVSub, dist_smul, IsUltrametricDist.isUltrametricDist_of_forall_norm_natCast_le_one, CantorScheme.VanishingDiam.dist_lt, EuclideanGeometry.dist_eq_of_two_zsmul_oangle_eq, dist_triangle4_left, disjoint_closedBall_closedBall_iff, ContractingWith.dist_le_of_fixedPoint, EuclideanGeometry.cospherical_iff_exists_mem_of_complete, Set.infsep_le_dist_of_mem, ODE.FunSpace.dist_iterate_next_le, Real.dist_le_of_mem_Icc_01, EuclideanGeometry.dist_orthogonalProjection_eq_zero_iff, EuclideanGeometry.dist_sq_smul_orthogonal_vadd_smul_orthogonal_vadd, BoxIntegral.integrable_iff_cauchy_basis, EuclideanGeometry.Sphere.isDiameter_iff_mem_and_mem_and_dist, EuclideanGeometry.exists_dist_eq_iff_exists_dist_orthogonalProjection_eq, Complex.dist_conj_conj, Real.dist_0_eq_abs, BoundedVariationOn.dist_le, dist_eq_norm_div, dist_le_dist_of_le_pi, EuclideanGeometry.angle_eq_arcsin_of_angle_eq_pi_div_two, dist_mul_mul_le, Affine.Triangle.dist_circumcenter_reflection_orthocenter_finset, dist_vadd_cancel_left, abs_dist, MeasureTheory.LocallyIntegrable.exists_contDiff_dist_le_of_forall_mem_ball_dist_le, ODE.FunSpace.dist_iterate_next_iterate_next_le, UpperHalfPlane.cosh_half_dist, EuclideanGeometry.Sphere.mul_dist_eq_zero_of_mem_sphere, dist_vsub_vsub_le, LipschitzWith.iff_le_add_mul, dist_self_sub_left, LipschitzOnWith.dist_le_mul, IsometryEquiv.dist_eq, Real.dist_le_of_mem_pi_Icc, EuclideanGeometry.triangle_congruent_iff_dist_eq, inner_vsub_vsub_left_eq_dist_sq_right_iff, Differentiable.dist, Affine.Simplex.Equilateral.dist_eq, UpperHalfPlane.exp_half_dist, ContDiffAt.dist, TensorProduct.dist_tmul_le, EuclideanGeometry.dist_div_cos_oangle_right_of_oangle_eq_pi_div_two, IsUltrametricDist.isUltrametricDist_iff_isNonarchimedean_nnnorm, dist_div_eq_dist_mul_right, MeasureTheory.MeasuredSets.dist_def, IsBoundedSMul.dist_smul_pair', Metric.Sum.dist_eq, NonUnitalNormedRing.dist_eq, EuclideanGeometry.dist_le_of_wbtw_of_inner_eq_zero, dist_left_lineMap, Isometry.dist_eq, Metric.infDist_le_infDist_add_dist, Dense.exists_dist_lt, WithLp.dist_pseudoMetricSpaceToProd, Measurable.dist, dist_indicator, ContDiff.dist, EuclideanGeometry.hasFDerivAt_inversion, dist_div_norm_sq_smul, lipschitzOnWith_iff_dist_le_mul, EuclideanGeometry.dist_div_cos_oangle_left_of_oangle_eq_pi_div_two, EuclideanGeometry.inversion_mem_perpBisector_inversion_iff, Metric.mem_closure_range_iff_nat, IsUltrametricDist.normedAlgebra_iff, EuclideanGeometry.dist_div_cos_angle_of_angle_eq_pi_div_two, dist_partial_sum', EuclideanGeometry.dist_of_mem_subset_mk_sphere, disjoint_ball_ball_iff, abs_dist_sub_le_dist_add_add, BoundedContinuousFunction.dist_set_exists, dist_neg_neg, dist_pi_def, EuclideanGeometry.Sphere.IsTangentAt.dist_sq_eq_of_mem, UpperHalfPlane.sinh_half_dist_add_dist, Metric.denseRange_iff, AffineSubspace.mem_perpBisector_iff_dist_eq, Similar.exists_pairwise_dist_eq, Metric.inductiveLimitDist_eq_dist, dist_eq_zero, UniformContinuous.dist, Complex.dist_mk, EuclideanGeometry.mul_dist_eq_mul_dist_of_cospherical_of_angle_eq_pi, Continuous.exists_contDiff_approx, tendsto_dist_right_cocompact_atTop, dist_add_right, BoundedContinuousFunction.bounded, dist_norm_norm_le', dist_anti_right_pi, DifferentiableOn.dist, dist_dist_dist_le, dist_smul₀, EuclideanSpace.dist_eq, Metric.uniformity_eq_comap_nhds_zero, Affine.Simplex.abs_signedInfDist_eq_dist_of_mem_affineSpan_range, EuclideanGeometry.sin_oangle_left_of_oangle_eq_pi_div_two, convexHull_exists_dist_ge2, ZeroAtInftyContinuousMap.bounded, dist_div_left, Metric.uniformContinuousOn_iff_le, absolutelyContinuousOnInterval_iff, dist_le_norm_add_norm', Real.sub_le_dist, Metric.exists_subseq_summable_dist_of_cauchySeq, ULift.dist_up_up, dist_add_left, EuclideanGeometry.Sphere.isIntTangent_iff_dist_center, SeminormedCommGroup.dist_eq, dist_lt_dist_add_dist_iff, EuclideanGeometry.dist_lt_of_angle_lt, IsClosed.exists_infDist_eq_dist, dist_prod_prod_le, EuclideanGeometry.Sphere.mem_coe', PiLp.dist_eq_of_L2, nndist_dist, dist_sub_eq_dist_add_right, dist_pi_const, Complex.dist_conj_comm, Metric.controlled_of_isUniformEmbedding, dist_pi_const_le, cauchySeq_bdd, EuclideanGeometry.oangle_right_eq_arccos_of_oangle_eq_pi_div_two, Metric.isUniformEmbedding_iff, dist_pointReflection_left, Affine.Triangle.dist_div_sin_angle_div_two_eq_circumradius, dist_eq_norm_vsub, Sbtw.dist_lt_max_dist, Metric.tendstoUniformlyOnFilter_iff, Metric.mem_closedBall, EuclideanGeometry.Sphere.isTangentAt_iff_dist_sq_eq_power, KuratowskiEmbedding.embeddingOfSubset_dist_le, EuclideanSpace.dist_sq_eq, EuclideanGeometry.law_cos, EuclideanGeometry.sin_oangle_left_mul_dist_of_oangle_eq_pi_div_two, Fin.dist_insertNth_insertNth, IsUltrametricDist.dist_eq_max_of_dist_ne_dist, UpperHalfPlane.dist_coe_le, Tactic.ComputeAsymptotics.Seq.FriendlyOperation.dist_le, EuclideanGeometry.dist_affineCombination, similar_iff_exists_pos_pairwise_dist_eq, signedDist_eq_dist_iff_vsub_mem_span, IsCompact.exists_mem_frontier_infDist_compl_eq_dist, HolderOnWith.dist_le, EuclideanGeometry.dist_smul_vadd_eq_dist, dist_birkhoffAverage_birkhoffAverage_le, ConvexBody.hausdorffDist_coe, Metric.Snowflaking.dist_ofSnowflaking_ofSnowflaking, AffineSubspace.mem_perpBisector_iff_inner_eq, SeparationQuotient.dist_mk, HasCompactSupport.exists_simpleFunc_approx_of_prod, UniformContinuous.exists_contDiff_dist_le, Tactic.ComputeAsymptotics.Seq.dist_eq_half_of_head, dist_self_add_right, EuclideanGeometry.dist_sq_mul_dist_add_dist_sq_mul_dist, Metric.continuousAt_iff, Metric.mem_sphere', NormedRing.dist_eq, dist_midpoint_midpoint_le', dist_algebraMap, UpperHalfPlane.sinh_half_dist, dist_self_div_left, EuclideanGeometry.cos_oangle_right_mul_dist_of_oangle_eq_pi_div_two, NNReal.dist_eq, UpperHalfPlane.dist_le_iff_le_sinh, AddOpposite.dist_op, Dilation.dist_eq, dist_mono_right_pi, PadicAlgCl.instIsUltrametricDist, dist_dist_dist_le_left, dist_right_lineMap, Metric.hausdorffDist_singleton, EuclideanGeometry.dist_inversion_mul_dist_center_eq, EuclideanGeometry.dist_div_sin_oangle_right_of_oangle_eq_pi_div_two, EuclideanGeometry.Sphere.IsTangentAt.dist_eq_of_mem_of_mem, Metric.continuousOn_iff', UpperHalfPlane.dist_coe_center_sq, Metric.dist_le_diam_of_mem', Tactic.ComputeAsymptotics.Seq.dist_le_one, dist_self_add_left, Metric.exists_mem_closure_infDist_eq_dist, IsUltrametricDist.isUltrametricDist_of_forall_norm_mul_le_max_norm, hofer, Similar.exists_pos_pairwise_dist_eq, dist_div_right, congruent_iff_dist_eq, HolderWith.dist_le, PiCountable.dist_eq_tsum, BoundedContinuousFunction.map_bounded', EuclideanGeometry.dist_center_inversion, dist_edist, Besicovitch.SatelliteConfig.inter, EuclideanGeometry.dist_sq_add_dist_sq_eq_two_mul_dist_midpoint_sq_add_half_dist_sq, EuclideanGeometry.cospherical_iff_exists_mem_of_finiteDimensional, Metric.isBounded_iff_exists_ge, EuclideanGeometry.Sphere.IsIntTangent.dist_center, KuratowskiEmbedding.embeddingOfSubset_coe, Metric.infDist_eq_iInf, Metric.isGLB_infDist, inner_vsub_vsub_left_eq_dist_sq_left_iff, BoxIntegral.hasIntegral_iff, UpperHalfPlane.tanh_half_dist, abs_signedDist_le_dist, EuclideanGeometry.tan_oangle_left_of_oangle_eq_pi_div_two, dist_midpoint_left, Metric.continuousOn_iff, Metric.cauchySeq_iff', dist_add_self_right, EuclideanGeometry.Sphere.IsTangent.radius_le_dist_center, Affine.Triangle.dist_div_sin_oangle_div_two_eq_circumradius, dist_zero_right, EuclideanGeometry.dist_inversion_center, dist_algebraMap', dist_dist_dist_le_right, Affine.Simplex.dist_incenter, EuclideanGeometry.inversion_dist_center', dist_le_pi_dist, ContinuousMap.uniform_continuity, dist_inf_sup_pi, UniformFun.dist_def, dist_add_dist_of_mem_segment, Metric.uniformity_basis_dist_le_pow, AbsoluteValue.Completion.extensionEmbedding_dist_eq_of_comp, dist_smul_add_one_sub_smul_le, SeminormedAddGroup.dist_eq, Metric.uniformContinuous_iff, dist_sum_sum_le, dist_norm_norm_le, Real.dist_mulExpNegMulSq_le_dist, tendsto_nhds_unique_dist, tendsto_iff_dist_tendsto_zero, uniformity_basis_dist_pow_of_lt_one, BoundedContinuousFunction.dist_le_two_norm, MeasureTheory.StronglyMeasurable.dist, dist_zero, ContinuousLinearMap.dist_le_opNorm, EuclideanGeometry.inversion_eq_lineMap, Metric.dist_lt_add_of_nonempty_ball_inter_closedBall, dist_pi_le_iff', swap_dist, Complex.dist_of_re_eq, Affine.Triangle.dist_orthocenter_reflection_circumcenter_finset, Congruent.dist_eq, dist_sq_lineMap_of_inner_eq_zero, Metric.diam_union, BoundedContinuousFunction.dist_mkOfCompact, Metric.uniformCauchySeqOn_iff, EuclideanGeometry.dist_orthogonalProjection_line_eq_iff_two_zsmul_oangle_eq, dist_le_Ico_sum_dist, EuclideanGeometry.cos_oangle_right_of_oangle_eq_pi_div_two, EuclideanGeometry.dist_orthogonalProjection_line_eq_of_two_zsmul_oangle_eq, properSpace_iff_isProperMap_dist, ContinuousMap.dist_le_iff_of_nonempty, CircleDeg1Lift.dist_map_zero_lt_of_semiconjBy, edist_dist, IsUltrametricDist.isUltrametricDist_of_forall_nnnorm_mul_le_max_nnnorm, dist_inv, Metric.uniformSpace_eq_bot, NNReal.dist_gm_am_le, BoundedContinuousFunction.dist_lt_iff_of_compact, dist_smul_pair, AffineIsometryEquiv.dist_pointReflection_self', WithLp.dist_toLp_fst, dist_vadd_vadd_le, congruent_iff_pairwise_dist_eq, ODE.FunSpace.dist_iterate_next_apply_le, dist_triangle8, AEMeasurable.dist, Set.Nontrivial.le_infsep_iff, disjoint_closedBall_ball_iff, EuclideanGeometry.Sphere.dist_orthogonalProjection_eq_radius_iff_isTangentAt, EuclideanGeometry.dist_sq_eq_dist_sq_add_dist_sq_iff_angle_eq_pi_div_two, Metric.tendsto_dist_right_atTop_iff, dist_one_right, Complex.dist_conj_self, IsUltrametricDist.isUltrametricDist_of_isNonarchimedean_nnnorm, BoundedContinuousFunction.dist_le_two_norm', similar_iff_exists_pos_dist_eq, EuclideanGeometry.dist_set_eq_iff_dist_orthogonalProjection_eq, Metric.uniformity_basis_dist_inv_nat_pos, Metric.isBounded_range_iff, DifferentiableAt.dist, BoxIntegral.Integrable.dist_integralSum_sum_integral_le_of_memBaseSet_of_iUnion_eq, NormedGroup.dist_eq, AffineIsometry.dist_map, Metric.ball_eq_ball', isClosedMap_dist, inner_vsub_vsub_right_eq_dist_sq_right_iff, MeasureTheory.LevyProkhorov.dist_finiteMeasure_def, ContDiffOn.dist, dist_mul_right, Real.dist_left_le_of_mem_uIcc, EuclideanGeometry.Sphere.IsDiameter.dist_left_right_div_two, dist_lineMap_lineMap, lipschitz_with_lipschitz_const_add, Affine.Triangle.dist_point_centroid, NormedAddTorsor.dist_eq_norm', Delone.DeloneSet.exists_dist_le_coveringRadius, dist_mul_self_right, dist_anti_left_pi, IsUltrametricDist.isUltrametricDist_of_isNonarchimedean_norm, ContinuousMap.dist_eq_iSup, Metric.NonemptyCompacts.dist_eq, LipschitzWith.dist, Metric.dist_le_add_of_nonempty_closedBall_inter_closedBall, AbsolutelyContinuousOnInterval.hasBasis_totalLengthFilter, Affine.Triangle.equilateral_iff_dist_eq_and_dist_eq, Complex.dist_eq_re_im, Metric.mem_ball', Metric.Sigma.dist_ne, Metric.isUniformEmbedding_iff', WithLp.dist_fst_le, Metric.mk_uniformity_basis, continuous_iff_continuous_dist, EuclideanGeometry.dist_center_eq_dist_center_of_mem_sphere, Metric.exists_dist_lt_of_hausdorffDist_lt', Metric.Sigma.dist_same, Metric.dist_mem_uniformity, exists_mem_frontier_infDist_compl_eq_dist, measurable_dist
toEDist 📖	CompOp	12 math math: nndist_edist, edist_le_ofReal, edist_lt_ofReal, coe_nnreal_ennreal_nndist, edist_lt_coe, edist_dist, edist_le_coe, edist_lt_top, Metric.uniformity_edist, edist_nndist, dist_edist, Metric.boundedSpace_iff_edist
toNNDist 📖	CompOp	175 math math: nndist_ofMul, PiLp.nndist_eq_sum, nndist_ofAdd, WithLp.prod_nndist_eq_of_L2, nndist_inv_inv, AntilipschitzWith.mul_le_nndist, nndist_self, Fin.nndist_insertNth_insertNth, nndist_pi_le_iff, AffineIsometry.nndist_map, nndist_edist, Complex.nndist_self_conj, nndist_eq_zero, nndist_mul_left, nndist_midpoint_right, nndist_smul₀, nndist_mul_right, EuclideanSpace.nndist_eq, coe_nndist, nndist_eq_nnnorm_div, nndist_right_lineMap, Similar.exists_nndist_eq, WithLp.nndist_fst_le, nndist_toMul, nndist_add_add_le, Complex.nndist_of_im_eq, nndist_left_lineMap, nndist_toDual, ULift.nndist_up_up, MeasureTheory.nndist_integral_add_measure_le_lintegral, nndist_vadd_cancel_right, WithLp.prod_nndist_eq_of_L1, Hamming.nndist_eq_hammingDist, similar_iff_exists_nndist_eq, nndist_smul_le, nndist_inv_inv₀, BoxIntegral.Box.nndist_le_distortion_mul, AddOpposite.nndist_op, PiLp.nndist_toLp_single_same, BoundedContinuousFunction.nnnorm_def, Dilation.nndist_eq, nndist_le_pi_nndist, Congruent.nndist_eq, PiLp.nndist_apply_le, BoundedContinuousFunction.nndist_set_exists, dist_le_coe, Isometry.nndist_eq, antilipschitzWith_iff_le_mul_nndist, nndist_triangle_right, nndist_vadd_left, nndist_comm, uniformContinuous_nndist, nndist_single_single, nndist_pi_const, coe_nnreal_ennreal_nndist, nndist_div_left, nndist_left_midpoint, nndist_one_left, ULift.nndist_eq, nndist_sub_right, isClosedMap_nndist, MulOpposite.nndist_op, NNReal.le_add_nndist, MeasureTheory.hausdorffMeasure_lineMap_image, nndist_midpoint_left, dist_nndist, Filter.Tendsto.nndist, nndist_midpoint_midpoint_le', nndist_center_homothety, nndist_vsub_vsub_le, WithLp.prod_nndist_eq_add, Complex.nndist_of_re_eq, WithLp.nndist_toLp_snd, nndist_mul_mul_le, nndist_triangle, AntilipschitzWith.le_mul_nndist, nndist_div_right, nndist_neg_neg, congruent_iff_pairwise_nndist_eq, nndist_lineMap_right, nndist_triangle_left, nndist_eq_nnnorm_sub, edist_lt_coe, BoundedContinuousFunction.nndist_coe_le_nndist, nndist_mulIndicator, nndist_pi_const_le, Congruent.pairwise_nndist_eq, BoundedContinuousFunction.nndist_eq_iSup, nndist_pi_def, NNReal.nndist_eq, EuclideanGeometry.dist_orthogonalProjection_eq_infNndist, nndist_vadd_right, nndist_eq_nnnorm_vsub, nndist_add_left, Real.nndist_eq, dist_lt_coe, nndist_nnnorm_nnnorm_le', nndist_zero_right, Subtype.nndist_eq, edist_le_coe, nndist_midpoint_midpoint_le, WithLp.prod_nndist_eq_sup, IsometryClass.nndist_eq, similar_iff_exists_pairwise_nndist_eq, Complex.nndist_conj_self, ContinuousLinearMap.nndist_le_opNNNorm, LipschitzWith.nndist_le, Metric.isBounded_iff_nndist, ContinuousMap.nndist_eq_iSup, nndist_vsub_cancel_left, Continuous.nndist, NNRat.nndist_eq, dist_pi_def, zero_eq_nndist, Complex.nndist_conj_comm, Complex.nndist_conj_conj, Metric.boundedSpace_iff_nndist, nndist_lineMap_lineMap, BoundedContinuousFunction.nndist_eq, nndist_vsub_cancel_right, nndist_sub_left, Unitization.nndist_inr, nndist_dist, nndist_vadd, nndist_indicator, Inseparable.nndist_eq_zero, Metric.inseparable_iff_nndist, measurable_nndist, nndist_eq_nnnorm, nndist_pi_lt_iff, nndist_homothety_center, UniformContinuous.nndist, HolderOnWith.nndist_le, nndist_nnnorm_nnnorm_le, nndist_zero_left, edist_nndist, NNReal.nndist_zero_eq_val', TensorProduct.nndist_tmul_le, IsometryEquiv.nndist_eq, isometry_iff_nndist_eq, nndist_vadd_cancel_left, AddOpposite.nndist_unop, lipschitzWith_lineMap, MeasureTheory.FiniteMeasure.testAgainstNN_lipschitz_estimate, congruent_iff_nndist_eq, nndist_right_midpoint, Measurable.nndist, MulOpposite.nndist_unop, antilipschitzWith_lineMap, Real.nndist_eq', nndist_vadd_vadd_le, EuclideanSpace.nndist_single_same, WithLp.nndist_toLp_fst, continuous_nndist, nndist_smul, nndist_self_homothety, NNReal.nndist_zero_eq_val, nndist_toAdd, HolderWith.nndist_le, nndist_homothety_self, BoundedContinuousFunction.apply_le_nndist_zero, nndist_add_right, BoundedContinuousFunction.nndist_le_two_nnnorm, BoundedContinuousFunction.NNReal.upper_bound, PiLp.nndist_eq_of_L2, nndist_eq_nnnorm_vsub', Similar.exists_pairwise_nndist_eq, WithLp.nndist_snd_le, nndist_lineMap_left, nndist_one_right, nndist_pi_eq_iff, PiLp.nndist_eq_iSup, isProperMap_nndist, PiLp.nndist_eq_of_L1, nndist_ofDual
toPseudoEMetricSpace 📖	CompOp	419 math math: Matrix.l2_opNorm_toEuclideanCLM, MeasureTheory.tendstoInMeasure_iff_measureReal_norm, ball_sub, IsometryEquiv.image_sphere, edist_eq_enorm_sub, Metric.thickening_eq_biUnion_ball, NormedGroup.to_isIsometricSMul_right, locallyLipschitz_neg_iff, LinearIsometryEquiv.coe_symm_toIsometryEquiv, infEdist_inv, mul_ball, IsometryEquiv.preimage_sphere, LinearIsometry.lipschitz, SemilinearIsometryClass.ediam_image, Matrix.cstar_nnnorm_def, Metric.eball_top_eq_univ, LipschitzWith.mk_one, AddMonoidHomClass.lipschitz_of_bound_nnnorm, LinearIsometryEquiv.antilipschitz, DilationEquiv.smulTorsor_symm_apply, infEdist_thickening, MeasureTheory.LevyProkhorov.eq_convergenceInDistribution, IsCompact.closedBall_mul, closure_thickening, Set.le_einfsep_of_forall_dist_le, IsCompact.mul_closedBall_one, MeasureTheory.tendstoInMeasure_of_tendsto_eLpNorm_of_stronglyMeasurable, AddMonoidHomClass.isometry_of_norm, Set.einfsep_lt_top_iff, lipschitzWith_lipschitz_const_add_edist, HasMFDerivWithinAt.prodMk, Metric.eball_ofReal, edist_zero_left, Dilation.ratio_unique_of_dist_ne_zero, edist_zero_eq_enorm, SemilinearIsometryClass.ediam_range, Metric.emetric_closedBall, AffineIsometryEquiv.edist_map, Dilation.mapsTo_sphere, ball_div_one, Metric.emetric_ball, AffineIsometryEquiv.toIsometryEquiv_refl, Metric.ediam_univ_of_noncompact, AntilipschitzWith.of_le_mul_dist, IsometryEquiv.constVSub_symm_apply, IsCompact.closedBall_zero_add, MeasureTheory.tendstoInMeasure_of_tendsto_eLpNorm_top, infEDist_neg_neg, antilipschitzWith_iff_le_mul_dist, MeasureTheory.LevyProkhorov.continuous_equiv_symm_probabilityMeasure, ediam_smul_le, ball_mul_one, Metric.isCover_iff_subset_cthickening, Convex.cthickening, Metric.closedEBall_ofReal, AbsolutelyContinuousOnInterval.boundedVariationOn, Metric.ball_subset_thickening, Metric.ediam_eq_top_iff_unbounded, blimsup_thickening_mul_ae_eq_aux, similar_iff_exists_dist_eq, IsometryEquiv.diam_image, Metric.mem_cthickening_of_dist_le, similar_iff_exists_nndist_eq, SemilinearIsometryClass.lipschitz, Congruent.of_nndist_eq, RegularNormedAlgebra.isometry_mul', Set.Finite.infsep_of_nontrivial, HasMFDerivWithinAt.prodMap, MeasureTheory.tendstoInMeasure_iff_norm, antilipschitzWith_iff_exists_mul_le_norm', Metric.mem_thickening_iff, AddMonoidHomClass.lipschitz_of_bound, LinearIsometry.edist_map, MeasureTheory.LevyProkhorov.continuous_equiv_probabilityMeasure, Finset.coe_infsep_of_offDiag_nonempty, LipschitzOnWith.of_dist_le_mul, Set.Nontrivial.infsep_of_fintype, Set.infsep_le_of_mem_of_edist_le, Dilation.coe_mkOfNNDistEq, LinearIsometryEquiv.toIsometryEquiv_injective, LipschitzWith.dist_left, MeasureTheory.tendstoInMeasure_iff_measureReal_dist, Set.Finite.infsep, Module.Basis.prod_addHaar, LipschitzWith.of_le_add, AffineIsometry.lipschitz, ball_mul, IsCompact.div_closedBall, blimsup_cthickening_ae_le_of_eventually_mul_le_aux, WithLp.edist_toLp_snd, HasFPowerSeriesWithinOnBall.prod, infEDist_smul₀, Dilation.nndist_eq, star_isometry, Metric.emetric_ball_top, UniformFun.isometry_ofFun_continuousMap, Set.Nontrivial.infsep_eq_iInf, holderWith_zero_iff, MulOpposite.isometry_opLinearEquiv, Matrix.toEuclideanCLM_toLp, NormedAddGroupHom.isometry_id, antilipschitzWith_iff_le_mul_nndist, Congruent.of_pairwise_nndist_eq, locallyLipschitzOn_neg_iff, ContinuousLinearMap.lipschitz, MeasureTheory.tendstoInMeasure_iff_dist, WithLp.prod_edist_eq_of_L2, ball_add_zero, neg_thickening, isometry_induced, IsCompact.cthickening_eq_biUnion_closedBall, MeasureTheory.LevyProkhorov.edist_finiteMeasure_def, edist_mul_mul_le, blimsup_cthickening_ae_le_of_eventually_mul_le, Metric.diam_thickening_le, lipschitzWith_one_norm', lipschitzWith_lipschitz_const_mul_edist, Isometry.of_dist_eq, Dilation.mapsTo_closedBall, cthickening_thickening, Set.infsep_eq_iInf, lipschitzOnWith_iff_norm_div_le, ContinuousLinearMap.lipschitz_apply, div_ball, LipschitzOnWith.mk_one, algebraMap_isometry, infEDist_neg, Set.infsep_pair, HasMFDerivAt.prodMap, similar_iff_exists_pairwise_dist_eq, ball_sub_zero, AddMonoidHomClass.antilipschitz_of_bound, Set.einfsep_eq_top_iff, convex_eball, RingHom.isometry, NumberField.mixedEmbedding.euclidean.volumePreserving_toMixed, IsCompact.mul_closedBall, LinearIsometryEquiv.coe_toIsometryEquiv, MeasureTheory.exists_null_frontier_thickening, add_ball_zero, Similar.of_exists_pos_dist_eq, Set.Nontrivial.infsep_lt_iff, IsContDiffImplicitAt.implicitFunction_apply, LinearIsometry.ediam_image, neg_cthickening, IsCompact.closedBall_one_mul, Metric.emetric_ball_nnreal, IsCompact.closedBall_div, Set.infsep_of_fintype, BoundedContinuousFunction.isometry_extend, ball_div, infEdist_smul₀, UniformFun.isometry_ofFun_boundedContinuousFunction, mem_emetric_ball_one_iff, LipschitzMul.lipschitz_mul, IsContDiffImplicitAt.implicitFunctionData_pt, edist_one_right, lipschitzWith_iff_norm_div_le, MonoidHomClass.lipschitz_of_bound_nnnorm, ContinuousLinearMap.lipschitzWith_of_opNorm_le, UniformSpace.Completion.coe_isometry, LipschitzWith.coordinate, similar_of_side_side, Set.Finite.infsep_exists_of_nontrivial, lipschitzOnWith_neg_iff, Metric.cthickening_eq_biUnion_closedBall, Matrix.ofLp_toEuclideanCLM, lipschitzWith_iff_norm_sub_le, DilationEquiv.smulTorsor_apply, ContinuousLinearEquiv.lipschitz, NormedAddGroup.to_isIsometricVAdd_left, isometry_iff_dist_eq, NormedAddGroup.to_isIsometricVAdd_right, MonoidHomClass.isometry_iff_norm, IsClosed.cthickening_eq_biUnion_closedBall, SemiNormedGrp₁.iso_isometry, thickening_closedBall, infEdist_inv_inv, Finset.coe_infsep, Isometry.of_nndist_eq, edist_one_eq_enorm, congruent_iff_pairwise_nndist_eq, SemilinearIsometryClass.antilipschitz, Metric.eball_top, edist_smul₀, Metric.cthickening_singleton, edist_eq_enorm_div, convex_closedEBall, IsContDiffImplicitAt.implicitFunctionData_rightFun_apply, IsCompact.sub_closedBall_zero, edist_add_add_le, Metric.thickening_ball, Metric.mem_thickening_iff_infDist_lt, Matrix.coe_toEuclideanCLM_eq_toEuclideanLin, mem_eball_one_iff, lipschitzWith_inv_iff, cthickening_closedBall, IsCompact.cthickening, ContinuousLinearMap.isometry_mul, Dilation.mapsTo_ball, MonoidHomClass.antilipschitz_of_bound, LinearIsometryEquiv.edist_map, Set.Nontrivial.infsep_anti, Metric.infEdist_eq_top_iff, LipschitzWith.dist_right, HasFPowerSeriesWithinAt.prod, Finset.coe_infsep_of_offDiag_empty, MeasureTheory.LevyProkhorov.edist_probabilityMeasure_def, LinearIsometry.isometry, IsometryEquiv.diam_preimage, infEDist_thickening, AffineIsometry.isometry, MeasureTheory.tendstoInMeasure_iff_measureReal_enorm, LinearIsometry.antilipschitz, Set.Nontrivial.infsep_exists_of_finite, Similar.of_exists_pos_pairwise_dist_eq, HasFTaylorSeriesUpToOn.prodMk, LipschitzOnWith.coordinate, LinearIsometryEquiv.isometry, LipschitzOnWith.iff_le_add_mul, lipschitzWith_iff_dist_le_mul, AffineIsometryEquiv.coe_toIsometryEquiv, Set.infsep_triple, IsCompact.closedBall_one_div, WithLp.prod_edist_eq_of_L1, LipschitzWith.of_le_add_mul, Metric.thickening_singleton, Trivialization.continuousLinearEquivAt_prod, ball_add, convexHull_ediam, similar_iff_exists_pairwise_nndist_eq, IsCompact.sub_closedBall, Set.infsep_le_dist_of_mem, infEdist_cthickening, lipschitzWith_one_nnnorm, IsometryEquiv.image_closedBall, thickening_thickening, Dilation.coe_mkOfDistEq, thickening_cthickening, add_ball, Similar.of_exists_pairwise_dist_eq, LipschitzWith.iff_le_add_mul, BoundedContinuousFunction.edist_eq_iSup, IsometryEquiv.dist_eq, IsometryEquiv.vaddConst_apply, Convex.lipschitz_gauge, Metric.emetric_closedBall_nnreal, SeminormedAddCommGroup.lipschitzWith_sub, IsCompact.closedBall_zero_sub, NormedAddTorsor.to_isIsIsometricVAdd, AddMonoidHomClass.isometry_iff_norm, ZeroAtInftyContinuousMap.isometry_toBCF, infEDist_cthickening, lipschitzOnWith_inv_iff, AffineIsometry.ediam_range, div_ball_one, ediam_smul₀, BoundedContinuousFunction.lipschitz_compContinuous, ContinuousMap.isometryEquivBoundedOfCompact_toEquiv, lipschitzOnWith_iff_dist_le_mul, UniformOnFun.edist_continuousRestrict, HasFPowerSeriesOnBall.prod, LipschitzOnWith.of_le_add, PiLp.edist_toLp_single_same, mul_ball_one, edist_vadd_vadd_le, IsometryEquiv.constVSub_apply, DilationEquiv.smulTorsor_ratio, Metric.ediam_le_of_forall_dist_le, AffineIsometryEquiv.ediam_image, ContinuousLinearMap.antilipschitz_of_bound, Set.Nontrivial.le_infsep, Metric.infEDist_eq_top_iff, edist_zero_right, MeasureTheory.exists_null_frontiers_thickening, Convex.lipschitzWith_gauge, MeasureTheory.tendstoInMeasure_of_tendsto_eLpNorm_of_ne_top, IsContDiffImplicitAt.implicitFunctionData_rightFun_pt, NormedAddGroupHom.lipschitz, Dilation.diam_range, ContinuousLinearMap.opNorm_le_iff_lipschitz, Dilation.diam_image, blimsup_cthickening_ae_eq_blimsup_thickening, LinearIsometryEquiv.toIsometryEquiv_trans, IsContDiffImplicitAt.implicitFunctionData_leftFun_apply, Metric.lipschitz_infDist_pt, Metric.ediam_of_unbounded, MeasureTheory.LevyProkhorov.continuous_ofMeasure_probabilityMeasure, LinearIsometry.ediam_range, Congruent.of_pairwise_dist_eq, MonoidHomClass.isometry_of_norm, AffineIsometryEquiv.lipschitz, IsometryEquiv.vaddConst_symm_apply, AffineIsometry.edist_map, HasFPowerSeriesAt.prod, Similar.of_exists_pairwise_nndist_eq, LinearIsometryEquiv.lipschitz, HasMFDerivAt.prodMk, similar_of_dist_mul_eq_dist_mul_eq, Topology.IsEmbedding.to_isometry, infEdist_neg, ediam_mul_le, blimsup_thickening_mul_ae_eq, LipschitzOnWith.of_le_add_mul', mem_emetric_ball_zero_iff, WithLp.edist_toLp_fst, MeasureTheory.tendstoInMeasure_iff_enorm, sub_ball_zero, NormedGroup.to_isIsometricSMul_left, similar_iff_exists_pos_pairwise_dist_eq, Metric.isCover_iff_subset_iUnion_closedBall, BoundedContinuousFunction.lipschitz_eval_const, MeasureTheory.LevyProkhorov.le_convergenceInDistribution, ConvexBody.hausdorffEDist_coe, IsometryEquiv.image_ball, cthickening_cthickening, IsCompact.closedBall_add, Dilation.dist_eq, ediam_add_le, DilationEquiv.smulTorsor_preimage_ball, ConvexBody.hausdorffEdist_coe, MeasureTheory.levyProkhorov_le_convergenceInDistribution, inv_cthickening, Metric.ediam_univ_eq_top_iff_noncompact, antilipschitzWith_inv_iff, MeasureTheory.LevyProkhorov.continuous_toMeasure_probabilityMeasure, Metric.eball_coe, cthickening_ball, Set.Nontrivial.einfsep_lt_top, blimsup_cthickening_mul_ae_eq, IsContDiffImplicitAt.implicitFunction_def, AffineIsometryEquiv.antilipschitz, NumberField.mixedEmbedding.euclidean.volumePreserving_toMixed_symm, Bornology.IsBounded.thickening, ContinuousMap.isometryEquivBoundedOfCompact_symm_apply, LinearIsometryEquiv.toIsometryEquiv_symm, AffineIsometryEquiv.coe_symm_toIsometryEquiv, BoundedContinuousFunction.lipschitz_evalx, Dilation.ratio_unique_of_nndist_ne_zero, congruent_iff_dist_eq, UniformOnFun.edist_continuousRestrict_of_singleton, AffineIsometry.antilipschitz, Similar.of_exists_dist_eq, Bornology.IsBounded.cthickening, lipschitzWith_one_nnnorm', Metric.isCover_closure, antilipschitzWith_neg_iff, IsCompact.div_closedBall_one, Bundle.Prod.contMDiffVectorBundle, MonoidHomClass.lipschitz_of_bound, Metric.closedEBall_coe, IsometryEquiv.nndist_eq, thickening_ball, Matrix.cstar_norm_def, isometry_iff_nndist_eq, Similar.of_exists_nndist_eq, lipschitzWith_lineMap, locallyLipschitz_inv_iff, edist_vsub_vsub_le, LipschitzWith.of_dist_le_mul, UniformFun.edist_continuousMapMk, mem_eball_zero_iff, congruent_iff_nndist_eq, edist_one_left, inv_thickening, SemiNormedGrp.iso_isometry_of_normNoninc, ContinuousMap.isometryEquivBoundedOfCompact_apply, Metric.closedBall_subset_cthickening_singleton, infEDist_inv_inv, IsCompact.add_closedBall_zero, Congruent.of_dist_eq, lipschitzWith_smul, edist_smul_le, UniformSpace.Completion.edist_eq, infEdist_neg_neg, IsometryEquiv.preimage_closedBall, sub_ball, Convex.thickening, LipschitzOnWith.of_dist_le', MeasureTheory.AEStronglyMeasurable.edist, PiLp.edist_eq_of_L1, MeasureTheory.tendsto_integral_meas_thickening_le, NormedAddGroupHom.antilipschitz_of_norm_ge, edist_indicator, AffineIsometryEquiv.isometry, LipschitzAdd.lipschitz_add, LipschitzWith.of_dist_le', IsometryEquiv.preimage_ball, Metric.cthickening_subset_iUnion_closedBall_of_lt, Metric.lipschitz_infNndist_pt, congruent_iff_pairwise_dist_eq, AffineIsometry.ediam_image, Metric.diam_cthickening_le, VectorBundle.prod, LipschitzOnWith.of_le_add_mul, Set.Nontrivial.le_infsep_iff, SemilinearIsometryClass.isometry, locallyLipschitzOn_inv_iff, Metric.closedBall_subset_cthickening, IsCompact.add_closedBall, AffineIsometryEquiv.toIsometryEquiv_symm, infEDist_inv, antilipschitzWith_iff_exists_mul_le_norm, similar_iff_exists_pos_dist_eq, lipschitzOnWith_iff_norm_sub_le, LipschitzWith.of_le_add_mul', ContinuousMap.edist_eq_iSup, lipschitzWith_neg_iff, PiLp.edist_eq_of_L2, HolderWith.smul_iff, IsContDiffImplicitAt.implicitFunctionData_leftFun_pt, AntilipschitzWith.of_le_mul_nndist, LipschitzWith.dist, LinearIsometryEquiv.ediam_image, edist_mulIndicator, Metric.IsCover.of_subset_iUnion_closedBall, IsCompact.closedBall_sub, lipschitzWith_one_norm, MeasureTheory.levyProkhorov_eq_convergenceInDistribution
toUniformSpace 📖	CompOp	10002 math, 1 bridge math: AnalyticWithinAt.const_smul, ContinuousMap.dense_setOf_contDiff, ArithmeticFunction.vonMangoldt.residueClass_eq, Unitary.openPartialHomeomorph_source, MeasureTheory.HasFiniteIntegral.of_subsingleton, SchwartzMap.norm_toLp_le_seminorm, Polynomial.fderiv, Matrix.l2_opNorm_toEuclideanCLM, ContDiffMapSupportedIn.coe_toBoundedContinuousFunction, Pi.comul_eq_adjoint, LinearMap.subset_bipolar, MeasureTheory.tendstoInMeasure_iff_measureReal_norm, LinearMap.det_toContinuousLinearMap, TestFunctionClass.instContinuousMapClass, Orientation.rightAngleRotationAux₁_rightAngleRotationAux₁, MeromorphicAt.meromorphicTrailingCoeffAt_add_eq_add, ValueDistribution.logCounting_zero, instSeparatingDual, MeasureTheory.Lp.instHasSolidNorm, TangentBundle.continuousLinearMapAt_model_space, Metric.equicontinuousAt_iff_right, hasFDerivAt_iff_hasDerivAt, absorbent_iff_eventually_nhdsNE_zero, comap_dist_left_atTop_eq_cocompact, ContinuousLinearEquiv.antilipschitz, MeasureTheory.Measure.integral_comp_inv_smul, TangentBundle.tangentMap_tangentBundle_pure, continuousAt_of_locally_lipschitz, VectorBundleCore.toFiberBundleCore_coordChange, HurwitzZeta.hasSum_int_hurwitzZetaOdd, InnerProductGeometry.cos_angle_add_of_inner_eq_zero, geometric_hahn_banach_open, iteratedDeriv_scomp_two, MeromorphicOn.deriv, TensorProduct.mapInclIsometry_apply, MeasureTheory.integrable_prodLp_iff, ContinuousLinearMap.rayleigh_smul, MeasureTheory.integrable_indicatorConstLp, Real.differentiableOn_arcosh, VitaliFamily.nonempty_interior, NumberField.mixedEmbedding.integral_comp_polarSpaceCoord_symm, Real.hasDerivAt_arccos, ContinuousMap.toLp_inj, AbsoluteValue.IsEquiv.isEmbedding_equivWithAbs, WeakFEPair.differentiableAt_Λ, ArithmeticFunction.vonMangoldt.summable_residueClass_non_primes_div, LinearIsometryEquiv.strictConvex_preimage, TemperedDistribution.lineDerivOpCLM_eq, NumberField.mixedEmbedding.fundamentalCone.expMapBasis_apply', PiTensorProduct.mapL_id, continuousSMul_sphere_ball, PiLp.continuousLinearEquiv_symm_apply, instCompactSpaceElemClosedBallOfProperSpace, MemHolder.nsmul, ContinuousMap.isUniformInducing_equivBoundedOfCompact, closure_diff_intrinsicFrontier, NumberField.mixedEmbedding.fundamentalDomain_integerLattice, aux_hasSum_of_le_geometric, Submodule.starProjection_apply_eq_isComplProjection, Orientation.oangle_sign_smul_add_right, DiffContOnCl.smul, MeasureTheory.Lp.toTemperedDistributionCLM_apply, InformationTheory.integrable_klFun_rnDeriv_iff, fderiv_iteratedFDeriv, Orientation.kahler_map_complex, Polynomial.differentiableWithinAt, Trivialization.pullback_linear, MeasureTheory.setIntegral_tilted, Metric.isPreconnected_ball, hasFPowerSeriesWithinAt_iff_exists_hasFPowerSeriesAt, FormalMultilinearSeries.comp_rightInv_aux1, Circle.periodic_exp, MeasureTheory.LpToLpRestrictCLM_coeFn, ContinuousLinearMap.hasFPowerSeriesOnBall, tendsto_zero_iff_meromorphicOrderAt_pos, UpperHalfPlane.mdifferentiable_num, Orientation.oangle_eq_zero_or_eq_pi_iff_right_eq_smul, TemperedDistribution.fourierInv_toTemperedDistributionCLM_eq, Complex.cos_eq_tsum, OpenPartialHomeomorph.map_extend_nhdsWithin_eq_image, IsBoundedLinearMap.differentiableAt, hasStrictFDerivAt_const_add_iff, ModularForm.mul_slash_SL2, cfcₙ_def, MeasureTheory.L1.SimpleFunc.norm_Integral_le_one, isConformalMap_conj, Bornology.IsBounded.uniformContinuousOn_smul, LinearMap.mkContinuous₂_norm_le', MeasureTheory.eLpNorm'_norm, hasStrictFDerivAt_apply, Real.continuousOn_rpowIntegrand₀₁_uncurry, differentiableWithinAt_finCons', MeasureTheory.eLpNormEssSup_const_smul_le, ContinuousMultilinearMap.norm_mkPiRing, ProbabilityTheory.integrable_cexp_mul_of_re_mem_integrableExpSet, differentiableAt_comp_const_add, fderiv_snd, ModelWithCorners.continuous_invFun, LinearIsometryEquiv.hasStrictFDerivAt, ZeroAtInftyContinuousMap.toBCF_injective, NormedSpace.exp_continuous, Bundle.Trivial.continuousLinearEquivAt_trivialization, EuclideanGeometry.dist_smul_vadd_sq, HasStrictFDerivAt.isLittleOTVS, Bundle.ContMDiffRiemannianMetric.isVonNBounded, ProbabilityTheory.tendsto_defaultRatCDF_atBot, SchwartzMap.lineDerivOpCLM_eq, ProbabilityTheory.stieltjesOfMeasurableRat_ae_eq, HurwitzZeta.differentiableAt_hurwitzZetaEven_sub_one_div, deriv_sub_const_fun, NNReal.summable_coe, real_inner_div_norm_mul_norm_eq_neg_one_iff, TensorProduct.enorm_lid, uniqueDiffOn_Icc, Metric.cauchySeq_iff, ConformalAt.differentiableAt, AnalyticOn.continuousOn, Orientation.oangle_ne_zero_and_ne_pi_iff_linearIndependent, isCompact_stdSimplex, differentiableAt_comp_neg, ProbabilityTheory.Kernel.tendsto_m_density, exists_continuous_sum_one_of_isOpen_isCompact, Orientation.oangle_add, ProbabilityTheory.paretoCDFReal_eq_lintegral, MeasureTheory.condExpInd_of_measurable, continuousAt_const_cpow, SpectrumRestricts.nnreal_of_nonneg, MeromorphicAt.fun_iterated_deriv, hasDerivWithinAt_Iio_iff_Iic, MeromorphicOn.codiscrete_setOf_meromorphicOrderAt_eq_zero_or_top, Real.integrableOn_rpowIntegrand₀₁_Ioi, SeparationQuotient.instNormOneClass, MeasureTheory.Lp.mul_meas_ge_le_pow_enorm', LinearMap.mkContinuous₂_apply, Matrix.frobenius_nnnorm_mul, TensorProduct.inner_tmul, AffineMap.hasStrictDerivAt_lineMap, ContinuousLinearMap.isPositive_iff_eq_sum_rankOne, Complex.differentiableAt_sin, Complex.tendsto_log_nhdsWithin_im_neg_of_re_neg_of_im_zero, Bundle.ContMDiffRiemannianMetric.contMDiff, NormedAddCommGroup.cauchy_series_of_le_geometric'', Bundle.mdifferentiableAt_proj, continuousOn_stereoToFun, Submodule.coe_continuous_linearProjOfClosedCompl', InnerProductSpace.isPositive_rankOne_self, SeparationQuotient.liftNormedAddGroupHom_normNoninc, SmoothBumpCovering.toSmoothPartitionOfUnity_eq_mul_prod, ModularForm.smul_slash, ProbabilityTheory.IsGaussian.memLp_id, LinearIsometryEquiv.comp_fderiv, completelyRegularSpace_iff_isOpen, MeasureTheory.condExpL1_smul, AffineIsometry.image_intrinsicClosure, ContinuousLinearMap.isBigO_comp, ContinuousAlternatingMap.opNorm_prod, summable_sigma_of_nonneg, LeftInvariantDerivation.lift_zero, ProbabilityTheory.condCDF_ae_eq, ContinuousMap.addEquivBoundedOfCompact_apply, RingHom.compLeftContinuousBounded_apply_apply, ProbabilityTheory.isGaussian_iff_gaussian_charFun, Complex.isOpen_re_lt_EReal, MeasureTheory.Lp.instIsScalarTower, hasSum_geometric_of_norm_lt_one, ContinuousLinearMap.mulLeftRight_isBoundedBilinear, DomAddAct.mk_vadd_indicatorConstLp, Real.differentiable_arctan, norm_cfcₙHom, ProperCone.innerDual_le_innerDual, LinearMap.mkContinuousOfExistsBound_apply, Real.map_exp_nhds, NormedCommGroup.tendsto_nhds_nhds, RCLike.map_apply, exists_contMDiffMap_zero_one_of_isClosed, differentiable_const_cpow_of_neZero, Real.differentiableAt_mulExpNegMulSq, NumberField.mixedEmbedding.normAtComplexPlaces_mixedSpaceOfRealSpace, OrthonormalBasis.orthogonalProjection_eq_sum, hasDerivWithinAt_ofNat, IsStarNormal.instNonUnitalContinuousFunctionalCalculus, ContinuousLinearMap.analyticWithinAt_bilinear, Complex.restrictScalars_one_smulRight', ProbabilityTheory.IdentDistrib.memLp_iff, MeasureTheory.aestronglyMeasurable_condExpInd, MeasureTheory.eLpNorm_condExp_le, Real.not_continuousAt_inv_log_neg_one, MeasureTheory.LipschitzWith.integrable_comp_iff_of_antilipschitz, Real.Angle.toReal_add_of_sign_eq_neg_sign, ContinuousLinearMap.compSL_apply, MeasureTheory.mem_lpMeasSubgroup_iff_aestronglyMeasurable, completedZeta_eq_tsum_of_one_lt_re, Complex.continuousOn_exp, ProbabilityTheory.lintegral_condCDF, ContinuousLinearMap.continuous₂, MeasureTheory.Martingale.smul, RCLike.geometric_hahn_banach_point_open, HasFPowerSeriesWithinAt.comp_sub, Orientation.oangle_add_swap, ContinuousLinearEquiv.differentiable, ContinuousLinearMap.opNorm_prod, hasDerivWithinAt_add_const_iff, IsSelfAdjoint.quasispectrumRestricts, contMDiffAt_extend, comap_gauge_nhds_zero_le, LinearMap.coe_toSeminorm, ContinuousLinearMap.integral_compLp, FormalMultilinearSeries.comp_partialSum, eventually_residual_irrational, mellin_eq_fourier, CuspFormClass.holo, SchwartzMap.instLineDerivLeftSMulReal, tendsto_birkhoffAverage_apply_sub_birkhoffAverage', LinearMap.adjoint_adjoint, HasFTaylorSeriesUpTo.differentiable, BumpCovering.eventuallyEq_one, CStarRing.norm_unitary_smul, DoubleCentralizer.star_snd, Asymptotics.isTheta_completion_right, bernsteinApproximation.apply_zero, ContinuousLinearMap.norm_inr_le_one, AnalyticOnNhd.smul, Affine.Simplex.orthogonalProjectionSpan_map, Asymptotics.IsBigO.rpow_rpow_nhdsGE_zero_of_le, TensorProduct.ext_iff_inner_left, NumberField.mixedEmbedding.lintegral_comp_polarCoord_symm, MeasureTheory.Measure.addHaar_image_continuousLinearMap, EuclideanGeometry.vsub_orthogonalProjection_mem_direction_orthogonal, ContDiffMapSupportedIn.coe_add, Matrix.IsHermitian.isClosedEmbedding_cfcAux, MeasureTheory.IntegrableOn.of_subsingleton, differentiableOn_star_iff, InnerProductSpace.toLinearIsometry_toDual, RCLike.ofRealCLM_apply, MeasureTheory.norm_indicatorConstLp_le, SchwartzMap.integral_sesq_fourier_fourier, tendsto_norm_sub_self_nhdsNE, Bornology.isVonNBounded_iff_tendsto_smallSets_nhds, PowerSeries.IsRestricted.smul, HurwitzZeta.differentiableAt_hurwitzZeta_sub_one_div, GaussianFourier.integrable_cexp_neg_mul_sq_add_real_mul_I, ModularFormClass.differentiableAt_comp_ofComplex, NormedAddGroupHom.completion_def, PeriodPair.hasFPowerSeriesAt_weierstrassPExcept, hasFDerivAt_comp_add_right, IsSelfAdjoint.commute_cfcHom, Real.hasFDerivAt_fourierChar_neg_bilinear_left, InnerProductSpace.span_gramSchmidtNormed, instIsManifoldRealEuclideanSpaceFinModelWithCornersSelfTopWithTopENatElemHAddNatOfNatSphere, Real.differentiableAt_arcsin, QuadraticMap.lineDeriv, hasStrictDerivAt_intCast, geometric_hahn_banach_point_point, tendsto_smoothingFun_of_ne_zero, NumberField.mixedEmbedding.fundamentalCone.interior_paramSet, cfcₙ_norm_nonneg, real_inner_div_norm_mul_norm_eq_neg_one_of_ne_zero_of_neg_mul, NumberField.mixedEmbedding.measurable_polarCoordReal_symm, NormedRing.inverse_one_sub_norm, LeftInvariantDerivation.leibniz, Ideal.toCharacterSpace_apply_eq_zero_of_mem, MeasureTheory.condExpInd_ae_eq_condExpIndSMul, MeasureTheory.convolution_eq_right', Metric.isCompact_iff_isClosed_bounded, EisensteinSeries.hasSum_e2Summand_symmetricIcc, hasFDerivAt_iff_hasGradientAt, NonUnitalIsometricContinuousFunctionalCalculus.isometric, HasFPowerSeriesOnBall.tendstoLocallyUniformlyOn, ProbabilityTheory.condCDF_nonneg, MeasureTheory.eLpNormEssSup_const_smul, RCLike.reCLM_apply, contMDiffWithinAt_iff_target, unitInterval.symmHomeomorph_apply, cfcₙHom_apply_mem_elemental, ContinuousMultilinearMap.cpolynomialOn, LinearIsometry.norm_compContinuousAlternatingMap, MeasureTheory.hausdorffMeasure_segment, MeasureTheory.integrable_withDensity_iff_integrable_coe_smul, HurwitzZeta.differentiableAt_hurwitzZetaEven, curveIntegral_smul, Affine.Simplex.smul_mongePoint_vsub_circumcenter_eq_sum_vsub, ContinuousLinearMap.isSelfAdjoint_iff_isSymmetric, NormedSpace.exp_zsmul, FDerivMeasurableAux.isOpen_A, DomMulAct.instSMulCommClassSubtypeAEEqFunMemAddSubgroupLp_1, UnitAddTorus.coe_mFourierBasis, ModularFormClass.qExpansionFormalMultilinearSeries_apply_norm, CFC.abs_eq_cfc_norm, Orientation.inner_rotation_pi_div_two_right_smul, intervalIntegral.intervalIntegrable_one_div_one_add_sq, extDeriv_constOfIsEmpty, RCLike.separate_convex_open_set, Bundle.contMDiffOn_zeroSection, Orientation.oangle_add_left_smul_rotation_pi_div_two, CFC.monotoneOn_one_sub_one_add_inv, ProbabilityTheory.tendsto_defaultRatCDF_atTop, Bundle.Trivial.symmL_trivialization, ProbabilityTheory.IsCondKernelCDF.toKernel_Iic, NumberField.canonicalEmbedding.mem_span_latticeBasis, iteratedDeriv_fun_sum, Path.continuousMapClass, Submodule.orthogonalDecomposition_symm_apply, hasStrictFDerivAt_list_prod_finRange', Asymptotics.IsEquivalent.add_const_of_norm_tendsto_atTop, MeasureTheory.integral_smul_nnreal_measure, VectorBundleCore.toFiberBundleCore_indexAt, CFC.sqrt_eq_one_iff', LinearIsometry.nnnorm_toContinuousLinearMap, ContinuousLinearMap.isStarProjection_iff_isSymmetricProjection, CFC.posPart_one, InnerProductSpace.rankOne_one_left_eq_innerSL, ContDiff.fderiv_succ, PeriodPair.hasSumLocallyUniformly_weierstrassP, Submodule.IsOrtho.starProjection_comp_starProjection, ContinuousMap.abs_mem_subalgebra_closure, Subalgebra.spectrum_sUnion_connectedComponentIn, ContDiffBump.normed_sub, ContMDiffMap.coeFnAlgHom_apply, Function.FactorizedRational.divisor, Complex.circleTransformDeriv_eq, ContinuousMap.HomotopyWith.coe_toContinuousMap, hasDerivAt_sqrt_mul_log, Asymptotics.isLittleO_completion_left, Manifold.pathELength_eq_lintegral_mfderiv_Ioo, ContinuousAffineMap.fderiv, iteratedDeriv_fun_add, DiffContOnCl.add_const, MeasureTheory.unifTight_iff_real, LSeries.term_sum, MeasureTheory.aefinStronglyMeasurable_iff_aemeasurable, ContinuousLinearMap.continuous_det, HurwitzZeta.hasSum_int_cosKernel₀, HasFiniteFPowerSeriesAt.neg, Complex.isOpenMap_im, IsometryEquiv.toRealLinearIsometryEquiv_symm_apply, nnnorm_cfcₙ_nnreal_le_iff, isSeparable_range_derivWithin, ProbabilityTheory.aemeasurable_exp_mul, HurwitzZeta.hasSum_int_hurwitzZetaEven, PiTensorProduct.mapLMonoidHom_apply, Complex.ofRealCLM_coe, Complex.kahler, Complex.norm_polarCoord_symm, MeasureTheory.SimpleFunc.setToSimpleFunc_smul_left, ClosedSubmodule.toSubmodule_orthogonal_eq, ContinuousLinearMap.map_add_add, ContinuousAlternatingMap.norm_constOfIsEmpty, ProbabilityTheory.eqOn_complexMGF_of_mgf', IsBoundedBilinearMap.hasFDerivAt, fderivWithin_comp_add_left, SeminormFamily.basisSets_smul_right, MeasureTheory.Measure.integral_comp_mul_right, ProbabilityTheory.IsCondKernelCDF.le_one, ContinuousLinearMap.sSup_unit_ball_eq_norm, SchwartzMap.inner_fourier_toL2_eq, ProbabilityTheory.IdentDistrib.integrable_iff, Complex.areaForm, Function.locallyFinsuppWithin.toClosedBall_support_subset_closedBall, SchwartzMap.toLp_fourierTransformInv_eq, intervalIntegral.inv_smul_integral_comp_div_add, ContinuousAlternatingMap.norm_ofSubsingleton_id_le, MeromorphicOn.divisor_fun_smul, finrank_real_complex_fact', PeriodPair.deriv_weierstrassP, ContinuousMap.dist_lt_iff, Metric.exists_continuous_real_forall_closedEBall_subset, nnnorm_cfc_lt, Real.deriv_negMulLog, Real.hasDerivAt_sigmoid, Metric.uniformContinuous_iff_le, MeasureTheory.L2.inner_indicatorConstLp_eq_inner_setIntegral, Manifold.IsImmersionAtOfComplement.target_subset_preimage_target, PeriodPair.coeff_weierstrassPExceptSeries, ProbabilityTheory.analyticOn_mgf, ContinuousMultilinearMap.norm_iteratedFDerivComponent_le, ContinuousLinearMap.analyticWithinAt, ContinuousAffineMap.differentiableWithinAt, summable_riemannZetaSummand, ContDiffWithinAt.contMDiffWithinAt, ContinuousMultilinearMap.analyticAt_uncurry_compContinuousLinearMap, ContinuousAlternatingMap.hasStrictFDerivAt_toContinuousMultilinearMap_comp_iff, Real.fourierIntegralInv_eq', AffineMap.hasDerivAtFilter, ContinuousLinearEquiv.toCompactConvergenceCLM_symm_apply, MeasureTheory.eLpNorm'_const', Asymptotics.isLittleO_completion_right, PositiveLinearMap.apply_le_of_isSelfAdjoint, complete_of_proper, Monotone.locallyIntegrable, ContinuousMap.Homotopy.extend_apply_of_one_le, Matrix.IsHermitian.det_abs, Matrix.posSemidef_iff_eq_conjTranspose_mul_self, ContDiffMapSupportedIn.norm_iteratedFDeriv_apply_le_seminorm, SlashInvariantForm.slash_action_eq', Metric.continuousWithinAt_iff', LinearMap.IsPositive.ne_zero_iff, SchwartzMap.add_apply, hasFDerivAtFilter_pi, ModularForm.mul_slash, OpenPartialHomeomorph.contDiff_unitBallBall_symm, ContinuousLinearMapWOT.le_nhds_iff_forall_inner_apply_le_nhds, deriv_abs, curveIntegrable_segment, differentiableAt_zpow, hasFDerivAt_multiset_prod, ContDiffOn.smul_const, Real.Angle.sin_add_pi_div_two, OpenPartialHomeomorph.map_extend_nhds_of_boundaryless, StieltjesFunction.rightLim_eq, AkraBazziRecurrence.tendsto_zero_sumCoeffsExp, LinearMap.isPositive_adjoint_comp_self, Absorbs.eventually_nhds_zero, Manifold.IsImmersionAt.map_target_subset_target, BoundedContinuousFunction.algebraMap_apply, Circle.exp_arg, Complex.exists_mem_frontier_isMaxOn_norm, Real.nnnorm_deriv_mulExpNegMulSq_le_one, Submodule.toLinearEquiv_orthogonalDecomposition_symm, ContinuousLinearMap.sSup_unitClosedBall_eq_nnnorm, continuousSMul_sphere_sphere, iteratedDeriv_succ, spectrum.instCompactSpace, geom_series_mul_shift, Real.deriv_binEntropy, locallyCompact_of_proper, CFC.monotone_nnrpow, intervalIntegral.integral_derivWithin_uIcc_of_contDiffOn_uIcc, mdifferentiableWithinAt_totalSpace, ContinuousLinearMap.continuousSMul, CFC.posPart_natCast, hasFTaylorSeriesUpToOn_top_iff_right, MeasureTheory.charFunDual_apply, DirichletCharacter.LSeries_eulerProduct_tprod, contMDiffWithinAt_vectorSpace_iff_contDiffWithinAt, ContinuousLinearMap.IsPositive.inner_left_eq_inner_right, Affine.Simplex.orthogonalProjection_vadd_smul_vsub_orthogonalProjection, MeasureTheory.Lp.const_smul_mem_Lp, uniqueDiffWithinAt_Iic, Real.Angle.cos_add, smoothSheafCommRing.nonunits_stalk, LSeries.term_convolution', CuspFormClass.zero_at_infty_comp_ofComplex, expNegInvGlue.hasDerivAt_polynomial_eval_inv_mul, LinearIsometry.isComplete_image_iff', HasFPowerSeriesWithinOnBall.hasSum_sub, PeriodPair.derivWeierstrassPExcept_sub, AffineIsometryEquiv.toHomeomorph_refl, MeasureTheory.isTightMeasureSet_of_tendsto_measure_norm_gt, Real.rpow_eq_nhds_of_neg, ContinuousMultilinearMap.analyticAt_uncurry_of_linear, tsum_eisSummand_eq_riemannZeta_mul_eisensteinSeries, isLittleO_exp_neg_mul_sq_cocompact, deriv_mem_iff, ProbabilityTheory.hasGaussianLaw_iff_charFunDual_map_eq, norm_jacobiTheta₂_term_fderiv_ge, Matrix.spectrum_toEuclideanLin, ContDiff.iteratedFDeriv_right, NumberField.canonicalEmbedding.latticeBasis_apply, norm_add_eq_iff_real, Complex.integral_comp_pi_polarCoord_symm, Real.summable_ofDigitsTerm, FormalMultilinearSeries.radius_pi_eq_iInf, ContinuousLinearMap.norm_inl_le_one, HasSolidNorm.continuousInf, CFC.tendsto_cfc_rpow_sub_one_log, MeasureTheory.norm_condExpL2_le, contDiffAt_norm_smul_iff, integrableOn_exp_mul_Iic, ProbabilityTheory.IsGaussian.integrable_dual, ContinuousLinearEquiv.contDiff_comp_iff, AlternatingMap.continuous_of_bound, SchwartzMap.pairing_apply_apply, Submodule.instStrictConvexSpace, InnerProductSpace.isIdempotentElem_rankOne_self, MeasureTheory.Lp.instIsOrderedAddMonoid, BumpCovering.toPartitionOfUnity_apply, Metric.contractibleSpace_ball, ContDiffMapSupportedIn.iteratedFDerivLM_apply, Matrix.cstar_nnnorm_def, MeasureTheory.weightedSMul_apply, ContinuousMultilinearMap.norm_map_snoc_le, AbsolutelyContinuousOnInterval.integral_deriv_eq_sub, MeasureTheory.FiniteMeasure.toWeakDualBCNN_apply, ContDiffMapSupportedInClass.instContinuousMapClass, ProbabilityTheory.HasSubgaussianMGF.integrable_exp_mul, egauge_prod_mk, ImplicitFunctionData.isInvertible_fderiv_prodFun, Padic.withValUniformEquiv_norm_le_one_iff, Trivialization.continuousLinearMapAt_apply, hasSum_choose_mul_geometric_of_norm_lt_one, ApproximatesLinearOn.lipschitz, summableLocallyUniformlyOn_iteratedDerivWithin_cexp, inseparable_one_iff_norm, tendsto_cobounded_iff_meromorphicOrderAt_neg, AddCircle.homeomorphCircle'_apply_mk, Real.hasStrictDerivAt_rpow_const_of_ne, Matrix.IsHermitian.cfc_eq, tsum_coe_mul_geometric_of_norm_lt_one', lp.inner_eq_tsum, Metric.mem_cocompact_iff_closedBall_compl_subset, NormedCommGroup.cauchySeq_iff, geometric_hahn_banach_open_point, MeasureTheory.Lp.cauchySeq_Lp_iff_cauchySeq_eLpNorm, Complex.isCoveringMap_exp, mdifferentiableOn_iff, CurveIntegrable.symm, StrongDual.polarSubmodule_eq_setOf, ContinuousLinearMap.continuous_integral_comp_L1, ContinuousLinearMap.isBigOWith_sub, ContDiffMapSupportedIn.structureMapCLM_eq_of_scalars, hasDerivWithinAt_Ioi_iff_Ici, ContinuousLinearMapWOT.tendsto_iff_forall_inner_apply_tendsto, Orientation.tan_oangle_add_left_smul_rotation_pi_div_two, ContDiff.hasStrictFDerivAt, PeriodPair.ω₁_div_two_notMem_lattice, CFC.sq_sqrt, ContinuousMap.attachBound_apply_coe, SeminormedGroup.uniformCauchySeqOnFilter_iff_tendstoUniformlyOnFilter_one, OrthonormalBasis.sum_inner_mul_inner, SeminormedGroup.disjoint_nhds, FormalMultilinearSeries.changeOriginSeriesTerm_apply, Matrix.l2_opNorm_mulVec, frontier_halfSpace, MeasureTheory.eLpNorm_mono_nnnorm_ae, Meromorphic.deriv, Asymptotics.isLittleOTVS_one, HasFTaylorSeriesUpTo.cont, Filter.inv_nhdsWithin_ne_zero, Real.binEntropy_continuous, ImplicitFunctionData.isCompl_ker, Metric.PiNatEmbed.continuous_distDenseSeq_inv, Complex.continuousWithinAt_arg_of_re_neg_of_im_zero, ProbabilityTheory.unitInterval.cdf_eq_real, ContinuousLinearMap.hasDerivAtFilter, Rat.continuous_coe_real, Asymptotics.isLittleO_const_iff, HasFPowerSeriesAt.locally_ne_zero, Polynomial.div_tendsto_atTop_leadingCoeff_div_of_degree_eq, MeasureTheory.Lp.edist_def, DoubleCentralizer.intCast_snd, MeasureTheory.Measure.toJordanDecomposition_toSignedMeasure_sub, Metric.frontier_closedBall_subset_sphere, span_fourier_closure_eq_top, Real.fourierIntegral_eq, Complex.GammaSeq_tendsto_Gamma, PeriodPair.basis_one, mdifferentiableWithinAt_iff_of_mem_maximalAtlas, Path.extend_extends, Finset.analyticAt_fun_sum, DoubleCentralizer.range_toProdMulOpposite, ContinuousLinearMap.comp_hasFiniteFPowerSeriesOnBall, ContinuousLinearMapWOT.withSeminorms, BoundedContinuousFunction.mkOfCompact_star, Submodule.re_inner_starProjection_eq_normSq, RCLike.conjCLE_norm, ProbabilityTheory.gammaCDFReal_eq_lintegral, ModelWithCorners.symm_continuousWithinAt_comp_right_iff, AffineSpace.cobounded_eq_iSup_sphere_asymptoticNhds, ProperCone.innerDual_univ, GenLoop.fromLoop_apply, ordinaryHypergeometric_radius_top_of_neg_nat₃, HasFPowerSeriesOnBall.add, OnePoint.isBoundedAt_iff_exists_SL2Z, Orientation.kahler_comp_rightAngleRotation', circleIntegral_def_Icc, tendsto_zpow_nhdsNE_zero_cobounded, Isometry.extensionHom_coe, MeasureTheory.inner_condExpL2_left_eq_right, MeasureTheory.integral_unique, setIntegral_withDensity_eq_setIntegral_smul₀, Nat.isUniformEmbedding_coe_real, ContinuousMap.toLp_denseRange, ContDiffBump.integrable, AnalyticOnNhd.compContinuousLinearMap, NormedAddCommGroup.cauchy_series_of_le_geometric', intervalIntegral.intervalIntegral_eq_integral_uIoc, not_bounded_iff_exists_ne_zero_mem_asymptoticCone, derivWithin_const, ZLattice.covolume_eq_det_inv, one_add_cpow_hasFPowerSeriesAt_zero, Orientation.two_zsmul_oangle_smul_left_of_ne_zero, BoxIntegral.HasIntegral.sum, differentiableWithinAt_neg_iff, Unitary.mem_pathComponentOne_iff, MeasureTheory.Lp.coeFn_add, ODE.FunSpace.isUniformInducing_toContinuousMap, contDiffWithinAtProp_self, ContDiffAt.contMDiffAt, unique_topology_of_t2, circleIntegrable_iff, LinearMap.polar_eq_iInter, Real.Angle.toCircle_add, hasFDerivAt_stereoInvFunAux, SchwartzMap.integral_clm_comp_lineDerivOp_right_eq_neg_left, ContinuousFunctionalCalculus.compactSpace_spectrum, DirichletCharacter.continuousOn_neg_logDeriv_LFunction_of_nontriv, ProbabilityTheory.IsGaussian.map_eq_gaussianReal, MeasureTheory.Martingale.stronglyAdapted, ProbabilityTheory.IsRatCondKernelCDFAux.tendsto_one_of_monotone, ContinuousLinearMap.comp_memLp, mdifferentiable_iff_target, Complex.tsum_exp_neg_mul_int_sq, not_integrableOn_Ioi_cpow, NormedCommGroup.nhds_one_basis_norm_lt, Real.fderiv_fourierChar_neg_bilinear_right_apply, LinearMap.IsSymmetric.diagonalization_apply_self_apply, EuclideanGeometry.orthogonalProjection_congr, IsBoundedBilinearMap.continuous_left, UpperHalfPlane.isOpenEmbedding_coe, LinearMap.IsPositive.re_inner_nonneg_right, MeasureTheory.Lp.eq_zero_iff_ae_eq_zero, stdSimplexHomeomorphUnitInterval_symm_apply_coe, intervalIntegral.integral_deriv_of_contDiffOn_uIcc, IsUltrametricDist.nnnorm_tprod_le_of_forall_le, Unitization.real_cfcₙ_eq_cfc_inr, norm_iteratedFDeriv_mul_le, ContDiffAt.fderiv_right_succ, ImplicitFunctionData.hasStrictFDerivAt_leftFun, contMDiffAt_iff_source, LipschitzWith.memLp_lineDeriv, Submodule.starProjection_orthogonal', RCLike.linearIndependent_of_ne_zero_of_wInner_one_eq_zero, WeakFEPair.hf_modif_int, Quaternion.continuous_imI, DoubleCentralizer.natCast_fst, lp.coeFn_star, hasFPowerSeriesOnBall_pi_iff, intervalIntegrable_bernoulliFun, NontrivialTopology.of_exists_norm_ne_zero', Polynomial.div_tendsto_atBot_leadingCoeff_div_of_degree_eq, ContinuousLinearMap.IsPositive.toLinearMap, MeasureTheory.Lp.ext_iff, Units.nhds, ContinuousLinearMap.norm_compLp_le, Submodule.toLinearEquiv_orthogonalDecomposition, ImplicitFunctionData.map_pt_mem_toOpenPartialHomeomorph_target, ContinuousMultilinearMap.changeOrigin_toFormalMultilinearSeries, differentiableWithinAt_abs_pos, ContinuousLinearEquiv.symm_toDiffeomorph, ImplicitFunctionData.pt_mem_toPartialHomeomorph_source, ContDiffBump.eventuallyEq_one, ContDiffMapSupportedIn.structureMapCLM_apply, Complex.uniformlyContinuous_im, OrthonormalBasis.toBasis_tensorProduct, TensorProduct.congrIsometry_refl_refl, eventually_enorm_mfderivWithin_symm_extChartAt_lt, ContinuousAlternatingMap.opNNNorm_pi, HasFPowerSeriesWithinAt.const_smul, Circle.exp_natCast_mul, norm_smul_inv_norm', ProbabilityTheory.tendsto_condCDF_atBot, MeasureTheory.UniformIntegrable.uniformIntegrable_of_ae_tendsto, ProbabilityTheory.integrable_preCDF, LipschitzWith.ae_lineDeriv_sum_eq, tangentMap_chart, SchwartzMap.lineDerivOp_fourier_eq, Orientation.inner_mul_inner_add_areaForm_mul_areaForm, SeparationQuotient.norm_liftNormedAddGroupHom_apply_le, Orientation.areaForm_le, MeasureTheory.isTightMeasureSet_iff_inner_tendsto, Seminorm.uniformContinuous_of_forall, isClosedEmbedding_cfcₙAux, det_fderivPolarCoordSymm, setIntegral_withDensity_eq_setIntegral_toReal_smul, MeasureTheory.Lp.indicatorConstLp_compMeasurePreserving, deriv_comp_const_sub, LeftInvariantDerivation.coe_derivation, TensorProduct.enorm_comm, Metric.mem_cocompact_of_closedBall_compl_subset, Metric.equicontinuousAt_iff_pair, innerSL_apply_apply, MeasureTheory.Lp.coeFn_const, Submodule.isOrtho_sup_right, RCLike.norm_expect_le, HasGradientAt.continuousOn, tendsto_rpow_mul_exp_neg_mul_atTop_nhds_zero, extChartAt_target_eventuallyEq, HasFPowerSeriesWithinOnBall.restrictScalars, TangentBundle.symmL_trivializationAt, NormedSpace.isVonNBounded_iff, CFC.abs_eq_cfcₙ_coe_norm, SmoothPartitionOfUnity.locallyFinite, MeasureTheory.LevyProkhorov.eq_convergenceInDistribution, ContinuousLinearEquiv.subsingleton_or_norm_symm_pos, Topology.RelCWComplex.continuousOn_symm, WithLp.enorm_snd_le, Metric.nhds_basis_closedBall_pow, MeasureTheory.IntegrableOn.of_finite, SeminormFamily.filter_eq_iInf, LipschitzWith.lipschitzWith_compLp, aemeasurable_smul_const, SchwartzMap.integral_bilin_fourierInv_eq, LinearMap.adjoint_innerₛₗ_apply, TestFunction.toBoundedContinuousFunctionCLM_eq_of_scalars, inner_sum, exists_smooth_one_nhds_of_subset_interior, ContinuousWithinAt.extChartAt_symm_preimage_inter_range_eventuallyEq, Real.differentiable_sinh, HasFTaylorSeriesUpTo.hasFDerivAt, Function.Periodic.cuspFunction_zero_eq_limUnder_nhds_ne, MeasureTheory.mem_L1_toReal_of_lintegral_ne_top, ContinuousAlternatingMap.hasStrictFDerivAt_compContinuousLinearMap, MeasureTheory.norm_indicatorConstLp, UpperHalfPlane.comp_ofComplex_of_im_pos, hasDerivAt_neg', ContMDiffWithinAt.mfderivWithin_const, MeasureTheory.Measure.toSphere_apply_aux, Orientation.neg_rotation, Metric.eventually_prod_nhds_iff, Unitary.conjStarAlgEquiv_unitaryLinearIsometryEquiv, AkraBazziRecurrence.isLittleO_deriv_one_add_smoothingFn, Unitization.splitMul_apply, GaussianFourier.integral_cexp_neg_mul_sq_norm, map_extChartAt_symm_nhdsWithin, inner_eq_norm_mul_iff, unitInterval.toNNReal_continuous, Metric.tendsto_atTop, ContinuousLinearMap.toBilinForm_apply, RCLike.map_same_eq_id, Sbtw.oangle_eq_add_pi_left, differentiable_fun_neg_iff, Topology.CWComplex.continuousOn, DoubleCentralizer.nnnorm_def', NumberField.mixedEmbedding.normAtPlace_polarCoord_symm_of_isComplex, ContinuousLinearEquiv.coe_toSpanNonzeroSingleton_symm, LinearMap.adjoint_eq_toCLM_adjoint, closure_one_eq, ClosedSubmodule.orthogonal_gc, Real.continuous_rpow_const, LinearMap.isPositive_id, DiffeologicalSpace.CorePlotsOn.isOpen_iff_preimages_plots, Complex.continuousOn_arg, bilinearIteratedFDerivTwo_eq_iteratedFDeriv, NumberField.mixedEmbedding.fundamentalCone.abs_det_completeBasis_equivFunL_symm, NormedSpace.image_isVonNBounded_iff, ContinuousMap.range_toLp, contMDiff_addInvariantVectorField, eqOn_dslope_sub_smul, deriv_mul_const_field, Rat.HeightOneSpectrum.adicCompletionIntegers.coe_padicIntEquiv_symm_apply, AkraBazziRecurrence.differentiableAt_one_add_smoothingFn, Submodule.orthogonalProjection_mem_subspace_eq_self, ContinuousLinearMap.nnnorm_def, ContinuousLinearMap.IsPositive.inner_nonneg_right, SmoothPartitionOfUnity.nonneg, ContinuousMap.Homotopy.apply_zero_path, DoubleCentralizer.zero_snd, LeftInvariantDerivation.left_invariant', Int.enorm_natCast, selfAdjoint.expUnitaryPathToOne_apply, FormalMultilinearSeries.norm_le_div_pow_of_pos_of_lt_radius, NormedRing.inverse_add_norm_diff_nth_order, hasDerivAt_bernoulliFun, Unitary.continuousOn_argSelfAdjoint, ContinuousLinearMap.norm_compContinuousMultilinearMap_le, FormalMultilinearSeries.le_changeOriginSeries_radius, Orientation.volumeForm_neg_orientation, QuasispectrumRestricts.nnreal_iff, HomotopyGroup.symmAt_indep, hasSum_one_div_nat_pow_mul_fourier, ContinuousLinearEquiv.comp_right_differentiableWithinAt_iff, Real.continuous_mul_log, derivWithin_fderivWithin, two_mul_riemannZeta_eq_tsum_int_inv_pow_of_even, closure_thickening, derivWithin_natCast, AddCircle.toCircle_add, CFC.nnnorm_sqrt, MeasureTheory.L1.ofReal_norm_eq_lintegral, ContinuousMap.dist_le_two_norm, AntitoneOn.memLp_isCompact, OpenPartialHomeomorph.continuousOn_univBall_symm, Set.instTietzeExtensionUnitBall, MeasureTheory.condExpIndL1Fin_smul, LinearMap.mkContinuous_apply, MultilinearMap.mkContinuousMultilinear_apply, ContDiffBump.integrable_normed, ContinuousMap.norm_le, instIsAddHaarMeasureVolume, Trivialization.mdifferentiableOn_section_baseSet_iff, InnerProductSpace.span_gramSchmidtNormed_range, ContinuousMap.isUltrametricDist, SchwartzMap.instContinuousSMul, SlashInvariantForm.quotientFunc_mk, ContinuousLinearMap.opNorm_comp_linearIsometryEquiv, Submodule.orthogonal_disjoint, InnerProductGeometry.angle_smul_right_of_pos, TemperedDistribution.lineDerivOp_fourier_eq, Complex.frontier_setOf_re_le, Int.isUniformEmbedding_coe_rat, WeakFEPair.symm_Λ₀_eq, ContDiffPointwiseHolderAt.isBigO, Real.deriv_log, PadicInt.norm_mahlerTerm, ModularForm.SL_slash, WithLp.instCompleteSpace, LinearMap.isSelfAdjoint_toContinuousLinearMap_iff, ContDiff.differentiable_deriv_two, AnalyticOn.comp_sub, SchwartzMap.decay', Module.Basis.ofZLatticeBasis_apply, ContinuousAlternatingMap.map_insertNth, intervalIntegral.integral_comp_sub_div, FormalMultilinearSeries.derivSeries_coeff_one, VonNeumannAlgebra.ext_iff, mdifferentiableOn_extChartAt, Polynomial.isCoveringMapOn_eval, Complex.ofRealCLM_norm, Submodule.starProjection_add_starProjection_orthogonal, contMDiff_neg_sphere, OrderedFinpartition.norm_compAlongOrderedFinpartition_le, LipschitzWith.completion_extension, tangentConeAt_nonempty_of_properSpace, dense_liouville, CircleDeg1Lift.tendsto_translationNumber_aux, instIsZLatticeComap, not_differentiableAt_norm_zero, mdifferentiableOn_symm_coordChangeL, ContinuousLinearMap.opNorm_lsmul_apply_le, intervalIntegral.integral_comp_mul_left, uniqueDiffOn_Iic, Real.continuous_arcsin, StarAlgebra.elemental.characterSpaceToSpectrum_coe, LipschitzWith.ae_exists_fderiv_of_countable, AnalyticAt.fun_const_smul, MeasureTheory.Lp.dist_def, BumpCovering.point_finite, tsum_choose_mul_geometric_of_norm_lt_one', OrthonormalBasis.orthogonalProjection_eq_sum_rankOne, ContinuousMap.norm_coe_le_norm, Submodule.mem_orthogonal_singleton_iff_inner_right, MeasureTheory.Lp.aestronglyMeasurable, Besicovitch.ae_tendsto_measure_inter_div_of_measurableSet, NumberField.mixedEmbedding.mem_idealLattice, MeromorphicOn.toMeromorphicNFOn_eq_self_on_nhdsNE, deltaGenerated_eq_coinduced, intervalIntegral.integral_comp_mul_sub, ContinuousMap.HomotopyWith.prop', cauchySeq_iff_tendsto_dist_atTop_0, SchwartzMap.bilinLeftCLM_apply, TopologicalSpace.Opens.CompleteCopy.dist_eq, Complex.borelSpace, ContinuousMap.setOfIdeal_ofSet_eq_interior, Set.Countable.exists_pos_hasSum_le, derivWithin_congr, ODE.FunSpace.range_toContinuousMap, InnerProductSpace.toDual_symm_apply, ContinuousLinearMap.fpowerSeriesBilinear_apply_zero, Real.tendsto_cos_pi_div_two, IsConformalMap.is_complex_or_conj_linear, NumberField.mixedEmbedding.fundamentalCone.completeBasis_apply_of_ne, TangentBundle.coe_chartAt_fst, HasGradientAt.hasDerivAt', derivWithin_comp_const_sub, IsHilbertSum.linearIsometryEquiv_symm_apply, SmoothBumpCovering.exists_immersion_euclidean, IsOpen.exists_msmooth_support_eq, OrderedFinpartition.norm_applyOrderedFinpartition_le, OpenPartialHomeomorph.tendsto_extend_comp_iff, ContinuousLinearMap.cpolynomialAt, HasMFDerivWithinAt.prodMk, differentiableOn_pi, hasSum_coe_mul_geometric_of_norm_lt_one', AffineMap.hasDerivWithinAt, Submodule.starProjection_singleton, HasFPowerSeriesAt.eventually_hasSum, MeromorphicOn.divisor_const, TopologicalSpace.IsCompletelyPseudoMetrizableSpace.complete, LeftInvariantDerivation.left_invariant, ContinuousMap.dist_le, SmoothPartitionOfUnity.locallyFinite', MeasureTheory.lpMeasSubgroupToLpTrim_neg, ProbabilityTheory.integrable_toReal_condExpKernel, MetricSpace.toIsCompletelyMetrizableSpace, torusIntegral_add, Bundle.RiemannianMetric.isVonNBounded, ContinuousMultilinearMap.norm_compContinuousLinearMapLRight_le, MeasureTheory.hasFiniteIntegral_iff_ofNNReal, MeasureTheory.Lp.simpleFunc.uniformContinuous, Orientation.tan_oangle_add_right_smul_rotation_pi_div_two, ProbabilityTheory.setIntegral_condCDF, MeasureTheory.locallyIntegrableOn_const, hasStrictFDerivAt_snd, tsum_coe_mul_geometric_of_norm_lt_one, MeasureTheory.le_eLpNorm_of_bddBelow, Complex.convexHull_reProdIm, CPolynomialAt.add, tendsto_norm_nhdsNE_one, one_mem_posTangentConeAt_iff_frequently, Real.hasDerivAt_sin, HasFPowerSeriesAt.neg, ContinuousLinearMap.measurable, LinearIsometryEquiv.coe_symm_toHomeomorph, Seminorm.continuous_of_forall', Complex.hasStrictDerivAt_tan, MeasureTheory.Lp.memLp, CPolynomialOn.iterated_deriv, ContDiff.continuous_deriv_one, NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_apply_comp_toReal, Path.Homotopy.map_apply, EuclideanGeometry.orthogonalProjection_contLinear, curveIntegralFun_smul, MeasureTheory.Lp.nnnorm_def, OpenPartialHomeomorph.map_extend_nhdsWithin_eq_image_of_subset, Module.Basis.exists_opNorm_le, ProbabilityTheory.IsCondKernelCDF.tendsto_atTop_one, ClosedSubmodule.mem_orthogonal', BoundedContinuousFunction.instSMulCommClass_1, Complex.closure_preimage_im, Metric.closedBall_mem_nhds, CFC.sqrt_rpow, ContDiffWithinAt.eventually, meromorphicOrderAt_add_of_ne, Real.summable_one_div_nat_add_rpow, egauge_ball_le_of_one_lt_norm, fourierIntegral_gaussian_innerProductSpace', MeasureTheory.Martingale.integrable, ContinuousAffineMap.differentiable, ProbabilityTheory.integral_gaussianReal_eq_integral_smul, MeasureTheory.charFun_toDual_symm_eq_charFunDual, QuotientAddGroup.norm_mk_eq_zero_iff_mem_closure, hasDerivWithinAt_iff_isLittleO, MeasureTheory.Measure.jordanDecompositionOfToSignedMeasureSub_toSignedMeasure, Nat.isUniformEmbedding_coe_rat, hasStrictFDerivAt_iff_isLittleOTVS, EuclideanGeometry.dist_orthogonalProjection_eq_iff_oangle_eq, Orientation.sin_oangle_add_left_mul_norm_of_oangle_eq_pi_div_two, not_IntegrableOn_Ioi_inv, derivWithin_fun_const_smul_field, NNReal.tendsto_dist_agmSequences_atTop_zero, ContinuousLinearEquiv.toCompactConvergenceCLM_apply, nontrivialTopology_iff_exists_nnnorm_ne_zero, MeasureTheory.Measure.instIsAddLeftInvariantMeasure, mdifferentiableWithinAt_iff_target_inter, Real.continuousAt_tan, ModelWithCorners.mdifferentiableOn_symm, differentiableWithinAt_fun_neg_iff, InnerProductSpace.canonicalCovariantTensor_eq_sum, Bundle.contMDiffWithinAt_zeroSection, MeasureTheory.lintegral_enorm_neg, ContinuousAlternatingMap.piLIE_apply_apply, Real.hasSum_log_one_add_inv, Matrix.PosSemidef.sqrt_eq_zero_iff, Real.differentiableOn_log, ProbabilityTheory.integral_continuousLinearMap_gaussianReal, Metric.diam_closure, combo_mem_ball_of_ne, FDerivMeasurableAux.le_of_mem_A, lintegral_fderiv_lineMap_eq_edist, MeasureTheory.HasFiniteIntegral.restrict_of_bounded, NumberField.InfiniteAdeleRing.algebraMap_apply, ContinuousLinearMap.isBigOWith_id, UnitAddTorus.mFourierSubalgebra_coe, TemperedDistribution.smulLeftCLM_compL_smulLeftCLM, curveIntegrable_fun_neg_iff, hasDerivWithinAt_zero, Path.ofLine_extend, Orientation.oangle_add_left_eq_arctan_of_oangle_eq_pi_div_two, iteratedDerivWithin_tsum_cexp_eq, MonotoneOn.intervalIntegrable, ContDiffAt.hasStrictDerivAt, Complex.continuousWithinAt_log_of_re_neg_of_im_zero, contMDiff_mulInvariantVectorField, ContinuousLinearEquiv.coe_toDiffeomorph_symm, MeasureTheory.isAddHaarMeasure_hausdorffMeasure, TensorProduct.ext_iff_inner_right_threefold', Complex.continuous_sin, MeasureTheory.lpMeasSubgroupToLpTrim_ae_eq, tangentCoordChange_def, signedDist_right_congr, differentiableWithinAt_inv, CurveIntegrable.zero, ContinuousMultilinearMap.contDiffAt, FormalMultilinearSeries.ofScalars_radius_eq_inv_of_tendsto_ENNReal, hasDerivAtFilter_ofNat, ProbabilityTheory.hasGaussianLaw_iff_charFun_map_eq, MeasureTheory.Measure.toSignedMeasure_le_toSignedMeasure_iff, Seminorm.continuous', CFC.exp_log, Complex.exp_eq_exp_ℂ, FormalMultilinearSeries.changeOriginSeries_summable_aux₃, curveIntegrable_smul_iff, ContinuousMap.toNNReal_neg_algebraMap, MeasureTheory.memLp_indicator_const, TensorProduct.toLinearEquiv_lidIsometry, NormedSpace.exp_series_hasSum_exp', HasFPowerSeriesOnBall.restrictScalars, Real.summable_one_div_int_pow, GaussianFourier.integral_cexp_neg_mul_sq_norm_add, Real.differentiableOn_arcsin, LinearMap.toContinuousLinearMap₁_coe, PeriodPair.eqOn_deriv_weierstrassPExcept_derivWeierstrassPExcept, ContinuousLinearMap.opNNNorm_le_iff, ContinuousLinearMap.isometry_mul_flip, PeriodPair.weierstrassP_coe, ContinuousMap.Homotopy.evalAt_eq, tendsto_cocompact_of_tendsto_dist_comp_atTop, ZSpan.smul, Meromorphic.fun_sum, BoundedContinuousFunction.evalCLM_apply, AnalyticOnNhd.eval_linearMap', NormedAddCommGroup.norm_toCompl, HasFPowerSeriesWithinAt.hasStrictFDerivWithinAt, Module.Basis.ofZLatticeComap_apply, map_extChartAt_symm_nhdsWithin', AffineEquiv.continuous_of_finiteDimensional, conformal_const_smul, MeasureTheory.SignedMeasure.exists_compl_positive_negative, UniformSpace.Completion.mem_uniformity_dist, ContinuousLinearEquiv.conjContinuousAlgEquiv_surjective, ContinuousLinearMap.adjoint_id, Complex.hasStrictFDerivAt_exp_real, NormedAddGroupHom.zero_completion, ClosedSubmodule.inf_orthogonal, NormedAddCommGroup.summable_imp_tendsto_iff_completeSpace, lp.coeFnAddMonoidHom_apply, LinearMap.coe_toContinuousLinearMap', ContDiffWithinAt.fun_smul, iteratedFDerivWithin_succ_eq_comp_left, ContinuousLinearMap.isPositive_natCast, summable_norm_mul_geometric_of_norm_lt_one, tendsto_birkhoffAverage_apply_sub_birkhoffAverage, ContinuousMultilinearMap.opNorm_zero_iff, ModularForm.prod_slash, ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_apply_of_gt, AkraBazziRecurrence.isTheta_deriv_rpow_p_mul_one_sub_smoothingFn, LipschitzWith.memLp_comp_iff_of_antilipschitz, EReal.nhds_coe, continuousAt_extChartAt, MeasureTheory.ComplexMeasure.HaveLebesgueDecomposition.imPart, Complex.isQuotientCoveringMap_npow, Summable.of_nnnorm_bounded, hasFDerivWithinAt_comp_smul_iff_smul, ContinuousLinearMap.isStarNormal_iff_norm_eq_adjoint, Submodule.starProjection_comp_starProjection_eq_zero_iff, Affine.Simplex.sign_signedInfDist_lineMap_incenter_touchpoint, FDerivMeasurableAux.differentiable_set_subset_D, uniqueDiffOn_Ioc, sum_cauchyPowerSeries_eq_integral, NumberField.mixedEmbedding.instIsAddHaarMeasureMixedSpaceVolume, MeasureTheory.condExpIndL1_add, Submodule.subtypeₗᵢ_toContinuousLinearMap, SchwartzMap.laplacianCLM_eq, CStarModule.innerSL_apply, instContinuousNegElemBallOfNat, MeromorphicOn.fun_smul, BoundedContinuousFunction.continuous_compContinuous, monomial_has_deriv_aux, continuous_equivFun_basis, DirichletCharacter.LSeries_twist_vonMangoldt_eq, LinearIsometryEquiv.conjStarAlgEquiv_apply, MeasureTheory.smul_convolution, StieltjesFunction.measure_Ioo, Real.vector_fourierIntegral_eq_integral_exp_smul, PadicInt.mahlerTerm_apply, iteratedFDerivWithin_comp_add_right', LinearMap.toMatrixOrthonormal_reindex, contDiff_one_iff_fderiv, NumberField.mixedEmbedding.fundamentalCone.compactSet_eq_union_aux₁, ContinuousMap.coeNNRealReal_apply, MeasureTheory.ConvolutionExistsAt.integrable, CompactlySupportedContinuousMap.nnrealPart_smul_neg, Matrix.IsHermitian.eigenvalues_eq, cfc_complex_eq_real, VectorBundleCore.mem_localTriv_target, egauge_add_add_le, UnitAddTorus.mFourierSubalgebra_closure_eq_top, Real.hasDerivAt_mul_log, contMDiff_equivTangentBundleProd_symm, IsBoundedLinearMap.differentiableWithinAt, Real.fourier_real_eq_integral_exp_smul, MeasureTheory.norm_indicatorConstLp_top, Asymptotics.isLittleOTVS_prodMk_left, Filter.tendsto_ofReal_iff', BoundedContinuousFunction.toContinuousMapLinearMap_apply, Asymptotics.IsEquivalent.tendsto_const, NumberField.mixedEmbedding.polarCoordReal_apply, Rat.not_countably_generated_cocompact, InnerProductGeometry.angle_smul_left_of_neg, iter_deriv_zpow', ProbabilityTheory.cdf_paretoMeasure_eq_integral, differentiableWithinAt_abs, PadicInt.coe_sum, MeasureTheory.integral_tilted, ContDiffAt.laplacian_CLM_comp_left, Complex.deriv_cos, WithSeminorms.continuousSMul, Real.tendsto_sigmoid_atTop, Matrix.exp_conj', CStarAlgebra.span_nonneg_inter_unitBall, hasLineDerivAt_iff_isLittleO_nhds_zero, Real.continuous_sinc, LinearIsometryEquiv.toHomeomorph_symm, Function.HasTemperateGrowth.sum, Complex.not_differentiableAt_Gamma_neg_nat, Real.deriv_arccos, RCLike.borelSpace, IntervalIntegrable.zero, CompactlySupportedContinuousMap.toBoundedContinuousFunction_apply, smul_unitClosedBall, ProbabilityTheory.setLIntegral_stieltjesOfMeasurableRat_rat, Real.hasStrictDerivAt_sinh, AddCircle.homeomorphCircle'_symm_apply, TestFunction.continuous_iff_continuous_comp, continuous_of_linear_of_boundₛₗ, MeasureTheory.integrable_const_mul_iff, isSelfAdjoint_iff_isStarNormal_and_spectrumRestricts, HasFiniteFPowerSeriesOnBall.sum, MeasureTheory.UniformIntegrable.integrable_of_tendstoInMeasure, MeasureTheory.L1.integral_smul, LocallyBoundedVariationOn.ae_differentiableWithinAt, MeasureTheory.Measure.toSphere_real_apply_univ, ContinuousLinearMap.opNorm_mul_flip_apply, ContinuousLinearMap.bilinearRestrictScalars_eq_restrictScalarsL_comp_restrictScalars, LinearMap.IsSymmetricProjection.ext_iff, ConvexOn.univ_sSup_of_countable_affine_eq, Real.hasFPowerSeriesOnBall_ofScalars_mul_add_zero, integrableOn_exp_Iic, ContinuousLinearMap.ebound, NormedAddGroupHom.instContinuousMapClass, LinearIsometry.isEmbedding, RCLike.hasSum_ofReal, CFC.negPart_algebraMap, InnerProductSpace.inner_left_rankOne_apply, Matrix.PosSemidef.commute_iff, cfcₙHom_nnreal_eq_restrict, contDiff_zero, instIsManifoldRealEuclideanSpaceFinOfNatNatEuclideanHalfSpaceModelWithCornersEuclideanHalfSpaceElemIcc, TestFunction.toBoundedContinuousFunctionCLM_apply, Metric.unitBall.instContinuousMul, RCLike.continuous_normSq, Conformal.const_smul, MeasureTheory.Lp.instFourierInvSMul, IsLocalFrameOn.coeff_apply_of_mem, hasFDerivWithinAt_sub_const_iff, ClosedSubmodule.orthogonal_injective, ProbabilityTheory.IsCondKernelCDF.nonneg, Orientation.oangle_neg_right, ContinuousAlternatingMap.norm_def, ContinuousLinearEquiv.hasTemperateGrowth, summable_norm_mul_geometric_of_norm_lt_one', stronglyMeasurable_derivWithin_Ioi, SchwartzMap.fderivCLM_apply, hasStrictDerivAt_abs_pos, deriv_sqrt_mul_log, ContinuousLinearMap.smul_compLp, isOpen_extChartAt_target, ProbabilityTheory.cdf_expMeasure_eq, hasMFDerivAt_extChartAt, hasDerivWithinAt_abs_pos, Submodule.norm_starProjection_apply_le, ContinuousLinearMap.norm_extendTo𝕜, ContinuousLinearMap.contMDiff, OpenPartialHomeomorph.extend_target_mem_nhdsWithin, ContinuousLinearMap.mdifferentiable, Rat.uniformContinuous_neg, Matrix.exp_neg, LinearIsometry.id_toContinuousLinearMap, HasSum.hasSum_at_zero, MeasureTheory.Measure.sub_toSignedMeasure_eq_toSignedMeasure_sub, Seminorm.continuousAt_zero_of_forall', HasFPowerSeriesAt.add, differentiableWithinAt_sub_const_iff, differentiable_descPochhammer_eval, VectorBundleCore.coordChange_self, Metric.tendsto_nhds_nhds, Metric.contractibleSpace_closedBall, differentiable_fst, tendsto_norm_div_self, ContinuousAlternatingMap.curryLeft_smul, Circle.isAddQuotientCoveringMap_exp, fderiv_const_smul_field, HasFTaylorSeriesUpToOn.comp_continuousAffineMap, instContMDiffAddSelf, LinearIsometry.map_starProjection', continuous_const_cpow, MeromorphicOn.fun_add, cfcHom_continuous, polynomialFunctions.starClosure_topologicalClosure, cfcL_apply, HasFDerivAtFilter.isBigOTVS_sub, threeAPFree_sphere, antideriv_bernoulliFun, NumberField.mixedEmbedding.commMap_apply_of_isComplex, innerₛₗ_apply_apply, AddCircle.integral_haarAddCircle, WithCStarModule.inner_def, Real.hasStrictFDerivAt_rpow_of_pos, hasFDerivWithinAt_inv, hasSum_nat_jacobiTheta, InnerProductSpace.HarmonicAt.const_smul, eventually_nhds_norm_smul_sub_lt, differentiableAt_sigmoid, CircleIntegrable.const_smul, exists_dist_slope_lt_pairwiseDisjoint_hasSum, DoubleCentralizer.pow_snd, LinearIsometry.coe_toContinuousLinearMap, HasFPowerSeriesWithinOnBall.tendstoLocallyUniformlyOn, BumpCovering.support_toPOUFun_subset, NumberField.InfinitePlace.Completion.norm_coe, PointwiseConvergenceCLM.tendsto_nhds, MeasureTheory.eLpNorm_le_of_ae_nnnorm_bound, Submodule.symmetric_isOrtho, SpectrumRestricts.nnreal_iff, iteratedDeriv_scomp_three, geometric_hahn_banach_compact_closed, ContDiffAt.continuousAt_fderiv, hasDerivWithinAt_pi, ContinuousMapZero.isometry_toContinuousMap, MeromorphicOn.add, differentiableOn_iteratedDerivWithin_cotTerm, ProbabilityTheory.IsCondKernelCDF.integral, smoothSheafCommRing.instLocalRing_stalk, Orientation.oangle_smul_left_of_neg, NormedSpace.isVonNBounded_ball, MeasureTheory.eLpNorm_mono_real, map_extChartAt_symm_nhdsWithin_range', deriv_const', norm_smul_inv_norm, ContinuousLinearEquiv.comp_hasFDerivAt_iff, MeromorphicAt.eq_nhdsNE_toMeromorphicNFAt, Real.Angle.continuousAt_sign, ContinuousLinearMap.eq_adjoint_iff, PeriodPair.hasSum_derivWeierstrassPExcept, Orientation.norm_div_cos_oangle_add_left_of_oangle_eq_pi_div_two, RealNormedSpace.noncompactSpace, modelWithCornersSelf_coe_symm, MeasureTheory.L2.inner_def, deriv.star, ContDiffAt.fderiv_succ, Orientation.volumeForm_map, ContMDiffVectorBundle.pullback, PiTensorProduct.toDualContinuousMultilinearMap_apply_apply, MeasureTheory.Measure.addHaar_ball_of_pos, WeakFEPair.hf_zero', Icc_isBoundaryPoint_bot, SchwartzMap.toLpCLM_apply, dist_birkhoffSum_birkhoffSum_le, Polynomial.div_tendsto_zero_iff_degree_lt, LinearMap.IsSymmetric.directSum_decompose_apply, Real.volume_val, Real.borel_eq_generateFrom_Iio_rat, deriv_abs_neg, Tactic.ComputeAsymptotics.Majorized.tendsto_zero_of_neg, TangentBundle.symmL_trivializationAt_eq_core, interior_closedBall, cfcHom_nonneg_iff, PartitionOfUnity.nonneg', OrderedFinpartition.norm_compAlongOrderedFinpartitionL_apply_le, Real.differentiableWithinAt_arccos_Ici, HasFPowerSeriesAt.comp, Complex.differentiableAt_GammaAux, ZeroAtInftyContinuousMap.instNormedStarGroup, Homeomorph.contDiff_unitBall, EuclideanGeometry.reflection_vadd_smul_vsub_orthogonalProjection, ContinuousLinearMap.IsPositive.smul_of_nonneg, fderiv_add_const, ContDiffAt.exists_forall_mem_closedBall_exists_eq_forall_mem_Ioo_hasDerivAt₀, gelfandStarTransform_naturality, InnerProductSpace.rankOne_apply, summable_condensed_iff_of_eventually_nonneg, isClosed_nonneg, LinearMap.polar_singleton, Orientation.oangle_add_right_eq_arcsin_of_oangle_eq_pi_div_two, AffineIsometryEquiv.comp_continuous_iff, Unitary.coe_linearIsometryEquiv_apply, BoxIntegral.integral_add, MeromorphicOn.divisor_pow, ModularForm.prod_slash_sum_weights, gelfandStarTransform_apply_apply, Real.summable_nat_rpow_inv, Submodule.reflection_singleton_apply, BoundedContinuousFunction.dist_toContinuousMap, RCLike.nonUnitalContinuousFunctionalCalculus, MeasureTheory.condExpIndL1Fin_add, smul_unitClosedBall_of_nonneg, HasFTaylorSeriesUpToOn.zero_eq', BoxIntegral.HasIntegral.tendsto, ProbabilityTheory.IdentDistrib.eLpNorm_eq, SchwartzMap.compCLMOfContinuousLinearEquiv_apply, HarmonicAt.analyticAt_complex_partial, Complex.instPathConnectedSpaceUnits, ProbabilityTheory.stronglyMeasurable_geometricPMFReal, integrableOn_Ioi_rpow_of_lt, Filter.inv_nhdsNE_zero, HasFPowerSeriesWithinOnBall.isBigO_image_sub_image_sub_deriv_principal, stereographic'_source, interior_convexHull_nonempty_iff_affineSpan_eq_top, ContDiff.continuous_deriv, cfc_apply_mkD, Real.aestronglyMeasurable_rpowIntegrand₀₁, Rat.borelSpace, NormedSpace.Dual.toWeakDual_continuous, MeasureTheory.Lp.compMeasurePreservingₗ_apply, Affine.Triangle.orthocenter_eq_smul_vsub_vadd_circumcenter, EuclideanGeometry.inter_eq_singleton_orthogonalProjection, WithSeminorms.withSeminorms_eq, BoundedContinuousFunction.toContinuousMapMonoidHom_apply, mdifferentiableWithinAt_section, HasFiniteFPowerSeriesAt.finite, ContinuousLinearMap.mkOfIsCompactOperator_mem_compactOperator, MeasureTheory.weightedSMul_nonneg, signedDist_left_congr, cfcₙ_eq_cfcₙL_mkD, MeasureTheory.convolution_integrand_bound_right_of_le_of_subset, ContinuousMap.toLp_norm_le, FormalMultilinearSeries.id_apply_one', TopologicalSpace.Opens.CompleteCopy.instCompleteSpace, TangentBundle.continuousLinearMapAt_trivializationAt_eq_core, stdSimplexHomeomorphUnitInterval_zero, ContinuousMultilinearMap.norm_smulRightL_le, HasSummableGeomSeries.summable_geometric_of_norm_lt_one, tensorIteratedFDerivTwo_eq_iteratedFDeriv, tsum_geometric_of_norm_lt_one, AnalyticOnNhd.iteratedFDeriv, map_extChartAt_symm_nhdsWithin_range, ContinuousLinearEquiv.contDiffAt_comp_iff, comap_norm_nhdsGT_zero, WeakFEPair.h_feq, differentiableAt_smul_iff, ContinuousLinearMap.precompL_apply, DoubleCentralizer.nnnorm_snd, egauge_univ, differentiableAt_comp_add_const, SeparationQuotient.nnnorm_mk', MeasureTheory.condExpL1_measure_zero, integrableOn_Ioi_norm_cpow_of_lt, ContinuousLinearEquiv.isBigO_comp, OnePoint.isBoundedAt_iff_forall_SL2Z, Complex.continuousOn_cos, CStarAlgebra.tendsto_mul_left_iff_tendsto_mul_right, MeasureTheory.Measure.addHaar_preimage_smul, IsClosed.lowerClosure_pi, setIntegral_withDensity_eq_setIntegral_toReal_smul', InformationTheory.leftDeriv_klFun_one, Module.Basis.parallelepiped_reindex, Submodule.reflection_apply, Real.circleAverage_sum, ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_eq_of_scalars, curveIntegralFun_segment, ZMod.completedLFunction_def_even, SchwartzMap.integral_fourierInv_smul_eq, ContinuousMultilinearMap.norm_mkPiAlgebra_le, Memℓp.star_mem, SlashInvariantForm.quotientFunc_smul, MeasureTheory.Measure.AddMonoidHom.continuous_of_measurable, map_extChartAt_nhdsWithin', ProbabilityTheory.stieltjesOfMeasurableRat_nonneg, Circle.exp_eq_exp, RCLike.reCLM_norm, RCLike.geometric_hahn_banach_closed_point, GenLoop.homotopyTo_apply, Besicovitch.SatelliteConfig.exists_normalized_aux2, differentiable_finCons', signedDist_triangle, Submodule.orthogonal_eq_bot_iff, TensorProduct.adjoint_map, Real.hasDerivAt_arcosh, curveIntegral_neg, summableLocallyUniformlyOn_iteratedDerivWithin_cotTerm, SchwartzMap.inner_toL2_toL2_eq, Complex.isOpen_slitPlane, HasGradientAt.continuousAt, MeasureTheory.AEEqFun.integrable_iff_mem_L1, MeasureTheory.SimpleFunc.memLp_zero, IsBoundedLinearMap.differentiable, circleIntegral.integral_fun_sum, VectorBundleCore.contMDiffOn_coordChange, PartitionOfUnity.locallyFinite, FormalMultilinearSeries.radius_le_smul, LinearIsometryEquiv.lTensor_apply, EuclideanGeometry.dist_eq_iff_eq_smul_rotation_pi_div_two_vadd_midpoint, DirichletCharacter.deriv_LFunction_eq_deriv_LSeries, ProbabilityTheory.gammaCDFReal_eq_integral, Metric.isPathConnected_ball, MeasureTheory.SignedMeasure.toComplexMeasure_apply, ModularForm.tsum_logDeriv_eta_q, Path.Homotopy.continuous_transAssocReparamAux, InnerProductSpace.gramSchmidt_def, AffineIsometryEquiv.continuousAt, EisensteinSeries.summable_left_one_div_linear_sub_one_div_linear, ConvexOn.monotoneOn_rightDeriv, tendsto_self_mul_const_pow_of_lt_one, MeasureTheory.Lp.simpleFunc.isDenseEmbedding, UniformSpace.Completion.uniformContinuous_dist, Polynomial.Chebyshev.isLocalMin_T_real, Real.expPartialHomeomorph_apply, CStarMatrix.toCLM_injective, MeasureTheory.integrable_piLp_iff, iteratedFDerivWithin_succ_const, Metric.equicontinuousAt_iff, Complex.integral_circleTransform, ContinuousLinearMap.isPositive_self_comp_adjoint, tendsto_norm_inv_nhdsNE_zero_atTop, dslope_eventuallyEq_slope_nhdsNE, iteratedDeriv_scomp_eq_sum_orderedFinpartition, trivialization_linear, formalMultilinearSeries_geometric_apply_norm_le, ContinuousLinearMap.hasFPowerSeriesAt, Bundle.Trivial.continuousLinearMapAt_trivialization, HasFPowerSeriesOnBall.hasSum_iteratedFDeriv, LinearMap.adjoint_toContinuousLinearMap, StrongFEPair.differentiable_Λ, Trivialization.contMDiffOn_symm_trans, hasDerivAt_iff_isLittleO, Path.extend_symm_apply, BoundedContinuousFunction.mkOfCompact_add, Absorbs.eventually_nhdsNE_zero, spectrum.isOpen_resolventSet, Affine.Simplex.orthogonalProjectionSpan_eq_point, intervalIntegral.intervalIntegrable_of_integral_ne_zero, LocallyBoundedVariationOn.ae_differentiableAt, Polynomial.toAddCircle_X_pow_eq_fourier, HasDerivWithinAt.hasFDerivWithinAt, MonotoneOn.intervalIntegrable_deriv, Unitary.linearIsometryEquiv_coe_apply, LDL.lowerInv_eq_gramSchmidtBasis, BoundedContinuousFunction.instSMulCommClass_2, ContDiffAt.differentiableAt, Function.HasTemperateGrowth.norm_iteratedFDeriv_le_uniform_aux, hasFPowerSeriesAt_const, EuclideanGeometry.angle_vadd_const, hasStrictFDerivAt_pi', fderiv_eq_deriv_mul, Path.Homotopy.target, UniformOnFun.continuousSMul_induced_of_image_bounded, MeasureTheory.UniformIntegrable.memLp_of_tendstoInMeasure, HasFPowerSeriesOnBall.const_smul, Orientation.abs_volumeForm_apply_of_orthonormal, ContinuousLinearMap.toSesqForm_apply_coe, signedDist_linear_apply_apply, FormalMultilinearSeries.nnnorm_mul_pow_le_of_lt_radius, ContinuousMultilinearMap.curry0_apply, hasFDerivAtFilter_sub_const_iff, norm_iteratedFDerivWithin_zero, ContinuousLinearMap.cpolynomialOn_uncurry_of_multilinear, inTangentCoordinates_eq_mfderiv_comp, FormalMultilinearSeries.radius_compNeg, intervalIntegral.intervalIntegrable_zpow, Circle.exp_two_pi_mul_int, cauchySeq_of_le_geometric, PiLp.coe_continuousLinearEquiv, setIntegral_withDensity_eq_setIntegral_toReal_smul₀, gelfandTransform_bijective, Polynomial.differentiableOn_aeval, SchwartzMap.integral_bilin_fourierIntegral_eq, MeasureTheory.Submartingale.integrable, fourier_gaussian_innerProductSpace, DomMulAct.smul_Lp_sub, ValueDistribution.logCounting_add_top_le, analyticOrderAt_add_eq_left_of_lt, Metric.tendsto_nhds, NormedRing.inverse_one_sub_nth_order, NumberField.mixedEmbedding.polarSpaceCoord_target, AddCircle.scaled_exp_map_periodic, mdifferentiableAt_iff, OnePoint.isZeroAt_iff_exists_SL2Z, LinearIsometryEquiv.adjoint_eq_symm, SchwartzMap.toLp_fourierInv_eq, NumberField.mixedEmbedding.negAt_apply_snd, extDeriv_fun_smul, TensorProduct.mapIsometry_id_id, Real.GammaIntegral_convergent, ContinuousAlternatingMap.toAlternatingMap_curryLeft, ordinaryHypergeometricSeries_radius_eq_one, Real.tendsto_atTop_csSup_of_monotoneOn_bddAbove_nat_Ici, Matrix.toEuclideanLin_apply, EReal.isOpenEmbedding_coe, BoundedContinuousFunction.isEmbedding_coeFn, Real.borel_eq_generateFrom_Ioo_rat, Real.hasSum_sinh, UniformSpace.metrizable_uniformity, IsContDiffImplicitAt.hasFDerivAt, Real.tendsto_eulerMascheroniSeq', iteratedDerivWithin_eq_iteratedFDerivWithin, Real.one_add_rpow_hasFPowerSeriesOnBall_zero, ProbabilityTheory.monotone_cdf, Submodule.IsOrtho.orthogonalProjection_comp_subtypeL, LinearMap.IsPositive.isPositive_smul_iff, ContinuousLinearMap.sSup_sphere_eq_nnnorm, analyticOrderAt_smul_eq_top_of_left, NormedSpace.isClosed_polar, VectorFourier.fourierPowSMulRight_eq_comp, upperClosure_interior_subset', ContinuousAlternatingMap.le_opNNNorm, IsEquivalent.summable_iff_nat, MeasureTheory.continuous_condExpIndL1, MeasureTheory.charFunDual_eq_charFun_map_one, HasFPowerSeriesOnBall.tendsto_partialSum_prod, EuclideanGeometry.orthogonalProjection_map, NormedField.discreteTopology_or_nontriviallyNormedField, hasFDerivWithinAt_pi', EisensteinSeries.E2_slash_action, LinearMap.mkContinuousOfExistsBound_coe, Complex.tendsto_exp_nhds_zero_iff, fourier_norm, IsHilbertSum.hasSum_linearIsometryEquiv_symm, MeasureTheory.Lp.nnnorm_eq_zero_iff, continuous_of_linear_of_bound, ContinuousLinearMap.opNorm_mul, Submodule.IsOrtho.map_iff, cfcHom_isClosedEmbedding, Complex.uniformContinuous_im, DoubleCentralizer.smul_toProd, mfderivWithin_projIcc_one, StieltjesFunction.measure_singleton, InnerProductSpace.harmonicOnNhd_comp_CLE_iff, sameRay_iff_inv_norm_smul_eq_of_ne, Complex.frontier_preimage_re, CuspForm.coe_trace, EisensteinSeries.e2Summand_summable, ContinuousAlternatingMap.constOfIsEmptyLIE_apply, ContinuousLinearMapWOT.le_nhds_iff_forall_dual_apply_le_nhds, ProbabilityTheory.Kernel.HasSubgaussianMGF.integrable_exp_add_compProd, indicator_thickening_eventually_eq_indicator_closure, comap_norm_nhds_zero, norm_sum_lt_of_strictConvexSpace, SmoothBumpFunction.continuous, iteratedDerivWithin_eq_iterate, UniformConvexOn.strictConvexOn, TemperedDistribution.smulLeftCLM_neg, analyticOrderAt_eq_top, Metric.inseparable_iff, Orientation.oangle_sign_sub_smul_left, MeasureTheory.SimpleFunc.integral_eq_sum_filter, egauge_zero_zero, Real.comap_exp_nhds_zero, PiTensorProduct.mapL_one, HomotopyGroup.isUnital_auxGroup, OpenPartialHomeomorph.univUnitBall_symm_apply_zero, Real.hasStrictDerivAt_arccos, DoubleCentralizer.toProdMulOpposite_injective, contDiffWithinAt_nat, deriv_const_add', AnalyticAt.frequently_zero_iff_eventually_zero, RCLike.conjCLE_apply, ContinuousLinearMap.norm_fst_le, Stirling.log_stirlingSeq_diff_hasSum, SchwartzMap.eLpNorm_lt_top, IsUltrametricDist.norm_tsum_le, ProbabilityTheory.integral_stieltjesOfMeasurableRat, MeasureTheory.Measure.quasiMeasurePreserving_smul, hasFDerivAt_snd, MeasureTheory.dominatedFinMeasAdditive_condExpInd, Complex.reCLM_nnnorm, DoubleCentralizer.norm_fst_eq_snd, MeasureTheory.L1.SimpleFunc.integral_add, Unitization.nnnorm_def, MeasureTheory.LevyProkhorov.continuous_equiv_symm_probabilityMeasure, IsUnit.cfcSqrt, CFC.continuousOn_log, ContinuousLinearMap.hasFiniteFPowerSeriesOnBall_uncurry_of_multilinear, Orientation.rightAngleRotation_def, ContinuousLinearMap.le_opNorm, MeasureTheory.SignedMeasure.toJordanDecomposition_zero, Function.locallyFinsuppWithin.logCounting_eval_zero, intervalIntegral.intervalIntegrable_inv_one_add_sq, ImplicitFunctionData.range_leftDeriv, Complex.instContinuousStar, QuotientGroup.norm_mk_eq_zero_iff_mem_closure, AddMonoidHomClass.continuous_of_bound, ENNReal.hasSum_toReal, NormedSpace.exp_hasFPowerSeriesOnBall, Topology.RelCWComplex.continuousOn, Function.HasTemperateGrowth.toTemperedDistribution_apply, Euclidean.closedBall_eq_image, NumberField.mixedEmbedding.fundamentalCone.expMap_target, Real.continuousOn_log, ContinuousLinearMap.flipMultilinear_apply_apply, ContinuousMultilinearMap.uncurrySum_apply, NumberField.mixedEmbedding.negAt_preimage, InformationTheory.not_differentiableWithinAt_klFun_Iio_zero, HasLineDerivAt.tendsto_slope_zero_right, ProbabilityTheory.Kernel.HasSubgaussianMGF.memLp_exp_mul, MeasureTheory.integrable_condExp, ContDiffPointwiseHolderAt.differentiableAt, ZLattice.comap_toAddSubgroup, OpenPartialHomeomorph.univUnitBall_apply_zero, Complex.hasDerivAt_GammaIntegral, NormedSpace.expSeries_summable, HasFPowerSeriesAt.eq_pow_order_mul_iterate_dslope, compactOperator_topologicalClosure, MeromorphicOn.divisor_natCast, RCLike.wInner_cWeight_eq_expect, Complex.deriv_ofReal_cpow_const, exists_continuous_zero_one_of_isClosed, Submodule.coe_orthogonalDecomposition_symm, UpperHalfPlane.comp_ofComplex, Complex.starConvex_ofReal_slitPlane, Real.Wallis.tendsto_W_nhds_pi_div_two, MeasureTheory.Lp.finStronglyMeasurable, Real.isOpenEmbedding_exp, Real.Angle.sign_two_nsmul_eq_neg_sign_iff, CuspForm.coeHom_apply, PiTensorProduct.mapL_smul, Complex.analyticOnNhd_univ_iff_differentiable, SchwartzMap.integral_sesq_fourier_eq, MDifferentiableWithinAt.differentiableWithinAt_writtenInExtChartAt, BoundedContinuousFunction.coe_toContinuousMapStarₐ, MeasureTheory.aestronglyMeasurable_condExpL2, NumberField.mixedEmbedding.fundamentalCone.volume_frontier_normLeOne, MeasureTheory.L1.SimpleFunc.setToL1S_add_left, Submodule.orthogonalProjection_bot, isAddHaarMeasure_basis_addHaar, DoubleCentralizer.norm_def', MeasureTheory.charFunDual_pi', ContinuousLinearMap.adjointAux_norm, differentiable_apply, CStarMatrix.norm_def', IsGreatest.nnnorm_cfc_nnreal, derivWithin_univ, NumberField.mixedEmbedding.iUnion_negAt_plusPart_ae, Rat.isDenseEmbedding_coe_real, SchwartzMap.memLp, Submodule.range_starProjection, MeasureTheory.eLpNorm_norm, HurwitzZeta.hasSum_nat_sinZeta, BoxIntegral.unitPartition.integralSum_eq_tsum_div, MeasureTheory.hasFiniteIntegral_toReal_of_lintegral_ne_top, ContinuousMap.instNormedStarGroup, MeasureTheory.Measure.addHaar_ball_mul, fderiv_neg, Real.instPathConnectedSpace, Real.norm_deriv_mulExpNegMulSq_le_one, ValueDistribution.logCounting_top, MeasureTheory.convolution_smul, ZLattice.module_finite, OpenPartialHomeomorph.continuousAt_extend_symm', LeftInvariantDerivation.lift_add, hasDerivAtFilter_natCast, EuclideanGeometry.angle_orthogonalProjection_self, ContinuousFunctionalCalculus.isCompact_spectrum, NormedAddGroupHom.extension_coe_to_fun, binomialSeries_radius_eq_one, EuclideanGeometry.orthogonalProjection_apply_mem, meromorphicOrderAt_ne_top_iff, ContinuousMap.norm_le_of_nonempty, HasFPowerSeriesAt.differentiableAt, MeasureTheory.SignedMeasure.singularPart_smul, Pi.counit_eq_adjoint, EisensteinSeries.G2_slash_action, uniformContinuous_norm, WithLp.unitization_algebraMap, ContinuousAlternatingMap.instContinuousSMul, LinearMap.toMatrixOrthonormal_apply_apply, MeasureTheory.condExpInd_nonneg, ContinuousLinearMap.fpowerSeries_apply_zero, Orientation.areaForm_to_volumeForm, stereoInvFunAux_apply, StrongFEPair.functional_equation, lp.norm_rpow_eq_tsum, Icc_isInteriorPoint_interior, derivWithin.fun_neg, Submodule.exists_add_mem_mem_orthogonal, Complex.summable_conj, Metric.uniformity_basis_dist_lt, SeparationQuotient.liftNormedAddGroupHomEquiv_apply, ContinuousAffineMap.norm_def, AnalyticAt.exists_eventuallyEq_sum_add_pow_mul, GaussianFourier.integrable_cexp_neg_mul_sq_norm_add_of_euclideanSpace, signedDist_le_dist, HasGradientWithinAt.continuousWithinAt, Real.not_continuousAt_deriv_mul_log_zero, ProbabilityTheory.integrable_condCDF, iteratedDeriv_succ', iteratedDerivWithin_one, MeasureTheory.withDensityᵥ_neg', Complex.continuousAt_arg, PeriodPair.latticeBasis_zero, OpenPartialHomeomorph.contDiff_univUnitBall, integrableOn_add_rpow_Ioi_of_lt, ZMod.LFunction_def_odd, cfcₙ_apply_mkD, AffineSubspace.isConnected_setOf_wOppSide, iteratedDeriv_smul_const, circleIntegral.integral_sub_inv_smul_sub_smul, InformationTheory.klDiv_eq_top_iff, Asymptotics.IsLittleO.tendsto_div_nhds_zero, ExistsContDiffBumpBase.w_compact_support, SchwartzMap.fourier_lineDerivOp_eq, Manifold.IsImmersionAtOfComplement.map_target_subset_target, Complex.starConvex_one_slitPlane, LinearMap.isBigOTVS_rev_comp, cfcₙHom_id, Asymptotics.IsEquivalent.add_isLittleO, MonoidHomClass.continuous_of_bound, ContinuousLinearMapWOT.inducingFn_apply, TemperedDistribution.instLineDerivLeftSMulReal, tangentBundle_model_space_coe_chartAt, meromorphicOrderAt_eq_top_iff, LindemannWeierstrass.exp_polynomial_approx, BoundedContinuousFunction.uniformContinuous_comp, ApproximatesLinearOn.approximatesLinearOn_iff_lipschitzOnWith, CStarMatrix.inner_toCLM_conjTranspose_left, Orientation.areaForm_neg_orientation, ProbabilityTheory.IsRatCondKernelCDFAux.tendsto_atBot_zero, MeasureTheory.L1.continuous_integral, hasStrictDerivAt_exp_smul_const, Real.hasSum_cosh, AffineBasis.interior_convexHull, ContinuousMap.setOfIdeal_ofSet_of_isOpen, EuclideanGeometry.inversion_vsub_center, ProbabilityTheory.tendsto_stieltjesOfMeasurableRat_atTop, isBoundedBilinearMap_comp, Complex.interior_setOf_le_re, EuclideanGeometry.dist_orthogonalProjection_eq_iff_angle_eq, MeasureTheory.uniformIntegrable_iff, HasFPowerSeriesWithinOnBall.uniform_geometric_approx, ENNReal.tendsto_toReal, IsBoundedLinearMap.continuous, SchwartzMap.smulLeftCLM_compCLMOfContinuousLinearEquiv, Filter.tendsto_ofReal_iff, MeasureTheory.Lp.stronglyMeasurable, IsUltrametricDist.norm_tprod_le, EuclideanSpace.instFactEqNatFinrankFin, differentiable_euclidean, SemilinearIsometryClass.continuous, NumberField.mixedEmbedding.stdBasis_apply_isComplex_snd, CFC.continuousOn_sqrt, FormalMultilinearSeries.nnnorm_changeOrigin_le, Monotone.ae_differentiableAt, hasStrictDerivAt_add_const_iff, hasLineDerivWithinAt_smul_iff, Metric.mem_closure_iff_infDist_zero, InnerProductGeometry.norm_add_eq_norm_sub_iff_angle_eq_pi_div_two, Finsupp.sum_inner, MeasureTheory.SimpleFunc.memLp_iff_integrable, contMDiffOn_iff_contDiffOn, ExistsContDiffBumpBase.u_continuous, TemperedDistribution.fourierInv_lineDerivOp_eq, MeasureTheory.L1.integrable_coeFn, SchwartzMap.injective_toLp, MeasureTheory.condExpL2_indicator_ae_eq_smul, mfderivWithin_comp_projIcc_one, conformalAt_const_smul, UpperHalfPlane.mdifferentiable_inv_denom, NumberField.mixedEmbedding.fundamentalCone.isCompact_compactSet, LeftInvariantDerivation.lift_smul, IsMIntegralCurveOn.hasDerivWithinAt, PartitionOfUnity.sum_eq_one', InnerProductGeometry.tan_angle_add_mul_norm_of_inner_eq_zero, ImplicitFunctionData.map_pt_mem_toPartialHomeomorph_target, FormalMultilinearSeries.rightInv_removeZero, Metric.hausdorffDist_self_closure, WithAbs.uniformSpace_comap_eq_of_comp, geom_series_succ, isCompactOperator_iff_isCompact_closure_image_ball, MeasureTheory.eLpNorm'_mono_nnnorm_ae, Asymptotics.isLittleO_pow_pow, ContinuousAlternatingMap.ofSubsingletonLIE_symm_apply, DoubleCentralizer.norm_def, ClosedSubmodule.orthogonal_closure'', hasStrictDerivAt_exp_smul_const', Complex.hasStrictFDerivAt_cpow', NumberField.mixedEmbedding.negAt_signSet_apply_isComplex, egauge_univ_pi, MeromorphicAt.fun_smul, NumberField.mixedEmbedding.fundamentalCone.volume_interior_eq_volume_closure, LinearIsometryEquiv.adjoint_toLinearMap_eq_symm, SmoothPartitionOfUnity.sum_finsupport', SchwartzMap.smulLeftCLM_real_smul, uniqueDiffWithinAt_iff_accPt, Real.dimH_univ_eq_finrank, InnerProductSpace.toDualMap_apply_apply, NNRealRMK.lintegral_rieszMeasure, Submodule.le_orthogonal_orthogonal, MeasureTheory.Measure.integral_comp_inv_mul_left, ContDiffBump.measure_closedBall_div_le_integral, Orientation.kahler_eq_zero_iff, AddChar.sum_apply_eq_ite, PositiveLinearMap.preGNS_norm_def, LinearMap.eq_adjoint_iff_basis_left, curveIntegralFun_trans_aeeq_right, Bundle.contMDiffAt_zeroSection, contDiff_succ_iff_fderiv, BoxIntegral.integralSum_add, PositiveLinearMap.leftMulMapPreGNS_apply, ContinuousLinearMap.opNNNorm_prod, ContinuousLinearEquiv.comp_differentiableOn_iff, Real.not_summable_indicator_one_div_natCast, Metric.ball_subset_interior_closedBall, Metric.uniformEquicontinuous_iff, tsum_geometric_le_of_norm_lt_one, BoundedContinuousFunction.integral_const_sub, MeasureTheory.measure_smul_average, contMDiffAt_mulInvariantVectorField, Metric.tendsto_atTop', extChartAt_preimage_mem_nhdsWithin', hasMellin_add, ContinuousMap.Homotopy.ulift_apply, isOpen_cpolynomialAt, InnerProductSpace.HarmonicOnNhd.comp_CLM, ZLattice.rank, Orientation.oangle_sign_sub_smul_right, Real.continuous_tan, hasDerivAtFilter_zero, ProperCone.innerDual_sUnion, Complex.integral_comp_polarCoord_symm, Complex.uniformContinuous_re, signedDist_apply_apply, spectrum.hasFPowerSeriesOnBall_inverse_one_sub_smul, ZSpan.quotientEquiv_apply_mk, GenLoop.loopHomeo_apply, PeriodPair.ω₂_div_two_notMem_lattice, Real.differentiableAt_rpow_const_of_ne, deriv.fun_neg', Orientation.oangle_smul_left_self_of_nonneg, UnitAddTorus.mFourierCoeff_toLp, ProbabilityTheory.gaussianReal_map_continuousLinearMap, Manifold.pathELength_def, MeasureTheory.Lp.simpleFunc.stronglyMeasurable, MeasureTheory.FiniteMeasure.injective_toWeakDualBCNN, Metric.isCompact_of_isClosed_isBounded, WeakDual.toStrongDual_inj, ODE.FunSpace.continuousOn_comp_compProj, Real.exp_sub_sum_range_succ_isLittleO_pow, BoxIntegral.Box.isCompact_Icc, IccLeftChart_extend_interior_pos, HurwitzZeta.differentiable_expZeta_of_ne_zero, AntitoneOn.derivWithin_nonpos, Real.hasDerivAt_arsinh, MeasureTheory.SignedMeasure.mutuallySingular_ennreal_iff, iteratedDerivWithin_const_add, ContinuousLinearMap.mulLeftRight_apply, SchwartzMap.differentiable, isModuleTopologyOfFiniteDimensional, PeriodPair.hasSum_derivWeierstrassP, MeasureTheory.Lp.dist_edist, LinearIsometryEquiv.fderiv, Orientation.areaForm_swap, curveIntegral_fun_smul, FormalMultilinearSeries.nnnorm_changeOriginSeries_le_tsum, hasSum_zeta_four, ContinuousLinearMap.holderₗ_apply_apply, contMDiffWithinAt_prod_module_iff, hasFDerivAt_add_const_iff, taylor_tendsto, PeriodPair.compl_lattice_diff_singleton_mem_nhds, NumberField.mixedEmbedding.euclidean.stdOrthonormalBasis_map_eq, dslope_sub_smul, hasDerivAt_id', ContinuousMultilinearMap.unit_le_opNorm, MeasureTheory.SignedMeasure.exists_isCompl_positive_negative, Real.uniformContinuous_const_mul, ext_inner_map, ProbabilityTheory.covarianceOperator_zero, integrableOn_Ioi_cpow_iff, ProbabilityTheory.IsGaussian.memLp_two_id, Bundle.ContinuousRiemannianMetric.symm, ContinuousMultilinearMap.curryRight_norm, ContinuousLinearMap.analyticOn_bilinear, MeasureTheory.memLp_const_iff, HurwitzZeta.differentiable_hurwitzZetaOdd, BoundedContinuousFunction.mkOfCompact_zero, Real.summable_abs_int_rpow, Submodule.instHasOrthogonalProjectionOfCompleteSpace, CompactlySupportedContinuousMap.toRealLinearMap_apply_apply, LSeries_deriv_eqOn, CPolynomialAt.exists_mem_nhds_cpolynomialOn, IndiscreteTopology.of_forall_nnnorm_eq_zero, FDerivMeasurableAux.norm_sub_le_of_mem_A, ContinuousLinearMap.deriv, ProbabilityTheory.Kernel.tendsto_density_atTop_ae_of_antitone, hasStrictFDerivAt_multiset_prod, OrthogonalFamily.linearIsometry_apply_dfinsupp_sum_single, InformationTheory.tendsto_rightDeriv_klFun_atTop, deriv_norm_ofReal_cpow, MeasureTheory.convolution_lsmul, TemperedDistribution.instFourierAdd, HurwitzZeta.differentiable_hurwitzZeta_sub_hurwitzZeta, PeriodPair.hasSumLocallyUniformly_derivWeierstrassP, Complex.sameRay_of_arg_eq, hasFDerivAt_sub_const_iff, SlashInvariantForm.coe_translate, NumberField.mixedEmbedding.normAtComplexPlaces_polarSpaceCoord_symm, MeasureTheory.Lp.norm_zero, MeasureTheory.ComplexMeasure.singularPart_add_withDensity_rnDeriv_eq, Path.truncate_self, ZeroAtInftyContinuousMap.isClosed_range_toBCF, curveIntegral_fun_zero, UpperHalfPlane.ofComplex_apply_of_im_nonpos, ProbabilityTheory.stieltjesOfMeasurableRat_le_one, meromorphicNFOn_smul_iff_right_of_analyticOnNhd, ModelWithCorners.uniqueDiffOn_preimage, LinearMap.nonneg_iff_isPositive, upperClosure_interior_subset, hasDerivAt_abs_neg, Orientation.kahler_swap, coe_innerSL_apply, ProbabilityTheory.IsGaussian.integrable_fun_id, cfcHom_le_iff, IsUnifLocDoublingMeasure.exists_measure_closedBall_le_mul'', strongConcaveOn_zero, Metric.PiNatEmbed.dist_def, MeasureTheory.Lp.simpleFunc.sub_toSimpleFunc, integral_withDensity_eq_integral_smul, MeasureTheory.L1.dist_eq_integral_dist, NumberField.tendsto_sub_one_mul_dedekindZeta_nhdsGT, NormedAddGroupHom.norm_completion, intervalIntegral.integral_comp_add_div, LinearMap.IsSymmetric.inner_map_self_eq_zero, StieltjesFunction.id_leftLim, cfcHom_id, ContinuousLinearMap.isCompact_image_coe_closedBall, MeasureTheory.L1.norm_def, Real.deriv_sqrt_aux, OrthonormalBasis.prod_apply, iteratedFDeriv_add_apply, deriv_fderiv, PeriodPair.hasFPowerSeriesAt_derivWeierstrassPExcept, BoundedContinuousFunction.instIsOrderedAddMonoid, RegularNormedAlgebra.isometry_mul', InnerProductGeometry.norm_add_eq_add_norm_iff_angle_eq_zero, Complex.frontier_setOf_im_lt, Orientation.rotation_rotation, cauchyPowerSeries_apply, summable_eisSummand, Real.Angle.two_nsmul_toReal_eq_two_mul_sub_two_pi, curveIntegralFun_symm_apply, MeasureTheory.SignedMeasure.mutuallySingular_singularPart, SeparationQuotient.norm_normedMk_eq_one, LinearIsometryEquiv.coe_toHomeomorph, uniformContinuous_dist, ContinuousLinearMap.isClosed_image_coe_closedBall, DoubleCentralizer.central, ModelWithCorners.hasMFDerivAt, SeparationQuotient.norm_normedMk_le, ModularFormClass.continuous, AddCircle.instIsAddHaarMeasureRealVolume, instNormedSpaceLieAddGroup, Matrix.PosSemidef.det_sqrt, MeasureTheory.integral_condExpL2_eq, AffineIsometryEquiv.continuousWithinAt, HasFPowerSeriesOnBall.coeff_zero, ProbabilityTheory.cdf_eq_real, ContinuousLinearMap.instStarOrderedRing, BoxIntegral.HasIntegral.smul, Real.deriv_rpow_const, CStarMatrix.toCLMNonUnitalAlgHom_eq_toCLM, TemperedDistribution.instFourierSMul, instIsContinuousRiemannianBundleTrivial, Metric.hausdorffDist_zero_iff_closure_eq_closure, integral_smul_const, Real.comap_exp_nhds_exp, FormalMultilinearSeries.norm_apply_eq_norm_coef, tendsto_norm_sub_self, VectorBundleCore.localTriv_symm_fst, lowerClosure_interior_subset', EuclideanGeometry.oangle_add, range_cfcₙHom, ContinuousMap.dist_apply_le_dist, HasFPowerSeriesWithinOnBall.differentiableOn, Metric.continuous_iff, MeasureTheory.FiniteMeasure.tendsto_iff_weakDual_tendsto, DomAddAct.instIsIsometricVAddSubtypeAEEqFunMemAddAddSubgroupLp, HasMFDerivWithinAt.prodMap, mdifferentiableAt_addInvariantVectorField, MeasureTheory.integrable_thickenedIndicator, Complex.isConnected_of_lowerHalfPlane, Real.tendsto_exp_neg_atTop_nhds_zero, hasDerivWithinAt_abs, extChartAt_target_mem_nhdsWithin, hasFPowerSeriesOnBall_const, Path.continuous_extend, MeasureTheory.eLpNorm'_le_nnreal_smul_eLpNorm'_of_ae_le_mul, tendsto_cobounded_of_meromorphicOrderAt_neg, ImplicitFunctionData.pt_mem_toOpenPartialHomeomorph_source, HurwitzZeta.hasSum_hurwitzZeta_of_one_lt_re, hasFDerivAtFilter_iff_isLittleO, Real.Angle.sin_add_pi, EisensteinSeries.summable_inv_of_isBigO_rpow_inv, ContinuousLinearEquiv.one_le_norm_mul_norm_symm, tendsto_smoothingFun_comp, TensorProduct.lidIsometry_apply, ContDiffMapSupportedIn.seminorm_le_iff, PartitionOfUnity.exists_finset_nhds, eventually_norm_mfderivWithin_symm_extChartAt_lt, Unitary.openPartialHomeomorph_symm_apply, ProbabilityTheory.IsRatCondKernelCDFAux.tendsto_integral_of_antitone, NumberField.mixedEmbedding.fundamentalCone.logMap_expMapBasis, Hyperreal.tendsto_iff_forall, ContinuousMultilinearMap.norm_compContinuous_linearIsometry_le, Path.extend_trans_of_le_half, ContinuousLinearMap.hasDerivAt, instPathConnectedSpaceElemForallRealStdSimplexOfNonempty, MeasureTheory.Integrable.of_isEmpty, BoundedVariationOn.intervalIntegrable_deriv, AkraBazziRecurrence.eventually_deriv_one_add_smoothingFn, UniqueMDiffOn.uniqueDiffOn_target_inter, rieszContentAux_image_nonempty, MeasureTheory.Measure.integral_comp_smul_of_nonneg, convex_halfSpace_re_le, Complex.reCLM_coe, DiffContOnCl.circleIntegral_sub_inv_smul, MeasureTheory.eLpNorm_mono_ae, PadicInt.fwdDiff_tendsto_zero, Complex.deriv_Gamma_add_one, Metric.isClosed_closedBall, ContMDiff.contMDiff_tangentMap, CompletelyPositiveMap.instLinearMapClassComplex, ArithmeticFunction.vonMangoldt.continuousOn_LFunctionResidueClassAux', DiscreteTopology.of_forall_le_norm, IsUltrametricDist.norm_tprod_le_of_forall_le_of_nonneg, MeasureTheory.eLpNorm_ofReal, Metric.disjoint_nhds_cobounded, Complex.continuous_re, Real.deriv_sinh, not_summable_of_antitone_of_neg, iteratedFDeriv_sum, hasFDerivAt_ringInverse, LinearMap.IsPositive.inner_nonneg_left, ContinuousMap.norm_eq_iSup_norm, norm_cfcₙ_lt, VectorField.mpullback_eq_pullback, ContinuousMultilinearMap.opNorm_smul_le, Real.continuousAt_rpow_const, contDiffAt_one_iff, Metric.closure_closedBall, Function.HasTemperateGrowth.fun_smul, Filter.HasBasis.isLittleOTVS_iff, LinearIsometry.enorm_map, iteratedFDerivWithin_comp_add_left, PartitionOfUnity.IsSubordinate.continuous_finsum_smul, IsBoundedSMul.toUniformContinuousConstSMul, ProbabilityTheory.IsMeasurableRatCDF.instIsProbabilityMeasure_stieltjesFunction, hasFTaylorSeriesUpTo_zero_iff, ContinuousLinearMap.instCStarRingId, LinearIsometry.isComplete_map_iff, WeakDual.coe_toStrongDual, NormedSpace.eq_zero_iff_forall_dual_eq_zero, orthonormal_fourier, Filter.inv_cobounded₀, hasFDerivAt_finCons, VectorBundleCore.localTrivAt_apply, Matrix.linfty_opNNNorm_eq_opNNNorm, MeasureTheory.Lp.simpleFunc.smul_toSimpleFunc, hasFDerivWithinAt_finCons, UpperHalfPlane.contMDiff_coe, PadicInt.compactSpace, norm_injOn_ray_right, hasGradientAt_iff_isLittleO, InformationTheory.hasDerivAt_klFun, MeasureTheory.setIntegral_condExpL2_indicator, ContinuousMap.toNNReal_algebraMap, MeasureTheory.eLpNorm_indicator_sub_le_of_dist_bdd, CuspForm.holo', integrableOn_Ioi_norm_cpow_iff, contMDiff_coe_sphere, Real.tsum_exp_neg_mul_int_sq, InnerProductSpace.nnnorm_rankOne, iteratedDeriv_fun_const_smul, AlternatingMap.coe_mkContinuous, PeriodPair.mem_lattice, Filter.IsIncreasingApproximateUnit.toIsApproximateUnit, ContinuousMultilinearMap.norm_restr, ContinuousMultilinearMap.norm_image_sub_le, ProbabilityTheory.isPosSemidef_covarianceBilin, MeasureTheory.L1.SimpleFunc.integral_eq_norm_posPart_sub, spectrum.gelfandTransform_eq, intervalIntegral.intervalIntegrable_sin, stereographic_apply_neg, instCountable_of_discrete_submodule, LinearIsometry.norm_toContinuousLinearMap, StarAlgHom.continuous_realContinuousMapOfNNReal, OrthonormalBasis.orthogonalProjection_apply_eq_sum, Orientation.kahler_comp_rightAngleRotation, EisensteinSeries.tsum_symmetricIco_linear_sub_linear_add_one_eq_zero, LiouvilleNumber.summable, differentiable_snd, MeasureTheory.SimpleFunc.setToSimpleFunc_add_left, TangentBundle.trivializationAt_fst, LeftInvariantDerivation.comp_L, ae_differentiableAt_norm, Real.hasSum_cos, IsOpen.exists_contMDiff_support_eq_aux, ArithmeticFunction.vonMangoldt.residueClass_apply, hasDerivAtFilter_iff_tendsto_slope, Real.sinhHomeomorph_symm_apply, ContinuousLinearMap.norm_toSpanSingleton, AffineMap.differentiableWithinAt, AffineIsometryEquiv.toContinuousAffineEquiv_symm, Matrix.PosSemidef.trace_eq_zero_iff, HasGradientWithinAt.differentiableWithinAt, Commute.cfc_real, ContinuousLinearMap.setIntegral_compLp, LinearMap.trace_eq_sum_inner, Icc_chartedSpaceChartAt_of_le_top, TemperedDistribution.delta_apply, modelWithCornersSelf_boundaryless, ContinuousAlternatingMap.curryLeft_apply_apply, NormedSpace.isVonNBounded_closedBall, MeasureTheory.memLp_haarAddCircle_iff, affinity_unitClosedBall, ContinuousLinearMap.flip_smul, ContinuousLinearMap.contDiffPointwiseHolderAt, Manifold.pathELength_eq_lintegral_mfderivWithin_Icc, Real.continuous_log, MeromorphicOn.divisor_inv, ContDiffBump.normed_le_div_measure_closedBall_rOut, curveIntegralFun_refl, extChartAt_target_union_compl_range_mem_nhds_of_mem, Bundle.Trivial.vectorBundle, ContDiffMapSupportedIn.coe_smul, ContinuousMap.spectrum_eq_preimage_range, Submodule.IsCompl.closedComplemented_of_isClosed, HasFPowerSeriesOnBall.comp_sub, Path.extend_apply, ContinuousLinearEquiv.isBigO_sub, HasFDerivAt.isBigOTVS_sub, mem_closure_one_iff_norm, MeasureTheory.LevyProkhorov.continuous_equiv_probabilityMeasure, PeriodPair.analyticOnNhd_derivWeierstrassPExcept, UniformSpace.Completion.nnnorm_coe, AddCircle.ergodic_nsmul_add, MeasureTheory.integrable_prod, InnerProductSpace.isSymmetricProjection_rankOne_self, PositiveLinearMap.gnsNonUnitalStarAlgHom_apply_coe, hasDerivWithinAt_neg, SchwartzMap.continuous, lp.summable_mul, NumberField.mixedEmbedding.convexBodySum_compact, ZeroAtInftyContinuousMap.dist_toBCF_eq_dist, ContinuousMap.continuous_toNNReal, Orientation.volumeForm_zero_pos, Real.continuous_sqrt, ContinuousMap.Homotopy.pathExtend_evalAt, MeromorphicOn.divisor_fun_pow, differentiableWithinAt_pow, Real.Angle.cos_add_pi, AddCircle.dense_addSubgroup_iff_ne_zmultiples, Bundle.ContinuousRiemannianMetric.continuous, hasMFDerivAt_neg, AddSubgroup.tendsto_zmultiples_subtype_cofinite, indiscreteTopology_iff_forall_norm_eq_zero, Matrix.IsHermitian.charpoly_cfc_eq, AnalyticAt.deriv, iteratedDerivWithin_cot_pi_mul_eq_mul_tsum_div_pow, NormedSpace.norm_expSeries_summable, meromorphicOrderAt_add_eq_left_of_lt, ContinuousLinearEquiv.hasMFDerivAt, contDiffWithinAt_iff_contDiffOn_nhds, MeasureTheory.ConvolutionExistsAt.integrable_swap, SchwartzMap.laplacianCLM_eq', Polynomial.deriv_aeval, EuclideanGeometry.oangle_add_swap, hasGradientWithinAt_iff_hasFDerivWithinAt, DoubleCentralizer.nnnorm_def, MultilinearMap.coe_mkContinuous, norm_inner_eq_norm_iff, Real.volume_eq_stieltjes_id, Metric.closedBall_mem_nhds_of_mem, DomAddAct.vadd_Lp_add, spectrum.isCompact, Real.circleAverage_eq_circleIntegral, HasFiniteFPowerSeriesOnBall.eq_partialSum, LSeries.summable_real_of_abscissaOfAbsConv_lt, ContinuousLinearMap.apply_norm_sq_eq_inner_adjoint_left, meromorphicOrderAt_add, Real.Angle.cos_add_pi_div_two, MeasureTheory.charFunDual_prod, ContinuousLinearMap.measurable_apply₂, IsLocalFrameOn.coeff_congr, continuousOn_tangentCoordChange, Real.GammaSeq_tendsto_Gamma, Metric.isBounded_closure_of_isBounded, ProbabilityTheory.Kernel.integrable_densityProcess, Submodule.Quotient.completeSpace, Real.Angle.two_nsmul_eq_zero_iff, nnnorm_cfcₙ_nnreal_lt, preimage_extChartAt_eventuallyEq_compl_singleton, CFC.sqrt_eq_rpow, inner_eq_norm_mul_iff_div, Submodule.topologicalClosure_eq_self, LinearMap.hasStrictDerivAt, instIsManifoldRealEuclideanSpaceFinOfNatNatModelWithCornersSelfTopWithTopENatCircle, SmoothBumpCovering.toSmoothPartitionOfUnity_apply, ContDiff.continuous_fderiv_apply, MeasureTheory.tendstoInMeasure_iff_measureReal_dist, lp.hasSum_single, FiniteDimensional.RCLike.properSpace_submodule, AffineMap.hasDerivAt_lineMap, Real.Angle.coe_add, Function.hasTemperateGrowth_iff_isBigO, range_stereographic_symm, Complex.comap_exp_nhds_zero, EisensteinSeries.G2_eq_tsum_symmetricIco, Complex.equivRealProdCLM_symm_apply, Real.hasSum_log_one_add, MeasureTheory.integral_smul, TemperedDistribution.instContinuousFourier, Complex.cos_eq_tsum', cfcₙ_neg, mellinInv_eq_fourierIntegralInv, ContinuousMultilinearMap.curryFinFinset_symm_apply_const, HasGradientAtFilter.hasDerivAtFilter', ContDiffOn.const_smul, WeakDual.CharacterSpace.continuousMapEval_bijective, MeasureTheory.Integrable.of_integral_ne_zero, cot_series_rep', Module.Basis.prod_addHaar, NNReal.continuous_coe, DirichletCharacter.differentiableAt_LFunction, CompactlySupportedContinuousMap.coe_toRealLinearMap, differentiableOn_dslope_of_notMem, LowerSemicontinuousOn.isClosed_re_epigraph, NumberField.canonicalEmbedding.integralBasis_repr_apply, Complex.interior_preimage_re, Complex.continuous_cosh, Real.tendsto_of_bddAbove_monotone, ZSpan.measureReal_fundamentalDomain, EuclideanGeometry.orthogonalProjection_apply', MeasureTheory.condExpIndSMul_empty, SmoothPartitionOfUnity.contDiffAt_finsum, memℓp_gen_iff, MeasureTheory.Submartingale.bddAbove_iff_exists_tendsto, fourier_one, Affine.Simplex.dist_sq_eq_dist_orthogonalProjection_sq_add_dist_orthogonalProjection_sq, Polynomial.isClosedMap_eval, isOpenEmbedding_stereographic_symm, LinearMap.IsSymmetric.hasEigenvalue_iSup_of_finiteDimensional, HasFPowerSeriesOnBall.fderiv_eq, MeasureTheory.lintegral_nnnorm_condExpL2_indicator_le, strictConvex_closedBall, mdifferentiableOn_iff_target, Real.totallyBounded_ball, Metric.closure_sphere, MeasureTheory.Measure.map_linearMap_addHaar_eq_smul_addHaar, Real.differentiableOn_rpow_const, PositiveLinearMap.instContinuousLinearMapClassComplexOfLinearMapClassOfOrderHomClass, Path.uniformContinuous_extend_left, MeromorphicOn.fun_deriv, ContinuousMultilinearMap.nnnorm_constOfIsEmpty, Rat.not_firstCountableTopology_opc, continuousMap_mem_polynomialFunctions_closure, lintegral_comp_pi_polarCoord_symm, SimplexCategory.toTop_obj, NumberField.mixedEmbedding.fundamentalCone.subset_interior_normLeOne, Asymptotics.IsLittleOTVS.zero, isBigO_rpow_top_log_smul, polarCoord_target, NormedSpace.inclusionInDoubleDual_norm_eq, differentiableAt_star_iff, lipschitzOnWith_cfc_fun_of_subset, eventually_nnnorm_sub_lt, HomotopyGroup.transAt_indep, VectorBundle.trivialization_linear', SchwartzMap.smulLeftCLM_sum, contMDiff_model, NNReal.isEmbedding_coe, MeasureTheory.SignedMeasure.absolutelyContinuous_iff_withDensityᵥ_rnDeriv_eq, AddCircle.denseRange_zsmul_iff, LinearIsometryEquiv.comp_hasFDerivWithinAt_iff', Metric.dense_iff_iUnion_ball, PadicInt.continuous_choose, MeromorphicAt.sum, AffineMap.hasDerivWithinAt_lineMap, PeriodPair.basis_zero, ContDiff.continuous, cfc_real_eq_nnreal, mfderiv_prod_eq_add_comp, TestFunction.coe_smul, has_fderiv_at_filter_real_equiv, Metric.mem_nhdsWithin_iff, NumberField.mixedEmbedding.negAt_signSet_apply_isReal, Matrix.PosSemidef.posSemidef_sqrt, Complex.closure_setOf_lt_im, aestronglyMeasurable_deriv, Real.hasDerivWithinAt_arccos_Ici, RightDerivMeasurableAux.differentiable_set_subset_D, Real.continuousAt_rpow_of_pos, EuclideanGeometry.orthogonalProjection_orthogonalProjection_of_le, unitary.linearIsometryEquiv_coe_symm_apply, PiTensorProduct.tprodL_toFun, MeasureTheory.setIntegral_condExpInd, Real.circleAverage_fun_sum, ContinuousLinearMap.isPositive_def, continuous_dist, Rat.HeightOneSpectrum.adicCompletion.padicEquiv_bijOn, ContinuousMap.dist_lt_of_dist_lt_modulus, ContinuousLinearMap.nnnorm_toSpanSingleton, Metric.eventually_nhds_iff, MeasureTheory.dense_of_generateFrom_isSetRing, InnerProductGeometry.norm_add_eq_add_norm_of_angle_eq_zero, ContinuousLinearEquiv.hasMFDerivWithinAt, ContinuousAlternatingMap.alternatizeUncurryFin_smul, InformationTheory.leftDeriv_klFun, ContDiffOn.contMDiffOn, contDiffAt_map_inverse, tendsto_integral_exp_smul_cocompact, BoxIntegral.Integrable.to_subbox_aux, MeasureTheory.integral_comp_rpow_Ioi_of_pos, EisensteinSeries.summable_of_isBigO_rpow_norm, Complex.hasDerivAt_Gammaℝ_one, Orientation.sin_oangle_add_right_mul_norm_of_oangle_eq_pi_div_two, SchwartzMap.toBoundedContinuousFunctionCLM_apply, AffineIsometryEquiv.continuousOn, ProbabilityTheory.eqOn_complexMGF_of_mgf, hasSum_jacobiTheta₂_term, StarAlgHom.realContinuousMapOfNNReal_apply, curveIntegral_segment, Asymptotics.isLittleOTVS_fun_neg_left, TestFunction.postcompCLM_apply, MeasureTheory.MemLp.of_discrete, hasDerivAt_iff_tendsto_slope_left_right, BoundedContinuousFunction.instStarModule, MeasureTheory.edist_indicatorConstLp_eq_enorm, tendsto_norm_div_self_nhdsNE, controlled_closure_of_complete, deriv_id'', hasFDerivAt_jacobiTheta₂_term, HasFTaylorSeriesUpToOn.hasFDerivWithinAt, Complex.continuousAt_cpow_const_of_re_pos, AddCircle.exists_norm_nsmul_le, Asymptotics.isBigOTVS_iff_smallSets, ContinuousAlternatingMap.norm_restrictScalars, Submodule.starProjection_top', ContinuousLinearMap.ker_closedComplemented_of_finiteDimensional_range, MeasureTheory.SignedMeasure.totalVariation_zero, LSeries_deriv, ProbabilityTheory.IsMeasurableRatCDF.tendsto_atBot_zero, Homeomorph.coe_unitBall_apply_zero, NormedAddGroupHom.completion_sub, indiscreteTopology_iff_forall_nnnorm_eq_zero, EuclideanGeometry.Sphere.isTangent_iff_isTangentAt_orthogonalProjection, OrthonormalBasis.toBasis_mulOpposite, Submodule.adjoint_subtypeL, Metric.isPreconnected_closedEBall, hasStrictFDerivAt_exp, NormedSpace.exp_conj, exists_nat_nat_continuous_surjective_of_completeSpace, summable_schlomilch_iff_of_nonneg, NumberField.mixedEmbedding.fundamentalDomain_idealLattice, OpenPartialHomeomorph.extend_image_target_mem_nhds, InnerProductSpace.HarmonicAt.eventually, AbsoluteValue.Completion.locallyCompactSpace, IsCoercive.range_eq_top, intervalIntegral.FTCFilter.nhdsWithinSingleton, LinearMap.isSymmetric_adjoint_mul_self, InnerProductGeometry.angle_add_le_pi_div_two_of_inner_eq_zero, UpperHalfPlane.contMDiff_inv_denom, ContinuousLinearMap.opNorm_mul_apply, gelfandStarTransform_symm_apply, Sbtw.oangle_eq_add_pi_right, ContinuousLinearMap.norm_smulRightL, AffineIsometry.comp_continuous_iff, Real.tendsto_exp_comp_nhds_zero, mul_neg_geom_series, deriv_const_mul_field', hasMFDerivWithinAt_extChartAt, Orientation.oangle_eq_zero_iff_sameRay, MeasureTheory.Submartingale.add_martingale, Submodule.reflection_orthogonalComplement_singleton_eq_neg, Complex.uniformlyContinuous_re, WithAbs.tendsto_one_div_one_add_pow_nhds_one, Real.continuousAt_const_rpow', ContinuousLinearEquiv.comp_fderiv, RCLike.summable_ofReal, derivWithin.neg, MonotoneOn.memLp_of_measure_ne_top, tendsto_norm_div_self_nhdsGE, WithSeminorms.uniformEquicontinuous_iff_exists_continuous_seminorm, ContinuousLinearMap.isBigO_id, SimplexCategory.toTop_map, EisensteinSeries.summable_norm_eisSummand, ContDiffAt.fderiv_right, Complex.differentiable_exp, AnalyticOn.compContinuousLinearMap, hasStrictFDerivAt_iff_isLittleO, MeasureTheory.convolution_def, contMDiffWithinAt_pi_space, Affine.Triangle.dist_circumcenter_reflection_orthocenter, MeasureTheory.norm_condExpL2_coe_le, ContinuousMultilinearMap.curryLeft_norm, CPolynomialAt.eventually_cpolynomialAt, MeasureTheory.setLIntegral_nnnorm_condExpL2_indicator_le, Complex.UnitDisc.isEmbedding_coe, HurwitzZeta.hasSum_nat_completedCosZeta, HasDerivAt.hasFDerivAt, tendsto_sub_mul_tsum_nat_cpow, MeasureTheory.mem_lpMeas_iff_aestronglyMeasurable, Polynomial.toAddCircle.integrable, intervalIntegral.FTCFilter.le_nhds, Besicovitch.ae_tendsto_rnDeriv, fourier_zero, InnerProductSpace.trace_rankOne, ContDiffBump.hasCompactSupport, HasFPowerSeriesOnBall.differentiableOn, ContinuousAlternatingMap.alternatizeUncurryFin_constOfIsEmptyLIE_comp, BoxIntegral.Integrable.toBoxAdditive_apply, MeasureTheory.Submartingale.smul_nonneg, RCLike.imLm_coe, Metric.uniformContinuous_infNndist_pt, LinearIsometryEquiv.coe_toContinuousLinearEquiv, deriv.neg, ContinuousMultilinearMap.uncurry0_norm, Metric.isPathConnected_closedEBall, circleIntegral.integral_add, fourier_neg', openSegment_subset_ball_of_ne, HasFPowerSeriesWithinOnBall.prod, NormedSpace.normalize_smul, IsBoundedBilinearMap.differentiableOn, MeasureTheory.integrable_withDensity_iff_integrable_smul', Real.differentiable_cos, Orientation.angle_eq_iff_oangle_eq_or_sameRay, NormedSpace.eq_iff_forall_dual_eq, mdifferentiableAt_totalSpace, MeasureTheory.eLpNorm'_congr_norm_ae, ContinuousLinearEquiv.integral_comp_comm, MeasureTheory.aestronglyMeasurable_condExpL1, Function.Periodic.boundedAtFilter_cuspFunction, deriv_zero, ContinuousMultilinearMap.le_opNorm, ContinuousAlternatingMap.alternatizeUncurryFin_alternatizeUncurryFinCLM_comp_apply, PartitionOfUnity.coe_finsupport, Bundle.Trivial.linearMapAt_trivialization, Affine.Simplex.ExcenterExists.sign_signedInfDist_touchpoint, cauchySeq_finset_iff_vanishing_norm, mdifferentiable_mulInvariantVectorField, isAddFundamentalDomain_Ioc, Metric.dense_iUnion_range_toInductiveLimit, MeasureTheory.HasFiniteIntegral.of_finite, hasStrictDerivAt_const_add_iff, iteratedFDeriv_const_smul_apply, Summable_cotTerm, SchwartzMap.delta_apply, InnerProductGeometry.angle_eq_zero_iff, Path.continuous_delayReflRight, AffineIsometry.toContinuousAffineMap_id, isBoundedBilinearMap_compMultilinear, ContinuousLinearEquiv.comp_right_fderiv, AnalyticAt.smul, SchwartzMap.norm_fourier_toL2_eq, hasLineDerivAt_smul_iff, Submodule.isIdempotentElem_starProjection, norm_cauchyPowerSeries_le, differentiableOn_finCons', MeasureTheory.Lp.boundedContinuousFunction_topologicalClosure, Real.qaryEntropy_continuous, IsUnifLocDoublingMeasure.exists_measure_closedBall_le_mul, MeasureTheory.Lp.SecondCountableTopology, Filter.tendsto_inv₀_cobounded, Real.one_div_one_sub_sq_hasFPowerSeriesOnBall_zero, hasFDerivAt_norm_rpow, derivWithin_ofNat, dist_birkhoffAverage_apply_birkhoffAverage, ProbabilityTheory.cdf_nonneg, IsSelfAdjoint.isClosed, ContinuousLinearMap.compL_apply, ContinuousLinearMap.lsmul_flip_inj, ContDiffMapSupportedIn.hasCompactSupport, mellinInv_eq_fourierInv, intervalIntegral.integrableOn_Ioo_rpow_iff, UniqueMDiffOn.uniqueMDiffOn_target_inter, ZSpan.repr_ceil_apply, GenLoop.instContinuousEval, MeasureTheory.Measure.addHaar_preimage_continuousLinearMap, Path.Homotopy.hcomp_half, HasFPowerSeriesOnBall.uniform_geometric_approx, ProperCone.innerDual_zero, DoubleCentralizer.neg_snd, mdifferentiableOn_prod_module_iff, contMDiffAt_iff_source_of_mem_source, summable_jacobiTheta₂_term_fderiv_iff, ContDiffMapSupportedIn.structureMapLM_eq_of_scalars, ZLattice.comap_equiv_apply, StieltjesFunction.iInf_rat_gt_eq, IsBoundedLinearMap.differentiableOn, sameRay_iff_of_norm_eq, MeromorphicOn.divisor_sub_const_self, ProbabilityTheory.IsMeasurableRatCDF.stronglyMeasurable_stieltjesFunction, MeasureTheory.Lp.instCompleteSpace, Metric.tendsto_nhdsWithin_nhds, ContinuousLinearMap.analyticAt, Isometry.completion_map, iteratedFDeriv_succ_const, contDiffWithinAt_zero, QuotientGroup.nhds_one_hasBasis, EuclideanGeometry.Sphere.tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center, Asymptotics.isBigOTVS_fun_neg_left, ZLattice.FG, sum_inner, CompactlySupportedContinuousMap.nnrealPart_add_le_add_nnrealPart, MeasureTheory.Martingale.add, Polynomial.div_tendsto_atBot_zero_of_degree_lt, instLieGroupRealEuclideanSpaceFinOfNatNatModelWithCornersSelfTopWithTopENatCircle, Path.Homotopy.hcomp_apply, UniformFun.isometry_ofFun_continuousMap, MeasureTheory.Lp.instFourierPair, fourier_gaussian_innerProductSpace', ContDiffAt.iteratedFDeriv_right, HurwitzZeta.hasSum_nat_hurwitzZetaEven, VectorFourier.fourierIntegral_const_smul, isCoveringMap_zpow, Matrix.linfty_opNNNorm_toMatrix, continuousWithinAt_dslope_of_ne, HasFTaylorSeriesUpToOn.cont, PartitionOfUnity.exists_finset_nhds_support_subset, HurwitzZeta.hasSum_int_cosKernel, Asymptotics.isBigOTVS_fun_neg_right, ZMod.completedLFunction_def_odd, measurable_deriv, NormedAddGroupHom.completion_coe, MeasureTheory.SignedMeasure.toJordanDecomposition_smul_real, RCLike.instContinuousMapUniqueHom, ContDiffAt.contDiffAt_norm_smul, Real.fourier_real_eq, ContinuousAlternatingMap.le_opNorm, ProbabilityTheory.ofReal_condCDF_ae_eq, ContinuousMultilinearMap.norm_mkPiAlgebraFin_zero, Path.continuous_delayReflLeft, ProbabilityTheory.IsMeasurableRatCDF.measure_stieltjesFunction_univ, intervalIntegral.intervalIntegrable_log, Asymptotics.IsEquivalent.smul, differentiableAt_apply, OnePoint.isZeroAt_infty_iff, Path.Homotopy.symm_apply, NormedSpace.expSeries_hasSum_exp, IsPicardLindelof.continuousOn, MeasureTheory.L1.integral_def, FormalMultilinearSeries.hasSum, hasDerivAt_abs_rpow, ContinuousLinearMap.IsPositive.conj_adjoint, ContinuousLinearMap.flip_apply, BoundedContinuousFunction.Lp_nnnorm_le, MeasureTheory.Measure.integral_comp_inv_smul_of_nonneg, Matrix.toEuclideanCLM_toLp, Real.hasSum_ofDigitsTerm_digits, WeakDual.CharacterSpace.homeoEval_naturality, signedDist_eq_zero_of_orthogonal, DomMulAct.edist_smul_Lp, hasSum_fourier_series_L2, CPolynomialOn.iteratedFDeriv, NumberField.mixedEmbedding.mem_span_fractionalIdealLatticeBasis, MeasureTheory.integrable_comp_div_iff, PeriodPair.isClosed_lattice, ContinuousLinearMap.isPositive_id, BoundedContinuousFunction.innerProbChar_zero, InnerProductGeometry.angle_add_eq_arctan_of_inner_eq_zero, FormalMultilinearSeries.coeff_eq_zero, Path.instContinuousEvalElemRealUnitInterval, Diffeology.instIsDTopologyCompatible, Complex.tendsto_normSq_cocompact_atTop, ProbabilityTheory.covarianceBilin_zero, NumberField.mixedEmbedding.instDiscreteTopologySubtypeMixedSpaceMemSubmoduleIntIdealLattice, CFC.posPart_algebraMap_nnreal, RCLike.conjCLE_coe, BoxIntegral.Integrable.cauchy_map_integralSum_toFilteriUnion, HasFPowerSeriesOnBall.sum, BoundedContinuousFunction.range_toLpHom, contDiffOn_stereoToFun, ZetaAsymptotics.term_tsum_of_lt, absorbs_iff_eventually_nhdsNE_zero, Real.finrank_eq_int_finrank_of_discrete, Metric.cobounded_le_cocompact, CStarAlgebra.instOrderClosedTopology, Units.instIsManifoldModelWithCornersSelf, AddCircle.ergodic_add_left, LeftInvariantDerivation.evalAt_coe, derivWithin_const_add, Matrix.IsHermitian.trace_eq_sum_eigenvalues, Unitary.coe_symm_linearIsometryEquiv_apply, fderiv_inverse, hasStrictFDerivAt_exp_smul_const', Polynomial.Chebyshev.isLocalMax_T_real, SchwartzMap.smulLeftCLM_fun_neg, HasFPowerSeriesOnBall.fderiv, range_cfcₙ, LinearMap.adjoint_rTensor, Real.Angle.coe_coeHom, ZSpan.measure_fundamentalDomain, convex_halfSpace_im_gt, Real.tendsto_cos_neg_pi_div_two, hasGradientAt_iff_isLittleO_nhds_zero, BoundedContinuousFunction.toLp_inj, Path.Homotopy.eval_apply, Matrix.PosSemidef.sqrt_eq_one_iff, LinearMap.IsPositive.add, ImplicitFunctionData.leftDeriv_fderiv_implicitFunction, EisensteinSeries.tendsto_zero_inv_linear_sub, Real.deriv_Gamma_nat, Metric.toUniformSpace_eq, NNRat.instContinuousSub, GaussianFourier.integrable_cexp_neg_mul_sum_add, HilbertBasis.hasSum_orthogonalProjection, ContinuousLinearMap.bilinearRestrictScalars_apply_apply, Complex.continuousOn_sin, LinearMap.adjoint_inner_right, Complex.hasStrictFDerivAt_cpow, BoundedContinuousFunction.toContinuousMapAddMonoidHom_apply, MeasureTheory.mem_lpMeas_indicatorConstLp, iteratedFDeriv_const_smul_apply', InnerProductSpace.adjoint_rankOne, FormalMultilinearSeries.compAlongComposition_nnnorm, tendsto_riemannZeta_sub_one_div, PiLp.hasFDerivAt_toLp, stereoInvFun_apply, MeasureTheory.Measure.innerRegularWRT_preimage_one_hasCompactSupport_measure_ne_top_of_group, PiTensorProduct.mapL_coe, ZetaAsymptotics.tendsto_Gamma_term_aux, NumberField.InfinitePlace.Completion.locallyCompactSpace, analyticAt_smul, MeasureTheory.Measure.HasTemperateGrowth.exists_integrable, CStarAlgebra.toCompleteSpace, NormedAddCommGroup.cauchySeq_iff, Manifold.IsImmersionAt.writtenInCharts, AnalyticWithinAt.continuousWithinAt, InnerProductSpace.rankOne_eq_zero, ContinuousLinearMap.lipschitz, Polynomial.differentiable_aeval, ProbabilityTheory.isGaussian_map_equiv_iff, DoubleCentralizer.range_toProd, Circle.exp_two_pi, Complex.polarCoord_apply, HurwitzZeta.continuousOn_cosKernel, egauge_le_one, Real.fourierIntegral_convergent_iff', BoundedContinuousFunction.toLp_injective, NormedAddCommGroup.denseRange_toCompl, Matrix.PosSemidef.sqrt_sq, hasDerivAt_deriv_iff, Seminorm.continuous, TensorProduct.ext_iff_inner_left_threefold', Convex.toWeakSpace_closure, instIsTopologicalDivisionRingReal, lp.singleAddMonoidHom_apply, Unitary.instLocPathConnectedSpace, MeasureTheory.SignedMeasure.absolutelyContinuous_ennreal_iff, Submodule.isOrtho_sSup_right, LinearIsometry.lTensor_apply, Complex.differentiable_iteratedDeriv_sin, AddChar.expect_apply_eq_zero_iff_ne_zero, ClosedSubmodule.bot_orthogonal_eq_top, LinearIsometry.norm_compContinuousMultilinearMap, ContinuousAlternatingMap.norm_curryLeft, extChartAt_target_mem_nhdsWithin_of_mem, hasDerivAtFilter_neg, NormedStarGroup.to_continuousStar, ContinuousMap.isUnit_iff_forall_isUnit, ContinuousMap.Homotopy.apply_one_path, Complex.hasStrictDerivAt_sinh, MeasureTheory.integral_indicatorConstLp, tsum_pow_div_one_sub_eq_tsum_sigma, MeasureTheory.Measure.toSphere_apply_univ, Real.hasDerivAt_binEntropy, Submodule.norm_sq_eq_add_norm_sq_starProjection, hasDerivAt_gronwallBound_shift, SeminormedAddGroup.disjoint_nhds_zero, PartitionOfUnity.sum_le_one', Bundle.ContMDiffRiemannianMetric.symm, EisensteinSeries.linear_right_summable, MeasureTheory.charFunDual_eq_prod_iff, InnerProductSpace.inner_right_rankOne_apply, HilbertBasis.hasSum_repr, ContDiff.differentiable_iteratedFDeriv, SchwartzMap.pairing_apply, Real.continuous_cosh, MeasureTheory.Measure.integral_comp_smul, MeasureTheory.Lp.coeFn_compMeasurePreserving, MeromorphicAt.tendsto_nhds_meromorphicTrailingCoeffAt, InnerProductSpace.HarmonicOnNhd.add, Asymptotics.isBigOTVS_iff_isBigO, ContinuousMultilinearMap.isLeast_opNorm, ContDiff.continuous_fderiv, UnitAddTorus.mFourier_add, continuous_polarCoord_symm, setIntegral_withDensity_eq_setIntegral_smul₀', Real.hasDerivAt_qaryEntropy, BoundedContinuousFunction.integrable, IsCoveringMap.liftPath_const, innerSL_inj, continuousAt_dslope_same, Rat.instOrderTopology, PositiveLinearMap.preGNS_inner_def, Metric.uniformity_basis_dist, MeasureTheory.SimpleFunc.memLp_iff_finMeasSupp, MeasureTheory.condExpIndSMul_smul, hasDerivAt_add_const_iff, intervalIntegral.FTCFilter.nhdsUIcc, hasDerivWithinAt_pow, hasDerivWithinAt_iff_hasFDerivWithinAt, Asymptotics.isLittleO_pow_id, LSeries_eq_mul_integral_of_nonneg, MeasureTheory.Measure.hausdorffMeasure_smul₀, ProbabilityTheory.analyticOnNhd_cgf, Ideal.IsMaximal.isClosed, MeasureTheory.ae_ae_add_linearMap_mem_iff, real_inner_div_norm_mul_norm_eq_one_iff, TensorProduct.ext_iff_inner_left_threefold, MDifferentiableAt.differentiableWithinAt_writtenInExtChartAt, MeasureTheory.lintegral_nnnorm_condExpL2_le, SmoothPartitionOfUnity.le_one, PeriodPair.periodic_derivWeierstrassP, EisensteinSeries.summable_linear_left_mul_linear_left, Monotone.ae_hasDerivAt, MeasureTheory.Lp.compMeasurePreservingₗᵢ_apply_coe, StrongFEPair.hf_zero', SimplexCategory.toTop₀_map, DoubleCentralizer.add_fst, Quaternion.expSeries_odd_of_imaginary, ProbabilityTheory.IsCondKernelCDF.setIntegral, MeasureTheory.integrable_withDensity_iff_integrable_smul₀', AffineSubspace.signedInfDist_eq_signedDist_of_mem, differentiableWithinAt_of_derivWithin_ne_zero, Real.borel_eq_generateFrom_Ioi_rat, LinearMap.IsSymmetric.coe_toSelfAdjoint, one_mem_posTangentConeAt_iff_mem_closure, BumpCovering.le_one, iteratedDeriv_const_smul, MeromorphicOn.divisor_intCast, Complex.tendsto_one_add_div_pow_exp, SchwartzMap.norm_fourierTransformCLM_toL2_eq, quasispectrum.isCompact, Real.integrable_sinc, HasFPowerSeriesWithinAt.coeff_zero, TensorProduct.inner_lid_lid, MeasureTheory.FiniteMeasure.tendsto_iff_forall_integral_tendsto, DiffContOnCl.deriv_eq_smul_circleIntegral, Real.coe_tanPartialHomeomorph, OrthonormalBasis.toBasis_map, NormedCommGroup.uniformity_basis_dist, ContDiffMapSupportedIn.uniformSpace_eq_iInf, hasFDerivAt_apply, derivWithin_div_const, NumberField.InfinitePlace.Completion.isClosed_image_extensionEmbedding, Matrix.piLp_ofLp_toEuclideanLin, UniformSpace.Completion.dist_eq, tendsto_pow_atTop_nhds_zero_iff_norm_lt_one, MeasureTheory.enorm_indicatorConstLp_le, Rat.cocompact_inf_nhds_neBot, cfcₙAux_id, ProbabilityTheory.stronglyMeasurable_poissonPMFReal, riemannZeta_eulerProduct_exp_log, MeasureTheory.Lp.norm_neg, LinearMap.IsSymmetric.diagonalization_symm_apply, PiTensorProduct.liftIsometry_tprodL, maximal_orthonormal_iff_basis_of_finiteDimensional, TensorProduct.norm_comm, NumberField.mixedEmbedding.polarCoordReal_source, contDiffWithinAt_iff_of_ne_infty, MeasureTheory.tendsto_of_uncrossing_lt_top, NormedSpace.inclusionInDoubleDual_norm_le, not_IntegrableOn_Ici_inv, AnalyticOnNhd.eval_linearMap, instIsBoundedSMulSeparationQuotient, UniformConvergenceCLM.continuousSMul, stereographic'_target, hasFTaylorSeriesUpToOn_pi', RCLike.rank_le_two, curveIntegral_segment_const, hasDerivWithinAt_one, deriv_comp_add_const, le_egauge_smul_left, IsSelfAdjoint.isConnected_spectrum_compl, Irrational.instOrderTopologySubtypeReal, BoundedContinuousFunction.norm_toContinuousMap_eq, MeasureTheory.dense_of_generateFrom_isSetSemiring, Memℓp.finset_sum, tendsto_measure_cthickening, WeakDual.isCompact_closedBall, MeasureTheory.L1.integral_eq_setToL1, MeasureTheory.enorm_integral_le_lintegral_enorm, ContinuousMultilinearMap.hasFTaylorSeriesUpTo_iteratedFDeriv, ContinuousLinearMap.isPositive_toLinearMap_iff, Affine.Simplex.signedInfDist_apply_self, BoxIntegral.BoxAdditiveMap.volume_apply, Quaternion.continuous_imJ, AntitoneOn.integrableOn_isCompact, TangentBundle.trivializationAt_apply, ConvexOn.sSup_of_countable_affine_eq, Real.differentiableAt_rpow_of_ne, exists_contMDiffMap_zero_one_nhds_of_isClosed, Circle.exp_sub, CFC.sqrt_eq_one_iff, IsBoundedSMul.continuousSMul, lp.singleContinuousAddMonoidHom_apply, Real.one_div_one_sub_hasFPowerSeriesOnBall_zero, ModelWithCorners.map_nhdsWithin_eq, Metric.uniformity_basis_dist_rat, RCLike.reCLM_coe, ContDiffBump.normed_convolution_eq_right, isClosedMap_pow, continuousSMul_closedBall_ball, MeasureTheory.Lp.nnnorm_neg, LinearMap.norm_mkContinuous₂_aux, InnerProductSpace.rankOne_eq_rankOne_iff_comm, Metric.uniformContinuous_infDist_Hausdorff_dist, InnerProductSpace.toDual_apply, AddCircle.ergodic_add_right, Real.differentiableAt_log, MeasureTheory.ComplexMeasure.equivSignedMeasure_apply, CStarAlgebra.norm_posPart_le, OrthonormalBasis.tensorProduct_repr_tmul_apply', ContDiffMapSupportedIn.continuous_iff_comp_withOrder, HasLineDerivAt.tendsto_slope_zero, contMDiffOn_pi_space, indiscreteTopology_iff_forall_nnnorm_eq_zero', Complex.tendsto_arg_nhdsWithin_im_nonneg_of_re_neg_of_im_zero, Real.exists_seq_rat_strictAnti_tendsto, EisensteinSeries.tendsto_e2Summand_atTop_nhds_zero, AbsolutelyContinuousOnInterval.integral_deriv_mul_eq_sub, Real.tendsto_sin_neg_pi_div_two, intervalIntegral.intervalIntegrable_cos, ContinuousLinearMap.holder_smul_left, MeromorphicOn.isClopen_setOf_meromorphicOrderAt_eq_top, tendsto_measure_Icc, ContinuousLinearMap.analyticWithinAt_uncurry_of_multilinear, ContinuousLinearMap.precompR_apply, HarmonicAt.differentiableAt_complex_partial, PiLp.enorm_apply_le, AffineIsometry.image_intrinsicInterior, ContinuousAlternatingMap.norm_alternatizeUncurryFinCLM_le, tendsto_logDeriv_euler_sin_div, SeminormedAddGroup.uniformCauchySeqOnFilter_iff_tendstoUniformlyOnFilter_zero, NumberField.mixedEmbedding.fundamentalCone.prod_deriv_expMap_single, Bundle.TotalSpace.isManifold, isSymmSndFDerivAt_iff_iteratedFDeriv, NormedSpace.exp_continuousMap_eq, LinearIsometry.isComplete_image_iff, EisensteinSeries.div_linear_zpow_differentiableOn, IsGreatest.nnnorm_cfcₙ_nnreal, Real.uniformContinuous_inv, UnitAddTorus.mFourier_zero, ContinuousMap.HomotopyLike.toContinuousMapClass, Real.tendsto_exp_nhds_zero_nhds_one, hasDerivAtFilter_one, EuclideanGeometry.angle_add_const, intervalIntegral.smul_integral_comp_mul_sub, MeromorphicOn.analyticAt_mem_codiscreteWithin, ContinuousLinearEquiv.differentiableAt, CStarAlgebra.span_nonneg_inter_unitClosedBall, ProbabilityTheory.IsGaussian.charFun_eq', Real.deriv_inv_log, MeasureTheory.Lp.coeFn_smul, ContMDiffAt.mfderiv_const, AnalyticOn.domDomCongr_iteratedFDeriv, smoothSheafCommRing.isUnit_stalk_iff, Matrix.PosSemidef.eq_sqrt_iff_sq_eq, FormalMultilinearSeries.coeff_ofScalars, contMDiff_vectorSpace_iff_contDiff, ContDiff.continuous_zero, UpperHalfPlane.ofComplex_apply_of_im_pos, signedDist_zero, MeasureTheory.condExpL1CLM_indicatorConstLp, Asymptotics.IsLittleO.isLittleOTVS, MeasureTheory.hasFiniteIntegral_iff_edist, hasDerivAt_ofNat, ProbabilityTheory.Kernel.HasSubgaussianMGF.integrable_exp_mul, LinearIsometryEquiv.reflections_generate, AffineSubspace.signedInfDist_eq_signedDist_orthogonalProjection, ContinuousLinearMap.ratio_le_opNorm, fderivWithin_sub_const, Submodule.map_orthogonal_equiv, Orientation.cos_oangle_add_left_of_oangle_eq_pi_div_two, iteratedFDerivWithin_eq_equiv_comp, RCLike.isUniformEmbedding_ofReal, ContDiffAt.laplacian_add, CompactlySupportedContinuousMap.toRealLinearMap_apply, DifferentiableAt.isBigOTVS_sub, Matrix.l2_opNNNorm_mulVec, aestronglyMeasurable_derivWithin_Ioi, MeasureTheory.integrable_comp, NumberField.mixedEmbedding.span_idealLatticeBasis, NumberField.mixedEmbedding.fundamentalCone.norm_expMapBasis, hasFDerivAt_prodMk_left, PartitionOfUnity.sum_eq_one, AffineIsometryEquiv.toContinuousAffineEquiv_refl, AkraBazziRecurrence.differentiableAt_one_sub_smoothingFn, IsContDiffImplicitAt.apply_implicitFunction, Orthonormal.inner_left_right_finset, AlternatingMap.mkContinuousAlternating_norm_le, MeromorphicOn.fun_iterated_deriv, frontier_range_modelWithCornersEuclideanHalfSpace, isometry_cfcₙHom, SchwartzMap.lineDerivOp_compCLMOfContinuousLinearEquiv, ContDiffMapSupportedIn.structureMapCLM_zero_apply, ClosedSubmodule.top_orthogonal_eq_bot, ContDiffWithinAt.const_smul, VonNeumannAlgebra.centralizer_centralizer', NNReal.map_coe_nhdsGT, FormalMultilinearSeries.mkPiRing_coeff_eq, intervalIntegral.intervalIntegrable_rpow, AkraBazziRecurrence.eventually_deriv_rpow_p_mul_one_sub_smoothingFn, HurwitzZeta.hasSum_nat_sinKernel, differentiableAt_inv_iff, Metric.uniformity_basis_dist_inv_nat_succ, SchwartzMap.integral_bilinear_deriv_right_eq_neg_left, OpenPartialHomeomorph.continuousWithinAt_writtenInExtend_iff, IsBoundedLinearMap.lim_zero_bounded_linear_map, AntitoneOn.memLp_top, ContinuousAlternatingMap.curryLeft_compContinuousAlternatingMap, MeasureTheory.eLpNorm'_neg, eventually_norm_sub_lt, SchwartzMap.norm_iteratedFDeriv_le_seminorm, ProbabilityTheory.covarianceBilinDual_zero, Irrational.eventually_forall_le_dist_cast_div_of_denom_le, Submodule.norm_orthogonalProjection_apply_le, StarAlgebra.elemental.bijective_characterSpaceToSpectrum, RealRMK.integral_rieszMeasure, Finsupp.inner_sum, LinearMap.deriv, GromovHausdorff.rep_gHSpace_compactSpace, BoundedContinuousFunction.memLp_top, dense_irrational, CFC.continuous_abs, contDiff_iff_iteratedDeriv, bernstein.variance, tsum_geometric_of_lt_one, Real.continuous_probChar, LeftInvariantDerivation.map_zero, PadicInt.coe_adicCompletionIntegersEquiv_symm_apply, NormedSpace.polar_ball_subset_closedBall_div, TensorProduct.norm_assoc, BoxIntegral.Integrable.dist_integralSum_sum_integral_le_of_memBaseSet, EuclideanSpace.instIsManifoldSphere, zeta_eq_tsum_one_div_nat_cpow, TensorProduct.nnnorm_tmul, InnerProductSpace.comp_rankOne, OrthonormalBasis.starProjection_eq_sum_rankOne, Metric.isUniformInducing_iff, SeminormedAddGroup.uniformCauchySeqOn_iff_tendstoUniformlyOn_zero, DoubleCentralizer.smul_fst, Orientation.abs_volumeForm_apply_of_pairwise_orthogonal, bernstein_apply, iteratedDerivWithin_const_smul_field, norm_fderiv_le_of_lipschitz, Real.isEquivalent_sin, continuousAt_cpow, tendsto_rpow_atTop_of_base_gt_one, ContDiffMapSupportedIn.zero_on_compl', InnerProductSpace.toDualMap_apply, Real.tendsto_sigmoid_atBot, gelfandTransform_map_star, geometric_hahn_banach_point_closed, AnalyticOnNhd.continuous, Quaternion.instCompleteSpaceReal, LiouvilleNumber.remainder_summable, MeasureTheory.L1.SimpleFunc.coe_negPart, hasFDerivWithinAt_finCons', Complex.interior_preimage_im, Orthonormal.inner_products_summable, Real.tendsto_harmonic_sub_log, continuousOn_cfc_nnreal, MeasureTheory.integrableOn_Lp_of_measure_ne_top, IsUnifLocDoublingMeasure.exists_measure_closedBall_le_mul', OpenPartialHomeomorph.continuousAt_extend, MeasureTheory.Lp.dist_eq_norm, Real.differentiable_exp, ContDiffOn.continuousOn_zero, TangentBundle.coordChange_model_space, NormedSpace.normalize_smul_of_pos, selfAdjoint.continuous_expUnitary, ContinuousLinearMap.adjoint_inner_left, Complex.isBigO_re_sub_re, AddChar.sum_apply_eq_zero_iff_ne_zero, MeasureTheory.condExpInd_disjoint_union, MeasureTheory.Lp.coeFn_le, PointwiseConvergenceCLM.isInducing_inducingFn, ImplicitFunctionData.hasStrictFDerivAt_implicitFunction_fderiv, FormalMultilinearSeries.nnnorm_compContinuousLinearMap_le, TensorProduct.inner_mapIncl_mapIncl, ValueDistribution.proximity_sum_top_le, isQuotientCoveringMap_npow, MeasureTheory.Lp.simpleFunc.add_toSimpleFunc, EuclideanGeometry.oangle_add_cyc3, MeasureTheory.Supermartingale.add_martingale, ProbabilityTheory.differentiableOn_mgf, AlternatingMap.mkContinuous_norm_le, Complex.comap_exp_nhdsNE, ContinuousLinearMap.isBoundedBilinearMap, WeakFEPair.Λ₀_eq, uniformContinuous_vsub, fdifferential_apply, ContinuousMultilinearMap.opNorm_nonneg, CompactlySupportedContinuousMap.integrable, Int.isClosedEmbedding_coe_real, InnerProductSpace.AlgebraOfCoalgebra.mul_def, fderivWithin_const_add, Real.hasStrictDerivAt_arcosh, MeasureTheory.Submartingale.add, UnitAddTorus.coeFn_mFourierLp, coe_ringEquiv_lpBCF, MeasureTheory.memLp_prod_iff, Matrix.l2_opNorm_conjTranspose_mul_self, egauge_pi, ContinuousLinearMap.apply_norm_eq_sqrt_inner_adjoint_right, compContinuousLinearMap_zero, Orientation.cos_oangle_add_right_mul_norm_of_oangle_eq_pi_div_two, HasLineDerivWithinAt.smul, MeromorphicOn.divisor_sub_const_of_ne, Affine.Simplex.orthogonalProjectionSpan_congr, ContinuousMultilinearMap.ofSubsingletonₗᵢ_symm_apply, Real.differentiableAt_cos, nonunits.isClosed, isClosed_preCantorSet, CompactlySupportedContinuousMap.nnrealPart_neg_toReal_eq, FormalMultilinearSeries.apply_eq_pow_smul_coeff, hasDerivAtFilter_id, FormalMultilinearSeries.le_radius_compContinuousLinearMap, GenLoop.ext_iff, uniformContinuous_nndist, SmoothBumpFunction.contMDiffAt, Differentiable.fderiv_two, CircleDeg1Lift.tendsto_translation_number', continuousMultilinearCurryFin0_symm_apply, MeasureTheory.setIntegral_condExpIndSMul, ContinuousLinearEquiv.integrable_comp_iff, MeasureTheory.weightedSMul_empty, Asymptotics.isBigOTVS_congr, AnalyticWithinAt.add, NumberField.mixedEmbedding.polarCoord_symm_apply, MeasureTheory.integrable_withDensity_iff_integrable_smul₀, OpenPartialHomeomorph.map_extend_symm_nhdsWithin, NumberField.InfinitePlace.Completion.extensionEmbeddingOfIsReal_coe, Affine.Simplex.mongePlane_def, ContinuousMap.dist_lt_iff_of_nonempty, MeasureTheory.Submartingale.eLpNorm_stoppedAbove_le, Polynomial.intervalIntegrable_mahlerMeasure, Complex.deriv_Gamma_nat, exists_continuous_one_zero_of_isCompact, Orientation.oangle_add_oangle_rev, IsUltrametricDist.norm_tsum_le_of_forall_le, MeasureTheory.ProbabilityMeasure.continuous_iff_forall_continuousMap_continuous_integral, cfcₙHom_predicate, Asymptotics.isBigOTVS_neg_right, Real.deriv_log', Circle.exp_neg, ProbabilityTheory.IsCondKernelCDF.setLIntegral, hasDerivAt_update, cfc_nnreal_eq_real, BumpCovering.toPartitionOfUnity_eq_mul_prod, ContinuousLinearMap.IsPositive.isSymmetric, MeasureTheory.indicatorConstLp_univ, ContinuousAlternatingMap.ofSubsingletonLIE_apply, extChartAt_mem_closure_interior, ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_apply, intervalIntegrable_sub_inv_iff, UniqueMDiffWithinAt.bundle_preimage', Real.one_div_sub_hasFPowerSeriesOnBall_zero, FormalMultilinearSeries.compAlongComposition_bound, HasFiniteFPowerSeriesOnBall.comp_sub, ProbabilityTheory.integrable_condVar, mfderiv_extChartAt_comp_mfderivWithin_extChartAt_symm, continuousMultilinearCurryRightEquiv_symm_apply, OrthonormalBasis.equiv_apply, RCLike.uniqueNonUnitalContinuousFunctionalCalculus, FormalMultilinearSeries.nnnorm_changeOriginSeriesTerm_apply_le, Metric.infDist_closure, ContMDiffMap.smul_comp, unitInterval.continuous_sigmoid, ContinuousLinearMap.lipschitz_apply, ContDiff.euclidean_dist, Trivialization.prod.isLinear, measurableSet_pi_polarCoord_target, cfcₙ_real_eq_complex, MeasureTheory.lpMeasToLpTrimLie_symm_indicator, AnalyticWithinAt.differentiableWithinAt, intervalIntegral.integral_comp_add_mul, fderiv_pow_ring, Complex.continuous_sinh, constFormalMultilinearSeries_apply_zero, Padic.instCompleteSpace, AnalyticAt.fun_smul, hasFTaylorSeriesUpToOn_top_iff', ContinuousLinearMap.lsmul_apply, MeasureTheory.SimpleFunc.memLp_of_finite_measure_preimage, MeasureTheory.setIntegral_rnDeriv_smul, instIsTopologicalRingReal, inTangentCoordinates_eq, isMIntegralCurveAt_iff, SeminormedAddCommGroup.cauchySeq_of_le_geometric, LinearIsometryEquiv.conjStarAlgEquiv_trans, FormalMultilinearSeries.radius_smul_eq, Path.truncate_zero_zero, selfAdjoint.unitarySelfAddISMul_coe, Bundle.ContMDiffRiemannianMetric.pos, hasFTaylorSeriesUpToOn_zero_iff, AffineIsometryEquiv.continuous, ContinuousMap.linearIsometryBoundedOfCompact_symm_apply, signedDist_triangle_left, ContinuousLinearMap.bilinearComp_zero_right, NormedAddGroupHom.extension_coe, TemperedDistribution.fourier_toTemperedDistributionCLM_eq, LinearMap.IsSymmetric.continuous, IsContMDiffRiemannianBundle.exists_contMDiff, Metric.isClosed_of_pairwise_le_dist, MeasureTheory.Lp.norm_const_le, map_extChartAt_nhds_of_boundaryless, ContinuousMap.ideal_isMaximal_iff, Complex.isOpen_compl_range_intCast, DiffContOnCl.circleIntegral_one_div_sub_center_pow_smul, deriv_const_mul_field, ZeroAtInftyContinuousMap.toBCF_apply, MeasureTheory.SignedMeasure.singularPart_add, Complex.nhdsWithin_lt_le_nhdsWithin_stolzSet, Complex.hasSum_ofReal, CuspFormClass.zero_at_infty, hasDerivAtFilter_add_const_iff, ContDiffMapSupportedIn.zero_on_compl, isBounded_iff_asymptoticCone_subset_singleton, HurwitzZeta.completedHurwitzZetaEven_residue_one, LinearIsometry.extend_apply, ProbabilityTheory.instIsGaussianMapHSub, Matrix.exp_nsmul, MeasureTheory.tendsto_indicator_ge, Complex.ofRealCLM_nnnorm, Complex.imCLM_norm, hasDerivAt_jacobiTheta₂_fst, Real.deriv2_binEntropy, InnerProductSpace.rank_rankOne, Summable.of_nnnorm, ArithmeticFunction.LSeries_vonMangoldt_eq_deriv_riemannZeta_div, MeasureTheory.integrableOn_Ioi_comp_mul_left_iff, isClosed_stdSimplex, LinearMap.toSeminorm_comp, CPolynomialOn.continuous, SmoothBumpCovering.sum_toSmoothPartitionOfUnity_eq, ContinuousAlternatingMap.toContinuousMultilinearMapLI_apply, UnitAddTorus.mFourier_neg, Submodule.isOrtho_top_left, AnalyticWithinAt.eventually_analyticWithinAt, interior_halfSpace, gauge_closure_zero, SimplexCategory.toTop₀_obj, IsometricContinuousFunctionalCalculus.toNonUnital, DiffContOnCl.const_smul, VectorFourier.fourierIntegral_convergent_iff, extChartAt_preimage_mem_nhds, InnerProductSpace.toDual_apply_apply, Real.Angle.sub_coe_pi_eq_add_coe_pi, Complex.continuousOn_norm_circleTransformBoundingFunction, Complex.continuousAt_Gamma_one, exists_continuous_nonneg_pos, intervalIntegral.intervalIntegrable_cpow, AlgHom.instContinuousLinearMapClassOfAlgHomClass, MeasureTheory.eLpNorm_sub_comm, ContinuousMap.sup_mem_closed_subalgebra, ContinuousLinearMap.adjointAux_apply, contMDiff_subtype_coe_Icc, ContinuousLinearMap.nonneg_iff_isPositive, Real.hasDerivAt_arcsin, ContinuousFunctionalCalculus.exists_cfc_of_predicate, MeasureTheory.Lp.coeFn_negPart_eq_max, integral_comp_polarCoord_symm, coe_lpBCFₗᵢ, ContinuousAffineMap.norm_contLinear_le, ContinuousLinearMap.inner_map_map_iff_adjoint_comp_self, AntitoneOn.intervalIntegrable, isClosed_nullSubgroup, CompactlySupportedContinuousMap.toRealPositiveLinear_apply, BoundedContinuousFunction.instIsScalarTower_1, Real.Angle.sin_eq_iff_coe_eq_or_add_eq_pi, Submodule.linearEquiv_det_reflection, HasFPowerSeriesAt.comp_sub, PeriodPair.differentiableOn_derivWeierstrassP, Matrix.SpecialLinearGroup.isClosedEmbedding_mapGLInt, ProperCone.innerDual_singleton, Complex.hasDerivAt_sinh, MeasureTheory.SimpleFunc.memLp_iff, PeriodPair.weierstrassPExcept_def, CurveIntegrable.intervalIntegrable_curveIntegralFun_trans_left, Submodule.IsOrtho.map, LinearIsometryEquiv.comp_differentiableOn_iff, LinearIsometryEquiv.comp_differentiableAt_iff, differentiable_inner, LeftInvariantDerivation.coe_sub, exists_locallyFinite_iUnion_eq_ball_radius_lt, HasFPowerSeriesWithinOnBall.sub, VectorBundleCore.baseSet_at, CFC.exp_eq_normedSpace_exp, MeasureTheory.IsFundamentalDomain.integrableOn_iff, CFC.abs_natCast, HasLineDerivAt.tendsto_slope_zero_left, BoundedContinuousFunction.AlgHom.compLeftContinuousBounded_apply_apply, ContinuousLinearMap.cpolyomialOn_uncurry_of_multilinear, tendsto_nhds_iff_meromorphicOrderAt_nonneg, ContDiffWithinAt.continuousLinearMap_comp, VectorBundleCore.mem_trivChange_source, CStarAlgebra.isStrictlyPositive_iff_isStrictlyPositive_sqrt_and_eq_sqrt_mul_sqrt, ContinuousMultilinearMap.hasFiniteFPowerSeriesOnBall, derivWithin_const_smul_field, LDL.lower_conj_diag, ContinuousAlternatingMap.norm_ofSubsingleton, Real.hasDerivAt_tan, OrderedFinpartition.compAlongOrderedFinpartitionₗ_apply_apply, hasFDerivAt_list_prod', HurwitzZeta.hasSum_int_cosZeta, Submodule.toLinearMap_starProjection_eq_isComplProjection, SeminormFamily.withSeminorms_iff_topologicalSpace_eq_iInf, intervalIntegral.FTCFilter.nhdsIcc, hasStrictFDerivAt_finCons, InnerProductSpace.rankOne_def, TensorProduct.nnnorm_map, Icc_chartedSpaceChartAt, Module.Basis.ofZLatticeBasis_span, contDiff_const_smul, BoundedContinuousFunction.mkOfCompact_apply, Real.deriv_tan_sub_id, ExistsContDiffBumpBase.u_int_pos, ContinuousLinearMap.coe_flipₗᵢ', HasMFDerivAt.prodMap, Real.leftDeriv_mul_log, WeakFEPair.h_feq', PiTensorProduct.norm_eval_le_injectiveSeminorm, MeasureTheory.weightedSMul_null, stereoToFun_apply, ContinuousLinearMap.adjointAux_inner_left, SchwartzMap.convolution_apply, deriv_inv, MeromorphicOn.negPart_divisor_add_of_analyticNhdOn_right, Submodule.sub_starProjection_mem_orthogonal, ContinuousLinearMap.fpowerSeriesBilinear_apply_add_three, MeasureTheory.Measure.MeasureDense.indicatorConstLp_subset_closure, PointwiseConvergenceCLM.equivWeakDual_apply, Real.differentiableAt_Gamma, hasSum_jacobiTheta₂_term_fderiv, Polynomial.fderiv_aeval, Module.Basis.addHaar_reindex, comap_norm_nhdsGT_zero', ContinuousLinearMap.norm_smulRight_apply, ContinuousMap.linearIsometryBoundedOfCompact_of_compact_toEquiv, ContinuousMap.Homotopy.extend_apply_coe, Orientation.norm_div_tan_oangle_add_left_of_oangle_eq_pi_div_two, Real.hasStrictDerivAt_cosh, differentiable_add_const_iff, ConvexOn.real_univ_sSup_of_countable_affine_eq, contDiff_iff_continuous_differentiable, dist_birkhoffAverage_birkhoffAverage, NumberField.mixedEmbedding.mem_span_latticeBasis, ZetaAsymptotics.tendsto_riemannZeta_sub_one_div_Gammaℝ, hasDerivAt_const, dslope_sub_smul_of_ne, Complex.tendsto_norm_tan_atTop, deriv_add_const', Orientation.tan_oangle_add_left_mul_norm_of_oangle_eq_pi_div_two, TemperedDistribution.fourierTransformInv_toTemperedDistributionCLM_eq, TopologicalSpace.Opens.CompleteCopy.dist_val_le_dist, HasFPowerSeriesWithinOnBall.uniform_geometric_approx', Module.Basis.equivFunL_symm_apply_repr, CircleDeg1Lift.continuous_iff_surjective, BoundedContinuousFunction.innerProbChar_apply, fderiv_const_add, ProbabilityTheory.analyticOn_cgf, continuousOn_extChartAt, MeasureTheory.eLpNorm_star, hasFDerivWithinAt_const_add_iff, UniformSpace.Completion.norm_toComplL, Real.zero_at_infty_fourierIntegral, ContDiffOn.differentiableOn, closure_upperClosure_comm_pi, Bornology.IsVonNBounded.tendsto_smallSets_nhds, ProbabilityTheory.covarianceBilin_comm, ProbabilityTheory.Kernel.tendsto_integral_density_of_monotone, iter_deriv_zpow, ContinuousAlternatingMap.constOfIsEmptyLIE_symm_apply, ContinuousMap.toLp_def, ContDiffAt.const_smul, Units.instLieGroupModelWithCornersSelf, ContinuousLinearMap.IsStarNormal.ker_adjoint_eq_ker, natCast_le_analyticOrderAt, Complex.hasDerivAt_Gammaℂ_one, ProbabilityTheory.Kernel.memL1_limitProcess_densityProcess, ProbabilityTheory.cdf_le_one, AnalyticAt.eventually_constant_or_nhds_le_map_nhds, Complex.hasSum_sin, Complex.tendsto_self_mul_Gamma_nhds_zero, iteratedDerivWithin_fun_const_smul_field, ImplicitFunctionData.map_nhds_eq, SchwartzMap.integral_bilin_fourier_eq, Real.isTopologicalBasis_Ioo_rat, gradient_eq_deriv', Complex.hasStrictDerivAt_const_cpow, ZetaAsymptotics.continuousOn_term, ContinuousLinearEquiv.contDiffPointwiseHolderAt, ContinuousMultilinearMap.analyticAt, ClosedSubmodule.orthogonal_eq_inter, Chebyshev.integrableOn_theta_div_id_mul_log_sq, PositiveLinearMap.toPreGNS_ofPreGNS, contDiffWithinAtProp_self_source, summable_iff_vanishing_norm, ContinuousMultilinearMap.prodL_apply, Orientation.kahler_neg_orientation, FormalMultilinearSeries.radius_inv_eq_limsup, Real.hasStrictDerivAt_log, hasFDerivWithinAt_iff_hasDerivWithinAt, IsSelfAdjoint.cfc_arg, mdifferentiableWithinAt_iff_image, MeasureTheory.L2.integral_inner_eq_sq_eLpNorm, AnalyticOnNhd.comp_sub, affinity_unitBall, MonotoneOn.intervalIntegrable_slope, OpenPartialHomeomorph.extend_coord_change_source_mem_nhdsWithin', EisensteinSeries.D2_inv, hasFTaylorSeriesUpToOn_succ_iff_right, EisensteinSeries.hasSum_e2Summand_symmetricIco, Real.sin_eq_tsum, ContinuousLinearMap.coe_flipMultilinearEquiv, Affine.Triangle.circumsphere_eq_of_dist_of_oangle, tendsto_rpow_div_mul_add, iteratedFDeriv_comp_add_left, indiscreteTopology_iff_forall_norm_eq_zero', NonUnitalAlgHom.coe_Lmul, tendsto_rpow_atTop_of_base_lt_one, ContinuousMultilinearMap.norm_map_init_le, NumberField.mixedEmbedding.euclidean.volumePreserving_toMixed, LeftInvariantDerivation.left_invariant'', ArithmeticFunction.vonMangoldt.not_summable_residueClass_prime_div, ContinuousAlternatingMap.hasStrictFDerivAt, ContinuousAffineMap.hasStrictFDerivAt, SchwartzMap.tsupport_lineDerivOp_subset, intervalIntegral.integrableOn_Ioo_cpow_iff, lp.coeFn_add, OpenPartialHomeomorph.extend_coord_change_source_mem_nhdsWithin, SchwartzMap.fourierInv_apply_eq, SchwartzMap.smulRightCLM_apply_apply, NormedSpace.expSeries_summable', Real.differentiableOn_Gamma_Ioi, Real.differentiableOn_mul_log, TestFunctionClass.instBoundedContinuousMapClass, LinearIsometryEquiv.conjStarAlgEquiv_refl, MeasureTheory.HasFiniteIntegral.of_bounded, CurveIntegrable.fun_zero, MeasureTheory.Submartingale.bddAbove_iff_exists_tendsto_aux, InnerProductSpace.laplacian_smul, InformationTheory.klDiv_def, MeasureTheory.finStronglyMeasurable_of_measurable, PartitionOfUnity.exists_isSubordinate_of_locallyFinite_t2space, MeasureTheory.L2.inner_indicatorConstLp_one, hasStrictFDerivAt_iff_hasStrictDerivAt, NNRat.instContinuousInv₀, MeasureTheory.L2.inner_indicatorConstLp_indicatorConstLp, ProbabilityTheory.Kernel.tendsto_densityProcess_atTop_empty_of_antitone, ProbabilityTheory.setIntegral_tilted_mul_eq_mgf', contDiff_nat_iff_iteratedDeriv, Path.source', MeasureTheory.exists_null_frontier_thickening, MeasureTheory.Lp.boundedContinuousFunction_dense, LinearMap.IsSymmetric.toSelfAdjoint_apply, MeasureTheory.Lp.constₗ_apply, Submodule.coe_continuous_linearProjOfClosedCompl, MeasureTheory.Lp.coe_nnnorm, hasSum_jacobiTheta₂'_term, InnerProductSpace.volume_ball, EuclideanGeometry.orthogonalProjection_subtype, Real.Angle.sin_two_nsmul, NumberField.mixedEmbedding.negAt_apply_isReal_and_notMem, MeasureTheory.JordanDecomposition.exists_compl_positive_negative, ProbabilityTheory.IsRatCondKernelCDF.tendsto_atTop_one, iteratedFDeriv_neg_apply, ProbabilityTheory.memLp_id_gaussianReal', circleIntegral.norm_two_pi_i_inv_smul_integral_le_of_norm_le_const, Submodule.coe_orthogonalDecomposition, EuclideanGeometry.two_zsmul_oangle_self_orthogonalProjection, VectorField.lieBracket_eq, Complex.tendsto_arg_nhdsWithin_im_neg_of_re_neg_of_im_zero, fderiv_norm_smul_neg, SchwartzMap.toTemperedDistributionCLM_apply_apply, EisensteinSeries.q_expansion_riemannZeta, Seminorm.continuousAt_zero', differentiableAt_fst, Real.continuousOn_cos, ContinuousLinearMapWOT.isInducing_inducingFn, SlashInvariantFormClass.periodic_comp_ofComplex, integrableOn_Ioi_deriv_ofReal_cpow, cfc_def, CompactlySupportedContinuousMap.toReal_apply, PositiveLinearMap.exists_norm_apply_le, NormedField.nhdsNE_neBot, contMDiff_iff_contDiff, DoubleCentralizer.star_fst, Real.fourierIntegral_real_eq_integral_exp_smul, Complex.map_exp_comap_re_atBot, HasFPowerSeriesWithinOnBall.continuousOn, MeasureTheory.Lp.mem_boundedContinuousFunction_iff, DomMulAct.instSMulCommClassSubtypeAEEqFunMemAddSubgroupLp_2, Real.deriv_mulExpNegMulSq, EuclideanHalfSpace.convex, StrongDual.polarSubmodule_eq_polar, NormedAddGroupHom.completion_add, fourier_coe_apply, Submodule.finrank_orthogonal_span_singleton, summable_prod_mul_pow, PiTensorProduct.liftEquiv_symm_apply, Complex.interior_setOf_le_im, RCLike.summable_conj, NNReal.continuousAt_rpow, MeasureTheory.integrable_comp_div_left, MeasureTheory.condExpIndSMul_add, TopologicalSpace.complete_completelyPseudoMetrizableMetric, RCLike.geometric_hahn_banach_point_point, Nat.Primes.not_summable_one_div, ContinuousLinearMap.fpowerSeries_apply_add_two, iteratedDeriv_mul, Orientation.oangle_eq_iff_eq_pos_smul_rotation_of_ne_zero, Metric.uniformContinuousOn_iff, periodizedBernoulli.continuous, GenLoop.continuous_fromLoop, contMDiff_iff_target, LinearMap.isPositive_natCast, fourierSubalgebra_separatesPoints, AffineSubspace.isConnected_setOf_wSameSide, FormalMultilinearSeries.nnnorm_changeOriginSeries_apply_le_tsum, curveIntegralFun_cast, TensorProduct.toLinearEquiv_congrIsometry, Asymptotics.isLittleOTVS_fun_neg_right, MeasureTheory.Lp.norm_fourier_eq, AnalyticAt.analyticOrderAt_deriv_add_one, Asymptotics.isBigO_completion_right, Complex.isEquivalent_sinh, cfcₙ_neg_id, ContDiffWithinAt.smul, ContinuousMultilinearMap.opNorm_zero, AnalyticOnNhd.is_constant_or_isOpenMap, IsBoundedBilinearMap.continuous, hasFDerivAt_exp_smul_const', mdifferentiableOn_extChartAt_symm, dense_differentiableAt_norm, Quaternion.exp_of_re_eq_zero, MeromorphicAt.iterated_deriv, normedAddGroupHomCompletionHom_apply, MeasureTheory.SignedMeasure.re_toComplexMeasure, lowerClosure_interior_subset, TemperedDistribution.smulLeftCLM_sub, Complex.one_add_cpow_hasFPowerSeriesAt_zero, FormalMultilinearSeries.ofScalars_norm_le, Matrix.exp_zsmul, Submodule.isOrtho_iSup_left, Seminorm.uniformSpace_eq_of_hasBasis, ContinuousLinearMap.hasFiniteFPowerSeriesOnBall, IsCoercive.bounded_below, HurwitzZeta.hasSum_nat_cosZeta, DiffContOnCl.continuousOn_ball, HurwitzZeta.continuousOn_evenKernel, Commute.cfcₙHom, ValueDistribution.proximity_add_top_le, iteratedFDerivWithin_comp_sub, Submodule.norm_subtypeL, NumberField.mixedEmbedding.fundamentalCone.expMap_basis_of_eq, AffineSubspace.closed_of_finiteDimensional, AkraBazziRecurrence.eventually_deriv_rpow_p_mul_one_add_smoothingFn, ContinuousMultilinearMap.norm_mkPiAlgebraFin_le_of_pos, fourierCoeff.const_smul, ContinuousLinearMapWOT.hasBasis_seminorms, MonotoneOn.intervalIntegral_deriv_mem_uIcc, ContinuousMap.nnnorm_lt_iff, MeasureTheory.SignedMeasure.mutuallySingular_iff, Submodule.mem_orthogonal', NumberField.mixedEmbedding.volume_preserving_negAt, ContinuousLinearMap.norm_iteratedFDeriv_le_of_bilinear, OnePoint.isZeroAt_iff_forall_SL2Z, StarAlgHom.realContinuousMapOfNNReal_apply_comp_toReal, ContDiff.continuous_iteratedDeriv, instPolynormableSpace, setIntegral_withDensity_eq_setIntegral_toReal_smul₀', hasFDerivAt_finCons', Affine.Simplex.ExcenterExists.sign_signedInfDist_lineMap_excenter_touchpoint, LinearMap.toMatrixOrthonormal_symm_apply, Real.deriv_qaryEntropy, ContinuousMultilinearMap.cpolyomialOn_uncurry_of_linear, closure_of_rat_image_lt, IsUltrametricDist.norm_fwdDiff_iter_apply_le, OpenPartialHomeomorph.continuousOn_extend_symm, contDiffPointwiseHolderAt_iff, ContinuousLinearMap.IsStarNormal.orthogonal_range, WithSeminorms.topology_eq_withSeminorms, mem_closure_zero_iff_norm, Real.deriv_arctan, hasSum_cauchyPowerSeries_integral, AffineSubspace.isPreconnected_setOf_wOppSide, SchwartzMap.coeFn_toLp, continuousSMul_sphere_closedBall, differentiableWithinAt_comp_sub, Matrix.posDef_gram_iff_linearIndependent, monotoneOn_deriv_descPochhammer_eval, MeasureTheory.Lp.instFourierSMul, SchwartzMap.smulLeftCLM_const, hasStrictFDerivAt_piLp, ProbabilityTheory.HasSubgaussianMGF.memLp_exp_mul, Asymptotics.isLittleO_pow_sub_pow_sub, UpperHalfPlane.contMDiff_num, MeasureTheory.Supermartingale.integrable, SmoothPartitionOfUnity.sum_eq_one', Circle.exp_inj, TopologicalSpace.UpgradedIsCompletelyMetrizableSpace.toCompleteSpace, Real.sinh_eq_tsum, VectorField.mlieBracketWithin_def, UpperHalfPlane.mdifferentiable_denom, mdifferentiableAt_prod_module_iff, BoundedContinuousFunction.uniformContinuous_coe, writtenInExtChartAt_model_space, BumpCovering.locallyFinite, Path.reparam_id, Metric.sphere.compactSpace, LinearMap.toMatrix_innerₛₗ_apply, Matrix.exp_sum_of_commute, strictConvexSpace_iff, intervalIntegral.smul_integral_comp_sub_mul, AffineSubspace.toContinuousAffineMap_subtypeₐᵢ, Real.cos_eq_tsum, ContinuousLinearMap.IsStarNormal.adjoint_apply_eq_zero_iff, Complex.continuous_conj, MeromorphicAt.iff_eventuallyEq_zpow_smul_analyticAt, MeasureTheory.Lp.norm_const', Function.locallyFinsuppWithin.toClosedBall_divisor, LSeries.term_convolution, HasFPowerSeriesAt.isBigO_image_sub_norm_mul_norm_sub, SchwartzMap.coeHom_injective, PointwiseConvergenceCLM.equivWeakDual_symm_apply, MeasureTheory.norm_condExpIndL1_le, MeasureTheory.IsAddFundamentalDomain.integrableOn_iff, MeasureTheory.Measure.withDensityᵥ_absolutelyContinuous, Real.continuous_sin, TensorProduct.toLinearEquiv_commIsometry, ProperCone.hyperplane_separation_point, NumberField.mixedEmbedding.fundamentalCone.prod_expMapBasis_pow, MeasureTheory.ComplexMeasure.integrable_rnDeriv, contMDiffOn_extChartAt, Polynomial.isProperMap_eval, PadicInt.completeSpace, MeasureTheory.eLpNorm_le_mul_eLpNorm_of_ae_le_mul, StieltjesFunction.countable_leftLim_ne, NumberField.mixedEmbedding.negAt_apply_isComplex, isBigO_riemannZeta_sub_one_div, SchwartzMap.norm_toLp, AffineMap.hasDerivAt, Real.continuousOn_logb, Complex.hasFDerivAt_cpow, ProbabilityTheory.isGaussian_iff_charFun_eq, Orientation.inner_rotation_pi_div_two_left_smul, MeasureTheory.Measure.toSignedMeasure_toMeasureOfZeroLE, isClosedMap_nndist, Nonneg.instNonUnitalIsometricContinuousFunctionalCalculus, Submodule.norm_sq_eq_add_norm_sq_projection, ContinuousAffineMap.contDiff, smul_sphere, FormalMultilinearSeries.radius_compContinuousLinearMap_linearIsometryEquiv_eq, ValueDistribution.logCounting_add_analyticOn, NumberField.mixedEmbedding.fundamentalCone.expMapBasis_closure_subset_compactSet, tangentCoordChange_comp, lipschitzOnWith_cfc_fun, Orientation.sin_oangle_add_left_of_oangle_eq_pi_div_two, Complex.differentiableAt_exp, MeasureTheory.Measure.toSignedMeasure_smul, OnePoint.isBoundedAt_iff, LinearIsometry.norm_iteratedFDeriv_comp_left, LinearMap.range_toContinuousLinearMap, SeminormedGroup.uniformCauchySeqOn_iff_tendstoUniformlyOn_one, Submodule.orthogonal_gc, Complex.not_continuousAt_Gamma_zero, fderiv_const_smul_of_invertible, Path.uniformContinuous, Complex.differentiable_Gammaℝ_inv, Quaternion.re_exp, Path.extend_of_one_le, ContinuousLinearEquiv.dimH_image, meromorphicOrderAt_eq_int_iff, ContinuousLinearMap.norm_precompR_le, hasFDerivWithinAt_pow', NumberField.mixedEmbedding.fundamentalCone.continuous_expMap, ContDiffMapSupportedIn.structureMapLM_apply_withOrder, continuous_circleMap, differentiableAt_jacobiTheta₂_fst, HasFTaylorSeriesUpToOn.continuousLinearMap_comp, Real.summable_nat_pow_inv, intervalIntegral.FTCFilter.nhdsRight, not_integrableOn_Ioi_rpow, AffineMap.differentiableAt, hasStrictDerivAt_finCons', Real.continuousAt_logb_iff, AbsolutelyContinuousOnInterval.uniformContinuousOn, Trivialization.contMDiffOn_localFrame_baseSet, Asymptotics.isLittleO_id_one, Complex.iter_deriv_exp, tendsto_measure_thickening, ProbabilityTheory.instIsGaussianDirac, MeromorphicOn.meromorphicNFAt_mem_codiscreteWithin, dist_iteratedFDerivWithin_zero, curveIntegral_restrictScalars, HasProdLocallyUniformlyOn_euler_sin_prod, MeromorphicOn.negPart_divisor_add_of_analyticNhdOn_left, HasFPowerSeriesOnBall.hasSum, NormedSpace.ofReal_exp_ℝ_ℝ, ContinuousLinearMap.isBoundedLinearMap_comp_right, ProbabilityTheory.setIntegral_stieltjesOfMeasurableRat, Circle.exp_add_two_pi, Matrix.PosSemidef.toLinearMap₂'_zero_iff, Submodule.starProjection_isSymmetric, MeasureTheory.Lp.smul_zero, convex_halfSpace_im_lt, ContDiffWithinAt.contDiffOn, Submodule.starProjection_apply, Real.Angle.two_nsmul_eq_iff_eq_of_abs_toReal_lt_pi_div_two, ContinuousLinearMap.hasFPowerSeriesOnBall_bilinear, Path.image_extend_of_subset, HasFPowerSeriesWithinAt.pi, tendsto_rpow_sub_one_log, MeasureTheory.L1.SimpleFunc.norm_eq_sum_mul, NormedSpace.isVonNBounded_iff', Polynomial.rootSet_derivative_subset_convexHull_rootSet, Submodule.HasOrthogonalProjection.map_linearIsometryEquiv', SmoothPartitionOfUnity.mem_finsupport, VonNeumannAlgebra.mem_carrier, Continuous.inner_bundle, IsSelfAdjoint.instNonUnitalContinuousFunctionalCalculus, MemHolder.add, MeasureTheory.hasFiniteIntegral_neg_iff, WeakDual.isSeqCompact_closedBall, differentiableOn_fun_neg_iff, hasStrictDerivAt_finCons, enorm_sub_le_lintegral_derivWithin_Icc_of_contDiffOn_Icc, Complex.differentiableAt_tan, PiTensorProduct.liftEquiv_apply, DomMulAct.mk_smul_indicatorConstLp, LinearIsometryEquiv.toHomeomorph_injective, DoubleCentralizer.add_snd, Real.continuous_negMulLog, ModularForm.differentiableAt_eta_tprod, MeasureTheory.Measure.integrable_measure_prodMk_left, MeasureTheory.norm_condExpInd_apply_le, has_antideriv_at_fourier_neg, ImplicitFunctionData.toPartialHomeomorph_coe, OpenPartialHomeomorph.univUnitBall_target, Real.differentiableAt_log_iff, hasFTaylorSeriesUpTo_top_iff', hasStrictDerivAt_zpow, NormedAddGroupHom.uniformContinuous, MeasureTheory.hasFiniteIntegral_const, IsOpen.exists_contMDiff_support_eq, fderivWithin_iteratedFDerivWithin, Real.uniformContinuous_neg, PadicInt.denseRange_natCast, ProbabilityTheory.cdf_gammaMeasure_eq_lintegral, UnitAddTorus.mFourier_norm, Orientation.rotation_neg_orientation_eq_neg, rescale_to_shell, toMeromorphicNFOn_eq_toMeromorphicNFAt_on_nhds, ContinuousLinearMap.rayleighQuotient_add, ContinuousMultilinearMap.contDiff, IsPicardLindelof.continuousOn_uncurry, MultilinearMap.mkContinuousLinear_norm_le, WithSeminorms.uniformEquicontinuous_iff_bddAbove_and_continuous_iSup, hasFDerivAt_iff_tendsto, GenLoop.toLoop_apply, VonNeumannAlgebra.centralizer_centralizer, WeakDual.exists_countable_separating, NumberField.mixedEmbedding.normAtComplexPlaces_normAtAllPlaces, LSeriesSummable.sum, mdifferentiable_iff, MeasureTheory.isTightMeasureSet_of_tendsto_measure_compl_closedBall, LinearMap.isSelfAdjoint_iff', Function.Periodic.continuous_qParam, tsum_geometric_two, FormalMultilinearSeries.not_summable_norm_of_radius_lt_nnnorm, MeasureTheory.SimpleFunc.norm_setToSimpleFunc_le_sum_opNorm, Orientation.areaForm'_apply, NumberField.mixedEmbedding.fundamentalCone.expMap_smul, Real.continuous_const_rpow, VectorBundleCore.coe_coordChange, IsGδ.setOf_irrational, OpenPartialHomeomorph.continuous_univBall, hasFDerivAtFilter_iff_hasDerivAtFilter, Metric.mem_closure_iff, ENNReal.continuous_ofReal, HurwitzZeta.hasSum_expZeta_of_one_lt_re, innerSLFlip_apply_apply, UniformContinuousOn.cexp, ContinuousLinearEquiv.mdifferentiableOn, PiCountable.dist_summable, ContinuousLinearMap.nnnorm_holder_apply_apply_le, HurwitzZeta.hasSum_int_evenKernel, Real.summable_exp_neg_nat, mdifferentiableWithinAt_iff_differentiableWithinAt, NNRat.tendsto_inv_atTop_nhds_zero_nat, Affine.Triangle.dist_orthocenter_reflection_circumcenter, iteratedDeriv_add, OrthogonalFamily.hasSum_linearIsometry, ODE.FunSpace.toContinuousMap_apply_eq_apply, Polynomial.hasFDerivAt, TestFunctionClass.map_hasCompactSupport, RCLike.ofReal_finsupp_sum, intervalIntegral.integral_smul_measure, hasSum_one_div_nat_pow_mul_cos, isOpen_setOf_affineIndependent, tendsto_zero_of_meromorphicOrderAt_pos, signedDist_smul_of_pos, MeasureTheory.BorelCantelli.integrable_process, Distribution.mapCLM_apply, OnePoint.IsZeroAt.smul_iff, finrank_euclideanSpace, FormalMultilinearSeries.norm_compContinuousLinearMap_le, Complex.continuous_exp, continuous_gauge, HurwitzZeta.hasSum_int_completedHurwitzZetaOdd, MeasureTheory.SignedMeasure.singularPart_zero, Real.hasStrictDerivAt_const_rpow_of_neg, BoundedContinuousFunction.continuous, hasDerivAt_inv, EuclideanGeometry.oangle_orthogonalProjection_self, tendsto_pow_const_mul_const_pow_of_abs_lt_one, LinearMap.IsPositive.isSelfAdjoint, MeasureTheory.FiniteMeasure.testAgainstNN_add, ContinuousLinearMap.bilinear_hasTemperateGrowth, Orientation.oangle_add_left_eq_arcsin_of_oangle_eq_pi_div_two, IsBoundedBilinearMap.isBoundedLinearMap_deriv, IsContinuousRiemannianBundle.exists_continuous, ContinuousAlternatingMap.fderivCompContinuousLinearMap_eq_alternatizeUncurryFin, Set.OrdConnected.null_frontier, differentiableOn_add_const_iff, MeasureTheory.Submartingale.stronglyMeasurable, DoubleCentralizer.norm_snd, Submodule.top_orthogonal_eq_bot, AkraBazziRecurrence.isTheta_deriv_rpow_p_mul_one_add_smoothingFn, ConvexOn.sSup_of_nat_affine_eq, MeasureTheory.Submartingale.eLpNorm_stoppedAbove_le', IsometricContinuousFunctionalCalculus.toContinuousFunctionalCalculus, Submodule.fst_orthogonalDecomposition_apply, LinearMap.coe_toContinuousLinearMap, ContinuousLinearMap.prodMapL_apply, ContinuousLinearMap.uncurryLeft_apply, MeasureTheory.Submartingale.ae_tendsto_limitProcess_of_uniformIntegrable, HilbertBasis.dense_span, DomAddAct.norm_vadd_Lp, Complex.frontier_preimage_im, Complex.one_div_sub_sq_hasFPowerSeriesOnBall_zero, DirichletCharacter.summable_neg_log_one_sub_mul_prime_cpow, Submodule.orthogonal_orthogonal_eq_closure, MeasureTheory.condExpL1_neg, AnalyticOn.const_smul, MeasureTheory.Lp.instTrivialStarSubtypeAEEqFunMemAddSubgroup, ContinuousLinearEquiv.nhds, continuousAt_clog, EisensteinSeries.linear_left_summable, ContDiffAt.derivWithin, ContinuousAlternatingMap.le_opNorm_mul_pow_of_le, AnalyticOnNhd.preimage_zero_mem_codiscrete, Submodule.smul_starProjection_singleton, Metric.tendsto_nhdsWithin_nhdsWithin, MeasureTheory.eLpNorm'_mono_ae, PeriodPair.hasSumLocallyUniformly_weierstrassPExcept, Finset.analyticOn_fun_sum, Bornology.IsBounded.isCompact_closure, Circle.invOn_arg_exp, ContinuousLinearMap.opNorm_comp_le, contMDiff_smul, isLittleO_log_rpow_nhdsGT_zero, MeromorphicOn.divisor_ofNat, VectorBundleCore.mem_source_at, DoubleCentralizer.nnnorm_fst, MeasureTheory.L1.nnnorm_integral_le, trivializationAt_model_space_apply, ContinuousLinearMap.isUnit_iff_isUnit_toLinearMap, MeasureTheory.Measure.addHaar_real_closedBall', UniformFun.continuousSMul_induced_of_range_bounded, LinearIsometryEquiv.continuousWithinAt, TensorProduct.ext_iff_inner_right, Real.tendsto_comp_exp_atBot, ContinuousMap.equivBoundedOfCompact_apply, HasFPowerSeriesWithinOnBall.image_sub_sub_deriv_le, instSeparatingDualRealOfIsTopologicalAddGroupOfContinuousSMulOfLocallyConvexSpaceOfT1Space, ContinuousAlternatingMap.curryLeft_compContinuousLinearMap, Complex.hasDerivAt_cos, MeasureTheory.Lp.norm_smul_le, intervalIntegral.intervalIntegrable_id, signedDist_lineMap_lineMap, Complex.ofRealCLM_apply, contMDiffOn_continuousLinearMapCoordChange, LinearEquiv.isPositive_symm_iff, AkraBazziRecurrence.differentiableOn_one_add_smoothingFn, UpperHalfPlane.ofComplex_apply_eq_of_im_nonpos, Complex.log_sub_self_isBigO, ContinuousMultilinearMap.curryFinFinset_apply_const, InnerProductSpace.enorm_rankOne, Function.HasTemperateGrowth.norm_iteratedFDeriv_le_uniform, Module.Basis.exists_opNNNorm_le, Module.Basis.addHaar_def, aestronglyMeasurable_smul_const_iff, MeasureTheory.SimpleFunc.FinMeasSupp.integrable, MeasureTheory.isClosed_aestronglyMeasurable, Orthonormal.inner_finsupp_eq_sum_right, PartitionOfUnity.finsum_smul_mem_convex, InnerProductSpace.continuousLinearMapOfBilin_zero, contDiffOn_zero, differentiableAt_complex_iff_differentiableAt_real, mfderiv_coe_sphere_injective, NNRat.instContinuousSMulOfIsScalarTowerOfRat, ContinuousMultilinearMap.compContinuousLinearMapLRight_apply, OpenPartialHomeomorph.map_extend_nhds, PiTensorProduct.mapL_mul, exists_continuous_zero_one_of_isCompact', IsUltrametricDist.isOpen_sphere, cfcHom_real_eq_restrict, OpenPartialHomeomorph.restrContDiff_target, intervalIntegral.inv_smul_integral_comp_sub_div, extChartAt_preimage_mem_nhdsWithin, SeparationQuotient.normedMk_eq_zero_iff, contMDiffOn_extChartAt_symm, ContinuousLinearMap.toLinearMap_innerSL_apply, ModelWithCorners.symm_map_nhdsWithin_range, extChartAt_target_mem_nhdsWithin', UniformConvexOn.convexOn, differentiableAt_comp_const_sub, HasFPowerSeriesAt.hasStrictDerivAt, Submodule.orthogonalFamily_self, EuclideanGeometry.dist_orthogonalProjection_eq_dist_iff_eq_of_mem, AnalyticOn.smul, NumberField.mixedEmbedding.mem_negAt_plusPart_of_mem, ContinuousLinearMap.continuousMultilinearMapOption_apply_eq_self, NumberField.Units.regOfFamily_of_isMaxRank, VectorPrebundle.pretrivialization_mem_atlas, Orientation.norm_div_cos_oangle_add_right_of_oangle_eq_pi_div_two, IsUnifLocDoublingMeasure.eventually_measure_le_doublingConstant_mul, Module.Basis.equivFunL_apply, OpenPartialHomeomorph.univBall_apply_zero, nonneg_iff_isSelfAdjoint_and_spectrumRestricts, MeasureTheory.Lp.coeFn_sup, IsBoundedBilinearMap.differentiableAt, NNReal.ContinuousMap.canLift, hasFDerivAt_list_prod_finRange', HomotopyGroup.mul_spec, ContDiffOn.differentiableOn_one, Bundle.mdifferentiableWithinAt_proj, LinearMap.IsSymmetric.adjoint_eq, BoundedContinuousFunction.probCharDual_zero, IsSelfAdjoint.dense_domain, LinearMap.isPositive_sum, ContinuousMultilinearMap.flipLinear_apply_apply, tendsto_integral_mul_one_add_inv_smul_sq_pow, Submodule.starProjection_norm_le, Asymptotics.isLittleO_iff_tendsto', ContinuousAlternatingMap.norm_toContinuousMultilinearMap, MeasureTheory.charFun_conv, HasGradientAt.hasFDerivAt, Complex.arg_eq_nhds_of_im_neg, ContinuousLinearMap.comp_hasFPowerSeriesWithinOnBall, MeasureTheory.eLpNormEssSup_le_nnreal_smul_eLpNormEssSup_of_ae_le_mul, expNegInvGlue.tendsto_polynomial_inv_mul_zero, MeasureTheory.hasFiniteIntegral_const_iff_isFiniteMeasure, LinearMap.hasDerivWithinAt, IsLocalFrameOn.contMDiffOn, Rat.uniformContinuous_add, summable_choose_mul_geometric_of_norm_lt_one, AffineSubspace.abs_signedInfDist_eq_dist_of_mem_affineSpan_insert, CStarMatrix.toCLM_apply_single, NumberField.InfinitePlace.Completion.isClosed_image_extensionEmbeddingOfIsReal, GromovHausdorff.toGHSpace_continuous, hasSum_two_pi_I_cauchyPowerSeries_integral, LinearIsometry.continuous, meromorphicOrderAt_add_of_top_left, FormalMultilinearSeries.comp_id, differentiableWithinAt_star_iff, ContinuousMultilinearMap.hasStrictFDerivAt, Submodule.inner_orthogonalProjection_eq_of_mem_right, range_cfcₙ_eq_range_cfcₙHom, fderivWithin_comp_smul_eq_fderivWithin_smul, ContinuousLinearMap.isLeast_opNNNorm, ZeroAtInftyContinuousMap.isBounded_image, ContinuousMap.nnnorm_smul_const, sameRay_iff_norm_add, tendsto_rpow_abs_mul_exp_neg_mul_sq_cocompact, Function.HasTemperateGrowth.add, Complex.tendsto_exp_comap_re_atBot, continuous_bernoulliFun, ContinuousMap.adjoin_id_eq_span_one_union, signedDist_vadd_left_swap, IsSelfAdjoint.spectrumRestricts, Submodule.isOrtho_iff_le, MeasureTheory.condExp_smul, SeparationQuotient.mk_eq_zero_iff, HurwitzZeta.continuousOn_oddKernel, NumberField.mixedEmbedding.fundamentalCone.closure_normLeOne_subset, Real.borel_eq_generateFrom_Ici_rat, intervalIntegral.FTCFilter.nhdsUniv, hasFTaylorSeriesUpTo_succ_nat_iff_right, OpenPartialHomeomorph.contDiffOn_univUnitBall_symm, iteratedFDeriv_add, UniformSpace.Completion.coe_isometry, MeasureTheory.Lp_toLp_restrict_add, CFC.abs_algebraMap, tsum_riemannZetaSummand, ordinaryHypergeometric_radius_top_of_neg_nat₂, hasFDerivWithinAt_piLp, MeasureTheory.norm_weightedSMul_le, extChartAt_preimage_mem_nhds', Complex.restrictScalars_one_smulRight, ContinuousLinearMapWOT.isEmbedding_inducingFn, PartitionOfUnity.nonneg, differentiableOn_piLp, contMDiffWithinAt_extChartAt_symm_range_self, differentiableAt_abs_neg, ClosedSubmodule.iInf_orthogonal, Asymptotics.isLittleOTVS_iff_smallSets, Complex.summable_ofReal, Orientation.oangle_eq_iff_eq_pos_smul_rotation_or_eq_zero, Complex.one_div_one_sub_pow_hasFPowerSeriesOnBall_zero, hasDerivAt_fourier_neg, ValueDistribution.characteristic_add_top_eventuallyLE, ProbabilityTheory.isGaussian_gaussianReal, MeasureTheory.eLpNormEssSup_mono_nnnorm_ae, HasFiniteFPowerSeriesOnBall.differentiableOn, MeasureTheory.eLpNormEssSup_le_of_ae_bound, EuclideanGeometry.reflection_apply_of_mem, StrongDual.dualPairing_separatingLeft, HasFPowerSeriesOnBall.neg, Metric.continuous_iff', deriv_abs_zero, ContinuousLinearMap.uncurryBilinear_apply, Asymptotics.continuousAt_iff_isLittleO, LinearMap.IsSymmetric.isSymmetric_smul_iff, VectorBundle.continuousOn_coordChange', LinearMap.isPositive_linearIsometryEquiv_conj_iff, ZSpan.coe_floor_self, ContinuousLinearEquiv.continuousAlternatingMapCongrRight_symm, ContinuousLinearMap.mfderiv_eq, Asymptotics.isLittleOTVS_iff_tendsto_div, hasStrictDerivAt_abs, hasFDerivAt_const_add_iff, Antitone.locallyIntegrable, fourier_eval_zero, Matrix.PosDef.commute_iff, ContinuousAlternatingMap.isLeast_opNorm, Matrix.IsHermitian.cfcAux_apply, SchwartzMap.fourierInv_lineDerivOp_eq, curveIntegralFun_trans_of_half_lt, Metric.isPreconnected_eball, RCLike.finrank_le_two, nontrivialTopology_iff_exists_nnnorm_ne_zero', EuclideanGeometry.Sphere.secondInter_smul, ContDiffMapSupportedIn.tsupport_subset, InnerProductSpace.harmonicAt_comp_CLE_iff, Complex.tendsto_euler_sin_prod, InnerProductSpace.coe_gramSchmidtBasis, EulerProduct.summable_and_hasSum_smoothNumbers_prod_primesBelow_geometric, Bundle.RiemannianMetric.symm, Metric.cthickening_eq_biUnion_closedBall, ZMod.completedLFunction_eq, ContinuousLinearMap.cpolynomialAt_uncurry_of_multilinear, NormedSpace.isVonNBounded_of_isBounded, strongConcaveOn_iff_convex, Filter.tendsto_cocompact_cocompact_of_norm, iteratedFDeriv_eq_equiv_comp, ContinuousMap.toNNReal_one, Complex.hasStrictDerivAt_log, ProbabilityTheory.Kernel.tendsto_integral_density_of_antitone, LinearMap.toContinuousLinearMap_eq_iff_eq_toLinearMap, ModelWithCorners.continuousWithinAt, closure_open_halfSpace, CFC.log_monotoneOn, MeasureTheory.condExpIndL1_smul, Path.extend_range, Real.Angle.toCircle_coe, instContinuousNegElemSphereOfNat, UnitAddTorus.orthonormal_mFourier, BoundedContinuousFunction.instContinuousEvalConst, ZLattice.module_free, Unitization.norm_eq_sup, IsBoundedBilinearMap.hasFDerivWithinAt, RCLike.toCompleteSpace, ProbabilityTheory.isGaussian_map, instIsZLatticeRealSpan, Affine.Simplex.orthogonalProjection_circumcenter, Real.hasDerivAt_cos, ContinuousMap.toLp_norm_eq_toLp_norm_coe, GenLoop.fromLoop_symm_toLoop, Matrix.ofLp_toEuclideanCLM, Quaternion.expSeries_even_of_imaginary, NumberField.mixedEmbedding.convexBodySumFun_continuous, hasFTaylorSeriesUpToOn_succ_nat_iff_right, Fourier.fourierIntegral_const_smul, AffineSubspace.signedInfDist_eq_const_of_mem, summable_pow_div_add, HurwitzZeta.continuousOn_sinKernel, hasDerivAtFilter_iff_isLittleO, Absorbent.eventually_nhdsNE_zero, NormedSpace.expSeries_div_summable, ProbabilityTheory.HasSubgaussianMGF.integrable, IsStrictlyPositive.nnrpow, CStarMatrix.toCLM_apply_eq_sum, mahler_natCast_eq, PiTensorProduct.mapL_comp, PadicInt.coe_adicCompletionIntegersEquiv_apply, MeromorphicAt.eventually_continuousAt, exists_nat_bool_continuous_surjective_of_compact, summable_descFactorial_mul_geometric_of_norm_lt_one, Metric.frontier_ball_subset_sphere, OpenPartialHomeomorph.extend_symm_preimage_inter_range_eventuallyEq_aux, Submodule.norm_starProjection, OpenPartialHomeomorph.continuousOn_writtenInExtend_iff, differentiableOn_pow, isCompactOperator_iff_image_closedBall_subset_compact, Real.disjoint_residual_ae, HurwitzZeta.hurwitzZeta_residue_one, contMDiffWithinAt_iff_target_of_mem_source, tsum_choose_mul_geometric_of_norm_lt_one, HasFPowerSeriesWithinAt.sub, ClosedSubmodule.sup_orthogonal, FormalMultilinearSeries.isLittleO_one_of_lt_radius, ContinuousMap.sup_mem_subalgebra_closure, hasDerivAt_exp_smul_const, RCLike.continuous_re, LinearIsometryEquiv.completeSpace_map, NormedSpace.algebraMap_exp_comm, Meromorphic.fun_smul, Bundle.contMDiffWithinAt_totalSpace, MeasureTheory.weightedSMul_add_measure, Unitary.linearIsometryEquiv_coe_symm_apply, nhds_comap_dist, Asymptotics.isBigOTVS_neg_left, MeasureTheory.Measure.NullMeasurableSet.const_smul, mdifferentiableOn_iff_of_subset_source, WithCStarModule.pi_norm, contMDiffWithinAt_iff_source_of_mem_maximalAtlas, ContDiff.comp_continuousLinearMap, HasFiniteFPowerSeriesAt.eventually_zero_of_bound_zero, Orientation.oangle_neg_left, exists_dual_vector, NumberField.mixedEmbedding.det_basisOfFractionalIdeal_eq_norm, ContDiffMapSupportedIn.locallyConvexSpace, hasFDerivWithinAt_comp_smul_smul_iff, MeasureTheory.finStronglyMeasurable_iff_measurable, MeasureTheory.SimpleFunc.memLp_top, tsum_geometric_of_abs_lt_one, MeasureTheory.continuous_integral_integral, NumberField.mixedEmbedding.fundamentalCone.normAtAllPlaces_mem_fundamentalCone_iff, NonUnitalCommCStarAlgebra.toCompleteSpace, fourierCoeff_toLp, ContinuousLinearMap.rayleighQuotient_le_norm, RCLike.instContinuousStar, differentiableAt_const_add_iff, Real.continuous_logb, EReal.continuousOn_toReal, ContinuousLinearEquiv.comp_right_hasFDerivAt_iff, MeromorphicOn.divisor_fun_zpow, DifferentiableWithinAt.isBigOTVS_sub, LinearMap.isPositive_toContinuousLinearMap_iff, ContinuousLinearMap.norm_def, OrthogonalFamily.summable_of_lp, ProbabilityTheory.IsGaussian.charFunDual_eq, Real.hasDerivAt_half_log_one_add_div_one_sub_sub_sum_range, coe_fourierBasis, ProbabilityTheory.variance_continuousLinearMap_gaussianReal, Complex.tsum_exp_neg_quadratic, HasFPowerSeriesWithinOnBall.tendstoLocallyUniformlyOn', HasFPowerSeriesAt.apply_eq_zero, tendsto_measure_Icc_nhdsWithin_right, CFC.monotone_rpow, derivWithin_mul_const_field, Real.differentiableWithinAt_arcsin_Ici, InnerProductGeometry.norm_div_sin_angle_add_of_inner_eq_zero, logDeriv_apply, ContinuousLinearMap.le_opNorm_of_le, iteratedDeriv_comp_const_smul, ProbabilityTheory.covarianceBilin_eq_covarianceBilinDual, Affine.Simplex.exists_forall_dist_eq_iff_exists_excenterExists_and_eq_excenter, TangentBundle.trivializationAt_source, norm_inner_eq_norm_tfae, Real.circleAverage_def, ContinuousMultilinearMap.opNorm_pi, curveIntegral_fun_add, ProbabilityTheory.Kernel.density_ae_eq_limitProcess, ContinuousLinearEquiv.lipschitz, BumpCovering.continuous_toPOUFun, iteratedDeriv_vcomp_three, intervalIntegral.integral_smul, LinearIsometryEquiv.toContinuousLinearEquiv_symm, Submodule.isCompl_orthogonal_of_hasOrthogonalProjection, CuspForm.coe_translate, InformationTheory.klDiv_ne_top_iff, RCLike.sqrt_map, MeasureTheory.condExp_def, ProbabilityTheory.Kernel.IsFiniteKernel.integrable, Real.hasDerivWithinAt_arcsin_Ici, signedDist_vadd_right, UniqueDiffWithinAt.smul_iff, PiNat.completeSpace, curveIntegral_fun_neg, HasStrictDerivAt.hasStrictFDerivAt, PeriodPair.derivWeierstrassP_sub_coe, NumberField.Ideal.tendsto_norm_le_div_atTop₀, InnerProductSpace.instIsContPerfPairRealInnerₗOfCompleteSpace, Isometry.completion_extension, RCLike.inner_tmul_eq, Complex.isAddQuotientCoveringMap_exp, AnalyticAt.analyticOrderAt_eq_natCast, inr_comp_cfcₙHom_eq_cfcₙAux, not_sameRay_iff_of_norm_eq, CFC.rpow_neg_one_eq_cfc_inv, differentiableAt_finCons, InnerProductSpace.gramSchmidt_triangular, HasFTaylorSeriesUpToOn.continuousOn, OpenPartialHomeomorph.restrContDiff_symm_apply, NormedSpace.equicontinuous_TFAE, hasDerivAt_taylorWithinEval_succ, Submodule.starProjection_map_apply, CFC.monotoneOn_one_sub_one_add_inv_real, IsMIntegralCurveAt.hasMFDerivAt, polarCoord_symm_apply, MemHolder.smul, LinearMap.star_eq_adjoint, MeasureTheory.lpMeasSubgroupToLpTrim_sub, SpectrumRestricts.real_iff, Matrix.l2_opNNNorm_mul, hasSum_geometric_two, NormedAddGroupHom.isClosed_ker, contDiffWithinAt_succ_iff_hasFDerivWithinAt', DiffContOnCl.circleAverage_smul_div, HurwitzZeta.differentiableAt_completedHurwitzZetaEven, lp.ext_continuousAddMonoidHom_iff, Rat.uniformContinuous_abs, Real.tsum_le_of_sum_range_le, Complex.cosh_eq_tsum, IsLocalFrameOn.eventually_eq_sum_coeff_smul, Bundle.mdifferentiableOn_proj, contDiffOn_succ_iff_hasFDerivWithinAt, MeasureTheory.SimpleFunc.integrable_iff, fderivWithin_add_const, NormedSpace.expSeries_radius_eq_top, differentiableWithinAt_euclidean, ContinuousLinearMap.continuousWithinAt_uncurry_of_multilinear, HasSolidNorm.toTopologicalLattice, LinearMap.IsSymmetric.orthogonalComplement_iSup_eigenspaces_eq_bot', OpenPartialHomeomorph.univUnitBall_source, NumberField.mixedEmbedding.volume_preserving_mixedSpaceToRealMixedSpace_symm, intervalIntegral.integral_comp_div, Affine.Simplex.orthogonalProjection_eq_circumcenter_of_exists_dist_eq, LinearIsometryEquiv.coe_coe, ContinuousLinearMap.opNorm_add_le, InnerProductGeometry.norm_div_tan_angle_add_of_inner_eq_zero, AddCircle.ergodic_nsmul, tendsto_integral_mulExpNegMulSq_comp, Metric.dense_iff, ContinuousLinearMap.sSup_sphere_eq_norm, SmoothBumpCovering.embeddingPiTangent_injective_mfderiv, DoubleCentralizer.neg_toProd, ModelWithCorners.mdifferentiableAt, FormalMultilinearSeries.radius_unshift, aestronglyMeasurable_derivWithin_Ici, MeasureTheory.locallyIntegrable_const, NNReal.coe_tsum_of_nonneg, Complex.frontier_setOf_lt_im, Real.continuous_logb', HasFPowerSeriesAt.fderiv_eq, LinearPMap.adjointDomainMkCLM_apply, Orientation.oangle_sign_smul_left, MeasureTheory.integrable_mul_const_iff, deriv_abs_pos, MeromorphicOn.divisor_apply, Matrix.isPositive_toEuclideanLin_iff, ContDiffPointwiseHolderAt.continuousLinearMap_comp, ContinuousLinearMap.coe_restrictScalarsIsometry, TensorProduct.enorm_tmul, PartitionOfUnity.locallyFinite', HasFPowerSeriesOnBall.tendstoUniformlyOn, ContinuousLinearMap.norm_inr, ContinuousLinearMap.toLinearMap_eq_iff_eq_toContinuousLinearMap, MeasureTheory.setAverage_eq, ImplicitFunctionData.implicitFunction_apply, CPolynomialAt.continuousAt, SchwartzMap.smulLeftCLM_smulLeftCLM_apply, Submodule.starProjection_bot, ConvexBody.isBounded, exists_polynomial_near_continuousMap, iInter_halfSpaces_eq, NormedRing.inverse_add, Subadditive.tendsto_lim, NumberField.mixedEmbedding.fundamentalCone.hasFDerivAt_expMap, ZSpan.isAddFundamentalDomain', continuousMultilinearCurryFin0_apply, CStarMatrix.ofMatrix_eq_ofMatrixL, EuclideanGeometry.oangle_add_oangle_add_oangle_eq_pi, Complex.interior_reProdIm, geometric_hahn_banach_closed_compact, EuclideanGeometry.Sphere.inv_tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center, HurwitzZeta.differentiableAt_one_completedHurwitzZetaEven_sub_completedHurwitzZetaEven, HasGradientAt.differentiableAt, ValueDistribution.logCounting_add_top_eventuallyLE, ModelWithCorners.nonempty_interior, Path.isUniformEmbedding_coe, ContinuousMap.inf_mem_subalgebra_closure, ContDiffAt.hasStrictFDerivAt, PiTensorProduct.dualSeminorms_bounded, LinearMap.hasBasis_weakBilin, NormedSpace.exp_sum, unitInterval.symmHomeomorph_symm_apply, Conformal.differentiable, FormalMultilinearSeries.radius_neg, Real.tendsto_mul_log_one_add_div_atTop, Real.differentiableAt_cosh, ProbabilityTheory.Kernel.continuous_integral_integral, extDeriv_smul, MeasureTheory.Measure.toSignedMeasure_apply, homeomorphUnitSphereProd_symm_apply_coe, DomMulAct.smul_Lp_neg, spectrum.isClosed, ProbabilityTheory.covarianceBilin_self_nonneg, taylorWithinEval_succ, QuotientAddGroup.nhds_zero_hasBasis, SchwartzMap.toBoundedContinuousFunction_apply, WeakBilin.locallyConvexSpace, Submodule.orthogonal_closure, unitInterval.continuous_qRight, MeasureTheory.SignedMeasure.toJordanDecomposition_neg, LinearMap.IsSymmetric.orthogonalFamily_eigenspace_inf_eigenspace, TensorProduct.inner_assoc_assoc, ContinuousMultilinearMap.curryMidEquiv_apply, NormedAddGroupHom.completion_coe_to_fun, conformalAt_iff_isConformalMap_fderiv, StrictConvexSpace.strictConvex_closedBall, exists_msmooth_support_eq_eq_one_iff, Real.fourier_eq, ApproximatesLinearOn.lipschitz_sub, EuclideanQuadrant.convex, ContinuousMultilinearMap.iteratedFDeriv_eq, instOrderTopologyReal, Complex.closure_preimage_re, ContinuousMap.nnnorm_lt_iff_of_nonempty, FormalMultilinearSeries.le_mul_pow_of_radius_pos, ZSpan.norm_fract_le, ContinuousMap.inf_mem_closed_subalgebra, HasFPowerSeriesOnBall.isBigO_image_sub_image_sub_deriv_principal, Real.continuousAt_arcsin, iteratedDeriv_const_add, MeasureTheory.L2.real_inner_indicatorConstLp_one_indicatorConstLp_one, fderiv_sub_const, CFC.continuousOn_nnrpow, ContinuousLinearMap.opNorm_mulLeftRight_apply_le, ContinuousLinearMap.analyticOnNhd_bilinear, Polynomial.hermite_eq_deriv_gaussian', MDifferentiableAt.mfderiv, ContinuousLinearMap.reApplyInnerSelf_apply, ZSpan.fundamentalDomain_reindex, ContinuousLinearEquiv.comp_hasFDerivWithinAt_iff', BoundedContinuousFunction.tendsto_integral_of_forall_integral_le_liminf_integral, tendsto_ne_zero_of_meromorphicOrderAt_eq_zero, Orientation.oangle_sign_smul_add_smul_smul_add_smul, ProbabilityTheory.indepFun_iff_charFunDual_prod', Affine.Simplex.direction_mongePlane, DoubleCentralizer.algebraMap_snd, AddCircle.continuous_toCircle, SeminormFamily.withSeminorms_iff_uniformSpace_eq_iInf, MeasureTheory.integrable_of_integral_eq_one, WeakDual.polar_def, cfc_neg, MeasureTheory.integrable_toReal_of_lintegral_ne_top, MeasureTheory.Measure.integral_comp_mul_left, RCLike.wInner_const_left, AnalyticAt.analyticOrderNatAt_eq_iff, Complex.isOpenQuotientMap_pow, uniqueDiffWithinAt_Ioo, MeasureTheory.eLpNorm_const_smul_le', RCLike.wInner_cWeight_const_left, MonotoneOn.derivWithin_nonneg, HurwitzZeta.hasSum_int_sinKernel, ProperCone.innerDual_union, CompactlySupportedContinuousMap.integralLinearMap_apply, MeasureTheory.integrable_smul_const, NormedSpace.invOf_exp, hasFiniteFPowerSeriesOnBall_const, LinearMap.le_def, tangentBundle_model_space_coe_chartAt_symm, Circle.exp_add, MeasureTheory.integral_condExpL2_eq_of_fin_meas_real, Path.Homotopy.trans_apply, geometric_hahn_banach_open_open, iteratedFDerivWithin_succ_apply_left, ProbabilityTheory.measurable_measure_stieltjesOfMeasurableRat, Orientation.areaForm_comp_linearIsometryEquiv, hasStrictFDerivAt_norm_sq, Submodule.starProjection_unit_singleton, EuclideanGeometry.angle_const_add, SmoothPartitionOfUnity.coe_finsupport, SchwartzMap.fourier_evalCLM_eq, LinearIsometryEquiv.comp_differentiableWithinAt_iff, support_deriv_subset, tangentBundleModelSpaceHomeomorph_coe, MeromorphicAt.meromorphicAt_add_iff_meromorphicAt₂, LinearMap.adjoint_toSpanSingleton, DoubleCentralizer.one_snd, OrthonormalBasis.coe_toBasis, ContDiff.differentiable_iteratedDeriv, ProbabilityTheory.stronglyMeasurable_stieltjesOfMeasurableRat, Complex.interior_setOf_im_le, Real.tendsto_log_nhdsGT_zero, ContinuousMultilinearMap.cpolynomialAt_uncurry_of_linear, OpenPartialHomeomorph.unitBallBall_target, RCLike.norm_nsmul, Emetric.exists_contMDiffMap_forall_closedBall_subset, ContinuousMultilinearMap.norm_mkPiAlgebra, MeasureTheory.stronglyAdapted_predictablePart', BoxIntegral.Integrable.sum_integral_congr, Metric.PiNatEmbed.exists_closed_embedding_to_hilbert_cube, isLittleO_abs_log_rpow_rpow_nhdsGT_zero, EisensteinSeries.norm_le_tsum_norm, hasDerivWithinAt_natCast, MeromorphicOn.divisor_fun_mul, Asymptotics.superpolynomialDecay_iff_isLittleO, BumpCovering.nonneg', Real.deriv_exp, IsMIntegralCurveAt.continuousAt, MeromorphicOn.divisor_zpow, hasFDerivWithinAt_tangentCoordChange, ContinuousLinearEquiv.toSpanNonzeroSingleton_symm_apply, ENNReal.continuousAt_toReal, Orientation.oangle_sign_smul_sub_left, ContinuousWithinAt.nhdsWithin_extChartAt_symm_preimage_inter_range, ContinuousLinearEquiv.analyticOn, MeasureTheory.Lp.simpleFunc.denseRange, SchwartzMap.hasFDerivAt, ContinuousMultilinearMap.opNorm_add_le, fderiv_pow_ring', QuasispectrumRestricts.real_iff, MeasureTheory.memL1_smul_of_L1_withDensity, ContinuousLinearMap.bilinearComp_apply, analyticAt_iff_analytic_fun_smul, unitInterval.instTietzeExtension, MeasureTheory.condExp_ae_eq_condExpL1, ContinuousMultilinearMap.instContinuousEval, differentiableAt_piLp, ProbabilityTheory.integrable_comp_snd_map_prodMk_iff, Submodule.reflection_sub, differentiableWithinAtProp_self_source, MeasureTheory.Measure.toSphere_apply', NormedSpace.exp_conj', TemperedDistribution.instLineDerivSMulReal, iteratedDeriv_comp_neg, range_cfcₙ_nnreal_eq_image_cfcₙ_real, cot_series_rep, SchwartzMap.evalCLM_apply_apply, MDifferentiableWithinAt.mfderivWithin, EisensteinSeries.summable_one_div_norm_rpow, isClosed_cantorSet, upperHemicontinuous_quasispectrum, InnerProductGeometry.angle_smul_right_of_neg, Affine.Triangle.inv_tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_circumcenter, ClosedSubmodule.mem_orthogonal, ContinuousMultilinearMap.norm_restrictScalars, NormedRing.inverse_add_norm, UpperHalfPlane.ofComplex_apply_eq_ite, IsSelfAdjoint.sq_spectrumRestricts, DiffContOnCl.smul_const, MeasureTheory.IsAddFundamentalDomain.hasFiniteIntegral_on_iff, Matrix.posDef_iff_eq_conjTranspose_mul_self, MeasureTheory.condExpIndL1_smul', Polynomial.differentiableAt_aeval, MeasureTheory.Measure.toTemperedDistribution_apply, WeakDual.CharacterSpace.compContinuousMap_apply, Subalgebra.frontier_subset_frontier, tendsto_integral_exp_smul_cocompact_of_inner_product, lipschitzOnWith_cfcₙ_fun, TangentBundle.chartAt, HurwitzZeta.completedCosZeta_residue_zero, LinearMap.re_inner_adjoint_mul_self_nonneg, hasDerivAt_id, Diffeomorph.contDiff, differentiable_pi, contDiff_smul_const, HasFTaylorSeriesUpToOn.fderivWithin, Real.hasDerivAt_rpow_const, CStarMatrix.toCLM_apply, ContinuousLinearEquiv.hasFDerivWithinAt, ContDiffAt.restrictScalars_iteratedFDeriv_eventuallyEq, InnerProductGeometry.angle_add_lt_pi_div_two_of_inner_eq_zero, ContinuousMultilinearMap.isLeast_opNNNorm, BoxIntegral.integralSum_biUnionTagged, Orientation.oangle_rotation_right, InnerProductSpace.nullSubmodule_le_ker_toDualMap_left, DoubleCentralizer.algebraMap_toProd, Real.tendsto_log_nhdsLT_zero, MeasureTheory.Integrable.re_im_iff, Path.Homotopy.continuous_reflTransSymmAux, ContinuousLinearEquiv.comp_right_hasFDerivWithinAt_iff, LinearMap.isPositive_self_comp_adjoint, EisensteinSeries.isBoundedAtImInfty_eisensteinSeries_SIF, RCLike.hasSum_conj, tendsto_ne_zero_iff_meromorphicOrderAt_eq_zero, differentiableAt_norm_smul, instModuleFinite_of_discrete_submodule, FormalMultilinearSeries.id_comp, circleIntegral.integral_smul, MeasureTheory.SignedMeasure.singularPart_neg, ContinuousLinearMap.norm_map_tail_le, continuous_coe_real_ereal, deriv_update, UpperHalfPlane.qParam_tendsto_atImInfty, Real.circleAverage_eq_integral_add, HasFPowerSeriesAt.restrictScalars, Real.iter_deriv_exp, contMDiffOn_symm_coordChangeL, tangentBundleCore_coordChange_model_space, intervalIntegral.inv_smul_integral_comp_div_sub, Module.Basis.prod_parallelepiped, summable_dirichletSummand, ContinuousLinearMap.instStarModuleId, IsLocalFrameOn.contMDiffAt, BoundedContinuousFunction.mem_Lp, ContDiff.smul_const, iteratedFDerivWithin_comp_add_right, Real.differentiable_iteratedDeriv_cos, NonUnitalSeminormedRing.toIsTopologicalRing, MeasureTheory.eLpNorm'_congr_nnnorm_ae, lp.coeFn_sum, Polynomial.hasFDerivAt_aeval, EuclideanGeometry.orthogonalProjection_affineSpan_singleton, LinearIsometryEquiv.toLinearEquiv_lTensor, MeasureTheory.lpMeasSubgroupToLpTrim_right_inv, DoubleCentralizer.instIsCentralScalar, InnerProductGeometry.angle_add_pos_of_inner_eq_zero, NormedField.continuousAt_inv, NormedSpace.polar_closure, ContDiffAt.restrictScalars_iteratedFDeriv, IsUnit.cfcNNRpow, exists_dual_vector'', ContinuousLinearMapWOT.instContinuousSMul, exists_msmooth_zero_iff_one_iff_of_isClosed, BoundedContinuousFunction.continuous_coe, deriv_zpow', PiTensorProduct.injectiveSeminorm_apply, InnerProductGeometry.tan_angle_add_of_inner_eq_zero, Homeomorph.unitBall_apply_coe, UniformSpace.Completion.norm_coe, ContinuousLinearMap.isBoundedLinearMap_comp_left, PartitionOfUnity.sum_finsupport_smul_eq_finsum, ModelWithCorners.map_nhds_eq, LeftInvariantDerivation.map_add, Real.continuous_sinh, BoundedContinuousFunction.Lp_norm_le, ProbabilityTheory.IsGaussian.memLp_dual, Complex.isConnected_of_upperHalfPlane, AnalyticOnNhd.codiscreteWithin_setOf_analyticOrderAt_eq_zero_or_top, NormedSpace.exp_units_conj', norm_fderiv_iteratedFDeriv, Complex.differentiable_sin, MeasureTheory.SignedMeasure.haveLebesgueDecomposition_smul_real, isConnected_setOf_sameRay_and_ne_zero, curveIntegralFun_neg, Real.continuousOn_exp, ZetaAsymptotics.term_tsum_one, Complex.continuous_normSq, DomAddAct.vadd_Lp_ae_eq, binomialSeries_radius_eq_top_of_nat, MeasureTheory.Lp.norm_constL_le, PeriodPair.weierstrassP_add_coe, meromorphicOrderAt_smul, Asymptotics.isLittleOTVS_map, isTheta_deriv_rpow_const_atTop, ProbabilityTheory.covarianceBilinDual_self_nonneg, IccLeftChart_extend_bot, conformalFactorAt_inner_eq_mul_inner', NumberField.mixedEmbedding.stdBasis_apply_isComplex_fst, hasFDerivAtFilter_snd, ContinuousAlternatingMap.fderivCompContinuousLinearMapCLM_apply, hasFDerivAt_pow, BoundedContinuousFunction.mkOfCompact_neg, TemperedDistribution.fourier_lineDerivOp_eq, convexHull_sphere_eq_closedBall, NumberField.mixedEmbedding.fundamentalCone.continuous_expMapBasis, Matrix.l2_opNNNorm_def, ContinuousMultilinearMap.instIsBoundedSMul, isOpen_deltaGenerated_iff, cfcₙHom_isClosedEmbedding, MeasureTheory.charFunDual_map_const_add, ContinuousMultilinearMap.iteratedFDeriv_comp_diagonal, extChartAt_target_eventuallyEq', Metric.mem_closure_range_iff, hasDerivAtFilter_sub_const_iff, tendsto_smoothingFun_of_map_one_le_one, Real.Angle.sign_two_nsmul_eq_sign_iff, MeasureTheory.charFunDual_map_add_const, Filter.tendsto_inv₀_nhdsWithin_ne_zero, spectrum.hasDerivAt_resolvent, ContinuousLinearMap.adjointAux_adjointAux, ImplicitFunctionData.differentiableAt_implicitFunction, Module.Basis.addHaar_eq_iff, PeriodPair.instProperSpaceSubtypeComplexMemSubmoduleIntLattice, FiberBundle.extChartAt, ContDiffMapSupportedIn.seminorm_le_iff_withOrder, MeasureTheory.Lp.simpleFunc.neg_toSimpleFunc, Polynomial.deriv_gaussian_eq_hermite_mul_gaussian, LinearMap.polar_gc, Orientation.rotation_trans, dslope_same, NormedAddCommGroup.tendsto_nhds_nhds, hasDerivAt_exp, Meromorphic.fun_add, Submodule.orthogonalProjection_apply_eq_linearProjOfIsCompl, ZSpan.span_top, DomMulAct.norm_smul_Lp, uniqueDiffWithinAt_Ioi, ModularForm.coeHom_apply, Path.continuous_uncurry_iff, analyticOrderAt_add_eq_right_of_lt, MeasureTheory.Measure.toSignedMeasure_add, hasFDerivAt_single, LeftInvariantDerivation.coe_add, signedDist_lineMap_left, MeasureTheory.condExpL2_indicator_of_measurable, LinearMap.IsSymmetric.orthogonalComplement_iSup_eigenspaces_eq_bot, Complex.hasDerivAt_logTaylor, Orientation.continuousAt_oangle, DirichletCharacter.differentiable_LFunction, ProbabilityTheory.covarianceBilin_real_self, iteratedDeriv_vcomp_eq_sum_orderedFinpartition, LinearMap.eq_adjoint_iff, MeasureTheory.Lp.add_smul, MeasureTheory.martingalePart_add_predictablePart, MeasureTheory.setIntegral_condExpL1CLM_of_measure_ne_top, iteratedDerivWithin_cot_pi_mul_eq_mul_tsum_zpow, nnnorm_cfcₙ_nnreal_lt_iff, Real.tendsto_rightDeriv_mul_log_atTop, OpenPartialHomeomorph.restrContDiff_source, Real.hasStrictDerivAt_arsinh, ModularForm.slash_action_eq'_iff, circleMap_preimage_codiscrete, PositiveLinearMap.gnsStarAlgHom_apply, iter_deriv_pow', SchwartzMap.tsupport_iteratedLineDerivOp_subset, MeasureTheory.integral_comp_rpow_Ioi, ContinuousAlternatingMap.toAlternatingMap_alternatizeUncurryFin, ContDiff.contMDiff, EuclideanGeometry.dist_sq_eq_dist_orthogonalProjection_sq_add_dist_orthogonalProjection_sq, bernsteinApproximation.apply_one, hasDerivAt_iff_tendsto_slope_zero, ConvexOn.convex_re_epigraph, EulerProduct.summable_and_hasSum_factoredNumbers_prod_filter_prime_geometric, tendsto_self_mul_const_pow_of_abs_lt_one, uniformity_dist, Complex.lintegral_comp_polarCoord_symm, SmoothPartitionOfUnity.sum_le_one', Asymptotics.isLittleOTVS_iff_isLittleO, Int.tendsto_zmultiplesHom_cofinite, OrthonormalBasis.tensorProduct_apply', ValueDistribution.characteristic_sub_characteristic_inv, integrable_rpow_mul_exp_neg_mul_sq, ImplicitFunctionData.hasStrictFDerivAt, Nat.isClosedEmbedding_coe_rat, NumberField.mixedEmbedding.span_latticeBasis, tsum_geometric_two', DomAddAct.vadd_Lp_sub, SchwartzMap.integral_pow_mul_iteratedFDeriv_le, zero_cpow_eq_nhds, WeakFEPair.hf_zero, LinearIsometry.norm_toContinuousLinearMap_comp, hasStrictFDerivAt_inv, Metric.continuousAt_iff', MeromorphicAt.eventually_analyticAt, BoundedContinuousFunction.coeFn_toLp, ContinuousLinearMap.isBigOWith_comp, HurwitzKernelBounds.summable_f_nat, ContinuousLinearMap.flip_add, ProbabilityTheory.IsCondKernelCDF.measurable, hasFiniteFPowerSeriesAt_const, MeasureTheory.IntegrableOn.finset, Circle.leftInverse_exp_arg, continuous_clm_apply, ContinuousLinearMap.hasTemperateGrowth, Orientation.nonneg_inner_and_areaForm_eq_zero_iff_sameRay, TestFunction.coe_add, Seminorm.uniformContinuous, Complex.continuousAt_ofReal_cpow, Subalgebra.spectrum_isBounded_connectedComponentIn, MeromorphicOn.eventually_codiscreteWithin_analyticAt, InformationTheory.klDiv_eq_integral_klFun, Orientation.oangle_sub_right_smul_rotation_pi_div_two, EuclideanGeometry.continuousAt_angle, AnalyticAt.eventually_constant_or_nhds_le_map_nhds_aux, MeasureTheory.hasFiniteIntegral_iff_ofReal, integrable_mul_exp_neg_mul_sq, LinearMap.isPositive_iff_complex, cfcₙHom_le_iff, bernstein_nonneg, VectorFourier.fourierSMulRight_apply, tendsto_fib_div_fib_succ_atTop, ContinuousLinearEquiv.isBigO_sub_rev, deriv_neg'', ContinuousLinearMap.isSelfAdjoint_iff', Submodule.sndL_comp_coe_orthogonalDecomposition, DoubleCentralizer.pow_toProd, UnitAddTorus.instContinuousSMulComplexSubtypeAEEqFunVolumeMemAddSubgroupLp, OrthonormalBasis.equiv_apply_euclideanSpace, measurable_fderiv_apply_const, MeasureTheory.Lp.instContinuousVAddDomAddAct, RCLike.continuous_ofReal, stereographic_neg_apply, StrongConcaveOn.strictConcaveOn, TemperedDistribution.lineDerivOp_toTemperedDistributionCLM_eq, NormedRing.inverse_add_norm_diff_second_order, MeasureTheory.Measure.addHaar_image_linearMap, continuousAt_gauge_zero, ProbabilityTheory.tendsto_stieltjesOfMeasurableRat_atBot, MeasureTheory.withDensityᵥ_neg, IsLocalFrameOn.coeff_apply_of_notMem, MeasureTheory.tendsto_ae_condExp, isSelfAdjoint_starProjection, BumpCovering.exists_finset_toPartitionOfUnity_eventuallyEq, InnerProductSpace.gramSchmidt_def', MeasureTheory.condExpL2_indicator_eq_toSpanSingleton_comp, Real.Angle.sin_add, NumberField.mixedEmbedding.fundamentalCone.expMap_symm_apply, GromovHausdorff.eq_toGHSpace, ContinuousMultilinearMap.uncurryRight_apply, instIsRiemannianManifoldModelWithCornersSelfReal, PartitionOfUnity.locallyFinite_tsupport, OpenPartialHomeomorph.extend_preimage_mem_nhds, eventually_norm_symmL_trivializationAt_self_comp_lt, SchwartzMap.instContinuousMapClass, Real.stronglyMeasurable_sinc, NumberField.mixedEmbedding.polarCoord_source, MeasureTheory.condExpL1CLM_indicatorConst, summable_of_ratio_norm_eventually_le, nnnorm_cfc_nnreal_lt, SmoothBumpCovering.embeddingPiTangent_ker_mfderiv, isSelfAdjoint_iff_isStarNormal_and_quasispectrumRestricts, SmoothBumpFunction.isClosed_image_of_isClosed, UpperHalfPlane.J_smul, fderiv_inv, MeasureTheory.mem_lpMeasSubgroup_toLp_of_trim, MeromorphicAt.fun_deriv, Asymptotics.isLittleO_norm_pow_norm_pow, Real.continuous_log', NormedSpace.normalize_smul_of_neg, ModelWithCorners.hasMFDerivWithinAt, tangentBundleCore_coordChange, derivWithin_comp_mul_left, SmoothPartitionOfUnity.sum_nonneg, ProbabilityTheory.Kernel.tendsto_densityProcess_fst_atTop_univ_of_monotone, MeasureTheory.L1.nnnorm_Integral_le_one, MeasureTheory.L1.SimpleFunc.integrable, Manifold.riemannianEDist_def, hasDerivAt_circleMap, instNonemptyElemWeakDualComplexCharacterSpaceOfNontrivial, curveIntegralFun_fun_zero, ProbabilityTheory.IsRatCondKernelCDFAux.tendsto_zero_of_antitone, Real.one_div_one_sub_rpow_hasFPowerSeriesOnBall_zero, MeasureTheory.ProbabilityMeasure.continuous_integral_boundedContinuousFunction, ContinuousLinearMap.bilinearComp_zero, MeasureTheory.integral_fun_norm_addHaar, MeasureTheory.lpMeasSubgroupToLpTrim_add, MeasureTheory.L1.integral_eq_norm_posPart_sub, signedDist_anticomm, MeasureTheory.Lp.instContinuousFourierInv, Metric.tendstoUniformlyOn_iff, BumpCovering.locallyFinite_tsupport, ZSpan.map, IsOpen.measure_eq_biSup_integral_continuous, PartitionOfUnity.continuous_finsum_smul, Unitary.openPartialHomeomorph_target, continuousAt_gauge, iteratedDeriv_eq_equiv_comp, SchwartzMap.smulLeftCLM_add, MeasureTheory.weightedSMul_smul, ContinuousLinearEquiv.norm_symm_pos, Submodule.sInf_orthogonal, Metric.closedBall_zero', norm_deriv_le_of_lipschitz, extChartAt_image_nhds_mem_nhds_of_boundaryless, UnitAddTorus.hasSum_mFourier_series_L2, CFC.rpow_le_rpow, Real.continuousAt_rpow_of_ne, ContinuousMultilinearMap.cpolynomialAt, MultilinearMap.mkContinuousLinear_norm_le', Real.taylor_tendsto, MeasureTheory.Lp.norm_const, ContinuousLinearMap.NonlinearRightInverse.right_inv, norm_fderivWithin_iteratedFDerivWithin, HasFTaylorSeriesUpToOn.shift_of_succ, TemperedDistribution.laplacian_eq_sum, MeasureTheory.eLpNorm_indicator_le_of_bound, tendsto_uniformity_iff_dist_tendsto_zero, curveIntegralFun_def', NumberField.mixedEmbedding.stdBasis_repr_eq_matrixToStdBasis_mul, NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_apply, WithCStarModule.pi_inner, MeasureTheory.instCompleteSpaceSubtypeAEEqFunMemAddSubgroupLpSubmoduleLpMeasOfFactLeMeasurableSpace, Orientation.areaForm_comp_rightAngleRotation, MeasureTheory.eLpNorm_neg, NumberField.mixedEmbedding.continuous_norm, IsMIntegralCurve.continuous, uniqueDiffOn_Icc_zero_one, AnalyticAt.add, MeasureTheory.lpNorm_nsmul, Bundle.contMDiffWithinAt_proj, ContinuousMap.instCStarRing, Polynomial.div_tendsto_leadingCoeff_div_of_degree_eq, MeasureTheory.ComplexMeasure.HaveLebesgueDecomposition.rePart, Submodule.isOrtho_span, IsStrictlyPositive.sqrt, MeasureTheory.lpMeasSubgroupToLpTrim_left_inv, contDiffOn_fderiv_coord_change, ContinuousLinearEquiv.continuousMultilinearMapCongrRight_symm, HasFPowerSeriesWithinAt.differentiableWithinAt, instIsTopologicalAddTorsor_1, tendsto_log_div_rpow_nhdsGT_zero, ZSpan.exist_unique_vadd_mem_fundamentalDomain, Real.tendsto_logb_nhdsNE_zero_of_base_lt_one, ContinuousMultilinearMap.ratio_le_opNorm, ContDiff.iterate_deriv, ZSpan.fundamentalDomain_subset_parallelepiped, Complex.continuousOn_tan, ContinuousLinearEquiv.subsingleton_or_nnnorm_symm_pos, not_summable_indicator_mod_of_antitone_of_neg, ZetaAsymptotics.zeta_limit_aux1, ContinuousLinearMap.norm_extendTo𝕜'_bound, sum_mem_ball_of_strictConvexSpace, ContinuousLinearEquiv.comp_hasFDerivWithinAt_iff, ContinuousAlternatingMap.toContinuousMultilinearMapCLM_comp_fderivCompContinuousLinearMap, ProbabilityTheory.measurable_stieltjesOfMeasurableRat, Quaternion.normSq_exp, Real.differentiableAt_arctan, le_egauge_smul_right, Matrix.PosSemidef.isUnit_sqrt_iff, unitary.joined, uniqueDiffWithinAt_Iio, SeminormFamily.basisSets_smul, hasDerivAt_iff_hasFDerivAt, MultilinearMap.continuous_of_bound, ZeroAtInftyContinuousMap.instCompleteSpace, CurveIntegrable.refl, IsSelfAdjoint.exp_nonneg, ContDiff.deriv', MeasureTheory.lintegral_nnnorm_condExpL2_indicator_le_real, ModelWithCorners.image_mem_nhdsWithin, HasFiniteFPowerSeriesOnBall.neg, RCLike.conj_tsum, derivWithin_intCast, ContinuousMapZero.norm_def, IsUltrametricDist.nnnorm_tsum_le_of_forall_le, ProbabilityTheory.exponentialCDFReal_eq_integral, differentiableWithinAt_abs_neg, ProbabilityTheory.stieltjesOfMeasurableRat_eq, TemperedDistribution.instContinuousLineDeriv, LinearMap.weakBilin_withSeminorms, Real.differentiableOn_negMulLog, cfc_eq_cfcL_mkD, norm_derivWithin_eq_norm_fderivWithin, ModularForm.differentiableAt_eta_of_mem_upperHalfPlaneSet, differentiableWithinAt_dslope_of_ne, iteratedFDeriv_zero_apply, LinearMap.polar_weak_closed, Real.convex_iff_isPreconnected, ContinuousLinearMap.le_def, Metric.closure_ball_subset_closedBall, ProbabilityTheory.integrable_exp_mul_gaussianReal, hasGradientAt_iff_tendsto, WeakDual.isClosed_closedBall, Real.Angle.two_zsmul_eq_iff, contDiff_succ_iff_fderiv_apply, cfcₙ_real_eq_nnreal, hasDerivAt_fourier, ProbabilityTheory.cdf_expMeasure_eq_integral, coe_lpPiLpₗᵢ, OpenPartialHomeomorph.contDiff_univBall, closure_zero_eq, ProbabilityTheory.instIsProbabilityMeasureCondCDF, Complex.continuousAt_cpow_zero_of_re_pos, NumberField.mixedEmbedding.polarSpaceCoord_symm_apply, stdSimplexHomeomorphUnitInterval_apply_coe, VectorBundleCore.localTriv_apply, SeparationQuotient.norm_liftNormedAddGroupHom_le, Complex.measurableEquivRealProd_symm_polarCoord_symm_apply, Orientation.oangle_add_cyc3, MeasureTheory.integrable_add_const_iff, MeasureTheory.Lp.simpleFunc.memLp, Besicovitch.ae_tendsto_measure_inter_div, LinearMap.isPositive_zero, DoubleCentralizer.zero_fst, Real.summable_one_div_nat_rpow, EuclideanGeometry.Sphere.direction_orthRadius_le_iff, LinearIsometryEquiv.coe_coe'', NumberField.mixedEmbedding.fundamentalCone.norm_normAtAllPlaces, MeasureTheory.integrable_comp_mul_left_iff, fderiv_update, Complex.instCompleteSpace, Metric.continuousWithinAt_iff, ContinuousLinearMap.IsPositive.re_inner_nonneg_left, MeasureTheory.ProbabilityMeasure.tendsto_iff_forall_integral_rclike_tendsto, Metric.sphere.instContinuousMul, Real.rightDeriv_mul_log, ProbabilityTheory.Kernel.integrable_density, nnnorm_cfc_nnreal_le, ContinuousLinearMap.measurable_comp, ZMod.LFunction_def_even, Metric.uniformity_basis_dist_le, ValueDistribution.characteristic_sum_top_le, BoxIntegral.BoxAdditiveMap.toSMul_apply, ProbabilityTheory.IsGaussian.map_rotation_eq_self, ContinuousLinearEquiv.coord_toSpanNonzeroSingleton, ProbabilityTheory.hasFiniteIntegral_prodMk_left, Complex.one_div_sub_pow_hasFPowerSeriesOnBall_zero, MeasureTheory.Lp.instAddLeftMono, IsSelfAdjoint.norm_eq_max_norm_posPart_negPart, fdifferential_comp, CStarMatrix.mul_entry_mul_eq_inner_toCLM, Real.continuousOn_sin, continuous_inner, homeomorphSphereProd_symm_apply_coe, ContinuousMap.HomotopyWith.extendProp, modelWithCornersSelf_prod, ModularFormClass.differentiableAt_cuspFunction, fourier_apply, Bundle.contMDiffAt_totalSpace, Diffeomorph.uniqueDiffOn_image, ContinuousLinearMap.le_opNorm₂, ContinuousLinearMap.lpPairing_eq_integral, Matrix.coe_toEuclideanCLM_eq_toEuclideanLin, ProbabilityTheory.isGaussian_iff_gaussian_charFunDual, Seminorm.continuous_iff, ContinuousLinearMap.norm_iteratedFDeriv_comp_left, ContinuousLinearMap.norm_uncurryMid, EuclideanGeometry.continuousAt_oangle, QuadraticForm.equivalent_sum_squares, Real.Angle.two_nsmul_toReal_eq_two_mul_add_two_pi, MeasureTheory.Lp.simpleFunc.norm_toSimpleFunc, RCLike.wInner_const_right, InnerProductSpace.rankOne_def', ContDiff.fderiv_apply, EuclideanGeometry.eq_or_eq_reflection_of_dist_eq, SchwartzMap.tendsto_cocompact, ContinuousLinearMap.opNorm_mul_le, LeftInvariantDerivation.coe_injective, ContinuousLinearMap.uncurryLeft_norm, Real.Angle.sign_pi_add, MeromorphicOn.divisor_restrict, hasFDerivAtFilter_fst, Metric.mk_uniformity_basis_le, Submodule.isClosed_orthogonal, ContinuousMap.Homotopy.curry_apply, differentiableWithinAt_comp_add_right, IndiscreteTopology.of_forall_nnnorm_eq_zero', ContinuousLinearMap.opNorm_subsingleton, mellin_eq_fourierIntegral, DeltaGeneratedSpace.isOpen_iff, hasStrictDerivAt_abs_neg, Orientation.inner_rightAngleRotation_left, Orientation.cos_oangle_add_right_of_oangle_eq_pi_div_two, ContinuousLinearMap.holder_smul_right, NormedSpace.exp_hasFPowerSeriesAt_zero, WithSeminorms.continuous_seminorm, HasFPowerSeriesOnBall.tendstoUniformlyOn', SchwartzMap.instBoundedContinuousMapClass, HasFPowerSeriesWithinOnBall.const_smul, PadicInt.continuousAddCharEquiv_of_norm_mul_symm_apply, InnerProductGeometry.angle_eq_angle_add_angle_iff, cfcHomSuperset_apply, NumberField.InfinitePlace.Completion.isClosed_image_extensionEmbedding_of_isReal, fderiv_apply_one_eq_deriv, ContinuousAlternatingMap.nnnorm_ofSubsingleton_id, HurwitzZeta.hasSum_nat_completedSinZeta, ProbabilityTheory.norm_uncenteredCovarianceBilinDual_le, NormedField.tendsto_norm_inv_nhdsNE_zero_atTop, GromovHausdorff.instCompleteSpaceGHSpace, MeasureTheory.stronglyMeasurable_llr, HasFTaylorSeriesUpToOn.compContinuousLinearMap, nnnorm_cfc_nnreal_le_iff, integrableOn_exp_mul_complex_Iic, HasFPowerSeriesOnBall.sub, SchwartzMap.integral_sesq_fourierIntegral_eq, MeromorphicAt.add, contDiffAt_succ_iff_hasFDerivAt, ContinuousLinearMap.IsPositive.inner_nonneg_left, Real.fourierIntegral_eq', Real.circleAverage_fun_smul, ContinuousLinearMap.apply_norm_eq_sqrt_inner_adjoint_left, MeasureTheory.L2.eLpNorm_inner_lt_top, LinearMap.adjoint_lTensor, Complex.frontier_setOf_le_re, OpenPartialHomeomorph.contDiffOn_restrContDiff_source, EuclideanGeometry.orthogonalProjection_vadd_smul_vsub_orthogonalProjection, MeasureTheory.Measure.measurePreserving_homeomorphUnitSphereProd, MeasureTheory.integrable_withDensity_iff_integrable_smul, ProbabilityTheory.paretoCDFReal_eq_integral, isPathConnected_stdSimplex, Polynomial.Chebyshev.isLocalExtr_T_real_iff, BoxIntegral.integralSum_fiberwise, norm_inner_div_norm_mul_norm_eq_one_of_ne_zero_of_ne_zero_mul, Quaternion.im_exp, LinearMap.toMatrixOrthonormal_apply, hasFPowerSeriesOn_cauchy_integral, MeasureTheory.condExpL1CLM_lpMeas, measurableSet_of_differentiableAt, Module.Basis.coe_parallelepiped, ProbabilityTheory.IsRatCondKernelCDF.tendsto_atBot_zero, Submodule.isSymmetricProjection_starProjection, UpperHalfPlane.contMDiff_denom_zpow, CFC.sqrt_sq, AntitoneOn.memLp_of_measure_ne_top, ContractingWith.tendsto_iterate_fixedPoint, cfcₙHom_eq_cfcₙ_extend, SmoothBumpCovering.exists_finset_toSmoothPartitionOfUnity_eventuallyEq, ContinuousLinearMap.mdifferentiableWithinAt, SeparatingDual.completeSpace_continuousLinearMap_iff, IsUltrametricDist.isOpen_closedBall, contDiffOn_tsum_cexp, convex_halfSpace_re_ge, OrthogonalFamily.inner_sum, NormedDivisionRing.to_continuousInv₀, EuclideanGeometry.inversion_def, deriv_circleMap, range_cfc_eq_range_cfcHom, InnerProductSpaceable.parallelogram_identity, LinearMap.IsPositive.smul_of_nonneg, ValueDistribution.characteristic_add_top_le, NormedSpace.vonNBornology_eq, NormedAddCommGroup.exists_norm_nsmul_le, PeriodPair.latticeBasis_one, ZeroAtInftyContinuousMap.norm_toBCF_eq_norm, ProbabilityTheory.exp_neg_integrableOn_Ioc, GromovHausdorff.ghDist_le_nonemptyCompacts_dist, MeasureTheory.Lp.mem_Lp_iff_memLp, curveIntegral_symm, ZeroAtInftyContinuousMap.instCStarRing, SchwartzMap.integral_bilinear_laplacian_right_eq_left, ClosedSubmodule.mem_orthogonal_toSubmodule_iff, instContinuousNegElemClosedBallOfNat, iteratedDeriv_fun_const_smul_field, IsBoundedLinearMap.hasFDerivAtFilter, EuclideanSpace.inner_eq_star_dotProduct, CauSeq.tendsto_limit, ZLattice.covolume_eq_det_mul_measureReal, hasDerivWithinAt_const, AnalyticOnNhd.continuousOn, FormalMultilinearSeries.compAlongComposition_norm, Polynomial.tendsto_nhds_iff, ContinuousLinearMap.isometry_mul, map_extChartAt_nhds', intervalIntegral.integral_comp_sub_mul, MeasureTheory.Submartingale.stoppedValue_leastGE_eLpNorm_le, MeasureTheory.hasFiniteIntegral_norm_iff, Circle.argEquiv_symm_apply, ContinuousLinearMap.isOpen_injective, MeasureTheory.eLpNorm_indicator_sub_indicator, isCoveringMapOn_npow, mdifferentiableWithinAt_iff', ContDiff.continuous_iteratedFDeriv', Real.tendsto_exp_atBot, AddCircle.toCircle_apply_mk, Rat.totallyBounded_Icc, OrthonormalBasis.sum_repr_symm, Metric.ball_mem_nhds, homeomorphUnitSphereProd_apply_fst_coe, CFC.rpow_sqrt_nnreal, tendsto_rpow_neg_nhdsGT_zero, MeasureTheory.Supermartingale.stronglyMeasurable, MeasureTheory.unifTight_iff_ennreal, Real.Angle.two_nsmul_eq_pi_iff, LeftInvariantDerivation.coe_neg, Complex.hasStrictDerivAt_cos, Trivialization.contMDiffOn_section_baseSet_iff, LipschitzWith.ae_differentiableAt, Orientation.kahler_apply_self, Complex.frontier_setOf_re_lt, MeasureTheory.Lp.const_mem_Lp, LinearMap.mkContinuous_coe, PeriodPair.weierstrassP_sub_coe, Real.differentiableWithinAt_arcsin_Iic, signedDist_triangle_right, Polynomial.hermite_eq_deriv_gaussian, UniqueMDiffOn.tangentBundle_proj_preimage, Affine.Simplex.orthogonalProjectionSpan_faceOpposite_eq_point_rev, curveIntegral_refl, NormedSpace.exp_nsmul, ContDiffAt.laplacian_add_nhds, Orientation.inner_smul_rotation_pi_div_two_right, DoubleCentralizer.sub_toProd, formalMultilinearSeries_geometric_apply_norm, OpenPartialHomeomorph.extend_target_eventuallyEq, ZSpan.instDiscreteTopologySubtypeMemSubmoduleIntSpanRangeCoeBasisRealOfFinite, HasFiniteFPowerSeriesOnBall.continuousOn, ContinuousLinearMap.continuous_uncurry_of_multilinear, Complex.analyticOn_univ_iff_differentiable, Valued.integer.coe_span_singleton_eq_closedBall, EReal.tendsto_coe, UniformConcaveOn.concaveOn, Complex.conjCLE_nnorm, differentiable_const_add_iff, Polynomial.differentiableOn, Path.Homotopy.cast_apply, Pi.orthonormalBasis.toBasis, hasSum_geom_series_inverse, LinearIsometry.map_starProjection, IsLocalFrameOn.coeff_apply_zero_at, TangentBundle.continuousLinearMapAt_trivializationAt, contMDiffWithinAt_comp_projIcc_iff, Orientation.inner_mul_areaForm_sub', constFormalMultilinearSeries_apply_of_nonzero, hasFDerivAt_polarCoord_symm, fourierIntegral_gaussian_innerProductSpace, egauge_ball_one_le_of_one_lt_norm, HasFTaylorSeriesUpToOn.add, NormedSpace.norm_expSeries_summable', continuous_norm', le_analyticOrderAt_add, tangentBundle_model_space_chartAt, TangentBundle.mem_chart_target_iff, AnalyticWithinAt.continuousWithinAt_insert, formalMultilinearSeries_geometric_eq_ofScalars, Real.continuous_exp, isQuotientCoveringMap_zpow, Real.circleAverage_smul, NumberField.mixedEmbedding.mixedSpaceToRealMixedSpace_apply, MeasureTheory.integrable_comp_sub_left, differentiableOn_neg, ContDiffMapSupportedIn.isUniformEmbedding_pi_structureMapCLM, ZSpan.isAddFundamentalDomain, ContinuousLinearMap.isSelfAdjoint_toLinearMap_iff, MeasureTheory.eLpNorm_congr_nnnorm_ae, ContinuousMap.Homotopy.extend_apply_of_mem_I, EuclideanGeometry.dist_orthogonalProjection_eq_infNndist, LinearMap.continuous_of_nonzero_on_open, Submodule.inf_orthogonal, MeasureTheory.HasFiniteIntegral.of_mem_Icc, intervalIntegral.intervalIntegrable_exp, curveIntegral_trans, ConvexOn.real_univ_sSup_affine_eq, MeasureTheory.SignedMeasure.toComplexMeasure_apply_re, MeasureTheory.weightedSMul_union, ProbabilityTheory.hasDerivAt_neg_exp_mul_exp, Real.deriv_arcsin, Complex.isBigO_im_sub_im, Metric.exists_isCompact_closedBall, mdifferentiableAt_iff_target_of_mem_source, hasSum_coe_mul_geometric_of_norm_lt_one, gronwallBound_continuous_ε, abs_signedDist_eq_dist_iff_vsub_mem_span, InnerProductSpace.innerSL_norm, MeasureTheory.uniformIntegrable_average, hasFDerivAt_exp_zero, cexp_neg_quadratic_isLittleO_abs_rpow_cocompact, NonUnitalIsometricContinuousFunctionalCalculus.toNonUnitalContinuousFunctionalCalculus, ArithmeticFunction.LSeries_vonMangoldt_eq, differentiableAt_fun_neg_iff, LinearIsometryEquiv.strictConvex_image, ProbabilityTheory.Kernel.tendsto_eLpNorm_one_densityProcess_limitProcess, BumpCovering.toFun_eq_coe, MeasureTheory.indicatorConstLp_add, MultilinearMap.mkContinuousMultilinear_norm_le', SchwartzMap.le_seminorm, DoubleCentralizer.nnnorm_fst_eq_snd, toWeakSpace_closedConvexHull_eq, WithCStarModule.inner_single_right, ConvexOn.monotoneOn_leftDeriv, Unitization.norm_def, ContinuousMap.toNNReal_mul_add_neg_mul_add_mul_neg_eq, EisensteinSeries.qExpansion_identity_pnat, Real.summable_exp_nat_mul_of_ge, Submodule.IsOrtho.le, Submodule.reflection_map, differentiableOn_neg_iff, tendsto_pow_atTop_nhds_zero_of_abs_lt_one, GenLoop.toLoop_apply_coe, ContDiffWithinAt.contDiffOn', tendsto_gauge_nhds_zero_nhdsGE, ModelWithCorners.continuous_toFun, Metric.isConnected_closedBall, SchwartzMap.eLpNorm_le_seminorm, InnerProductSpace.span_gramSchmidt_Iic, NumberField.Units.instDiscrete_unitLattice, Complex.isCoveringMapOn_exp, LinearMap.IsSymmetric.direct_sum_isInternal, UpperHalfPlane.petersson_slash_SL, Submodule.det_reflection, DomAddAct.vadd_Lp_neg, ContinuousLinearMap.measurable_apply, selfAdjoint.star_coe_unitarySelfAddISMul, deriv_neg', summable_one_div_pow_of_le, Orientation.kahler_rotation_left', NumberField.mixedEmbedding.fundamentalCone.closure_paramSet, Real.differentiable_sin, MeasureTheory.Lp.simpleFunc.coeFn_le, hasFDerivAtFilter_iff_isLittleOTVS, MeasureTheory.setIntegral_rnDeriv_smul', zeta_eq_tsum_one_div_nat_add_one_cpow, IsBoundedBilinearMap.fderiv, FormalMultilinearSeries.radius_le_radius_continuousLinearMap_comp, ContinuousMultilinearMap.norm_ofSubsingleton_id_le, Complex.continuous_cos, DirichletCharacter.differentiableAt_completedLFunction, ContinuousAlternatingMap.curryLeft_same, BoundedContinuousFunction.instContinuousEval, NumberField.mixedEmbedding.euclidean.instDiscreteTopologySubtypeMixedSpaceMemSubmoduleIntIntegerLattice, ContinuousMultilinearMap.curryRight_apply, TensorProduct.inner_comm_comm, MeasureTheory.Lp.instFourierPairInv, ContDiff.fourierPowSMulRight, ContinuousLinearEquiv.toSpanNonzeroSingleton_coord, IsUltrametricDist.norm_tsum_le_of_forall_le_of_nonneg, MeasureTheory.eLpNorm_const_smul_le, Submodule.inner_orthogonalProjection_eq_of_mem_left, ContMDiffWithinAt.mfderivWithin, Units.isOpen, convex_halfSpace_im_ge, ContinuousLinearMap.sSup_unit_ball_eq_nnnorm, differentiableWithinAt_pi, HasFPowerSeriesOnBall.uniform_geometric_approx', Polynomial.hasDerivWithinAt_aeval, tendsto_dist_left_cocompact_atTop, intervalIntegral.smul_integral_comp_mul_left, Orientation.oangle_eq_zero_or_eq_pi_iff_not_linearIndependent, hasSum_choose_mul_geometric_of_norm_lt_one', Real.continuous_arctan, ContinuousLinearMap.extendTo𝕜_apply, ContDiffMapSupportedIn.toBoundedContinuousFunctionLM_eq_of_scalars, frontier_sphere', CStarAlgebra.rpow_neg_one_le_rpow_neg_one, integrableOn_Ioi_rpow_iff, ContinuousMultilinearMap.curryFinFinset_symm_apply_piecewise_const, eventually_norm_symmL_trivializationAt_comp_self_lt, ContinuousLinearMap.IsPositive.add, HasFPowerSeriesWithinOnBall.comp_sub, Real.eulerMascheroniConstant_eq_neg_deriv, Metric.PiNatEmbed.continuous_distDenseSeq, not_sameRay_iff_abs_lt_norm_sub, CPolynomialOn.deriv, MeasureTheory.HasFiniteIntegral.of_isEmpty, Real.not_differentiableAt_inv_log_zero, ProbabilityTheory.IsGaussian.integral_dual, ContinuousLinearEquiv.comp_right_hasFDerivWithinAt_iff', uniformConcaveOn_zero, instNoncompactSpaceReal, CurveIntegrable.fun_neg, enorm_sub_le_lintegral_deriv_of_contDiffOn_Icc, Orientation.abs_areaForm_le, Real.deriv_mul_log, ZLattice.exists_forall_abs_repr_le_norm, egauge_le_of_smul_mem, IsOpen.exists_msmooth_support_eq_aux, SeminormedAddCommGroup.mem_closure_iff, MeasureTheory.memLp_pi_iff, NumberField.mixedEmbedding.polarCoord_target, Affine.Simplex.mongePoint_eq_smul_vsub_vadd_circumcenter, AnalyticAt.iterated_deriv, hasStrictFDerivAt_pow', Complex.continuousAt_arg_coe_angle, AddCircle.denseRange_zsmul_coe_iff, Polynomial.hasStrictDerivAt_aeval, MeasureTheory.Measure.addHaar_image_continuousLinearEquiv, AnalyticOn.iteratedFDeriv_comp_perm, ContinuousLinearMap.norm_single, CauSeq.cauchySeq, ContinuousMapZero.toNNReal_mul_add_neg_mul_add_mul_neg_eq, ext_chart_model_space_apply, Asymptotics.superpolynomialDecay_iff_isBigO, DoubleCentralizer.one_fst, ContinuousLinearMap.norm_extendTo𝕜', InnerProductGeometry.angle_smul_smul, integrableOn_rpow_mul_exp_neg_rpow, HasFPowerSeriesAt.has_fpower_series_iterate_dslope_fslope, AnalyticWithinAt.comp_sub, MeasureTheory.Lp.simpleFunc.toLp_zero, NumberField.mixedEmbedding.fundamentalCone.hasFDerivAt_expMapBasis, ContinuousMapZero.toContinuousMapHom_toNNReal, StrongDual.polar_univ, ModularForm.SL_slash_def, Path.Homotopy.coeFn_injective, cauchySeq_iff_le_tendsto_0, CFC.log_pow', NumberField.mixedEmbedding.normAtPlace_polarCoord_symm_of_isReal, Real.tendsto_abs_tan_of_cos_eq_zero, OpenPartialHomeomorph.contDiff_unitBallBall, PeriodPair.hasSum_weierstrassP, convex_halfSpace_re_lt, MeasureTheory.ProbabilityMeasure.toWeakDualBCNN_apply, differentiableAt_iff_comp_const_sub, linearIndependent_of_ne_zero_of_inner_eq_zero, MeasureTheory.L2.inner_indicatorConstLp_eq_setIntegral_inner, Padic.toEquiv_withValUniformEquiv_eq_toEquiv_withValRingEquiv, InnerProductGeometry.cos_angle_add_mul_norm_of_inner_eq_zero, UpperHalfPlane.ofComplex_apply, MeasureTheory.L1.SimpleFunc.integralCLM'_L1_eq_integral, ModelWithCorners.convex_range, Quaternion.summable_coe, summable_iff_not_tendsto_nat_atTop_of_nonneg, ContDiffMapSupportedIn.postcompCLM_apply, LinearIsometry.comp_continuous_iff, curveIntegrable_symm, SeparationQuotient.inner_mk_mk, NontrivialTopology.of_exists_norm_ne_zero, TemperedDistribution.smulLeftCLM_add, DoubleCentralizer.coeHom_apply, summable_norm_pow_mul_geometric_div_one_sub, ContinuousAlternatingMap.curryLeft_zero, signedDist_neg, IsContDiffImplicitAt.bijective, PeriodPair.coeff_weierstrassPSeries, eHolderNorm_nsmul, ContDiffBump.integral_normed_smul, ContMDiffFiberwiseLinear.hasGroupoid, ProbabilityTheory.IsRatCondKernelCDFAux.integrable, exists_contMDiff_zero_iff_one_iff_of_isClosed, hasSum_geometric_two', dslope_eventuallyEq_slope_of_ne, ContinuousMultilinearMap.analyticOn_uncurry_of_linear, PeriodPair.isOpen_compl_lattice_diff, ProbabilityTheory.instIsGaussianMapHAdd_1, isCompact_sphere, ContinuousAlternatingMap.restrictScalarsLI_apply, Complex.restrictScalars_toSpanSingleton, integrableOn_exp_mul_Ioi, ProbabilityTheory.measure_cdf, Orientation.oangle_sign_smul_right, Bundle.contMDiffOn_proj, Orientation.normSq_kahler, contDiffWithinAtProp_self_target, ProbabilityTheory.IsCondKernelCDF.integrable, ContinuousMultilinearMap.opNNNorm_prod, Complex.tendsto_one_add_div_cpow_exp, ContinuousLinearEquiv.comp_right_differentiableOn_iff, Metric.isOpen_ball, UniformSpace.Completion.coe_toComplₗᵢ, ContinuousLinearMap.opENorm_comp_le, tendsto_norm_one, hasGradientAt_iff_hasFDerivAt, Complex.hasSum_cos', Asymptotics.IsTheta.isThetaTVS, MeasureTheory.Lp.coeFn_nonneg, Submodule.toLinearMap_orthogonalProjection_eq_linearProjOfIsCompl, Complex.closure_setOf_re_lt, ProbabilityTheory.integrable_of_mem_integrableExpSet, Complex.deriv_cosh, curveIntegrable_neg_iff, ProbabilityTheory.IndepFun.charFunDual_map_add_eq_mul, NumberField.mixedEmbedding.fundamentalCone.hasDerivAt_expMap_single, PeriodPair.derivWeierstrassP_coe, HasFPowerSeriesOnBall.tendsto_partialSum, writtenInExtChartAt_extChartAt, tendsto_iff_norm_div_tendsto_zero, ProbabilityTheory.HasCondSubgaussianMGF.memLp_exp_mul, MeromorphicNFOn.divisor_nonneg_iff_analyticOnNhd, continuousAt_extChartAt_symm, maximal_orthonormal_iff_orthogonalComplement_eq_bot, nontrivialTopology_iff_exists_norm_ne_zero, MeasureTheory.nnnorm_indicatorConstLp_le, locallyFinsuppWithin.logCounting_divisor, MeromorphicAt.meromorphicAt_add_iff_meromorphicAt₁, iteratedFDeriv_one_apply, ContinuousLinearEquiv.iteratedFDeriv_comp_left, DomMulAct.dist_smul_Lp, SemilinearIsometryClass.toContinuousSemilinearMapClass, Bundle.contMDiff_proj, cfcₙHom_map_quasispectrum, ContinuousAlternatingMap.toContinuousMultilinearMap_curryLeft, contMDiffAt_iff_target_of_mem_source, HasFPowerSeriesOnBall.factorial_smul, Real.differentiableAt_tan, MeasureTheory.Lp.instFourierInvAdd, ContinuousAlternatingMap.norm_image_sub_le', Real.differentiable_cosh, NumberField.InfinitePlace.Completion.extensionEmbedding_coe, NumberField.mixedEmbedding.negAt_symm, HasFPowerSeriesWithinAt.prod, IsSelfAdjoint.instIsometricContinuousFunctionalCalculus, MeasureTheory.memLp_piLp_iff, ContMDiffMap.coe_smul, Memℓp.star_iff, iteratedFDeriv_succ_apply_right, Asymptotics.IsEquivalent.const_add_of_norm_tendsto_atTop, fourierSubalgebra_coe, NumberField.InfinitePlace.denseRange_algebraMap_pi, Submodule.isOrtho_top_right, FormalMultilinearSeries.leftInv_coeff_one, MetricSpace.instT0Space, AnalyticOn.add, IsContDiffImplicitAt.eventually_implicitFunction_apply_eq, Matrix.exp_conj, ContinuousLinearMap.hasMFDerivAt, Polynomial.toAddCircle_monomial_eq_smul_fourier, TensorProduct.assocIsometry_apply, sameRay_iff_inv_norm_smul_eq, Matrix.toLin_conjTranspose, mdifferentiableOn_continuousLinearMapCoordChange, derivWithin_one, hasDerivAtFilter_intCast, CompletelyRegularSpace.completely_regular, Orthonormal.inner_finsupp_eq_sum_left, cfcHom_nnreal_eq_restrict, continuousAt_const_cpow', fderiv_deriv, BoxIntegral.integral_smul, GenLoop.loopHomeo_symm_apply, Complex.hasStrictDerivAt_sin, Complex.polarCoord_source, Metric.isOpen_iff, hasFPowerSeriesAt_pi_iff, mfderivWithin_eq_fderivWithin, MeasureTheory.eLpNorm'_const_smul, Module.Basis.continuous_toMatrix, MeasureTheory.Lp.coeFn_lpSMul, norm_cfcₙ_le, MeasureTheory.Submartingale.stronglyAdapted, ProbabilityTheory.integral_tilted_mul_eq_mgf, NormedField.continuousAt_zpow, TestFunction.tsupport_subset, hasDerivWithinAt_univ, Asymptotics.isLittleOTVS_neg_right, LinearIsometryEquiv.hasFDerivAt, ContDiffBump.apply, MeasureTheory.Lp.simpleFunc.coeFn_zero, isProperMap_dist, RCLike.continuous_conj, EMetric.exists_continuous_real_forall_closedBall_subset, ModelWithCorners.coe_extChartAt_transContinuousLinearEquiv_symm, intervalIntegral.intervalIntegrable_const, Orientation.oangle_sign_add_smul_left, NumberField.mixedEmbedding.polarCoord_symm_eq, tsum_geometric_inv_two_ge, differentiableAt_add_const_iff, MeasureTheory.UniformIntegrable.aestronglyMeasurable, ContinuousLinearEquiv.contDiffWithinAt_comp_iff, Real.tendsto_tan_pi_div_two, upperHemicontinuous_spectrum_nnreal, Matrix.PosSemidef.sq_sqrt, uniqueMDiffWithinAt_iff, VectorField.eventuallyEq_mpullback_mpullbackWithin_extChartAt, continuous_barycentric_coord, signedDist_vsub_self_rev, BumpCovering.ind_apply, ImplicitFunctionData.fderiv_implicitFunction_apply_eq_iff, Real.probChar_apply', LinearIsometryEquiv.rTensor_apply, AnalyticAt.comp_sub, EuclideanGeometry.Sphere.dist_orthogonalProjection_eq_radius_iff_isTangent, ContinuousLinearMap.analyticOnNhd_uncurry_of_multilinear, InnerProductSpace.isStarProjection_rankOne_self, deriv_sub_const, coord_norm', ProperCone.relative_hyperplane_separation, OrderedFinpartition.compAlongOrderedFinpartitionL_apply, ContinuousAlternatingMap.piLIE_symm_apply_apply, ContinuousAlternatingMap.le_opNorm_mul_pow_card_of_le, Real.tendsto_log_comp_add_sub_log, Complex.exp_sub_sum_range_succ_isLittleO_pow, ContinuousLinearMapWOT.ext_dual_iff, MeasureTheory.ProbabilityMeasure.coe_toWeakDualBCNN, extChartAt_model_space_eq_id, MeasureTheory.condExpIndSMul_nonneg, contDiff_clm_apply_iff, Complex.continuousOn_prod_circle_transform_function, BoxIntegral.Box.exists_seq_mono_tendsto, HasFPowerSeriesAt.hasFDerivAt, lp.summable_inner, Seminorm.cont_withSeminorms_normedSpace, WeakDual.isClosed_polar, hasStrictFDerivAt_finCons', Icc_chartedSpaceChartAt_of_top_le, analyticAt_iff_analytic_smul, map_extChartAt_nhdsWithin, spec_cfcₙAux, interior_sphere, ModelWithCorners.continuousOn_symm, MeromorphicOn.sum, ClosedSubmodule.orthogonal_eq_top_iff, eventually_enorm_mfderiv_extChartAt_lt, UniformConcaveOn.strictConcaveOn, enorm_tangentSpace_vectorSpace, QuadraticMap.lineDifferentiableAt, ContinuousMap.norm_lt_iff, FormalMultilinearSeries.norm_mul_pow_le_mul_pow_of_lt_radius, hasFDerivAt_exp_smul_const, LinearIsometryEquiv.norm_iteratedFDeriv_comp_right, HasFPowerSeriesOnBall.eventually_hasSum, ContinuousMap.norm_lt_iff_of_nonempty, NNRealRMK.le_rieszMeasure_of_isCompact_tsupport_subset, LinearMap.mkContinuous₂_norm_le, MeasureTheory.Integrable.comp_fst_iff, OrthonormalBasis.enorm_eq_one, DifferentiableWithinAtProp_self, LipschitzWith.completion_map, signedDist_linear_apply, UpperHalfPlane.isZeroAtImInfty_iff, coe_addEquiv_lpBCF_symm, NumberField.mixedEmbedding.negAt_apply_isReal_and_mem, LeftInvariantDerivation.map_smul, hasFDerivAt_jacobiTheta₂, Orientation.rotation_eq_matrix_toLin, FormalMultilinearSeries.zero_radius, Real.hasDerivAt_log, MeasureTheory.addHaarMeasure_eq_volume_pi, oneTangentSpaceIcc_def, intervalIntegral.integral_const_of_cdf, dist_birkhoffSum_apply_birkhoffSum, IsUltrametricDist.frontier_closedBall_eq_empty, Complex.isHomeomorphicTrivialFiberBundle_re, cfcHom_eq_cfc_extend, MeasureTheory.ConvolutionExistsAt.add_distrib, IsSymmSndFDerivAt.iteratedFDeriv_cons, Metric.uniformity_basis_dist_pow, Real.continuous_inv, ContinuousLinearMap.hasFPowerSeriesAt_bilinear, Path.continuous, MeasureTheory.tendstoInMeasure_iff_measureReal_enorm, NumberField.mixedEmbedding.polarSpaceCoord_target', intervalIntegral.integral_const', MeasureTheory.L1.dist_def, InnerProductSpaceable.add_left, VectorPrebundle.totalSpaceMk_isInducing, ContinuousLinearMap.comp_analyticOn, hasStrictDerivAt_const, ModelWithCorners.uniqueMDiffOn, ModelWithCorners.hasMFDerivWithinAt_symm, IccRightChart_extend_top_mem_frontier, Bundle.Trivial.trivialization.isLinear, ContinuousLinearMap.coeFn_compLpL, OpenPartialHomeomorph.extend_image_nhds_mem_nhds_of_boundaryless, hasStrictFDerivAt_list_prod_attach', CompactlySupportedContinuousMap.toReal_add, ProbabilityTheory.IsMeasurableRatCDF.stieltjesFunction_eq, NumberField.mixedEmbedding.volume_negAt_plusPart, deriv_single, ProbabilityTheory.IsMeasurableRatCDF.measure_stieltjesFunction_Iic, stronglyMeasurable_deriv, StrongDual.norm_toLpₗ_le, ContDiffMapSupportedIn.iteratedFDeriv_zero_on_compl, CircleIntegrable.sum, hasFDerivWithinAt_euclidean, Real.continuousOn_rpowIntegrand₀₁_Ici, ClosedSubmodule.mem_orthogonal_iff, Orientation.oangle_sub_left_smul_rotation_pi_div_two, EuclideanGeometry.orthogonalProjection_eq_orthogonalProjection_iff_vsub_mem, HasFPowerSeriesWithinAt.restrictScalars, DoubleCentralizer.sub_fst, tangentConeAt_real_subset_isRCLikeNormedField, ProperCone.innerDual_insert, ProbabilityTheory.IsCondKernelCDF.tendsto_atBot_zero, Module.Basis.parallelepiped_eq_map, ContDiffMapSupportedIn.norm_apply_le_seminorm, Complex.deriv_tan, integral_withDensity_eq_integral_toReal_smul, contDiffOn_clm_apply, ContinuousLinearMap.le_opNNNorm, nnnorm_cfc_le, SmoothPartitionOfUnity.sum_eq_one, MeasureTheory.Lp.instIsCentralScalar, ModelWithCorners.continuousAt, isCauSeq_iff_cauchySeq, MeromorphicAt.frequently_eq_iff_eventuallyEq, LinearMap.IsSymmetricProjection.hasOrthogonalProjection_range, FormalMultilinearSeries.id_apply_zero, SchwartzMap.hasDerivAt, MeasureTheory.eLpNorm_lt_top_of_finite, MeasureTheory.tendsto_eLpNorm_condExp, Submodule.starProjection_orthogonal, OnePoint.IsBoundedAt.smul_iff, exists_continuous_zero_one_of_isCompact, ContDiffBump.continuous, PiTensorProduct.mapLMultilinear_apply_apply, Orientation.oangle_eq_iff_eq_norm_div_norm_smul_rotation_or_eq_zero, ContinuousLinearMap.instNonnegSpectrumClassRealId, iteratedDeriv_comp_two, MeasureTheory.eLpNorm_one_condExp_le_eLpNorm, LinearMap.mem_polar_singleton, ContinuousLinearMap.uncurryMid_apply, ContinuousMap.setOfIdeal_eq_compl_singleton, hasFDerivAt_update, signedDist_self, comap_norm_nhds_one, Complex.hasDerivAt_cosh, iteratedDeriv_eq_iterate, isBoundedBilinearMap_apply, HasFPowerSeriesWithinOnBall.coeff_zero, FormalMultilinearSeries.analyticOnNhd, fderiv_comp_add_right, EisensteinSeries.tendsto_zero_inv_linear, MeasureTheory.L1.norm_integral_le, Unitization.nnreal_cfcₙ_eq_cfc_inr, hasDerivAtFilter_iff_tendsto, MeromorphicOn.divisor_fun_inv, ProperCone.dual_flip_dual, ProbabilityTheory.measure_stieltjesOfMeasurableRat_univ, RCLike.ofRealCLM_norm, unitInterval.tendsto_sigmoid_atTop, HasFPowerSeriesAt.eventually_differentiableAt, ModelWithCorners.continuous, integrable_inv_one_add_sq, Matrix.IsHermitian.eigenvectorUnitary_coe, Submodule.ClosedComplemented.of_finiteDimensional, ENNReal.tsum_coe_ne_top_iff_summable_coe, Complex.sqrt_map, InnerProductSpace.HarmonicOnNhd.const_smul, ContinuousAffineMap.hasFDerivAtFilter, hasStrictFDerivAt_ringInverse, curveIntegrable_cast_iff, MeasureTheory.setIntegral_indicatorConstLp, ProbabilityTheory.exponentialCDFReal_eq, signedDist_vsub_self, ContinuousLinearMap.mul_apply', ModelWithCorners.continuousWithinAt_symm, ContDiffOn.continuousLinearMap_comp, HurwitzZeta.differentiableAt_hurwitzZeta, stereographic_target, MeasureTheory.SignedMeasure.rnDeriv_smul, ContDiff.smul, MeromorphicNFOn.zero_set_eq_divisor_support, Unitary.norm_map, ContinuousMap.realToNNReal_apply, Rat.HeightOneSpectrum.adicCompletionIntegers.coe_padicIntEquiv_apply, SeparationQuotient.norm_mk', ProbabilityTheory.isGaussian_conv, Affine.Simplex.exists_forall_signedInfDist_eq_iff_eq_incenter, LinearMap.instStarModuleId, IsPicardLindelof.exists_forall_mem_closedBall_eq_hasDerivWithinAt_continuousOn, RCLike.linearIndependent_of_ne_zero_of_wInner_cWeight_eq_zero, Submodule.starProjection_apply_mem, MeasureTheory.hausdorffMeasure_smul_right_image, instIsUniformAddGroupReal, signedDist_smul, Rat.not_countably_generated_nhds_infty_opc, ENNReal.tendsto_toReal_zero_iff, VectorPrebundle.mem_trivialization_at_source, LinearIsometryEquiv.symm_conjStarAlgEquiv_apply_apply, MeasureTheory.eLpNorm_mono_ae_real, InnerProductSpace.rankOne_comp_rankOne, TemperedDistribution.fourierTransform_apply, ContinuousLinearMap.opNorm_zero, NormedAddGroupHom.ker_completion, MeasureTheory.convolution_lsmul_swap, Orientation.oangle_add_right_smul_rotation_pi_div_two, MeromorphicOn.circleAverage_log_norm, EuclideanGeometry.dist_eq_iff_dist_orthogonalProjection_eq, ProbabilityTheory.Kernel.continuous_integral_integral_comp, not_sameRay_iff_norm_add_lt, StieltjesFunction.measure_Icc, mdifferentiableAt_neg, Real.continuous_cos, geometric_hahn_banach_point_open, Real.hasStrictDerivAt_arctan, HasFTaylorSeriesUpToOn.prodMk, ContinuousMultilinearMap.norm_iteratedFDeriv_le, Complex.interior_setOf_re_le, ContDiffAt.domDomCongr_iteratedFDeriv, Quaternion.tsum_coe, DirichletCharacter.deriv_LFunctionTrivChar₁_apply_of_ne_one, isSeparable_range_deriv, ImplicitFunctionData.implicitFunction_apply_image, intervalIntegrable_posLog_norm_meromorphicOn, Orientation.inner_smul_rotation_pi_div_two_left, taylor_isLittleO, CFC.abs_ofNat, AnalyticAt.hasFPowerSeriesAt, BoxIntegral.hasIntegral_const, ZLattice.volume_image_eq_volume_div_covolume, hasDerivAtFilter_finCons', Complex.isOpen_im_gt_EReal, MeasureTheory.Supermartingale.smul_nonpos, Prod.fst_exp, MeasureTheory.SignedMeasure.haveLebesgueDecomposition_smul, LinearIsometry.toLinearMap_rTensor, SemiNormedGrp.completion_obj_str, MeromorphicAt.eventually_eq_zero_or_eventually_ne_zero, MeasureTheory.eLpNorm_congr_norm_ae, PiLp.hasStrictFDerivAt_apply, ContinuousMap.toLp_injective, Circle.exp_zero, hasStrictFDerivAt_fst, Metric.isCompact_closure_iff_exists_finite_isCover, CFC.negPart_one, Matrix.toEuclideanLin_eq_toLin, ModelWithCorners.continuous_symm, LinearMap.mkContinuous_norm_le', setIntegral_withDensity_eq_setIntegral_smul, UniqueMDiffOn.uniqueDiffOn_inter_preimage, DoubleCentralizer.pow_fst, mdifferentiableWithinAt_iff_target_inter', Rat.not_secondCountableTopology_opc, tendsto_logDeriv_euler_cot_sub, SlashInvariantForm.coe_trace, isConformalMap_complex_linear_conj, MeromorphicAt.meromorphicTrailingCoeffAt_smul, PiTensorProduct.mapL_apply, MeasureTheory.indicatorConstLp_sub, RightDerivMeasurableAux.A_mem_nhdsGT, LinearIsometryEquiv.submoduleMap_symm_apply_coe, hasDerivWithinAt_finCons', Euclidean.closedBall_eq_preimage, mellin_comp_rpow, Matrix.isHermitian_iff_isSymmetric, tendsto_norm', cfcₙHomSuperset_id, Quaternion.continuous_im, ContinuousAffineMap.hasFDerivAt, NumberField.mixedEmbedding.iUnion_negAt_plusPart_union, deriv.fun_neg, LSeries_differentiableOn, Asymptotics.Filter.Tendsto.isBigOTVS_one, Matrix.PosSemidef.inv_sqrt, ContinuousMultilinearMap.norm_iteratedFDeriv_le', support_iteratedFDeriv_subset, uniqueDiffOn_Iio, MeasureTheory.Measure.toSphereBallBound_mul_measureReal_unitBall_le_toSphere_ball, hasStrictFDerivAt_finset_prod, AffineSubspace.isPreconnected_setOf_wSameSide, ProbabilityTheory.IsMeasurableRatCDF.measurable_stieltjesFunction, AnalyticOnNhd.deriv, instContMDiffInv₀ModelWithCornersSelf, differentiableAt_riemannZeta, Submodule.le_orthogonal_iff_le_orthogonal, fderiv_fun_neg, ProbabilityTheory.memLp_id_gaussianReal, contMDiffOn_iff_source_of_mem_maximalAtlas, Complex.tendsto_partialGamma, intervalIntegral.smul_integral_comp_mul_add, Complex.exp_sub_sum_range_isBigO_pow, curveIntegral_zero, deriv_zpow, Function.HasTemperateGrowth.fun_add, DomAddAct.edist_vadd_Lp, hasFDerivAt_comp_sub, Complex.tendsto_norm_tan_of_cos_eq_zero, riemannZeta_eulerProduct, Complex.isOpenQuotientMap_zpow_compl_zero, LipschitzWith.locallyIntegrable_lineDeriv, InnerProductSpace.laplacian_eq_iteratedFDeriv_stdOrthonormalBasis, NumberField.mixedEmbedding.homeoRealMixedSpacePolarSpace_apply_fst_ofIsReal, Submodule.IsOrtho.comap_iff, UpperHalfPlane.eventuallyEq_coe_comp_ofComplex, InnerProductSpace.rankOne_comp, SmoothBumpCovering.embeddingPiTangent_injOn, contMDiffWithinAt_extChartAt_symm_target_self, MeasureTheory.L1.aemeasurable_coeFn, Unitary.joined, EisensteinSeries.summable_linear_sub_mul_linear_add, Real.Angle.continuous_coe, Submodule.mem_orthogonal, AddCircle.compactSpace, ContinuousAffineMap.norm_image_zero_le, StrongDual.mem_polarSubmodule, exists_dual_vector', Asymptotics.isLittleOTVS_fun_comm, MeasureTheory.measureReal_abs_dual_gt_le_integral_charFunDual, FormalMultilinearSeries.apply_eq_prod_smul_coeff, MeasureTheory.SignedMeasure.totalVariation_neg, ContinuousMap.instIsBoundedSMul, ContinuousMapZero.toNNReal_add_add_neg_add_neg_eq, Orientation.kahler_rightAngleRotation_left, Asymptotics.isLittleOTVS_comm, AbsoluteValue.Completion.isClosedEmbedding_extensionEmbedding_of_comp, IndiscreteTopology.of_forall_norm_eq_zero', hasFPowerSeriesWithinAt_pi_iff, CircleIntegrable.const_fun_smul, tangentMap_chart_symm, UniqueMDiffWithinAt.bundle_preimage, isCompactOperator_iff_isCompact_closure_image_closedBall, MeasureTheory.eLpNorm_const_smul, Real.hasDerivAt_mulExpNegMulSq, hasDerivWithinAt_comp_mul_left_smul_iff, MeasureTheory.integrable_condExpL2_of_isFiniteMeasure, ModelWithCorners.symm_map_nhdsWithin_image, hasDerivAt_iff_isLittleO_nhds_zero, Real.tendstoLocallyUniformlyOn_rpow_sub_one_log, SchwartzMap.tsupport_smulLeftCLM_subset, Orientation.kahler_comp_linearIsometryEquiv, HurwitzZeta.hasSum_nat_hurwitzZetaOdd, PadicInt.hasSum_mahler, Function.Periodic.invQParam_tendsto, InnerProductSpace.toMatrix_rankOne, AkraBazziRecurrence.eventually_deriv_one_sub_smoothingFn, separate_convex_open_set, contMDiffAt_vectorSpace_iff_contDiffAt, eventually_norm_symmL_trivializationAt_lt, MeasureTheory.isTightMeasureSet_of_inner_tendsto, differentiableAt_comp_add_left, ContinuousMultilinearMap.le_opNorm_mul_pow_card_of_le, cfcₙHom_real_eq_restrict, PeriodPair.latticeEquiv_symm_apply, CFC.abs_algebraMap_nnreal, deriv_const, ContDiffMapSupportedIn.structureMapCLM_apply_withOrder, differentiableAt_euclidean, FormalMultilinearSeries.changeOriginSeries_summable_aux₁, AnalyticAt.fun_add, hasFDerivAtFilter_finCons, MeasureTheory.ComplexMeasure.im_apply, PiTensorProduct.liftIsometry_comp_mapL, Function.locallyFinsuppWithin.logCounting_divisor_eq_circleAverage_sub_const, Real.smoothTransition.continuousAt, EuclideanGeometry.dist_orthogonalProjection_eq_infDist, contMDiffWithinAt_iff_contDiffWithinAt, Complex.closure_setOf_lt_re, geom_series_mul_one_add, iteratedFDeriv_smul_const_apply, UnitAddTorus.mFourierSubalgebra_separatesPoints, Complex.betaIntegral_convergent, MeasureTheory.Measure.addHaar_smul_of_nonneg, MeasureTheory.condExpIndL1Fin_disjoint_union, EisensteinSeries.tsum_tsum_symmetricIco_sub_eq, OrthonormalBasis.reindex_toBasis, ContinuousLinearMap.opNorm_le_iff, Real.Angle.sin_eq_iff_eq_or_add_eq_pi, RCLike.geometric_hahn_banach_open, Asymptotics.isLittleO_iff_exists_eq_mul, EuclideanGeometry.orthogonalProjection_mem, mdifferentiableOn_iff_of_mem_maximalAtlas', MeasureTheory.Lp.instIsBoundedSMul, InnerProductSpace.isSymmetric_rankOne_self, PointedContMDiffMap.instIsScalarTowerSomeENatTopContMDiffMapModelWithCornersSelf, RCLike.ofReal_expect, Real.differentiableOn_arccos, Orientation.oangle_smul_right_of_neg, Metric.uniformEquicontinuous_iff_right, Metric.mem_nhds_iff, tendsto_zero_iff_norm_tendsto_zero, ContinuousMap.coe_toLp, Real.fourierIntegral_convergent_iff, NumberField.canonicalEmbedding.mem_rat_span_latticeBasis, Commute.cfcHom, Bundle.mdifferentiableWithinAt_zeroSection, CPolynomialOn.continuousOn, Real.hasDerivAt_cosh, PeriodPair.hasSumLocallyUniformly_derivWeierstrassPExcept, Real.tendsto_deriv_mul_log_atTop, fderiv_const_sub, continuousMultilinearCurryLeftEquiv_apply, Orientation.abs_areaForm_of_orthogonal, ProbabilityTheory.Kernel.tendsto_setIntegral_densityProcess, Orientation.sin_oangle_add_right_of_oangle_eq_pi_div_two, LipschitzOnWith.ae_differentiableWithinAt_real, LeftInvariantDerivation.coe_smul, lp.hasSum_norm, HasFPowerSeriesAt.deriv, ModularForm.summable_logDeriv_one_sub_eta_q, upperHemicontinuous_quasispectrum_nnreal, HasFPowerSeriesWithinAt.continuousWithinAt_insert, IsBoundedBilinearMap.hasStrictFDerivAt, LinearIsometryEquiv.symm_rTensor, NormedSpace.instPathConnectedSpace, DomMulAct.instIsIsometricSMulSubtypeAEEqFunMemAddSubgroupLp, differentiable_pow, indicator_cthickening_eventually_eq_indicator_closure, IsUltrametricDist.nonarchimedeanAddGroup, Affine.Simplex.orthogonalProjectionSpan_restrict, uniqueMDiffWithinAt_iff_inter_range, FormalMultilinearSeries.ofScalars_radius_eq_zero_of_tendsto, ProbabilityTheory.Kernel.stronglyMeasurable_countableFiltration_densityProcess, Tactic.ComputeAsymptotics.Seq.instCompleteSpaceStream', LSeries_sum, LinearMap.polar_eq_biInter_preimage, Matrix.toEuclideanLin_conjTranspose_eq_adjoint, LinearMap.eq_adjoint_iff_basis, MeasureTheory.Lp.antitone, cfc_apply_mem_elemental, TensorProduct.commIsometry_symm, isStarProjection_starProjection, tendsto_gauge_nhds_zero, isClosed_nullSubmodule, Metric.cauchy_iff, MeasureTheory.eLpNorm_norm_rpow, MeasureTheory.integral_rnDeriv_smul, UpperHalfPlane.comp_ofComplex_of_im_le_zero, unitary.norm_map, Asymptotics.IsBigOTVS.rfl, Path.subpathAux_continuous, Set.EqOn.iteratedFDerivWithin, Complex.hasDerivAt_sin, ContinuousLinearEquiv.fderiv, fourierCoeff_eq_intervalIntegral, Real.map_exp_atBot, CStarAlgebra.conjugate_le_norm_smul', continuousOn_extChartAt_symm, NumberField.mixedEmbedding.continuous_normAtPlace, uniformContinuous_norm', Metric.isClosed_sphere, Asymptotics.IsLittleOTVS.bot, SchwartzMap.tsupport_fderivCLM_subset, ContinuousAlgEquiv.eq_continuousLinearEquivConjContinuousAlgEquiv, toIsCompletelPseudoMetrizableSpace, ContinuousLinearMap.isBigOTVS_comp, ContDiffAt.smul_const, Metric.mem_uniformity_dist, SeparatingDual.completeSpace_of_completeSpace_continuousLinearMap, UpperHalfPlane.continuous_im, ContinuousLinearEquiv.mdifferentiableWithinAt, hfdifferential_apply, tendsto_mod_div_atTop_nhds_zero_nat, ContinuousLinearMap.NonlinearRightInverse.right_inv', ContinuousLinearEquiv.mdifferentiable, AnalyticAt.exists_eq_sum_add_pow_mul, TangentBundle.trivializationAt_eq_localTriv, Tactic.ComputeAsymptotics.Seq.instCompleteSpaceSeq, ContinuousLinearMap.restrictScalarsIsometry_toLinearMap, ContinuousLinearMap.integral_comp_L1_comm, ContDiffWithinAt.continuousWithinAt, Complex.closure_reProdIm, curveIntegralFun_add, ContinuousMap.canLift, ContinuousOn.ofReal_map_toNNReal, CompactlySupportedContinuousMap.toNNRealLinear_apply, ContinuousLinearMap.opNorm_zero_iff, MeasureTheory.Measure.map_addHaar_smul, InnerProductSpace.gramSchmidt_def'', Real.hasDerivAt_fourierChar, numDerangements_tendsto_inv_e, AnalyticOnNhd.fderiv, WStarAlgebra.exists_predual, span_fourierLp_closure_eq_top, Orientation.oangle_add_right_eq_arctan_of_oangle_eq_pi_div_two, TopologicalSpace.complete_completelyMetrizableMetric, Real.tendsto_of_bddBelow_antitone, PMF.integral_eq_sum, AnalyticAt.exists_mem_nhds_analyticOnNhd, hasDerivAt_intCast, SeparationQuotient.nnnorm_mk, Orientation.kahler_rotation_left, multipliable_sineTerm, GromovHausdorff.HD_below_aux2, PiTensorProduct.liftIsometry_symm_apply, writtenInExtChartAt_extChartAt_symm, nnnorm_cfcₙHom, ModularFormClass.hasSum_qExpansion_of_abs_lt, SchwartzMap.smulLeftCLM_neg, intervalIntegral.inv_smul_integral_comp_div, ContinuousLinearMap.opNNNorm_mul, ContinuousMultilinearMap.iteratedFDerivComponent_apply, Complex.isUniformEmbedding_ofReal, differentiableOn_inverse, mdifferentiable_addInvariantVectorField, Complex.conjCLE_enorm, ContinuousLinearEquiv.comp_differentiableAt_iff, Metric.isBounded_closure_iff, Real.differentiableWithinAt_arccos_Iic, NormedField.completeSpace_iff_isComplete_closedBall, CFC.nnnorm_rpow, deriv_one, MeasureTheory.L1.measurable_coeFn, DirichletCharacter.LSeries_eulerProduct_hasProd, spectrum.differentiableOn_inverse_one_sub_smul, MeasureTheory.aestronglyMeasurable_condExpL1CLM, controlled_closure_range_of_complete, HasFPowerSeriesAt.const_smul, ContDiffMapSupportedIn.norm_iteratedFDeriv_apply_le_seminorm_withOrder, intervalIntegral.integral_derivWithin_Icc_of_contDiffOn_Icc, iteratedFDeriv_succ_eq_comp_right, Complex.hasSum_conj, SchwartzMap.iteratedPDeriv_eq_iteratedFDeriv, ValueDistribution.logCounting_sum_top_eventuallyLE, ContinuousMultilinearMap.changeOriginSeries_support, PeriodPair.deriv_derivWeierstrassPExcept_self, ContinuousLinearEquiv.comp_hasFDerivAt_iff', WeakFEPair.functional_equation₀, SchwartzMap.inner_fourierTransformCLM_toL2_eq, CFC.nnrpow_le_nnrpow, MeasureTheory.SimpleFunc.setToSimpleFunc_zero, CPolynomialOn.add, frontier_closedBall, curveIntegralFun_sub, Asymptotics.isBigOTVS_fun_comm, mdifferentiableWithinAt_comp_projIcc_iff, ContDiffMapSupportedIn.seminorm_apply, LinearMap.tripolar_eq_polar, inner_map_self_eq_zero, RCLike.toIsOrderedAddMonoid, FormalMultilinearSeries.isLittleO_of_lt_radius, tsupport_iteratedFDeriv_subset, nhdsWithin_extChartAt_target_eq_of_mem, MeasureTheory.continuous_integral, Complex.hasStrictDerivAt_exp, NormedAddCommGroup.tendsto_nhds_zero, MemHolder.nnHolderNorm_nsmul, aemeasurable_withDensity_iff, Real.zero_at_infty_fourier, Matrix.exp_units_conj', ContinuousMap.nonUnitalStarAlgebraAdjoin_id_subset_ker_evalStarAlgHom, Orientation.inner_sq_add_areaForm_sq, ContinuousMultilinearMap.hasFDerivAt, Real.enorm_exp_I_mul_ofReal_sub_one_le, signedDist_smul_of_neg, MeasureTheory.Lp.simpleFunc.isBoundedSMul, MeasureTheory.lpNorm_const_smul, HomotopyGroup.one_def, ContinuousLinearMap.rotation_apply, Diffeology.isOpen_iff_preimages_plots, Padic.denseRange_ratCast, MeasureTheory.SignedMeasure.singularPart_sub, lp.tsum_mul_le_mul_norm', circleAverage_sub_sub_inv_smul_of_differentiable_on, DoubleCentralizer.algebraMap_fst, AnalyticOnNhd.isClopen_setOf_analyticOrderAt_eq_top, differentiableOn_euclidean, RCLike.reLm_coe, mdifferentiableWithinAt_iff_of_mem_source', nnnorm_tsum_le, hasDerivWithinAt_diff_singleton, fderiv_continuousLinearEquiv_comp, Real.hasFPowerSeriesOnBall_linear_zero, differentiableAt_abs_pos, Real.Angle.coe_nsmul, EisensteinSeries.q_expansion_bernoulli, SchwartzMap.convolution_continuous_left, ContinuousLinearMap.adjoint_toSpanSingleton, MeasureTheory.Lp.coe_posPart, IsStarNormal.instContinuousFunctionalCalculus, ContinuousLinearMap.toBilinForm_injective, integrableOn_exp_neg_Ioi, Path.target', circleIntegral.integral_smul_const, Complex.hasStrictDerivAt_cosh, InnerProductSpace.mem_span_gramSchmidt, ContinuousMultilinearMap.nnnorm_ofSubsingleton, aemeasurable_deriv, NumberField.mixedEmbedding.fundamentalCone.expMap_single_symm_apply, NormedAddCommGroup.uniformity_basis_dist, VectorPrebundle.mem_base_pretrivializationAt, Set.instTietzeExtensionUnitClosedBall, ContinuousLinearMap.continuousOn_uncurry_of_multilinear, tsum_prod_pow_eq_tsum_sigma, ContinuousLinearMap.norm_compContinuousAlternatingMap_le, mdifferentiableWithinAt_iff_source_of_mem_maximalAtlas, ContDiff.continuous_iteratedFDeriv, mdifferentiableOn_iff_differentiableOn, InnerProductGeometry.angle_add_eq_arccos_of_inner_eq_zero, TangentBundle.symmL_model_space, HasFPowerSeriesWithinAt.isBigO_sub_partialSum_pow, Asymptotics.superpolynomialDecay_iff_norm_tendsto_zero, continuous_negPart, DiffContOnCl.continuousOn, ProbabilityTheory.IsMeasurableRatCDF.continuousWithinAt_stieltjesFunctionAux_Ici, ContDiffMapSupportedIn.seminorm_eq_bot_of_gt, MeasureTheory.integrable_condExpL2_indicator, Metric.tendstoLocallyUniformlyOn_iff, Real.hasDerivAt_Gamma_one_half, iteratedFDeriv_comp_add_left', ProbabilityTheory.isPosSemidef_covarianceBilinDual, ImplicitFunctionData.range_rightDeriv, Metric.isPathConnected_closedBall, tangentCoordChange_self, CStarAlgebra.span_nonneg_inter_closedBall, toSpanSingleton_derivWithin, HasFPowerSeriesWithinAt.isBigO_image_sub_norm_mul_norm_sub, CStarAlgebra.isClosed_nonneg, fderiv_norm_smul, InnerProductSpace.laplacian_eq_iteratedFDeriv_complexPlane, ContinuousAlternatingMap.isLeast_opNNNorm, expNegInvGlue.continuous_polynomial_eval_inv_mul, NumberField.mixedEmbedding.injective_mixedSpaceOfRealSpace, MeasureTheory.TendstoInMeasure.tendstoInDistribution, MeasureTheory.SimpleFunc.integral_eq_sum_of_subset, MeasureTheory.Lp.zero_smul, NontrivialTopology.of_exists_nnnorm_ne_zero, Real.instCompleteSpace, EuclideanGeometry.dist_orthogonalProjection_eq_zero_iff, CStarAlgebra.isStrictlyPositive_iff_isUnit_sqrt_and_eq_sqrt_mul_sqrt, HurwitzZeta.hasSum_int_oddKernel, Real.Angle.sign_add_pi, NumberField.mixedEmbedding.fundamentalCone.expMapBasis_pos, HasFiniteFPowerSeriesOnBall.eq_partialSum', continuousAt_cpow_const, mdifferentiableWithinAt_iff, starₗᵢ_toContinuousLinearEquiv, CFC.abs_intCast, Rat.uniformSpace_eq, LinearIsometry.enorm_toContinuousLinearMap, GaussianFourier.tendsto_verticalIntegral, apply_le_nnnorm_cfc_nnreal, coe_lpBCFₗᵢ_symm, MeromorphicOn.AnalyticOnNhd.divisor_nonneg, range_mfderiv_coe_sphere, Diffeology.IsPlot.continuous, Real.Angle.toReal_add_of_sign_pos_sign_neg, MeromorphicOn.eventually_analyticAt_or_mem_compl, ContinuousMap.Homotopy.extend_of_mem_I, Complex.wedgeIntegral_add_wedgeIntegral_eq, uniqueMDiffOn_iff_uniqueDiffOn, coe_lpPiLpₗᵢ_symm, IsBoundedBilinearMap.toContinuousLinearMap_apply, ContinuousMultilinearMap.norm_mkPiAlgebraFin_le, VectorBundleCore.localTrivAt_apply_mk, BoundedContinuousFunction.coe_zsmulRec, differentiable_piLp, ClosedSubmodule.inf_orthogonal_eq_bot, HasFPowerSeriesOnBall.pi, Metric.hausdorffDist_closure₂, ContinuousLinearEquiv.continuousAlternatingMapCongrLeft_apply, Submodule.reflection_eq_self_iff, Complex.UnitDisc.continuous_coe, MeasureTheory.weightedSMul_union', MeasureTheory.Measure.addHaar_closedBall_mul_of_pos, stereographic_source, ContinuousMultilinearMap.piₗᵢ_symm_apply, RCLike.wInner_one_const_right, Commute.cfc, TopologicalSpace.exists_isInducing_l_infty, AlgHom.coe_toContinuousLinearMap, ContDiff.iteratedFDeriv_right', Metric.hausdorffDist_closure, summable_geometric_of_abs_lt_one, Matrix.posSemidef_iff_eq_sum_vecMulVec, ProbabilityTheory.Kernel.IsMarkovKernel.integrable, contMDiffAt_extChartAt, Affine.Simplex.sign_signedInfDist_touchpoint_empty, ContinuousLinearMap.norm_id_le, deriv.neg', Irrational.eventually_forall_le_dist_cast_div, AnalyticAt.analyticOrderAt_ne_top, MeasureTheory.SignedMeasure.singularPart_add_withDensity_rnDeriv_eq, intervalIntegrable_log_cos, SchwartzMap.pairing_continuous_left, ConvexOn.univ_sSup_affine_eq, ContinuousMap.toNNReal_apply, MultilinearMap.mkContinuous_norm_le, Matrix.ofLp_toEuclideanLin_apply, Real.one_add_rpow_hasFPowerSeriesAt_zero, lipschitzOnWith_cfcₙ_fun_of_subset, range_cfc_nnreal_eq_image_cfc_real, signedDist_vadd_right_swap, ProbabilityTheory.integral_condCDF, differentiableAt_const_cpow_of_neZero, DomMulAct.smul_Lp_zero, uniformContinuous_nnnorm, mfderiv_extChartAt_comp_mfderivWithin_extChartAt_symm', tsum_dirichletSummand, AnalyticOnNhd.codiscrete_setOf_analyticOrderAt_eq_zero_or_top, ProbabilityTheory.IsRatStieltjesPoint.tendsto_atTop_one, SchwartzMap.integralCLM_apply, frontier_closedBall', InnerProductSpace.rankOne_one_right_eq_toSpanSingleton, PolynormableSpace.withSeminorms', Real.differentiable_mulExpNegMulSq, EuclideanGeometry.exists_dist_eq_iff_exists_dist_orthogonalProjection_eq, ContinuousMap.neg_norm_le_apply, ProbabilityTheory.condCDF_le_one, hasDerivAt_one, NumberField.mixedEmbedding.volume_preserving_homeoRealMixedSpacePolarSpace, FormalMultilinearSeries.radius_shift, Polynomial.fourierCoeff_toAddCircle_natCast, ContDiffBump.tsupport_eq, UniformSpace.Completion.uniformity_dist, MeasureTheory.stronglyMeasurable_condExp, ContinuousLinearEquiv.comp_right_differentiableAt_iff, Real.differentiableAt_arccos, ConvexOn.real_univ_sSup_of_nat_affine_eq, Real.summable_pow_div_factorial, ArithmeticFunction.vonMangoldt.LSeries_residueClass_lower_bound, ContDiffAt.contDiffOn, SimpleGraph.tendsto_turanDensity, OpenPartialHomeomorph.interior_extend_target_subset_interior_range, isClosedEmbedding_cfcₙHom_of_cfcHom, Complex.conjCLE_apply, ContinuousMap.spectrum_eq_range, NormedAddGroupHom.completion_toCompl, NormedSpace.polar_ball, AnalyticAt.const_smul, IsZLattice.span_top, summable_condensed_iff_of_nonneg, Real.not_DifferentiableAt_log_mul_zero, EReal.continuous_coe_iff, innerSLFlip_apply, IndiscreteTopology.of_forall_norm_eq_zero, ContinuousLinearEquiv.differentiableOn, NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_injective, FormalMultilinearSeries.div_le_radius_compContinuousLinearMap, ContinuousLinearEquiv.hasStrictFDerivAt, InnerProductGeometry.norm_add_sq_eq_norm_sq_add_norm_sq_iff_angle_eq_pi_div_two, iccLeftChart_extend_zero, coe_addEquiv_lpBCF, LinearMap.mkContinuous_norm_le, SmoothBumpCovering.comp_embeddingPiTangent_mfderiv, AnalyticWithinAt.exists_mem_nhdsWithin_analyticOn, EuclideanGeometry.Sphere.IsTangentAt.eq_orthogonalProjection, fderivWithin_derivWithin, MeasureTheory.Submartingale.tendsto_eLpNorm_one_limitProcess, Submodule.ker_starProjection, ProbabilityTheory.Kernel.tendsto_densityProcess_limitProcess, ContDiffMapSupportedInClass.instBoundedContinuousMapClass, CircleDeg1Lift.tendsto_translation_number₀, ContinuousLinearEquiv.mfderiv_eq, hasDerivAt_const_mul, hasLineDerivAt_iff_tendsto_slope_zero, differentiableAt_comp_add_right, MeasureTheory.lpMeasSubgroupToLpTrim_norm_map, InnerProductSpace.toContinuousLinearMap_toDualMap, MeasureTheory.SignedMeasure.singularPart_smul_nnreal, ProbabilityTheory.covarianceBilin_real, NNReal.instOrderTopology, Complex.differentiable_one_div_Gamma, Real.tendsto_tan_neg_pi_div_two, NormedAddGroupHom.completion_neg, MeasureTheory.SimpleFunc.eLpNorm'_eq, ContinuousLinearEquiv.comp_contDiffWithinAt_iff, Real.Angle.natCast_mul_eq_nsmul, MeasureTheory.integral_const, IsBoundedBilinearMap.continuous_right, tsum_geometric_inv_two, Affine.Triangle.dist_circumcenter_reflection_orthocenter_finset, IsSelfAdjoint.commute_cfcₙHom, completeSpace_of_cauSeq_isComplete, ContinuousLinearMap.measurable_coe, Euclidean.ball_eq_preimage, ContinuousLinearMap.analyticOn, ContinuousLinearMap.nndist_le_opNNNorm, Real.not_summable_one_div_natCast, CStarAlgebra.star_left_conjugate_le_norm_smul, NNRealRMK.le_rieszMeasure_of_tsupport_subset, norm_iteratedFDeriv_prod_le, contDiff_nat_iff_continuous_differentiable, MeasureTheory.L1.SimpleFunc.setToL1S_zero_left, hasFDerivAt_pow', NumberField.Ideal.tendsto_norm_le_div_atTop, NumberField.mixedEmbedding.fundamentalCone.expMap_apply, MeasureTheory.Lp.simpleFunc.coe_smul, SchwartzMap.iteratedLineDerivOp_eq_iteratedFDeriv, SchwartzMap.lineDerivOp_fourierInv_eq, LinearIsometryEquiv.symm_conjStarAlgEquiv, OrderedFinpartition.compAlongOrderFinpartition_apply, Submodule.topologicalClosure_eq_top_iff, InformationTheory.rightDeriv_klFun_one, hasDerivAt_abs, NumberField.mixedEmbedding.stdBasis_apply_isReal, DirichletCharacter.LSeries_eulerProduct_exp_log, mdifferentiableOn_coordChangeL, Finset.analyticOnNhd_sum, BoundedContinuousMapClass.toContinuousMapClass, LinearIsometryEquiv.coe_symm_toContinuousLinearEquiv, HasFiniteFPowerSeriesOnBall.add, Path.truncate_zero_one, MeasureTheory.Lp.smul_def, ContinuousLinearMap.opNorm_mulLeftRight_apply_apply_le, IsLocalFrameOn.eq_iff_coeff, iteratedDeriv_comp_const_sub, ContDiffAt.iteratedFDeriv_comp_perm, Polynomial.hasDerivAt, Complex.not_differentiableAt_Gamma_zero, ContinuousLinearEquiv.continuousAlternatingMapCongrRight_apply, AbsoluteValue.Completion.isometry_extensionEmbedding_of_comp, ContinuousLinearMap.opNorm_lsmul_le, MeromorphicNFAt.eventuallyEq_nhdsNE_iff_eventuallyEq_nhds, TensorProduct.enorm_assoc, MeasureTheory.Lp.norm_exponent_zero, hasFDerivWithinAt_comp_add_right, MeasureTheory.Lp.smul_neg, contMDiffWithinAt_extChartAt_symm_target, BumpCovering.sum_toPartitionOfUnity_eq, MeasureTheory.hasFiniteIntegral_toReal_iff, Orientation.inner_eq_zero_iff_eq_zero_or_eq_smul_rotation_pi_div_two, InformationTheory.rightDeriv_klFun, MultilinearMap.mkContinuousMultilinear_norm_le, writtenInExtChartAt_sumSwap_eventuallyEq_id, dense_addSubgroupClosure_pair_iff, IsUnifLocDoublingMeasure.eventually_measure_le_scaling_constant_mul', Path.extend_one, IsMIntegralCurveOn.continuousWithinAt, interior_range_modelWithCornersEuclideanHalfSpace, WeakDual.CharacterSpace.norm_le_norm_one, SchwartzMap.sum_apply, Bundle.contMDiff_zeroSection, AkraBazziRecurrence.differentiableOn_one_sub_smoothingFn, MeasureTheory.L1.stronglyMeasurable_coeFn, Matrix.linfty_opNorm_toMatrix, ConvexOn.real_sSup_of_countable_affine_eq, hasDerivAt_natCast, NumberField.mixedEmbedding.instDiscreteTopologySubtypeMixedSpaceMemSubmoduleIntIntegerLattice, Real.tendsto_logb_comp_add_sub_logb, ContinuousMap.coeFn_toLp, NonUnitalSeminormedRing.toContinuousMul, Submodule.reflection_bot, Real.Angle.zsmul_eq_iff, ProbabilityTheory.differentiableOn_complexMGF, PartitionOfUnity.sum_le_one, closure_ordConnected_inter_rat, Metric.isUniformEmbedding_bot_of_pairwise_le_dist, ContinuousMultilinearMap.opNNNorm_pi, innerSL_apply_norm, Real.hasDerivAt_Gamma_one, FiberBundle.extChartAt_target, InnerProductSpace.toDual_apply_eq_toDualMap_apply, Real.hasStrictDerivAt_cos, PeriodPair.deriv_weierstrassPExcept_same, MeasureTheory.ComplexMeasure.equivSignedMeasureₗ_symm_apply, NonUnitalContinuousFunctionalCalculus.exists_cfc_of_predicate, ContinuousLinearMap.isPositive_def', Function.Periodic.qParam_tendsto, Orientation.oangle_add_cyc3_neg_left, Real.continuousAt_log_iff, LinearMap.adjoint_inner_left, MemHolder.nnHolderNorm_smul, ODE.FunSpace.continuous_compProj, GromovHausdorff.compactSpace_optimalGHCoupling, MeasureTheory.eLpNorm_mono, Unitary.isPathConnected_ball, continuousAt_jacobiTheta, OpenPartialHomeomorph.unitBallBall_source, iter_deriv_inv, PeriodPair.analyticOnNhd_derivWeierstrassP, Matrix.frobenius_norm_mul, Circle.exp_int_mul_two_pi, BoxIntegral.Integrable.tendsto_integralSum_toFilteriUnion_single, AkraBazziRecurrence.deriv_smoothingFn, Real.not_differentiableAt_rpow_const_zero, ProperCone.innerDual_empty, Complex.Gammaℝ_residue_zero, stdSimplexHomeomorphUnitInterval_one, Matrix.star_dotProduct_gram_mulVec, OpenPartialHomeomorph.univUnitBall_apply, hasStrictFDerivAt_exp_zero, ContinuousLinearMap.norm_compL_le, AnalyticAt.differentiableAt, integrableOn_Ioi_cpow_of_lt, Seminorm.continuousAt_zero_of_forall, RCLike.hasSum_iff, ContinuousMultilinearMap.hasStrictFDerivAt_compContinuousLinearMap, SeminormFamily.withSeminorms_iff_nhds_eq_iInf, Metric.cobounded_eq_cocompact, ContMDiffVectorBundle.contMDiffOn_coordChangeL, MeasureTheory.Measure.addHaar_preimage_linearMap, EulerSine.antideriv_cos_comp_const_mul, deriv_natCast, ProbabilityTheory.condVar_of_sigmaFinite, Metric.disjoint_cobounded_nhds, curveIntegral_eq_intervalIntegral_deriv, ContDiffMapSupportedIn.toBoundedContinuousFunctionCLM_eq_of_scalars, Complex.instTietzeExtension, LinearIsometryEquiv.toContinuousLinearMap_toLinearIsometry, meromorphicOrderAt_smul_of_ne_zero, AccPt.uniqueDiffWithinAt, tendsto_norm, ContinuousMap.Homotopy.continuous, HasFPowerSeriesAt.sub, MeasureTheory.SimpleFunc.memLp_of_isFiniteMeasure, MeasureTheory.JordanDecomposition.toSignedMeasure_smul, MeasureTheory.Lp.instSMulCommClass, ContDiffAt.continuousLinearMap_comp, BoxIntegral.integralSum_smul, ContinuousMultilinearMap.norm_domDomCongr, ZetaAsymptotics.continuousOn_term_tsum, StarAlgHom.realContinuousMapOfNNReal_injective, Orientation.norm_div_sin_oangle_add_left_of_oangle_eq_pi_div_two, HasFTaylorSeriesUpTo.continuous, hasDerivWithinAt_zpow, ZSpan.quotientEquiv.symm_apply, contMDiff_prod_module_iff, EuclideanGeometry.reflection_eq_iff_orthogonalProjection_eq, NumberField.mixedEmbedding.convexBodyLT_convex, Real.tendsto_integral_exp_smul_cocompact, Complex.instT2Space, Monotone.deriv_nonneg, tendsto_closedBall_smallSets, MeasureTheory.setIntegral_tilted', VectorBundleCore.IsContMDiff.contMDiffOn_coordChange, Submodule.ker_orthogonalProjection, Orientation.kahler_mul, Metric.uniformity_edist, LinearMap.IsSymmetric.hasEigenvalue_iInf_of_finiteDimensional, GaussianFourier.integral_cexp_neg_mul_sum_add, OpenPartialHomeomorph.contDiffOn_restrContDiff_target, Submodule.reflection_map_apply, Complex.continuous_ofReal_cpow_const, mdifferentiableAt_section, ProbabilityTheory.eq_condKernel_of_measure_eq_compProd_real, sameRay_iff_norm_sub, ProbabilityTheory.covarianceBilinDual_comm, LinearIsometryEquiv.continuousAt, TensorProduct.dist_tmul_le, Real.uniformContinuous_abs, mfderivWithin_extChartAt_symm_comp_mfderiv_extChartAt', ProbabilityTheory.isGaussian_iff_charFunDual_eq, BoxIntegral.integralSum_disjUnion, Real.tendsto_arctan_atTop, SchwartzMap.integral_smul_lineDerivOp_right_eq_neg_left, MeasureTheory.L1.SimpleFunc.integral_smul, ContinuousMultilinearMap.curry0_norm, ContinuousMap.linearIsometryBoundedOfCompact_toAddEquiv, ContinuousLinearMap.opNNNorm_mul_flip_apply, ContinuousLinearMap.compLeftContinuousBounded_apply, Submodule.sup_orthogonal_of_hasOrthogonalProjection, tendsto_rpow_div, measurableSet_of_differentiableWithinAt_Ioi, MeasureTheory.L2.inner_indicatorConstLp_one_indicatorConstLp_one, TensorProduct.norm_lid, MeasureTheory.lpTrimToLpMeas_ae_eq, ContinuousLinearMap.norm_fst, ContinuousAlternatingMap.nnnorm_toContinuousMultilinearMap, Real.differentiable_iteratedDeriv_sin, Meromorphic.add, SmoothPartitionOfUnity.exists_pos_of_mem, OrderedFinpartition.applyOrderedFinpartition_apply, ContinuousMap.nnnorm_eq_iSup_nnnorm, Asymptotics.IsEquivalent.tendsto_nhds_iff, HasFPowerSeriesOnBall.hasFDerivAt, MeasureTheory.charFun_eq_charFunDual_toDualMap, AffineIsometry.toContinuousAffineMap_injective, Matrix.instIsOrderedAddMonoid, continuousAt_extChartAt', Complex.one_div_one_sub_cpow_hasFPowerSeriesOnBall_zero, SchwartzMap.instLocallyConvexSpace, MeasureTheory.UniformIntegrable.memLp, egauge_eq_zero_iff, HurwitzZeta.differentiableAt_completedCosZeta, fourier_neg, differentiableAt_neg_iff, ContinuousLinearMap.opNNNorm_comp_le, lp.single_add, cfcHom_isStrictlyPositive_iff, Submodule.starProjection_orthogonalComplement_singleton_eq_zero, Bundle.mdifferentiable_proj, Submodule.isOrtho_iSup_right, TensorProduct.toLinearEquiv_assocIsometry, ContinuousMultilinearMap.analyticOn, DomAddAct.vadd_Lp_const, FormalMultilinearSeries.changeOriginSeries_summable_aux₂, Orientation.oangle_smul_smul_self_of_nonneg, MeromorphicNFAt.smul_analytic, OpenPartialHomeomorph.extend_symm_continuousWithinAt_comp_right_iff, AnalyticOnNhd.add, AkraBazziRecurrence.isEquivalent_deriv_rpow_p_mul_one_add_smoothingFn, Real.deriv_sigmoid, MemHolder.nnHolderNorm_add_le, LSeries.tendsto_cpow_mul_atTop, Submodule.IsOrtho.disjoint, ContinuousMultilinearMap.curryMid_apply, iteratedDeriv_eq_iteratedFDeriv, norm_cfc_le, ZLattice.volume_image_eq_volume_div_covolume', ProperCone.dual_dual_flip, MeasureTheory.Measure.addHaar_preimage_continuousLinearEquiv, ArithmeticFunction.vonMangoldt.LSeries_residueClass_eq, PiTensorProduct.mapL_opNorm, EuclideanGeometry.orthogonalProjection_orthogonalProjection, EisensteinSeries.tendsto_double_sum_S_act, iter_deriv_inv', toMatrix_innerSL_apply, WeakDual.CharacterSpace.mem_spectrum_iff_exists, ClosedSubmodule.sInf_orthogonal, ContinuousMap.toLp_comp_toContinuousMap, Function.HasTemperateGrowth.smul, PiTensorProduct.toDualContinuousMultilinearMap_le_projectiveSeminorm, one_add_rpow_hasFPowerSeriesAt_zero, HomotopyGroup.inv_spec, MeasureTheory.integrable_const_iff, HasStrictFDerivAt.isBigOTVS_sub, DoubleCentralizer.mul_fst, Matrix.PosSemidef.re_dotProduct_nonneg, rescale_to_shell_zpow, Complex.integrable_pow_mul_norm_one_add_mul_inv, ZeroAtInftyContinuousMap.isometry_toBCF, iteratedFDeriv_comp_add_right, MeasureTheory.Measure.addHaar_ball_mul_of_pos, Orientation.rightAngleRotation_trans_neg_orientation, Orientation.volumeForm_robust', EuclideanGeometry.orthogonalProjection_vsub_mem_direction, tendsto_norm_cocompact_atTop', Complex.sinh_eq_tsum, exists_smooth_zero_one_of_isClosed, ModelWithCorners.mdifferentiable, BoundedContinuousFunction.toContinuousMapStarₐ_apply_apply, continuousAt_jacobiTheta₂, iteratedFDeriv_zero_fun, tendsto_measure_cthickening_of_isClosed, ModelWithCorners.range_eq_closure_interior, Submodule.HasOrthogonalProjection.exists_orthogonal, HurwitzZeta.hasSum_nat_hurwitzZetaEven_of_mem_Icc, CFC.exists_measure_nnrpow_eq_integral_cfcₙ_rpowIntegrand₀₁, ModelWithCorners.range_subset_closure_interior, ContinuousLinearEquiv.comp_contDiffOn_iff, ProbabilityTheory.IsRatStieltjesPoint.tendsto_atBot_zero, ModelWithCorners.convex_range', NormedSpace.Dual.dual_norm_topology_le_weak_dual_topology, CFC.spectrum_abs, MeasureTheory.Lp.smul_comm, Polynomial.isOpenQuotientMap_eval, SchwartzMap.continuous_toLp, Path.range_coe, CStarAlgebra.rpow_neg_one_le_one, Manifold.IsImmersionAt.target_subset_preimage_target, SchwartzMap.coe_coeHom, Submodule.starProjection_top, separatesPoints_continuous_of_t35Space_Icc, NormedSpace.toLocallyConvexSpace, seminormFromConst_isLimit, EulerSine.antideriv_sin_comp_const_mul, hasFDerivAt_sub_const, Set.Countable.isTotallyDisconnected, MeasureTheory.isComplete_aestronglyMeasurable, Submodule.iInf_orthogonal, exists_lt_rieszContentAux_add_pos, ContinuousLinearMap.norm_restrictScalars, Complex.differentiableAt_cosh, Affine.Simplex.sum_inv_height_sq_smul_vsub_eq_zero, TestFunction.hasCompactSupport', ContinuousMap.nndist_eq_iSup, MeasureTheory.Lp.simpleFunc.isUniformEmbedding, signedDist_vadd_left, Asymptotics.IsBigO.rpow_rpow_nhdsGE_zero_of_le_of_imp, ModularGroup.tendsto_lcRow0, MeasureTheory.hasFiniteIntegral_const_iff, tangentBundleModelSpaceHomeomorph_coe_symm, ProbabilityTheory.integrable_kernel_prodMk_left, AffineSpace.asymptoticNhds_le_cobounded, HasFPowerSeriesWithinOnBall.tendstoUniformlyOn, Real.comap_exp_nhdsGT_zero, Pretrivialization.continuousLinearMap_apply, derivWithin_sub_const_fun, EuclideanGeometry.oangle_add_oangle_rev, MeasureTheory.L1.integral_zero, ContinuousLinearMap.hasFDerivAt_uncurry_of_multilinear, NormedSpace.sInter_polar_eq_closedBall, Complex.differentiableAt_Gamma_nat_add_one, ContDiffBump.convolution_eq_right, TemperedDistribution.instFourierInvSMul, hasFDerivWithinAt_fst, PadicInt.totallyBounded_univ, ExistsContDiffBumpBase.w_def, Affine.Simplex.orthogonalProjection_eq_circumcenter_of_dist_eq, IsEquivalent.summable_iff, measurable_derivWithin_Ioi, MeasureTheory.Measure.setIntegral_comp_smul, PositiveLinearMap.ofPreGNS_toPreGNS, Complex.deriv_cos', Complex.imCLM_coe, ModelWithCorners.transContinuousLinearEquiv_range, ContDiffOn.smul, OpenPartialHomeomorph.map_extend_nhdsWithin, ContinuousMap.norm_restrict_mono_set, lp.hasSum_inner, iteratedDeriv_comp_eq_sum_orderedFinpartition, TensorProduct.nnnorm_assoc, WeakFEPair.hf_modif_FE, Complex.isQuotientMap_im, tangentBundleCore_localTriv_baseSet, tendsto_mul_add_inv_atTop_nhds_zero, FormalMultilinearSeries.analyticAt_changeOrigin, ContinuousLinearMap.opNorm_mul_apply_le, PiTensorProduct.tprodL_apply, CStarMatrix.normedSpaceCore, mfderivWithin_extChartAt_symm_comp_mfderiv_extChartAt, HasFPowerSeriesWithinAt.continuousWithinAt, HasFPowerSeriesAt.tendsto_partialSum, circleAverage_log_norm_factorizedRational, Diffeomorph.uniqueDiffOn_preimage, deriv_pow_field, ZSpan.repr_fract_apply, cfc_apply_pi, SmoothBumpCovering.embeddingPiTangent_injective, ContinuousLinearMap.orthogonal_range, contDiff_one_iff_hasFDerivAt, MeasureTheory.charFunDual_prod', HasFiniteFPowerSeriesAt.add, Submodule.lipschitzWith_starProjection, HasFPowerSeriesAt.hasDerivAt, ContinuousLinearMap.isPositive_iff_complex, Real.instContinuousMapUniqueHom, instIsContMDiffRiemannianBundleTrivial, MeromorphicOn.min_divisor_le_divisor_add, SchwartzMap.toLp_fourierTransform_eq, MeasureTheory.setLIntegral_nnnorm_condExpIndSMul_le, Real.summable_pow_mul_exp_neg_nat_mul, LinearIsometry.completeSpace_map, HasFPowerSeriesAt.eventually_hasSum_sub, deriv_comp_neg, ContinuousLinearMap.isThetaTVS_comp, exists_contMDiff_support_eq_eq_one_iff, AnalyticAt.eventually_eq_or_eventually_ne, DiffContOnCl.two_pi_i_inv_smul_circleIntegral_sub_inv_smul, fourierIntegral_half_period_translate, BoxIntegral.integralSum_sub_partitions, MeasureTheory.continuous_indicatorConstLp_set, ordinaryHypergeometricSeries_eq_zero_iff, Polynomial.hasDerivAt_aeval, ProbabilityTheory.measure_stieltjesOfMeasurableRat_Iic, MeasureTheory.withDensityᵥ_zero, ContinuousLinearMap.comp_cpolynomialOn, MeasureTheory.stronglyMeasurable_charFun, PeriodPair.instDiscreteTopologySubtypeComplexMemSubmoduleIntLattice, MeasureTheory.condExpIndL1_of_not_measurableSet, ContMDiffSection.contMDiff, ContinuousLinearMap.opNorm_smul_le, Quaternion.norm_exp, iteratedFDerivWithin_comp_add_left', InnerProductSpace.span_gramSchmidt, ProbabilityTheory.IsRatCondKernelCDFAux.integrable_iInf_rat_gt, MeasureTheory.Lp.smul_add, MeasureTheory.withDensitySMulLI_apply, Asymptotics.isLittleOTVS_congr, IsBoundedBilinearMap.deriv_apply, hasDerivAt_gronwallBound, hasDerivWithinAt_const_add_iff, MeasureTheory.Measure.addHaar_nnreal_smul, Quaternion.continuous_coe, Real.uniformContinuous_add, Complex.continuous_ofReal, ContinuousMap.comp_attachBound_mem_closure, EuclideanGeometry.hasFDerivAt_inversion, Finset.analyticOnNhd_fun_sum, InformationTheory.continuous_klFun, Orientation.kahler_map, isBigO_deriv_ofReal_cpow_const_atTop, MeasureTheory.convolutionExistsAt_iff_integrable_swap, ContinuousMultilinearMap.le_opNorm_mul_prod_of_le, Complex.not_continuousAt_Gamma_neg_nat, PiLp.hasFDerivAt_ofLp, TemperedDistribution.instFourierInvAdd, InformationTheory.stronglyMeasurable_klFun, dist_div_norm_sq_smul, NormedField.tendsto_norm_zpow_nhdsNE_zero_atTop, Metric.eventually_nhds_prod_iff, MeasureTheory.Lp.fourierInv_toTemperedDistribution_eq, MeasureTheory.memLp_prodLp_iff, Polynomial.C_eq_or_isOpenQuotientMap_eval, NNReal.isUniformEmbedding_coe, torusIntegral_smul, ZLattice.comap_comp, MeasureTheory.JordanDecomposition.toSignedMeasure_neg, stronglyMeasurable_derivWithin_Ici, ContinuousMap.isometryEquivBoundedOfCompact_toEquiv, NumberField.mixedEmbedding.fundamentalCone.injective_expMapBasis, Metric.continuous_infNndist_pt, norm_iteratedFDeriv_one, uniformContinuous_nnnorm', posTangentConeAt_mono, hasDerivAt_ofReal_cpow_const, EisensteinSeries.summable_e2Summand_symmetricIcc, LinearIsometryEquiv.comp_differentiable_iff, CFC.norm_abs, hasDerivAt_norm_rpow, Orientation.oangle_sign_add_left, ZSpan.instDiscreteTopologySubtypeMemAddSubgroupToAddSubgroupIntSpanRangeCoeBasisRealOfFinite, NumberField.mixedEmbedding.homeoRealMixedSpacePolarSpace_apply_fst_ofIsComplex, UnitAddTorus.hasSum_prod_mFourierCoeff, OrthonormalBasis.span_apply, isConformalMap_id, Padic.withValUniformEquiv_cast_apply, Real.differentiableAt_tan_of_mem_Ioo, Real.not_continuousAt_deriv_qaryEntropy_zero, GromovHausdorff.instSecondCountableTopologyGHSpace, ContinuousMultilinearMap.analyticOnNhd, AffineSubspace.isPreconnected_setOf_sOppSide, NumberField.mixedEmbedding.latticeBasis_apply, ClosedSubmodule.orthogonal_toSubmodule_eq, MeasureTheory.integrable_comp_mul_right_iff, LeftInvariantDerivation.map_sub, EuclideanGeometry.vsub_orthogonalProjection_mem_direction, ContinuousLinearEquiv.continuousMultilinearMapCongrLeft_apply, ContinuousMap.Homotopy.coe_toContinuousMap, contMDiff_equivTangentBundleProd, SeparationQuotient.normedMk_apply, ContinuousLinearMap.isStarProjection_iff_isIdempotentElem_and_isStarNormal, Matrix.PosSemidef.dotProduct_mulVec_zero_iff, spectrum.exp_mem_exp, differentiableAt_finCons', ContinuousLinearMap.isPositive_iff, MeasureTheory.Measure.addHaar_submodule, Unitization.isUniformEmbedding_addEquiv, TensorProduct.mapIsometry_apply, SmoothPartitionOfUnity.sum_finsupport_smul_eq_finsum, tendsto_rpow_neg_div, differentiableWithinAt_inverse, ContinuousMultilinearMap.compContinuousLinearMapL_apply, AnalyticAt.analyticAt_localInverse, NormedSpace.exp_neg, signedDist_apply_linear_apply, VectorBundleCore.inCoordinates_eq, SchwartzMap.integral_mul_deriv_eq_neg_deriv_mul, DomMulAct.smul_Lp_ae_eq, TemperedDistribution.fourierInv_apply, AnalyticAt.eventually_eq_zero_or_eventually_ne_zero, MeromorphicOn.extract_zeros_poles, VectorField.pullbackWithin_eq, Matrix.IsHermitian.cfcAux_id, cfcₙAux_mem_range_inr, Asymptotics.IsLittleO.tendsto_inv_smul_nhds_zero, ContinuousLinearMap.norm_bilinearRestrictScalars, eventuallyConst_nhdsNE_iff_meromorphicOrderAt_sub_eq_top, MeasureTheory.SimpleFunc.integrable_of_isFiniteMeasure, inseparable_zero_iff_norm, MonotoneOn.integrableOn_isCompact, PiTensorProduct.liftIsometry_apply_apply, ContinuousMultilinearMap.prodL_symm_apply, ValueDistribution.logCounting_add_const, ContinuousMap.adjoin_id_eq_span_one_add, Path.extend_symm, LeftInvariantDerivation.map_neg, derivWithin_fun_const, Complex.sin_eq_tsum, MeasureTheory.Lp.simpleFunc.isUniformInducing, ContinuousLinearMap.norm_inl, MeasureTheory.Measure.addHaar_singleton_add_smul_div_singleton_add_smul, MonotoneOn.exists_tendsto_deriv_liminf_lintegral_enorm_le, isOpen_analyticAt, ContinuousMultilinearMap.analyticWithinAt_uncurry_of_linear, NumberField.mixedEmbedding.lintegral_comp_polarCoordReal_symm, MeasureTheory.integrable_swap_iff, IsHilbertSum.linearIsometryEquiv_symm_apply_dfinsupp_sum_single, DiscreteTopology.of_forall_le_dist, BoundedContinuousFunction.integral_add_const, differentiableAt_jacobiTheta₂_snd, ContinuousLinearEquiv.comp_differentiable_iff, ENNReal.continuous_truncateToReal, cfcₙ_norm_sq_nonneg, SchwartzMap.instFourierSMul, Padic.coe_withValRingEquiv, HasFPowerSeriesOnBall.prod, Unitization.nnnorm_eq_sup, Orientation.two_zsmul_oangle_smul_right_self, Path.subpath_continuous_family, SchwartzMap.fourierTransformCLM_apply, ODE.FunSpace.intervalIntegrable_comp_compProj, Metric.mem_closure_range_iff_nat, AffineSubspace.signedInfDist_singleton, HasFPowerSeriesWithinOnBall.neg, NumberField.mixedEmbedding.measurable_polarCoord_symm, norm_deriv_eq_norm_fderiv, MeasureTheory.L1.integral_add, Metric.totallyBounded_iff, MeasureTheory.Lp.mem_Lp_iff_eLpNorm_lt_top, Affine.Simplex.coe_orthogonalProjection_vadd_smul_vsub_orthogonalProjection, SeminormedGroup.disjoint_nhds_one, Circle.surjOn_exp_neg_pi_pi, DiffContOnCl.add, tendsto_rpow_neg_atTop, ContinuousMap.apply_le_norm, MeasureTheory.aestronglyMeasurable_condExpIndSMul, DoubleCentralizer.zero_toProd, LSeries.tendsto_atTop, continuous_real_toNNReal, hasSum_one_div_nat_pow_mul_sin, SlashInvariantForm.slash_S_apply, ProbabilityTheory.Kernel.tendsto_densityProcess_fst_atTop_ae_of_monotone, UniqueMDiffOn.bundle_preimage, Orientation.coe_basisRightAngleRotation, PointwiseConvergenceCLM.tendsto_nhds_atTop, AkraBazziRecurrence.differentiableAt_smoothingFn, BoundedContinuousFunction.norm_mkOfCompact, NumberField.InfinitePlace.Completion.extensionEmbedding_of_isReal_coe, TemperedDistribution.fourierTransform_toTemperedDistributionCLM_eq, ContinuousLinearMap.bilinearComp_zero_left, one_add_cpow_hasFPowerSeriesOnBall_zero, ContinuousLinearMap.nnnorm_smulRight_apply, MeromorphicAt.fun_sum, deriv_id, hasFPowerSeriesWithinOnBall_pi_iff, hasDerivAt_zero, NumberField.mixedEmbedding.fundamentalCone.expMap_source, MeasureTheory.Lp.constL_apply, Real.tendsto_arctan_atBot, MeasureTheory.IsFundamentalDomain.hasFiniteIntegral_on_iff, SchwartzMap.fderivCLM_fourier_eq, BoundedContinuousFunction.star_apply, ContinuousMultilinearMap.instContinuousSMul, CStarModule.inner_mul_inner_swap_le, MeasureTheory.Integrable.comp_snd_iff, Complex.hasSum_conj', MeasureTheory.L2.mem_L1_inner, Bundle.ContinuousRiemannianMetric.pos, BoxIntegral.Integrable.tendsto_integralSum_toFilter_prod_self_inf_iUnion_eq_uniformity, Complex.isOpen_im_lt_EReal, ContinuousLinearEquiv.contDiffOn_comp_iff, mellin_const_smul, nontrivialTopology_iff_exists_norm_ne_zero', ContDiffAt.exists_forall_mem_closedBall_exists_eq_forall_mem_Ioo_hasDerivAt, BoxIntegral.integrable_iff_cauchy, TemperedDistribution.instLineDerivAdd, BoundedContinuousFunction.mkOfCompact_one, SchwartzMap.derivCLM_apply, Real.Angle.two_nsmul_coe_div_two, ContDiffAt.fderiv, Matrix.toLin_finTwoProd_toContinuousLinearMap, HasFPowerSeriesOnBall.eventually_hasSum_sub, TensorProduct.toLinearMap_mapIsometry, RCLike.map_nonneg_iff, ContinuousMultilinearMap.opNNNorm_le_iff, contMDiffWithinAt_iff_source, MeasureTheory.L1.integral_eq_integral, NumberField.mixedEmbedding.fundamentalCone.expMapBasis_apply'', NormedSpace.exp_smul, MeromorphicOn.negPart_divisor_add_le_max, SchwartzMap.isBigO_cocompact_zpow_neg_nat, Real.deriv_cos, NonUnitalContinuousFunctionalCalculus.isCompact_quasispectrum, IsCoercive.continuousLinearEquivOfBilin_apply, Circle.exp_intCast_mul, LinearMap.toContinuousLinearMap₁_apply, VectorBundleCore.continuousOn_coordChange, Polynomial.div_tendsto_atBot_zero_iff_degree_lt, DomMulAct.instSMulCommClassSubtypeAEEqFunMemAddSubgroupLp, integrableOn_Ioi_exp_neg_mul_sq_iff, LinearIsometryEquiv.continuousOn, MeasureTheory.integral_fun_fst, Orientation.volumeForm_zero_neg, Bundle.contMDiffAt_section, MeasureTheory.martingalePart_eq_sum, Real.continuousAt_const_rpow, Real.differentiableAt_binEntropy, Real.smoothTransition.continuous, Complex.hasStrictDerivAt_cpow_const, Unitary.inner_map_map, Orientation.oangle_eq_iff_eq_norm_div_norm_smul_rotation_of_ne_zero, WithAbs.isUniformInducing_of_comp, tendsto_mulIndicator_thickening_mulIndicator_closure, OpenPartialHomeomorph.nhdsWithin_extend_target_eq, SmoothPartitionOfUnity.sum_finsupport, MeasureTheory.eLpNormEssSup_indicator_eq_eLpNormEssSup_restrict, Real.hasDerivAt_arctan', TensorProduct.enorm_map, Orientation.areaForm_map, ContDiff.iterate_deriv', nhdsWithin_extChartAt_target_eq, Real.enorm_rpow_of_nonneg, ContinuousMap.linearIsometryBoundedOfCompact_apply_apply, Asymptotics.isEquivalent_iff_tendsto_one, Metric.contractibleSpace_eball, differentiable_neg, deriv_comp_mul_left, hasDerivAt_neg, UniformSpace.Completion.dist_comm, instIsAddHaarMeasureProdRealVolume, OrthonormalBasis.toMatrix_orthonormalBasis_mem_unitary, MeasureTheory.Lp.simpleFunc.coe_indicatorConst, ProbabilityTheory.stronglyMeasurable_gaussianPDFReal, hasDerivAtFilter_finCons, ContinuousLinearMap.adjoint_comp, deriv_bernoulliFun, PiTensorProduct.norm_eval_le_projectiveSeminorm, iteratedFDeriv_zero_eq_comp, isCompactOperator_iff_image_ball_subset_compact, det_fderivPiPolarCoordSymm, isConformalMap_iff, hasFTaylorSeriesUpToOn_succ_iff_left, BoundedContinuousFunction.coe_star, Padic.isUniformInducing_cast_withVal, PadicInt.continuous_multichoose, ContDiffOn.continuousOn, Complex.hasSum_taylorSeries_neg_log, Real.tsum_le_of_sum_le, Polynomial.hasStrictDerivAt, injOn_pi_polarCoord_symm, Path.Homotopy.continuous_transReflReparamAux, cantorToHilbert_continuous, IsConformalMap.comp, cfcHomSuperset_id, NormedCommGroup.nhds_basis_norm_lt, Real.deriv2_qaryEntropy, Asymptotics.isTheta_completion_left, ContinuousLinearEquiv.isBigO_comp_rev, Real.differentiableAt_exp, Metric.isConnected_closedEBall, Real.locallyFinite_volume, zero_at_infty_of_norm_le, Real.hasStrictDerivAt_arcsin, MeasureTheory.condExpIndL1_disjoint_union, hasStrictFDerivAt_sub_const_iff, Metric.continuous_infDist_pt, SchwartzMap.integral_clm_comp_deriv_right_eq_neg_left, norm_withSeminorms, contMDiffWithinAt_iff_source_of_mem_source, CFC.monotone_sqrt, GromovHausdorff.toGHSpace_lipschitz, HasFPowerSeriesWithinOnBall.add, ENNReal.tsum_coe_eq_top_iff_not_summable_coe, Commute.cfcₙ, ContinuousLinearMap.add_compLp, ENNReal.summable_toReal, curveIntegralFun_restrictScalars, NumberField.mixedEmbedding.commMap_apply_of_isReal, MeasureTheory.Lp.inner_fourier_eq, contDiff_smul, NNRat.instContinuousSMulNNReal, EuclideanGeometry.Sphere.IsTangent.isTangentAt, comap_gauge_nhds_zero, AffineMap.hasStrictDerivAt, LipschitzWith.ae_differentiableAt_of_real, ProperCone.mem_innerDual, EuclideanGeometry.Sphere.two_zsmul_oangle_center_add_two_zsmul_oangle_eq_pi, InnerProductSpace.toLinearMap_rankOne, instSecondCountableTopologyContinuousLinearMapIdOfFiniteDimensional, ContinuousLinearMap.comp_hasFPowerSeriesOnBall, meromorphicNFAt_smul_iff_right_of_analyticAt, ZLattice.isAddFundamentalDomain, SchwartzMap.memLp_top, BumpCovering.eventuallyEq_one', NormedSpace.of_real_exp_ℝ_ℝ, ContinuousLinearMap.adjointAux_inner_right, IsClosed.diffContOnCl_iff, HasDerivWithinAt.Ioi_iff_Ioo, MeasureTheory.L1.aestronglyMeasurable_coeFn, MeromorphicOn.smul, Finset.analyticOn_sum, Real.Angle.continuous_sin, NormedAddCommGroup.toCompl_apply, Metric.eventually_notMem_cthickening_of_infEdist_pos, Bundle.RiemannianMetric.pos, NumberField.mixedEmbedding.polarCoord_apply, TemperedDistribution.instLineDerivSMulComplex, ContinuousLinearEquiv.isOpen, euler_sineTerm_tprod, tendsto_sub_mul_tsum_nat_rpow, frontier_ball, CStarAlgebra.conjugate_le_norm_smul, AnalyticAt.differentiableWithinAt, NormedField.discreteTopology_of_bddAbove_range_norm, hasSum_zeta_two, TensorProduct.commIsometry_apply, ContinuousLinearEquiv.coe_toDiffeomorph, deriv_intCast, summable_geometric_iff_norm_lt_one, NumberField.mixedEmbedding.hasFDerivAt_polarCoordReal_symm, norm_midpoint_lt_iff, CFC.sqrt_eq_cfc, ArithmeticFunction.vonMangoldt.continuousOn_LFunctionResidueClassAux, exists_continuousMap_one_of_isCompact_subset_isOpen, continuousMultilinearCurryRightEquiv_symm_apply', MeasureTheory.integral_comp_mul_right_Ioi, MeasureTheory.condExpInd_smul', Finset.analyticAt_sum, ContinuousLinearMap.isBigO_sub, ContinuousAlternatingMap.fderivCompContinuousLinearMap_apply, AffineSubspace.isConnected_setOf_sOppSide, DoubleCentralizer.norm_fst, Orientation.oangle_add_oangle_rev_neg_left, measurable_smul_const, IsGδ.setOf_liouville, WeakFEPair.functional_equation, ProbabilityTheory.analyticOnNhd_mgf, SchwartzMap.smul_apply, ContDiffMapSupportedIn.continuousSMul, Real.differentiable_iteratedDeriv_cosh, Real.hasStrictDerivAt_sin, StrongDual.zero_mem_polar, TensorProduct.congrIsometry_symm, summable_pow_mul_geometric_of_norm_lt_one, Subalgebra.frontier_spectrum, BoundedContinuousFunction.coe_toContinuousMapₐ, ContDiffMapSupportedIn.structureMapLM_zero_injective, toSpanSingleton_deriv, ContinuousLinearMapWOT.continuous_inducingFn, GaussianFourier.integrable_cexp_neg_mul_sq_norm_add, Metric.isConnected_ball, BoundedContinuousFunction.add_norm_nonneg, ContinuousAlternatingMap.norm_ofSubsingleton_id, tendsto_indicator_cthickening_indicator_closure, Metric.compactSpace_iff_isBounded_univ, Complex.equivRealProdCLM_symm_apply_re, OpenPartialHomeomorph.restrContDiff_apply, MeasureTheory.ProbabilityMeasure.continuous_iff_forall_continuous_integral, LinearMap.isStarProjection_toContinuousLinearMap_iff, ContinuousLinearMap.IsPositive.orthogonalProjection_comp, VectorField.mpullbackWithin_eq_pullbackWithin, MeromorphicOn.divisor_smul, Manifold.pathELength_eq_lintegral_mfderiv_Icc, ProbabilityTheory.tendsto_cdf_atTop, TorusIntegrable.add, Metric.denseRange_iff, MeasureTheory.UnifTight.exists_measurableSet_indicator, eHolderNorm_add_le, exists_locallyFinite_subset_iUnion_ball_radius_lt, ContinuousMap.HomotopyWith.prop, HasFDerivAtFilter.isLittleOTVS, NumberField.mixedEmbedding.continuous_normAtAllPlaces, LinearMap.IsSymmetric.orthogonal_range, MeasureTheory.Lp.eLpNorm_lt_top, MeasureTheory.integrable_withDensity_iff_integrable_coe_smul₀, NNRat.instOrderTopology, iteratedDerivWithin_eq_equiv_comp, ContinuousMultilinearMap.nnnorm_ofSubsingleton_id_le, Polynomial.differentiableAt, QuasispectrumRestricts.nnreal_of_nonneg, MeasureTheory.L2.integrable_inner, uniqueDiffOn_Ioi, Besicovitch.card_le_of_separated, MeasureTheory.exists_null_frontiers_thickening, dimH_orthogonalProjection_le, LinearIsometry.toContinuousLinearMap_injective, BoundedContinuousFunction.toLp_norm_le, intervalIntegral.intervalIntegrable_pow, AbsolutelyContinuousOnInterval.uniformlyContinuousOn, NormedSpace.expSeries_div_hasSum_exp, instDiscreteTopologySubtypeMemSubmoduleIntComap, Pretrivialization.continuousOn_continuousLinearMapCoordChange, ContDiffMapSupportedIn.seminorm_postcompLM_le, Real.BohrMollerup.tendsto_logGammaSeq, ContinuousMultilinearMap.cpolynomialOn_uncurry_compContinuousLinearMap, MeasureTheory.Lp.continuous_negPart, MeasureTheory.integrable_smul_iff, ModelWithCorners.isInteriorPoint_iff, ContinuousMultilinearMap.bound, Path.id_apply, DoubleCentralizer.coe_fst, MeasureTheory.Lp.coeFn_negPart, Complex.one_div_one_sub_sq_hasFPowerSeriesOnBall_zero, ContinuousMultilinearMap.analyticWithinAt_uncurry_compContinuousLinearMap, HurwitzZeta.differentiable_cosZeta_of_ne_zero, ContinuousMap.equivBoundedOfCompact_symm_apply, TangentBundle.trivializationAt_baseSet, ContinuousMultilinearMap.norm_mkPiAlgebraFin_succ_le, IsSelfAdjoint.instContinuousFunctionalCalculus, ContDiffPointwiseHolderAt.fderiv, CompactlySupportedContinuousMap.toReal_smul, Orientation.inner_rightAngleRotationAux₁_right, hasFDerivAt_pi_polarCoord_symm, curveIntegral_fun_sub, Int.instDiscreteTopologySubtypeRealMemAddSubgroupZmultiples, HasFiniteFPowerSeriesOnBall.finite, Meromorphic.iterated_deriv, Real.tendsto_sum_pi_div_four, SeparationQuotient.liftNormedAddGroupHom_apply, Submodule.re_inner_starProjection_nonneg, IsPicardLindelof.exists_eq_forall_mem_Icc_hasDerivWithinAt, norm_cfcₙ_one_sub_one_add_inv_lt_one, BoundedContinuousFunction.norm_sub_nonneg, MeromorphicOn.intervalIntegrable_log, summable_of_sum_le, MeasureTheory.integrable_neg_iff, map_extChartAt_nhdsWithin_eq_image', NumberField.mixedEmbedding.latticeBasis_repr_apply, MeasureTheory.Integrable.of_subsingleton, Submodule.adjoint_orthogonalProjection, CFC.abs_eq_cfcₙ_norm, Filter.HasBasis.isBigOTVS_iff, norm_tangentSpace_vectorSpace, VectorBundleCore.trivializationAt, Complex.deriv_cpow_const, InformationTheory.not_differentiableWithinAt_klFun_Ioi_zero, Real.fourierChar_apply', continuousOn_cfcₙ_nnreal, MeasureTheory.lintegral_enorm_eq_lintegral_edist, ContinuousMapZero.instCStarRing, EuclideanGeometry.reflection_apply', ContDiffWithinAt.smul_const, NormedField.instCompletableTopField, MeasureTheory.condExp_of_sigmaFinite, hasFDerivWithinAt_iff_hasGradientWithinAt, iteratedDerivWithin_succ, CurveIntegrable.smul, BoxIntegral.Integrable.smul, TemperedDistribution.laplacian_toTemperedDistributionCLM_eq, mdifferentiableAt_mulInvariantVectorField, ContinuousAffineMap.differentiableOn, cfcₙHom_continuous, IsUltrametricDist.norm_tprod_le_of_forall_le, Submodule.id_eq_sum_starProjection_self_orthogonalComplement, Submodule.isOrtho_bot_right, LinearMap.adjoint_comp, FormalMultilinearSeries.min_radius_le_radius_add, ContinuousAlternatingMap.opNorm_le_iff, CFC.abs_sq, hasStrictDerivAt_one, Complex.summable_one_div_nat_cpow, ODE.FunSpace.continuous, EuclideanGeometry.oangle_self_orthogonalProjection, ContinuousAffineMap.norm_comp_le, MeasureTheory.L1.SimpleFunc.norm_eq_integral, IsStarNormal.instNonUnitalIsometricContinuousFunctionalCalculus, PartitionOfUnity.le_one, MeasureTheory.SignedMeasure.haveLebesgueDecomposition_neg, signedDist_right_lineMap, SchwartzMap.instZeroAtInftyContinuousMapClass, MeasureTheory.condExpIndL1_of_measure_eq_top, tendsto_dist_right_cocompact_atTop, NonUnitalCStarAlgebra.toCompleteSpace, ProbabilityTheory.uncenteredCovarianceBilin_zero, Nat.isClosedEmbedding_coe_real, mdifferentiableAt_iff_source_of_mem_source, contMDiffAt_prod_module_iff, LinearMap.IsPositive.inner_nonneg_right, Real.tendsto_div_pow_mul_exp_add_atTop, VonNeumannAlgebra.coe_toStarSubalgebra, Matrix.toEuclideanLin_apply_piLp_toLp, MeasureTheory.SimpleFunc.setToSimpleFunc_eq_sum_filter, IsUpperSet.null_frontier, Asymptotics.isLittleOTVS_iff_tendsto_inv_smul, logDeriv_prod_sineTerm_eq_sum_cotTerm, circleIntegrable_def, Complex.differentiableAt_Gamma_one, IsManifold.of_discreteTopology, Real.differentiable_fourierChar, Path.extend_zero, InnerProductSpace.span_gramSchmidt_Iio, mdifferentiableAt_iff_of_mem_source, ContinuousAlternatingMap.curryLeft_add, NumberField.AdeleRing.algebraMap_fst_apply, lintegral_comp_polarCoord_symm, Metric.eventually_notMem_thickening_of_infEdist_pos, HasFPowerSeriesAt.pi, ContinuousMap.Homotopy.extend_zero, ProbabilityTheory.setIntegral_tilted_mul_eq_mgf, hasFDerivAt_comp_add_left, MeasureTheory.ProbabilityMeasure.toWeakDualBCNN_continuous, iteratedDerivWithin_succ', Rat.instIsTopologicalRing, analyticWithinAt_iff_exists_analyticAt, HasFPowerSeriesWithinOnBall.tendstoUniformlyOn', tendsto_pow_const_mul_const_pow_of_lt_one, ContDiffMapSupportedIn.toBoundedContinuousFunctionLM_apply, hasStrictDerivAt_pi, ContDiff.hasStrictDerivAt, LinearIsometry.strictConvexSpace_range_iff, VectorFourier.fourierPowSMulRight_apply, cfcₙHomSuperset_continuous, summable_prod_eisSummand, continuous_nnnorm, instTotallySeparatedSpaceOfIsUltrametricDist, uniqueDiffOn_Ico, mdifferentiable_jacobiTheta, BumpCovering.nonneg, Nat.Primes.summable_rpow, Matrix.linfty_opNorm_eq_opNorm, inner_eq_norm_mul_iff_real, MeasureTheory.FiniteMeasure.continuous_integral_boundedContinuousFunction, interior_extChartAt_target_nonempty, Metric.eventually_nhds_iff_ball, ContinuousAlternatingMap.prodLIE_apply, Submodule.mem_orthogonal_singleton_iff_inner_left, ProbabilityTheory.Kernel.eLpNorm_densityProcess_le, MeasureTheory.L1.SimpleFunc.norm_integral_le_norm, SeparationQuotient.mk_eq_one_iff, MeasureTheory.Submartingale.smul_nonpos, Manifold.IsImmersionAtOfComplement.writtenInCharts, RCLike.ofReal_tsum, Real.deriv_cos', Path.coe_toContinuousMap, SmoothBumpCovering.support_toSmoothPartitionOfUnity_subset, isBigO_deriv_rpow_const_atTop, bernsteinApproximation_uniform, Bundle.Trivial.contMDiffVectorBundle, polarCoord_apply, hasDerivAt_pow, SchwartzMap.decay, OpenPartialHomeomorph.isOpen_extend_target, contDiff_succ_iff_deriv, ModelWithCorners.uniqueDiffWithinAt_image, WithCStarModule.inner_single_left, LinearIsometryEquiv.comp_hasFDerivAt_iff', IsUltrametricDist.nnnorm_tprod_le, Submodule.mem_adjoint_iff, Real.not_summable_natCast_inv, NormedRing.inverse_add_norm_diff_first_order, ContinuousMap.Homotopy.map_one_left, FormalMultilinearSeries.summable_nnnorm_mul_pow, ContinuousLinearMap.isBoundedLinearMap, Asymptotics.isLittleO_norm_pow_id, LinearMap.isSymmetric_iff_isSelfAdjoint, Real.deriv_rpow_const', Real.continuous_fourierChar, ContinuousLinearMap.opNorm_le_iff_lipschitz, CPolynomialOn.fderiv, MeasureTheory.isAddHaarMeasure_volume_pi, NumberField.mixedEmbedding.normAtPlace_negAt, PadicInt.mahlerEquiv_apply, Polynomial.div_tendsto_atTop_zero_of_degree_lt, SchwartzMap.convolution_flip, Real.differentiableAt_arcosh, Orientation.tan_oangle_add_left_of_oangle_eq_pi_div_two, continuousSMul_closedBall_closedBall, ContinuousLinearMap.opNorm_flip, Module.Basis.parallelepiped_map, cfcₙ_apply_pi, AlternatingMap.measure_def, MeasureTheory.Integrable.of_mem_Icc, LinearIsometryEquiv.comp_continuousOn_iff, ContDiffAt.differentiableAt_one, InnerProductGeometry.sin_angle_add_of_inner_eq_zero, MeasureTheory.charFunDual_dirac, MeasureTheory.ConvolutionExistsAt.distrib_add, LinearMap.isSymmetric_iff_sesqForm, tendsto_one_iff_norm_tendsto_zero, FormalMultilinearSeries.radius_compContinuousLinearMap_le, MeasureTheory.eLpNormEssSup_lt_top_iff_isBoundedUnder, hasDerivWithinAt_derivWithin_iff, hasDerivAt_sub_const_iff, Metric.uniformity_eq_comap_nhds_zero, hasStrictDerivAt_exp, ContinuousLinearMap.IsPositive.adjoint_conj, Rat.instIsUniformAddGroup, EisensteinSeries.G2_eq_tsum_cexp, WeakFEPair.hg_int, LinearIsometryEquiv.reflections_generate_dim, Complex.isometryOfOrthonormal_apply, IsConformalMap.smul, hasMFDerivAt_iff_hasFDerivAt, iteratedFDeriv_prodMk, isCoveringMap_npow, intervalIntegral.smul_integral_comp_mul_right, ProbabilityTheory.cdf_expMeasure_eq_lintegral, Irreducible.maximalIdeal_eq_closedBall, LinearMap.isSymmetricProjection_iff_eq_coe_starProjection, Complex.frontier_setOf_le_re_and_le_im, Real.tendsto_Icc_vitaliFamily_left, tendsto_measure_Icc_nhdsWithin_right', Complex.sameRay_iff, Complex.instContinuousMapUniqueHom, MeasureTheory.eLpNorm'_const_smul_le, SchwartzMap.lineDerivOp_apply_eq_fderiv, deriv_add_const, intervalIntegral.integral_comp_div_add, Real.hasStrictDerivAt_sqrt, mdifferentiableAt_iff_differentiableAt, Real.tendsto_eulerMascheroniSeq, PositiveLinearMap.leftMulMapPreGNS_mul_eq_comp, Complex.hasDerivAt_Gamma_one, ContinuousLinearMap.exist_extension_of_finiteDimensional_range, NumberField.mixedEmbedding.homeoRealMixedSpacePolarSpace_apply, Orientation.areaForm_map_complex, Metric.eventually_notMem_cthickening_of_infEDist_pos, Real.continuousOn_tan, LinearMap.isSymmetricProjection_iff_eq_coe_starProjection_range, CFC.log_pow, hasFDerivWithinAt_pi, BoxIntegral.integral_const, PeriodPair.hasSum_weierstrassPExcept, intervalIntegral.integral_smul_const, MeasureTheory.Lp.neg_smul, Complex.HadamardThreeLines.eventuallyle, MeasureTheory.hausdorffMeasure_orthogonalProjection_le, BumpCovering.exists_finset_toPOUFun_eventuallyEq, Metric.totallyBounded_of_finite_discretization, Polynomial.deriv, LinearIsometryEquiv.toContinuousLinearEquiv_refl, GenLoop.Homotopic.equiv, ContinuousMultilinearMap.uncurry0_apply, differentiableWithinAt_apply, HilbertBasis.summable_inner_mul_inner, mdifferentiableWithinAt_iff_target_of_mem_source, OpenPartialHomeomorph.continuousAt_extend_symm, Polynomial.div_tendsto_zero_of_degree_lt, contDiffAt_zero, ContinuousLinearMap.isPositive_iff', Seminorm.continuous_of_lowerSemicontinuous, LinearIsometryEquiv.comp_hasFDerivAt_iff, derivWithin_const_add_fun, mdifferentiableWithinAt_extChartAt_symm, Real.hasDerivAt_tan_of_mem_Ioo, OrderedFinpartition.norm_compAlongOrderedFinpartition_sub_compAlongOrderedFinpartition_le, Submodule.finrank_add_finrank_orthogonal, contMDiffOn_comp_projIcc_iff, map_extChartAt_nhdsWithin_eq_image, NumberField.mixedEmbedding.finrank, Orientation.two_zsmul_oangle_smul_right_of_ne_zero, ContinuousLinearMap.star_eq_adjoint, SchwartzMap.integral_fourier_smul_eq, Real.dimH_segment, ODE.FunSpace.instCompleteSpace, Real.iter_deriv_rpow_const, AffineMap.differentiableOn, Complex.imCLM_nnnorm, ImplicitFunctionData.right_map_implicitFunction, SmoothBumpFunction.contMDiff, ModelWithCorners.mdifferentiableOn, Submodule.orthogonal_eq_top_iff, modelWithCornersSelf_partialEquiv, Path.truncate_const_continuous_family, ContinuousMultilinearMap.curryLeft_apply, ContinuousAlternatingMap.hasFDerivWithinAt, contMDiffWithinAt_extChartAt_symm_range, differentiableAt_pow, MeasureTheory.Lp.instOrderClosedTopologySubtypeAEEqFunMemAddSubgroupOfClosedIciTopology, ValueDistribution.logCounting_sum_top_le, AlgHom.toContinuousLinearMap_norm, ContDiffAt.laplacian_CLM_comp_left_nhds, ContDiff.differentiable, Rat.instNoncompactSpace, iteratedDeriv_comp_three, NumberField.mixedEmbedding.polarCoordReal_symm_target_ae_eq_univ, EisensteinSeries.qExpansion_identity, PiLp.hasFDerivAt_apply, exists_continuous_one_zero_of_isCompact_of_isGδ, Submodule.lipschitzWith_orthogonalProjection, Affine.Simplex.abs_signedInfDist_eq_dist_of_mem_affineSpan_range, Polynomial.hasFDerivWithinAt_aeval, LinearIsometryEquiv.toContinuousLinearEquiv_trans, ContDiffAt.fun_smul, HasFPowerSeriesWithinAt.neg, UniformSpace.Completion.enorm_coe, NormedAddGroupHom.ker_le_ker_completion, Orientation.inner_rightAngleRotation_right, CStarAlgebra.isStrictlyPositive_TFAE, UpperHalfPlane.contMDiffAt_ofComplex, NNReal.summable_mk, Real.hasDerivAt_exp, ContMDiffOn.contMDiffOn_tangentMapWithin, fourierSubalgebra_closure_eq_top, ModularForm.prod_fintype_slash, GaussianFourier.integral_cexp_neg_sum_mul_add, MeasureTheory.UniformIntegrable.spec, UniformSpace.Completion.coe_toComplL, derivWithin_comp_add_const, LinearMap.IsSymmetric.orthogonalComplement_iSup_eigenspaces, NumberField.mixedEmbedding.fractionalIdealLatticeBasis_apply, MeasureTheory.LevyProkhorov.continuous_ofMeasure_probabilityMeasure, Asymptotics.isThetaTVS_comm, derivWithin.star, hasStrictDerivAt_inv, Metric.infDist_pos_iff_notMem_closure, RCLike.wInner_one_const_left, eventually_norm_mfderivWithin_symm_extChartAt_comp_lt, summable_norm_iff, AlternatingMap.mkContinuousLinear_norm_le, ModularFormClass.bounded_at_infty_comp_ofComplex, asymptoticCone_subset_singleton_of_bounded, OpenPartialHomeomorph.extend_preimage_mem_nhdsWithin, ProbabilityTheory.HasSubgaussianMGF.memLp, OrderedFinpartition.applyOrderedFinpartition_update_left, LinearMap.continuous_of_isClosed_ker, Unitization.complex_cfcₙ_eq_cfc_inr, orthogonalFamily_iff_pairwise, ZSpan.map_fundamentalDomain, Complex.sameRay_iff_arg_div_eq_zero, Affine.Simplex.ExcenterExists.signedInfDist_excenter, Real.hasSum_sin, Complex.arg_eq_nhds_of_im_pos, derivWithin_zero, ContinuousMultilinearMap.norm_compContinuous_linearIsometryEquiv, Metric.secondCountable_of_countable_discretization, ModularForm.holo', FormalMultilinearSeries.radius_le_radius_derivSeries, Orientation.volumeForm_apply_le, ContinuousAlternatingMap.curryLeftLI_apply, ContDiffBump.eventuallyEq_one_of_mem_ball, ContinuousMapClass.toCocompactMapClass_of_norm, LDL.diag_eq_lowerInv_conj, deriv_comp_const_add, eventuallyConst_iff_analyticOrderAt_sub_eq_top, ContinuousLinearMap.norm_single_le_one, NumberField.mixedEmbedding.polarSpaceCoord_apply, tsum_eisSummand_eq_tsum_sigma_mul_cexp_pow, Padic.coe_withValRingEquiv_symm, deriv_const_add, iteratedFDerivWithin_zero_eq_comp, HasFiniteFPowerSeriesAt.sub, Metric.uniformContinuousOn_iff_le, Submodule.inf_orthogonal_eq_bot, differentiableAt_iff_comp_add_const, Complex.starConvex_slitPlane, MeasureTheory.eLpNormEssSup_lt_top_of_ae_bound, ContinuousLinearMap.norm_compSL_le, BoxIntegral.Box.volume_apply, MeasureTheory.norm_condExpInd_le, ContinuousLinearEquiv.uniqueDiffOn_preimage_iff, BoundedContinuousFunction.toContinuousMapₐ_apply, curveIntegralFun_trans_aeeq_left, MeasureTheory.BorelCantelli.stronglyAdapted_process, SmoothPartitionOfUnity.finite_tsupport, Metric.lipschitz_infDist, ProbabilityTheory.analyticOn_complexMGF, Asymptotics.isLittleO_one_iff, ContDiffMapSupportedIn.withSeminorms, differentiableWithinAt_snd, NormedSpace.noncompactSpace, WeakFEPair.hf_int, AnalyticOn.fun_const_smul, Submodule.isOrtho_sSup_left, ProbabilityTheory.Kernel.eLpNorm_density_le, Bundle.Trivial.trivialization.coordChangeL, MeasureTheory.withDensityᵥ_smul, ContDiffAt.exists_eventually_eq_hasDerivAt, CStarAlgebra.norm_negPart_le, polarCoord_source_ae_eq_univ, DiffContOnCl.const_add, LinearMap.polar_isClosed, ContinuousMultilinearMap.analyticWithinAt, NumberField.mixedEmbedding.negAt_apply_norm_isReal, Hyperreal.isSt_iff_tendsto, hasSum_geometric_of_abs_lt_one, fderiv_star, MeasureTheory.integrable_comp_smul_iff, derivWithin_fun_const_smul', MeasureTheory.Measure.addHaar_preimage_linearEquiv, innerₛₗ_apply, hasFDerivAtFilter_iff_tendsto, cfcₙ_nnreal_eq_real, InnerProductSpace.laplacian_eq_iteratedFDeriv_orthonormalBasis, NormedSpace.continuousOn_exp, HasFDerivWithinAt.isBigOTVS_sub, Affine.Simplex.orthogonalProjectionSpan_reindex, ContDiffMapSupportedIn.support_subset, Complex.log_sub_logTaylor_isBigO, CFC.sqrt_algebraMap, differentiable_completedZeta₀, innerSL_apply, OrthonormalBasis.coe_toBasis_repr, CFC.posPart_algebraMap, abs_real_inner_div_norm_mul_norm_eq_one_of_ne_zero_of_ne_zero_mul, ContinuousLinearEquiv.hasFDerivAt, ContMDiffMap.smul_comp', hasStrictFDerivAt_list_prod, SchwartzMap.integral_bilinear_lineDerivOp_right_eq_neg_left, iteratedDeriv_const_smul_field, CFC.sqrt_one, HurwitzZeta.hasSum_int_sinZeta, CFC.log_le_log, NonUnitalContinuousFunctionalCalculus.compactSpace_quasispectrum, Metric.secondCountable_of_almost_dense_set, spectrum.resolvent_tendsto_cobounded, Complex.differentiable_sinh, InnerProductSpace.isIdempotentElem_rankOne_self_iff, Matrix.isUnit_exp, IsUltrametricDist.frontier_ball_eq_empty, ContinuousLinearMap.opNorm_nonneg, intervalIntegral.FTCFilter.nhds, AntitoneOn.integrableOn_of_measure_ne_top, ProbabilityTheory.stronglyMeasurable_condCDF, ContDiffBump.hasCompactSupport_normed, OpenPartialHomeomorph.contDiffOn_univBall_symm, VectorBundleCore.mem_localTriv_source, IsCompact.measure_eq_biInf_integral_hasCompactSupport, Pretrivialization.continuousLinearMap_symm_apply, iteratedDerivWithin_cot_sub_inv_eq_add_mul_tsum, CompactlySupportedContinuousMap.nnrealPart_apply, div_le_egauge_ball, hasDerivAtFilter_pi, stereographic_apply, StrongDual.polar_empty, ArithmeticFunction.LSeries_zeta_eulerProduct_exp_log, Orientation.rotation_apply, NormedAddGroupHom.completion_comp, ContinuousLinearMap.coe_flipₗᵢ, MeasureTheory.Measure.toSignedMeasure_apply_measurable, ContinuousAlternatingMap.fderivCompContinuousLinearMap_of_isEmpty, MeasureTheory.Measure.HasTemperateGrowth.exists_eLpNorm_lt_top, MeasureTheory.Lp.coeFn_zero, HasFPowerSeriesOnBall.iteratedFDeriv_eq_sum_of_completeSpace, NormedAddCommGroup.tendsto_atTop, ModularFormClass.hasSum_qExpansion_of_norm_lt, Submodule.inner_starProjection_left_eq_right, Real.tendsto_pow_logb_div_mul_add_atTop, PiLp.proj_apply, ContinuousLinearMap.normOneClass, MeasureTheory.mem_lpMeas_self, ContinuousLinearMap.opNNNorm_subsingleton, NumberField.mixedEmbedding.fundamentalCone.expMap_add, ContMDiffAt.mfderiv, CompactlySupportedContinuousMap.eq_toRealPositiveLinear_toReal, ContinuousLinearMap.IsPositive.spectrumRestricts, Real.deriv_fourierChar, CFC.nnrpow_eq_cfcₙ_real, OrthonormalBasis.sum_repr, MeasureTheory.norm_Lp_toLp_restrict_le, hasDerivAtFilter_const_add_iff, LinearMap.continuous_iff_isClosed_ker, homeomorphSphereProd_apply_snd_coe, MonoidHomClass.uniformContinuous_of_bound, TemperedDistribution.derivCLM_toTemperedDistributionCLM_eq, cpow_eq_nhds', MeasureTheory.Lp.coe_LpSubmodule, MeasureTheory.integrableOn_condExpL2_of_measure_ne_top, differentiableAt_snd, ContinuousAlternatingMap.neg_one_pow_smul_map_removeNth_add_eq_zero_of_eq, IsCoercive.ker_eq_bot, not_summable_iff_tendsto_nat_atTop_of_nonneg, hasDerivWithinAt_abs_neg, TestFunction.instLocallyConvexSpaceReal, ContinuousMultilinearMap.norm_mkPiAlgebra_of_empty, ModularFormClass.bdd_at_infty_slash, ContinuousLinearEquiv.analyticOnNhd, StieltjesFunction.ae_hasDerivAt, IsConformalMap.injective, InnerProductSpaceable.innerProp, NormedDivisionRing.to_isTopologicalDivisionRing, Real.rpow_eq_nhds_of_pos, jacobiTheta_eq_tsum_nat, LinearIsometry.strictConvexSpace_range, LeftInvariantDerivation.coe_zero, hasSum_sq_fourierCoeff, contDiff_infty_iff_deriv, PartitionOfUnity.sum_nonneg, Metric.eball_contractible, ContinuousLinearMap.opNorm_neg, PositiveLinearMap.norm_apply_le_of_nonneg, EReal.tendsto_toReal, ContinuousLinearMap.holder_add_right, MeasureTheory.Lp.enorm_def, differentiableWithinAt_smul_iff, MeasureTheory.condExpInd_disjoint_union_apply, ContinuousLinearMap.analyticOn_uncurry_of_multilinear, ProbabilityTheory.measure_condCDF_Iic, iteratedDeriv_one, Complex.differentiable_iteratedDeriv_sinh, polynomialFunctions.topologicalClosure, FormalMultilinearSeries.changeOrigin_eval, LSeries.term_sum_apply, NormedRing.inverse_continuousAt, LinearMap.toSeminorm_ball_zero, differentiableWithinAt_add_const_iff, Real.differentiableAt_negMulLog, LinearIsometryEquiv.hasFDerivWithinAt, ContinuousAlternatingMap.norm_alternatizeUncurryFin_le, ProbabilityTheory.HasSubgaussianMGF.aestronglyMeasurable, Submodule.fstL_comp_coe_orthogonalDecomposition, Meromorphic.sum, UpperHalfPlane.contMDiffAt_iff, Metric.eventually_notMem_thickening_of_infEDist_pos, Besicovitch.tendsto_filterAt, contMDiffOn_extend_symm, StrongConvexOn.strictConvexOn, iter_deriv_inv_linear_sub, Orientation.kahler_apply_apply, RCLike.imCLM_coe, Module.Basis.ofZLatticeBasis_comap, MeasureTheory.FiniteMeasure.toWeakDualBCNN_continuous, isStarProjection_iff_eq_starProjection_range, ContinuousLinearMap.add_compLpL, AbsolutelyContinuousOnInterval.uniformity_eq_comap_totalLengthFilter, Orientation.inner_rightAngleRotationAux₁_left, MeasureTheory.integral_indicator_const, UpperHalfPlane.instIsManifoldComplexModelWithCornersSelfTopWithTopENat, MeasureTheory.Lp.simpleFunc.aestronglyMeasurable, StieltjesFunction.id_apply, Complex.nhdsWithin_stolzCone_le_nhdsWithin_stolzSet, AnalyticAt.continuousAt, SchwartzMap.toZeroAtInfty_toBCF, ModelWithCorners.toHomeomorph_apply, MeasureTheory.Lp.tendsto_Lp_iff_tendsto_eLpNorm', CompactlySupportedContinuousMap.toReal_nonneg, separatesPoints_continuous_of_t35Space, Path.extend_extends', VonNeumannAlgebra.mem_commutant_iff, not_summable_of_ratio_norm_eventually_ge, Real.tendsto_logb_nhdsGT_zero_of_base_lt_one, exists_embedding_euclidean_of_compact, UnitAddTorus.mFourierBasis_repr, MeasureTheory.condExpIndL1Fin_ae_eq_condExpIndSMul, Complex.differentiableAt_sinh, HasFPowerSeriesAt.prod, LinearMap.toSeminorm_apply, nonneg_iff_isSelfAdjoint_and_quasispectrumRestricts, Real.continuousAt_rpow, hasDerivAt_ofReal_cpow_const', hasStrictDerivAt_natCast, LinearIsometryEquiv.toLinearIsometry_rTensor, Complex.hasDerivAt_Gamma_one_half, Function.Periodic.differentiable_qParam, Orientation.areaForm_apply_self, ModularForm.slash_def, MeasureTheory.Lp.norm_measure_zero, Complex.continuous_tan, ProbabilityTheory.measurable_measure_condCDF, CFC.sqrt_le_sqrt, MeasureTheory.ComplexMeasure.absolutelyContinuous_ennreal_iff, LeftInvariantDerivation.toDerivation_injective, Submodule.starProjection_minimal, PeriodPair.differentiableOn_weierstrassPExcept, EuclideanGeometry.orthogonalProjection_linear, HasFPowerSeriesAt.isBigO_sub_partialSum_pow, ContinuousLinearMap.contMDiffWithinAt, MeasureTheory.tendsto_indicatorConstLp_set, Orientation.oangle_smul_add_right_eq_zero_or_eq_pi_iff, lineDeriv_smul, MeasureTheory.integrable_rnDeriv_smul_iff, AlternatingMap.mkContinuousAlternating_norm_le_max, LipschitzWith.coeFn_compLp, PiTensorProduct.mapL_pow, LinearMap.continuous_of_isClosed_graph, summable_of_sum_range_le, Asymptotics.isLittleO_id_const, DoubleCentralizer.natCast_toProd, Real.differentiable_fourierChar_neg_bilinear_right, OrthonormalBasis.sum_rankOne_eq_id, ProbabilityTheory.strong_law_ae_simpleFunc_comp, Complex.conjCLE_norm, MeasureTheory.Lp.ker_toTemperedDistributionCLM_eq_bot, hasDerivAt_finCons', MeasureTheory.Lp.toTemperedDistribution_toLp_eq, MeasureTheory.SignedMeasure.rnDeriv_neg, ProbabilityTheory.stronglyMeasurable_gammaPDFReal, Complex.differentiableAt_log, fourierBasis_repr, LeftInvariantDerivation.evalAt_mul, absorbs_iff_eventually_nhds_zero, cfcHom_predicate, MeasureTheory.SignedMeasure.integrable_rnDeriv, differentiableAt_completedZeta, AffineSubspace.signedInfDist_def, NNReal.coeNNRealReal_zero, MeasureTheory.Measure.addHaar_closedBall, ContinuousLinearMap.unit_le_opNorm, ZeroAtInftyContinuousMap.isBounded_range, PeriodPair.derivWeierstrassPExcept_add_coe, NumberField.mixedEmbedding.fundamentalCone.expMapBasis_apply, HasFPowerSeriesWithinAt.add, Path.truncate_continuous_family, Metric.isPathConnected_eball, Submodule.starProjection_mem_subspace_eq_self, Complex.norm_deriv_le_of_forall_mem_sphere_norm_le, MeasureTheory.BoundedContinuousFunction.inner_toLp, Complex.isQuotientMap_re, ContinuousLinearMap.adjoint_inner_right, Submodule.angle_coe, exists_extension_norm_eq, NormedAddGroupHom.extension_def, CFC.negPart_def, HasMFDerivAt.prodMk, CStarModule.continuous_inner, ProbabilityTheory.integrable_exp_mul_of_le, instSecondCountableTopologyReal, SeminormedCommGroup.to_isUniformGroup, ContinuousLinearMap.norm_id, MeasureTheory.submartingale_iff_condExp_sub_nonneg, instIsTopologicalAddGroupReal, FormalMultilinearSeries.id_apply_of_one_lt, ContinuousMultilinearMap.nnnorm_ofSubsingleton_id, CuspFormClass.zero_at_infty_slash, MeasureTheory.Lp.coeFn_neg, tendsto_fib_succ_div_fib_atTop, NontrivialTopology.of_exists_nnnorm_ne_zero', HasFiniteFPowerSeriesOnBall.hasStrictFDerivAt, TensorProduct.norm_tmul, ContDiff.contDiff_fderiv_apply, LinearMap.isPositive_iff, MeasureTheory.L1.norm_Integral_le_one, Metric.contractibleSpace_closedEBall, ProbabilityTheory.instIsProbabilityMeasure_stieltjesOfMeasurableRat, TopologicalSpace.IsCompletelyMetrizableSpace.complete, ContinuousLinearMap.measurable_apply', ContDiffMapSupportedIn.coe_coeHom, VectorFourier.fourierIntegral_comp_add_right, NormedSpace.closedBall_inv_subset_polar_closedBall, ContinuousMap.addEquivBoundedOfCompact_symm_apply, InnerProductSpace.isOpen_setOf_harmonicAt, ContDiffMapSupportedIn.postcompLM_apply, PeriodPair.differentiableOn_weierstrassP, MeromorphicOn.fun_sum, ProbabilityTheory.IsGaussian.integral_dual_conv_map_neg_eq_zero, UnitAddTorus.span_mFourier_closure_eq_top, ContDiff.dimH_range_le, signedDist_lineMap_right, analyticOrderAt_smul, ContinuousLinearMap.norm_smulRightL_le, TemperedDistribution.laplacian_apply_apply, MeasureTheory.Lp.coeFn_abs, DoubleCentralizer.one_toProd, Metric.isUniformEmbedding_iff, MeasureTheory.stronglyAdapted_predictablePart, MeasureTheory.withDensityᵥ_smul', ModularForm.is_invariant_one', Real.expPartialHomeomorph_symm_apply, AkraBazziRecurrence.isLittleO_deriv_one_sub_smoothingFn, HasFPowerSeriesOnBall.image_sub_sub_deriv_le, NormedSpace.expSeries_radius_pos, Complex.imCLM_enorm, TemperedDistribution.smulLeftCLM_smulLeftCLM_apply, IsUltrametricDist.nonarchimedeanGroup, hasDerivAtFilter_const, Metric.nhds_basis_ball_inv_nat_succ, SchwartzMap.tsupport_derivCLM_subset, CFC.sqrt_rpow_nnreal, Affine.Simplex.orthogonalProjectionSpan_eulerPoint_mem_ninePointCircle, isLocalHomeomorph_circleExp, hasDerivAt_single, deriv_fun_const_smul_field, MeasureTheory.Measure.toSignedMeasure_sub_apply, tendsto_integral_exp_inner_smul_cocompact, OrthonormalBasis.coe_toBasis_repr_apply, EisensteinSeries.tendsto_tsum_one_div_linear_sub_succ_eq, mdifferentiableWithinAt_iff_source_of_mem_source, RCLike.enorm_conj, LinearIsometryEquiv.toContinuousLinearEquiv_injective, PadicInt.norm_mahler_eq, MeasureTheory.Lp.norm_eq_zero_iff, VectorField.leibniz_identity_lieBracket, UpperHalfPlane.mdifferentiable_coe, Real.hasSum_arctan, ContinuousLinearMap.coe_symm_flipMultilinearEquiv, IsBoundedLinearMap.tendsto, SeparationQuotient.norm_mk, PiLp.coe_symm_continuousLinearEquiv, differentiableOn_apply, Trivialization.contMDiffOn_symm, ZLattice.normBound_spec, instContinuousStarReal, HasFPowerSeriesOnBall.continuousOn, nnnorm_cfc_nnreal_lt_iff, Metric.tendstoUniformlyOnFilter_iff, LinearIsometryEquiv.star_eq_symm, ContinuousLinearEquiv.dimH_preimage, NumberField.mixedEmbedding.homeoRealMixedSpacePolarSpace_apply_snd, ContinuousLinearMap.reApplyInnerSelf_continuous, Real.tendsto_abs_tan_atTop, Manifold.lintegral_norm_mfderiv_Icc_eq_pathELength_projIcc, hasStrictFDerivAt_add_const_iff, SchwartzMap.integral_smul_laplacian_right_eq_left, differentiableAt_pi, Complex.arg_eq_nhds_of_re_pos, Orientation.norm_div_tan_oangle_add_right_of_oangle_eq_pi_div_two, TopologicalSpace.exists_embedding_l_infty, Real.Angle.eq_add_pi_of_two_zsmul_eq_of_sign_eq_neg, FormalMultilinearSeries.radius_prod_eq_min, Metric.inseparable_iff_nndist, tendsto_norm_nhdsNE_zero, AddMonoidHomClass.uniformContinuous_of_bound, ModelWithCorners.isClosed_range, OrthonormalBasis.coe_equiv_euclideanSpace, differentiable_norm_rpow, VectorFourier.fourierIntegral_probChar, summable_cotTerm, MeasureTheory.eLpNorm_eq_zero_and_zero_of_ae_le_mul_neg, AffineIsometryEquiv.coe_symm_toContinuousAffineEquiv, ContinuousLinearEquiv.continuousAlternatingMapCongr_apply, CompactlySupportedContinuousMap.nnrealPart_smul_pos, continuousAt_jacobiTheta₂', Affine.Simplex.sign_signedInfDist_incenter, Affine.Simplex.ExcenterExists.sign_signedInfDist_excenter, ContinuousMap.polynomial_comp_attachBound, IsUltrametricDist.isClopen_sphere, VectorFourier.norm_fourierSMulRight_le, AlternatingMap.measure_parallelepiped, RCLike.wInner_one_eq_sum, IsSelfAdjoint.self_add_I_smul_cfcSqrt_sub_sq_mem_unitary, summable_norm_geometric_of_norm_lt_one, ContinuousAffineMap.hasFDerivWithinAt, Asymptotics.isLittleO_iff_tendsto, IsContDiffImplicitAt.comp_implicitFunctionAux_eq_snd, CompareReals.compare_uc_symm, ContinuousAlternatingMap.nnnorm_ofSubsingleton, norm_cfcHom, IsMIntegralCurveOn.continuousOn, RCLike.toContinuousLinearMap_complexLinearIsometryEquiv, EisensteinSeries.eisSummand_extension_differentiableOn, MeasureTheory.charFunDual_map, ModelWithCorners.continuousAt_symm, hasFDerivWithinAt_add_const_iff, summable_geometric_two', HasFiniteFPowerSeriesOnBall.fderiv', Orientation.two_zsmul_oangle_smul_left_self, Memℓp.summable, Monotone.intervalIntegrable, Orientation.kahler_rotation_right, Complex.ofRealCLM_enorm, Complex.arg_pow_coe_angle, Submodule.orthogonalProjectionFn_eq, Fourier.fourierIntegral_def, Complex.isOpenQuotientMap_pow_compl_zero, uniqueDiffWithinAt_Ici, DirichletCharacter.LFunctionTrivChar_isBigO_near_one_horizontal, ZSpan.discreteTopology_pi_basisFun, ContinuousMultilinearMap.currySum_apply, isOpenMap_barycentric_coord, TensorProduct.nnnorm_comm, Submodule.IsOrtho.ge, NNReal.tendsto_coe, ApproximatesLinearOn.continuousOn, Affine.Simplex.signedInfDist_affineCombination, Metric.nhds_basis_ball, Complex.deriv_sinh, TemperedDistribution.lineDerivOp_apply_apply, ImplicitFunctionData.toOpenPartialHomeomorph_coe, CompactlySupportedContinuousMap.integralPositiveLinearMap_toFun, MeasureTheory.ComplexMeasure.re_apply, MeasureTheory.Lp.coeFn_sub, Polynomial.differentiableWithinAt_aeval, Metric.isClosedEmbedding_of_pairwise_le_dist, Submodule.bot_orthogonal_eq_top, intervalIntegral.intervalIntegrable_cpow', Complex.deriv_sin, Real.one_div_sub_pow_hasFPowerSeriesOnBall_zero, signedDist_apply, closure_ball, UniformSpace.Completion.inner_coe, Unitization.norm_splitMul_snd_sq, curveIntegral_cast, interior_closedBall', geom_series_mul_neg, MeasureTheory.memLp_neg_iff, ContinuousLinearMap.IsPositive.conj_starProjection, MeasureTheory.integrable_pi_iff, WeakDual.CharacterSpace.equivAlgHom_coe, ContinuousMap.HomotopyWith.continuous, Real.coe_tanPartialHomeomorph_symm, EuclideanGeometry.angle_self_orthogonalProjection, MeasureTheory.tendstoInMeasure_iff_enorm, measurable_fderiv, MeasureTheory.eLpNormEssSup_lt_top_of_ae_nnnorm_bound, continuousMultilinearCurryRightEquiv_apply', ContinuousLinearMap.flipₗᵢ'_symm, NormedAddGroupHom.completion_coe', le_egauge_ball_one, MeasureTheory.Lp.meas_ge_le_mul_pow_enorm, EuclideanSpace.inner_toLp_toLp, NumberField.mixedEmbedding.polarSpaceCoord_source, Metric.lipschitz_infDist_set, cfc_real_eq_complex, Bundle.contMDiffAt_proj, UnitAddTorus.hasSum_sq_mFourierCoeff, TemperedDistribution.lineDerivOp_fourierInv_eq, CFC.norm_rpow, HasFPowerSeriesWithinOnBall.continuousWithinAt_insert, MonotoneOn.memLp_isCompact, not_integrableOn_Ici_inv, Submodule.map_orthogonal, Complex.hasSum_taylorSeries_log, fourierCoeffOn_eq_integral, ProbabilityTheory.IsGaussian.charFunDual_eq_of_integral_eq_zero, ContinuousMap.toNNReal_neg_one, DoubleCentralizer.natCast_snd, VonNeumannAlgebra.coe_commutant, ContDiffMapSupportedIn.bounded_iteratedFDeriv, AffineEquiv.coe_toHomeomorphOfFiniteDimensional_symm, HasFTaylorSeriesUpToOn.differentiableOn, MeasureTheory.SimpleFunc.integral_const, MeromorphicOn.negPart_divisor_add_le_add, frontier_sphere, CompactConvergenceCLM.continuousSMul, Circle.expHom_apply, MeromorphicAt.deriv, HasFiniteFPowerSeriesOnBall.hasFDerivAt, homeomorphUnitSphereProd_apply_snd_coe, ProbabilityTheory.IsRatCondKernelCDFAux.tendsto_atTop_one, ProbabilityTheory.isGaussian_map_equiv, differentiableWithinAt_const_sub_iff, tendsto_pow_const_div_const_pow_of_one_lt, contMDiffAt_addInvariantVectorField, ordinaryHypergeometric_radius_top_of_neg_nat₁, hasStrictDerivAt_zero, intervalIntegral.intervalIntegrable_rpow', MonotoneOn.integrableOn_of_measure_ne_top, PeriodPair.hasSum_sumInvPow, VectorBundleCore.coordChange_linear_comp, Real.differentiableAt_sinh, ContinuousAlternatingMap.alternatizeUncurryFin_add, Units.contMDiff_val, DirichletCharacter.LFunctionTrivChar_residue_one, contMDiff_tangentBundleModelSpaceHomeomorph, MeasureTheory.addHaarMeasure_eq_volume, Complex.hasDerivAt_tan, ContinuousLinearMap.isBigOTVS_fun_comp, Orientation.oangle_sign_smul_add_smul_right, Module.Basis.ofZLatticeComap_repr_apply, Real.Angle.nsmul_toReal_eq_mul, signedDist_eq_dist_iff_vsub_mem_span, Real.continuous_ofDigits, ProbabilityTheory.covarianceBilin_map_const_add, uniqueDiffOn_Ioo, Real.continuousAt_logb, HasSolidNorm.orderClosedTopology, Real.differentiable_iteratedDeriv_sinh, AffineSubspace.direction_perpBisector, Complex.lintegral_comp_pi_polarCoord_symm, TestFunction.hasCompactSupport, Besicovitch.multiplicity_le, curveIntegralFun_symm, NumberField.mixedEmbedding.fundamentalCone.setLIntegral_expMapBasis_image, RCLike.instOrderClosedTopology, NumberField.mixedEmbedding.fundamentalCone.expMap_single_apply, FormalMultilinearSeries.coeff_iterate_fslope, HasFPowerSeriesOnBall.changeOrigin, EisensteinSeries.eisensteinSeries_tendstoLocallyUniformlyOn, HasFPowerSeriesAt.eq_zero, ContinuousLinearMap.coeFn_compLp, DomMulAct.nnnorm_smul_Lp, ProbabilityTheory.setLIntegral_condCDF, ContinuousLinearMap.flip_zero, FormalMultilinearSeries.leftInv_removeZero, ZetaAsymptotics.term_welldef, modelWithCornersSelf_coe, conformalAt_iff_differentiableAt_or_differentiableAt_comp_conj, deriv_const_smul', exp_neg_integrableOn_Ioi, intervalIntegral.integral_comp_mul_right, ImplicitFunctionData.prod_map_implicitFunction, LSeriesHasSum.sum, ContinuousLinearMap.extendTo𝕜'_apply, hasFDerivWithinAt_comp_sub, derivWithin_comp_sub_const, ClosedSubmodule.orthogonal_disjoint, continuous_descPochhammer_eval, CompletelyPositiveMap.map_cstarMatrix_nonneg', IsLocalFrameOn.coeff_eq_of_eq, Metric.closedBall_infDist_compl_subset_closure, ContDiff.differentiable_iteratedDeriv', iteratedFDerivWithin_const_of_ne, ContinuousMultilinearMap.norm_ofSubsingleton, ContinuousAt.inner_bundle, ContinuousLinearMap.isAdjointPair_inner, AddCircle.instProperlyDiscontinuousVAddSubtypeAddOppositeRealMemAddSubgroupOpZmultiples, VectorFourier.norm_fourierPowSMulRight_le, NormedSpace.norm_expSeries_div_summable, CStarMatrix.uniformEmbedding_ofMatrix, TensorProduct.norm_map, EuclideanGeometry.dist_smul_vadd_eq_dist, derivWithin_Ioi_eq_Ici, dist_birkhoffAverage_birkhoffAverage_le, Complex.equivRealProdCLM_symm_apply_im, ContinuousLinearMap.coe_le_coe_iff, AddChar.linearIndependent, MeasureTheory.integral_singleton, summable_pow_mul_jacobiTheta₂_term_bound, ContinuousLinearEquiv.continuousMultilinearMapCongrRight_apply, intervalIntegral.integral_comp_div_sub, coe_ringEquiv_lpBCF_symm, hasFDerivAtFilter_finCons', ContinuousLinearEquiv.analyticWithinAt, integrable_exp_neg_mul_sq_iff, Complex.polarCoord_symm_apply, SmoothPartitionOfUnity.mem_fintsupport_iff, AnalyticAt.eventually_analyticAt, MeasureTheory.Measure.integrableOn_toReal_rnDeriv, not_integrableOn_Ioi_inv, Emetric.exists_smooth_forall_closedBall_subset, ProbabilityTheory.norm_uncenteredCovarianceBilin_le, ConvexBody.hausdorffDist_coe, MeasureTheory.SimpleFunc.integrable_iff_finMeasSupp, UnitAddTorus.mFourier_single, Real.hasFDerivAt_fourierChar_neg_bilinear_right, MeasureTheory.lintegral_nnnorm_condExpIndSMul_le, EuclideanGeometry.orthogonalProjection_eq_self_iff, LinearIsometryEquiv.differentiableAt, LipschitzWith.continuous_compLp, summable_bernoulli_fourier, ContinuousWithinAt.inner_bundle, ModularFormClass.differentiableOn_cuspFunction_ball, LinearIsometryEquiv.differentiable, ProbabilityTheory.IsMeasurableRatCDF.measurable_measure_stieltjesFunction, Unitization.splitMul_injective, MeasureTheory.eLpNorm'_const_smul_le', isInvertible_mfderiv_extChartAt, ProbabilityTheory.measure_condCDF_univ, Antitone.deriv_nonpos, lp.norm_eq_tsum_rpow, not_summable_one_div_on_primes, WeakFEPair.f_modif_aux1, ZMod.differentiable_completedLFunction₀, SeparationQuotient.dist_mk, Cube.insertAt_boundary, ContinuousMap.ker_evalStarAlgHom_inter_adjoin_id, MeasureTheory.Lp.smul_assoc, ContDiffMapSupportedIn.continuous_iff_comp, ContinuousMultilinearMap.norm_map_insertNth_le, PeriodPair.periodic_weierstrassP, HasFPowerSeriesAt.coeff_zero, Submodule.orthogonal_le_orthogonal_iff, DoubleCentralizer.sub_snd, intervalIntegrable_log_norm_meromorphicOn, ModelWithCorners.coe_transContinuousLinearEquiv, ProbabilityTheory.lintegral_stieltjesOfMeasurableRat, MonotoneOn.nnnorm_cfc, Submodule.orthogonal_le_iff_orthogonal_le, ModularFormClass.holo, ProperSpace.isCompact_closedBall, ContDiffOn.comp_continuousLinearMap, Seminorm.uniformContinuous', VectorFourier.norm_fourierSMulRight, AffineIsometryEquiv.comp_continuousOn_iff, mdifferentiableWithinAt_prod_module_iff, Polynomial.differentiable, MeasureTheory.integrable_condExpIndSMul, MeasureTheory.FiniteMeasure.isEmbedding_toWeakDualBCNN, PadicInt.isOpenEmbedding_coe, mdifferentiableAt_iff_target, InnerProductSpace.volume_closedBall, ContinuousLinearEquiv.coord_norm', PNat.instNoncompactSpace, completedRiemannZeta_residue_one, IsUltrametricDist.isClopen_closedBall, HasFPowerSeriesOnBall.hasSum_sub, EisensteinSeries.summable_e2Summand_symmetricIco, ContinuousLinearMap.nnnorm_id, GaussianFourier.integrable_cexp_neg_sum_mul_add, stereographic'_symm_apply, Asymptotics.IsBigO.id_rpow_of_le_one, differentiableOn_abs, contMDiff_pi_space, MeasureTheory.LevyProkhorov.le_convergenceInDistribution, contMDiffAt_extChartAt', Bundle.Trivial.symmₗ_trivialization, WithCStarModule.pi_norm_sq, NormedAddCommGroup.nhds_zero_basis_norm_lt, OrthonormalBasis.toMatrix_orthonormalBasis_self_mul_conjTranspose, Probability.stronglyMeasurable_cauchyPDFReal, MeasureTheory.eLpNorm_const_lt_top_iff, Complex.hasSum_sinh, NormedSpace.norm_smul_normalize, ContinuousLinearMap.isPositive_zero, div_le_egauge_closedBall, NumberField.mixedEmbedding.polarCoord_target_eq_polarCoordReal_target, hasStrictFDerivAt_inv', LinearMap.mem_span_iff_bound, cfcₙL_apply, homeomorphSphereProd_apply_fst_coe, MeasureTheory.ProbabilityMeasure.continuous_integral_continuousMap, ProbabilityTheory.integrable_toReal_condDistrib, uniqueMDiffWithinAt_iff_uniqueDiffWithinAt, Circle.arg_exp, hasDerivAt_mul_const, uniformContinuous_vadd, Metric.continuousAt_iff, MeromorphicAt.meromorphicTrailingCoeffAt_add_eq_left_of_lt, MeasureTheory.ConvolutionExists.distrib_add, Metric.nhds_basis_closedBall, MeasureTheory.Lp.toTemperedDistribution_apply, SchwartzMap.smulLeftCLM_sub, Submodule.snd_orthogonalDecomposition_apply, summable_geometric_two, cfcHomSuperset_continuous, Orientation.norm_div_sin_oangle_add_right_of_oangle_eq_pi_div_two, TemperedDistribution.smulLeftCLM_const, MeasureTheory.Martingale.ae_eq_condExp_limitProcess, SchwartzMap.smulLeftCLM_apply_apply, deriv_inv', deriv_descPochhammer_eval_eq_sum_prod_range_erase, Probability.integrable_cauchyPDFReal, strongConvexOn_iff_convex, cfcₙ_apply_mem_elemental, LipschitzWith.compLp_zero, Module.Basis.ofZLatticeBasis_repr_apply, MeasureTheory.integrable_toReal_iff, Real.not_continuousAt_inv_log_one, Orientation.oangle_eq_pi_iff_sameRay_neg, CFC.posPart_def, MeasureTheory.charFunDual_pi, strongConvexOn_zero, CFC.nnrpow_eq_rpow, SchwartzMap.fourier_fderivCLM_eq, SpectrumRestricts.nnreal_iff_spectralRadius_le, Unitary.conjStarAlgAut_symm_unitaryLinearIsometryEquiv, ConvexBody.hausdorffEDist_coe, PartitionOfUnity.finite_tsupport, integrable_mulExpNegMulSq_comp_restrict_of_isCompact, hasStrictFDerivAt_exp_smul_const, FormalMultilinearSeries.radius_eq_top_iff_summable_norm, MeasureTheory.SimpleFunc.integral_eq, CircleDeg1Lift.tendsto_translationNumber, integrableOn_rpow_mul_exp_neg_mul_sq, integral_withDensity_eq_integral_toReal_smul₀, VectorPrebundle.totalSpaceMk_preimage_source, MonotoneOn.memLp_top, SchwartzMap.fourier_convolution_apply, BoxIntegral.Integrable.tendsto_integralSum_sum_integral, Complex.hasStrictFDerivAt_log_real, Complex.differentiableAt_Gamma, Filter.Tendsto.pathExtend, MeasureTheory.SimpleFunc.setToSimpleFunc_const', Asymptotics.isBigOTVS_map, MeasureTheory.condExpL1_zero, iteratedFDeriv_two_apply, ContinuousMultilinearMap.analyticOnNhd_uncurry_compContinuousLinearMap, Real.summable_one_div_nat_pow, LinearIsometry.norm_toContinuousLinearMap_le, Real.hasStrictDerivAt_tan, MeasureTheory.Lp.compMeasurePreserving_continuous, Real.borelSpace, Submodule.starProjection_le_starProjection_iff, TestFunction.coe_toBoundedContinuousFunction, iteratedFDerivWithin_zero_fun, TangentBundle.coe_chartAt_symm_fst, ContDiffAt.smul, ExistsContDiffBumpBase.w_integral, CFC.cfcₙ_rpowIntegrand₀₁_eq_cfcₙ_rpowIntegrand₀₁_one, ENNReal.continuousOn_toReal, RCLike.wInner_cWeight_const_right, TemperedDistribution.smulLeftCLM_sum, mahler_apply, NumberField.mixedEmbedding.fundamentalCone.compactSet_ae, StieltjesFunction.measure_Ico, Metric.unitClosedBall.instContinuousMul, NumberField.InfinitePlace.Completion.WithAbs.ratCast_equiv, Real.tendsto_euler_sin_prod, NumberField.mixedEmbedding.fundamentalCone.abs_det_fderiv_expMapBasis, eventually_residual_liouville, ContinuousLinearMap.analyticOnNhd, fderiv_fst, iter_deriv_inv_linear, MeasureTheory.FiniteMeasure.continuous_iff_forall_continuousMap_continuous_integral, MeasureTheory.JordanDecomposition.toSignedMeasure_zero, EisensteinSeries.summable_right_one_div_linear_sub_one_div_linear_succ, NumberField.mixedEmbedding.instIsAddHaarMeasureRealMixedSpaceVolume, HurwitzZeta.differentiableAt_cosZeta, AffineMap.differentiable, Irreducible.maximalIdeal_pow_eq_closedBall_pow, ContDiffAt.continuousAt, ProbabilityTheory.IsGaussian.memLp_two_fun_id, Complex.hasSum_sin', jacobiTheta₂_fderiv_undef, MeasureTheory.Lp.coeFn_posPart, Int.isUniformEmbedding_coe_real, ContinuousAlternatingMap.differentiable, WeakDual.toStrongDual_apply, AffineEquiv.coe_toHomeomorphOfFiniteDimensional, ContinuousLinearEquiv.uniqueDiffOn_image_iff, ModelWithCorners.isClosedEmbedding, ContinuousMap.elemental_id_eq_top, NumberField.mixedEmbedding.euclidean.finrank, ZeroAtInftyContinuousMap.tendsto_iff_tendstoUniformly, LinearMap.eq_adjoint_iff_basis_right, instPerfectSpace, Complex.arg_eq_nhds_of_re_neg_of_im_pos, ContinuousLinearMap.hasMFDerivWithinAt, ContinuousLinearEquiv.nnnorm_symm_pos, pi_polarCoord_symm_target_ae_eq_univ, InnerProductSpace.laplacian_smul_nhds, Bundle.contMDiffWithinAt_section, MeasureTheory.Measure.toSphereBallBound_mul_measure_unitBall_le_toSphere_ball, Real.differentiable_fourierChar_neg_bilinear_left, Submodule.instOrthogonalCompleteSpace, UniformSpace.Completion.dist_triangle, NNReal.tendsto_coe', continuous_nnnorm', FormalMultilinearSeries.enorm_compContinuousLinearMap_le, ConvexBody.hausdorffEdist_coe, EisensteinSeries.summable_linear_right_add_one_mul_linear_right, ModularForm.is_invariant_const, AffineBasis.centroid_mem_interior_convexHull, EReal.isEmbedding_coe, Urysohns.CU.continuous_lim, MeasureTheory.levyProkhorov_le_convergenceInDistribution, MeasureTheory.isTightMeasureSet_iff_tendsto_measure_norm_gt, Orthonormal.enorm_eq_one, IsSelfAdjoint.commute_cfcₙ, fderiv_norm_smul_pos, gelfandTransform_isometry, FormalMultilinearSeries.le_radius_pi, Real.hasDerivAt_arctan, NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_expMap_symm, continuousMultilinearCurryLeftEquiv_symm_apply, MeasureTheory.integral_def, Path.Homotopy.source, WithLp.unitization_mul, MeasureTheory.Measure.addHaar_closedBall_mul, IsUnit.integrable_smul_iff, hasDerivAt_exp_smul_const', Bundle.mdifferentiableOn_zeroSection, Metric.ediam_univ_eq_top_iff_noncompact, hasFDerivAtFilter_const_add_iff, meromorphicOrderAt_add_eq_right_of_lt, DoubleCentralizer.instStarModule, WeakDual.CharacterSpace.compContinuousMap_comp, intervalIntegral.FTCFilter.nhdsLeft, MeasureTheory.L1.norm_sub_eq_lintegral, iteratedFDeriv_comp_add_right', VectorBundleCore.localTriv.isLinear, Affine.Simplex.ExcenterExists.signedInfDist_excenter_eq_mul_sum_inv, ProbabilityTheory.geometricPMFRealSum, tendsto_seminormFromConst_seq_atTop, geometric_hahn_banach_closed_point, instOrderIsoClassContinuousLinearMapIdOfNonUnitalAlgEquivClassOfStarHomClassOfContinuousMapClass, hasDerivWithinAt_id, ContinuousMultilinearMap.smulRightL_apply, Complex.betaIntegral_convergent_left, ContinuousLinearMap.contDiff, hasSum_one_div_pow_mul_fourier_mul_bernoulliFun, MeasureTheory.LevyProkhorov.continuous_toMeasure_probabilityMeasure, polynomialFunctions_closure_eq_top', Complex.continuousAt_cpow_of_re_pos, TemperedDistribution.instContinuousFourierInv, NumberField.mixedEmbedding.measurableSet_negAt_plusPart, differentiable_star_iff, ContinuousLinearMap.instBorelSpace, MeasureTheory.norm_indicatorConstLp', LinearMap.isStarProjection_iff_isSymmetricProjection, LinearIsometryEquiv.toLinearEquiv_rTensor, CStarAlgebra.star_right_conjugate_le_norm_smul, innerₛₗ_apply_coe, MeasureTheory.SignedMeasure.toComplexMeasure_apply_im, Finset.analyticWithinAt_sum, AnalyticOn.differentiableOn, AffineIsometryEquiv.coe_toHomeomorph, Complex.sin_eq_tsum', ProbabilityTheory.measurable_condCDF, NumberField.mixedEmbedding.homeoRealMixedSpacePolarSpace_symm_apply, PiLp.inner_apply, SchwartzMap.integrable, bernstein.probability, TestFunction.instContinuousSMulReal, MeasureTheory.integral_comp_mul_left_Ioi, IsBoundedLinearMap.hasFDerivAt, MeasureTheory.Lp.neg_smul_neg, AkraBazziRecurrence.growsPolynomially_deriv_rpow_p_mul_one_sub_smoothingFn, Complex.one_add_cpow_hasFPowerSeriesOnBall_zero, Complex.reCLM_norm, Orientation.tan_oangle_add_right_mul_norm_of_oangle_eq_pi_div_two, ContMDiffSection.mdifferentiable', MulOpposite.toContinuousLinearEquiv_opLinearIsometryEquiv, ContinuousLinearMap.norm_snd_le, ModularForm.SL_slash_apply, MeasureTheory.Measure.instIsLocallyFiniteMeasureMeasure, contMDiff_tangentBundleModelSpaceHomeomorph_symm, completelyRegularSpace_iff, ContinuousMap.norm_smul_const, Submodule.orthogonalDecomposition_apply, iteratedFDeriv_succ_eq_comp_left, IsUnifLocDoublingMeasure.eventually_measure_le_scaling_constant_mul, LinearIsometryEquiv.comp_hasFDerivWithinAt_iff, MeasureTheory.isometry_lpMeasSubgroupToLpTrim, Submodule.isOrtho_self, OpenPartialHomeomorph.ball_subset_univBall_target, LinearIsometryEquiv.toLinearIsometry_lTensor, Metric.continuousOn_iff', ContinuousMapZero.toNNReal_neg_smul, MeasureTheory.integrable_condExpL1, Real.Angle.abs_toReal_add_eq_two_pi_sub_abs_toReal_add_abs_toReal, ContinuousLinearMap.smul_compLpL, summable_geometric_of_norm_lt_one, isClosed_nullAddSubgroup, unitary.isPathConnected_ball, continuousOn_cfc_nnreal_setProd, differentiableAt_of_deriv_ne_zero, FormalMultilinearSeries.summable_norm_mul_pow, ContinuousLinearMap.contMDiffOn, ProbabilityTheory.instIsGaussianMapHAdd, VonNeumannAlgebra.instStarMemClass, Rat.isUniformEmbedding_coe_real, ModelWithCorners.coe_extChartAt_transContinuousLinearEquiv, ZMod.LFunction_residue_one, LinearIsometry.isComplete_map_iff', Metric.exists_mem_closure_infDist_eq_dist, contMDiffOn_coordChangeL, NumberField.mixedEmbedding.euclidean.volumePreserving_toMixed_symm, NumberField.mixedEmbedding.convexBodySum_convex, IsBoundedLinearMap.hasFDerivWithinAt, OrthonormalBasis.toMatrix_orthonormalBasis_conjTranspose_mul_self, ContinuousLinearMap.nnbound, ContinuousMap.polynomial_comp_attachBound_mem, PeriodPair.mul_ω₁_add_mul_ω₂_mem_lattice, range_cfcHom, ContinuousLinearMap.opNorm_mulLeftRight_le, Matrix.SpecialLinearGroup.discreteSpecialLinearGroupIntRange, DoubleCentralizer.intCast_fst, Circle.coe_exp, convex_halfSpace_im_le, Polynomial.Chebyshev.isLocalExtr_T_real, MeasureTheory.measure_smul_setAverage, ClosedSubmodule.orthogonal_closure, ContDiffPointwiseHolderAt.iteratedFDeriv, ContinuousLinearMap.norm_compLpL_le, contMDiffOn_model_symm, ZSpan.vadd_mem_fundamentalDomain, DomMulAct.smul_Lp_const, riemannZeta_eulerProduct_tprod, NumberField.Ideal.tendsto_norm_le_and_mk_eq_div_atTop, LinearMap.toSeminormFamily_apply, MeasureTheory.ComplexMeasure.toComplexMeasure_to_signedMeasure, MeasureTheory.Measure.LinearMap.quasiMeasurePreserving, nnnorm_tangentSpace_vectorSpace, ProbabilityTheory.stronglyMeasurable_betaPDFReal, CFC.abs_one, mfderiv_eq_fderiv, cpow_eq_nhds, hasGradientWithinAt_iff_tendsto, OrthonormalBasis.toMatrix_orthonormalBasis_mem_orthogonal, ContDiffMapSupportedIn.structureMapCLM_zero_injective, ContinuousMap.isometryEquivBoundedOfCompact_symm_apply, ContinuousAlternatingMap.neg_one_pow_smul_map_insertNth, derivWithin_add_const, ProbabilityTheory.IsMeasurableRatCDF.tendsto_stieltjesFunction_atTop, TemperedDistribution.fourier_apply, RCLike.iInter_halfSpaces_eq, StrongDual.polar_zero, Memℓp.add, fderiv_comp_add_left, CStarAlgebra.nonneg_TFAE, ContinuousMultilinearMap.piₗᵢ_apply, meromorphicAt_smul_iff_of_ne_zero, nnnorm_cfcHom, Matrix.PosSemidef.sqrt_mul_self, Orientation.areaForm_rightAngleRotation_right, MeasureTheory.setIntegral_condExpL1CLM, MeasureTheory.L1.hasFiniteIntegral_coeFn, ContDiffAt.continuousAt_iteratedFDeriv, ZSpan.fract_apply, iteratedFDeriv_apply_eq_iteratedDeriv_mul_prod, NormedRing.inverse_one_sub_nth_order', NormedSpace.exp_add_of_commute, Real.deriv_arcsin_aux, Complex.differentiable_cosh, Orientation.oangle_sign_add_right, WeakDual.CharacterSpace.equivAlgHom_symm_coe, ContinuousMultilinearMap.ofSubsingletonₗᵢ_apply, Complex.tendsto_log_nhdsWithin_im_nonneg_of_re_neg_of_im_zero, fourier_add', RCLike.continuous_im, ProperCone.hyperplane_separation, Module.Basis.map_addHaar, Circle.exp_zsmul, ContinuousLinearMap.cpolynomialOn, ProbabilityTheory.IsCondKernelCDF.lintegral, ContinuousAlternatingMap.nnnorm_ofSubsingleton_id_le, MeasureTheory.hasFiniteIntegral_congr', LinearMap.coe_toContinuousLinearMap_symm, tsum_of_nnnorm_bounded, fderiv_comp_sub, InnerProductGeometry.norm_add_sq_eq_norm_sq_add_norm_sq', HasFPowerSeriesAt.continuousAt, ContinuousAlternatingMap.nnnorm_constOfIsEmpty, hasStrictFDerivAt_list_prod', Complex.frontier_setOf_le_re_and_im_le, Real.differentiableAt_qaryEntropy, ContinuousLinearMap.le_opENorm, continuousMultilinearCurryFin1_symm_apply, MeasureTheory.Measure.setIntegral_comp_smul_of_pos, NNReal.hasSum_coe, EuclideanGeometry.orthogonalProjection_vsub_mem_direction_orthogonal, differentiableWithinAt_comp_add_left, Trivialization.symmL_apply, ContinuousMultilinearMap.opNorm_le_iff, ProbabilityTheory.Kernel.HasSubgaussianMGF.ae_aestronglyMeasurable, AnalyticAt.exists_eventuallyEq_pow_smul_nonzero_iff, Real.tendsto_sin_pi_div_two, intervalIntegral.integral_comp_mul_add, Complex.continuousAt_Gamma, StrongDual.mem_polar_iff, FormalMultilinearSeries.radius_pi_le, Affine.Simplex.exists_forall_signedInfDist_eq_iff_excenterExists_and_eq_excenter, EisensteinSeries.eisensteinSeries_SIF_MDifferentiable, tsum_sq_fourierCoeff, Prod.snd_exp, MeasureTheory.lpMeasToLpTrim_ae_eq, Submodule.orthogonal_eq_inter, LinearIsometryEquiv.toHomeomorph_trans, ContinuousLinearMap.mdifferentiableOn, MeasureTheory.eLpNorm_condExpL2_le, PadicInt.mahlerEquiv_symm_apply, ContinuousLinearMap.lsmul_flip_apply, aemeasurable_derivWithin_Ici, Orientation.inner_smul_rotation_pi_div_two_smul_left, closure_diff_intrinsicInterior, ContinuousAlternatingMap.alternatizeUncurryFin_curryLeft, hasDerivAt_iff_tendsto, Real.exp_eq_exp_ℝ, ContinuousLinearEquiv.toSpanNonzeroSingleton_apply_coe, Complex.differentiable_iteratedDeriv_cos, SchwartzMap.coe_apply, MeasureTheory.Measure.addHaar_ball, real_inner_div_norm_mul_norm_eq_one_of_ne_zero_of_pos_mul, ContinuousLinearEquiv.coord_self, sub_smul_dslope, AkraBazziRecurrence.isLittleO_deriv_smoothingFn, Real.differentiable_arsinh, UniformOnFun.continuousSMul_submodule_of_image_bounded, ContinuousLinearMap.compContinuousAlternatingMapCLM_apply_apply, MeasureTheory.eLpNorm_sub_le_of_dist_bdd, NumberField.mixedEmbedding.fundamentalCone.sum_expMap_symm_apply, MeasureTheory.condExp_bot', ContinuousAlternatingMap.unit_le_opNorm, riemannZeta_residue_one, RCLike.geometric_hahn_banach_compact_closed, SchwartzMap.smulLeftCLM_ofReal, Orientation.oangle_smul_right_of_pos, Circle.exp_eq_one, norm_iteratedFDeriv_smul_le, Complex.ofReal_tsum, MeasureTheory.ComplexMeasure.equivSignedMeasureₗ_apply, Metric.Sum.mem_uniformity_iff_glueDist, ContDiffAt.differentiableAt_iteratedFDeriv, LinearMap.IsPositive.adjoint_eq, PiCountable.dist_eq_tsum, abs_real_inner_div_norm_mul_norm_eq_one_iff, LinearIsometryEquiv.comp_continuous_iff, continuousAt_extChartAt_symm'', ContinuousLinearMap.sSup_unitClosedBall_eq_norm, mem_tangentConeAt_iff_exists_seq_norm_tendsto_atTop, iteratedDeriv_vcomp_two, integrable_exp_neg_mul_sq, ContinuousLinearEquiv.coord_norm, ContinuousAlternatingMap.opNNNorm_le_iff, StarAlgebra.elemental.continuous_characterSpaceToSpectrum, fderiv_norm_rpow, ContinuousMultilinearMap.nnnorm_smulRight, ContMDiffSection.mdifferentiableAt, ProbabilityTheory.instIsGaussianProdProdOfSecondCountableTopologyEither, VectorBundleCore.mem_localTrivAt_baseSet, BoundedContinuousFunction.map_bounded', ContinuousLinearMap.norm_map_iff_adjoint_comp_self, AddChar.coe_complexBasis, PartitionOfUnity.mem_fintsupport_iff, CurveIntegrable.trans, MeasureTheory.L1.integral_eq', Matrix.toEuclideanLin_eq_toLin_orthonormal, IsBoundedBilinearMap.differentiable, NormedSpace.isUnit_exp, Polynomial.toAddCircle_X_eq_fourier_one, isTheta_deriv_ofReal_cpow_const_atTop, MeasureTheory.lpMeasToLpTrim_smul, Real.hasStrictDerivAt_const_rpow, Complex.differentiable_cos, Submodule.starProjection_orthogonal_val, VectorField.lieBracketWithin_eq, MeasureTheory.FiniteMeasure.continuous_integral_continuousMap, Real.hasSum_pow_div_log_of_abs_lt_one, ContinuousMultilinearMap.cpolynomialAt_uncurry_compContinuousLinearMap, isStarProjection_iff_eq_starProjection, ContinuousLinearMap.norm_adjoint_comp_self, LinearPMap.mem_adjoint_domain_iff, IsPicardLindelof.exists_forall_mem_closedBall_eq_hasDerivWithinAt_lipschitzOnWith, OpenPartialHomeomorph.continuousOn_extend, cauchySeq_of_le_geometric_two, ContDiffBump.tsupport_normed_eq, Orientation.inner_smul_rotation_pi_div_two_smul_right, RCLike.geometric_hahn_banach_point_closed, LinearMap.IsSymmetricProjection.le_iff_range_le_range, summable_norm_pow_mul_geometric_of_norm_lt_one, Asymptotics.IsLittleO.sum_range, hasDerivWithinAt_intCast, differentiableWithinAt_zpow, ProbabilityTheory.Kernel.tendsto_eLpNorm_one_restrict_densityProcess_limitProcess, MeasureTheory.Lp.simpleFunc.denseRange_coeSimpleFuncNonnegToLpNonneg, CircleIntegrable.out, SeminormedAddCommGroup.toIsTopologicalAddGroup, VonNeumannAlgebra.instSubringClass, UniformSpace.Completion.continuous_inner, Irrational.eventually_forall_le_dist_cast_rat_of_den_le, EuclideanGeometry.eq_orthogonalProjection_of_eq_subspace, NumberField.mixedEmbedding.fundamentalCone.normAtAllPlaces_image_preimage_expMapBasis, MeasureTheory.exists_eLpNorm_indicator_le, SchwartzMap.integrable_pow_mul, ContinuousMultilinearMap.norm_map_cons_le, ContinuousMultilinearMap.norm_smulRight, Real.circleAverage_add, EuclideanGeometry.orthogonalProjection_apply, BumpCovering.toPOUFun_eq_mul_prod, LSeries_hasDerivAt, PadicInt.denseRange_intCast, Metric.isConnected_eball, CStarAlgebra.span_nonneg_inter_ball, CFC.log_exp, Real.expPartialHomeomorph_source, MeasureTheory.SignedMeasure.null_of_totalVariation_zero, Complex.one_div_one_sub_hasFPowerSeriesOnBall_zero, AkraBazziRecurrence.continuous_sumCoeffsExp, LeftInvariantDerivation.commutator_apply, EuclideanGeometry.Sphere.direction_orthRadius, ContinuousMap.toNNReal_add_add_neg_add_neg_eq, ContinuousLinearEquiv.continuousMultilinearMapCongrLeft_symm, mdifferentiableWithinAt_iff_of_mem_source, UpperHalfPlane.mdifferentiableAt_iff, mulIndicator_cthickening_eventually_eq_mulIndicator_closure, MeasureTheory.Measure.toSphere_eq_zero_iff_finrank, fourier_add_half_inv_index, NNRealRMK.integral_rieszMeasure, ContinuousMapZero.elemental_eq_top, Metric.isCover_closure, ContinuousMapZero.adjoin_id_dense, ContinuousAlternatingMap.bound, NormedField.noncompactSpace, ContinuousLinearMap.hasDerivWithinAt, Real.Angle.two_nsmul_neg_pi_div_two, isCompact_cantorSet, LeftInvariantDerivation.commutator_coe_derivation, PeriodPair.analyticOnNhd_weierstrassPExcept, differentiableWithinAt_piLp, LinearIsometry.rTensor_apply, hasStrictFDerivAt_pow, FormalMultilinearSeries.derivSeries_apply_diag, Path.extend_of_le_zero, NormedSpace.polar_closedBall, CompactlySupportedContinuousMap.monotone_of_nnreal, derivWithin_comp_const_add, Submodule.norm_orthogonalProjection, AnalyticAt.fderiv, ContinuousLinearEquiv.differentiableWithinAt, EReal.nhds_coe_coe, Matrix.l2_opNNNorm_conjTranspose_mul_self, ContinuousMapZero.toNNReal_smul, Real.continuousAt_log, iteratedDeriv_fun_mul, fderiv_comp_smul, integrable_mulExpNegMulSq_comp, Submodule.instHasOrthogonalProjectionTop, integrable_cexp_quadratic, MeasureTheory.Measure.toSignedMeasure_restrict_eq_restrict_toSignedMeasure, AffineSubspace.signedInfDist_apply_self, EuclideanGeometry.orthogonalProjection_vsub_orthogonalProjection, ContinuousLinearMap.opNorm_lsmul, MeasureTheory.hasFiniteIntegral_iff_norm, LinearIsometry.toLinearMap_lTensor, EuclideanGeometry.orthogonalProjection_mem_orthogonal, ImplicitFunctionData.toPartialHomeomorph_apply, coe_innerₛₗ_apply, HasFiniteFPowerSeriesAt.continuousAt, isCoveringMapOn_zpow, lp.star_apply, FormalMultilinearSeries.norm_changeOriginSeriesTerm, HurwitzZeta.completedHurwitzZetaEven_residue_zero, PiLp.hasStrictFDerivAt_ofLp, MeromorphicAt.fun_add, TemperedDistribution.smulLeftCLM_smul, ContinuousMultilinearMap.fderivCompContinuousLinearMap_apply, Module.Basis.continuous_coe_repr, ContinuousLinearMap.norm_id_of_nontrivial_seminorm, NormedRing.inverse_add_nth_order, Unitization.uniformity_eq_aux, curveIntegral_add, HasGradientAt.hasDerivAt, MeasureTheory.FiniteMeasure.continuous_iff_forall_continuous_integral, TensorProduct.nndist_tmul_le, InnerProductGeometry.angle_eq_pi_iff, hasDerivAt_exp_zero, HasFTaylorSeriesUpTo.zero_eq', deriv_circleMap_eq_zero_iff, Complex.imCLM_apply, MeasureTheory.charFun_map_eq_charFunDual_smul, SchwartzMap.isBigO_cocompact_zpow, ContinuousLinearEquiv.analyticAt, FDerivMeasurableAux.isOpen_B, Int.tendsto_coe_cofinite, Real.tendsto_log_nat_add_one_sub_log, HurwitzZeta.tendsto_hurwitzZeta_sub_one_div_nhds_one, MeasureTheory.integrable_withDensity_iff, summable_geometric_of_lt_one, exists_tsupport_one_of_isOpen_isClosed, InnerProductSpace.continuousLinearMapOfBilin_apply, NumberField.mixedEmbedding.normAtAllPlaces_mixedSpaceOfRealSpace, ContinuousMultilinearMap.norm_def, NNReal.coe_tsum, NormedSpace.double_dual_bound, instFieldContMDiffRing, hasGradientWithinAt_iff_isLittleO, curveIntegralFun_trans_of_lt_half, OpenPartialHomeomorph.map_extend_symm_nhdsWithin_range, fourierCoeffOn.const_smul, NormedDivisionRing.to_hasContinuousInv₀, NNRat.instIsTopologicalSemiring, NumberField.mixedEmbedding.det_fderivPolarCoordRealSymm, Matrix.cstar_norm_def, ContinuousMap.ker_evalStarAlgHom_eq_closure_adjoin_id, PointwiseConvergenceCLM.withSeminorms, abs_integral_sub_setIntegral_mulExpNegMulSq_comp_lt, PeriodPair.indep, interior_sphere', AddCircle.pathConnectedSpace, MeasureTheory.convolution_eq_swap, Real.Angle.tan_add_pi, Real.fourierInv_eq, CFC.isUnit_nnrpow_iff, Real.continuousOn_rpowIntegrand₀₁, isInvertible_mfderivWithin_extChartAt_symm, ModelWithCorners.coe_transContinuousLinearEquiv_symm, Real.differentiable_rpow_const, ProbabilityTheory.integrable_exp_mul_of_mem_Icc, isConformalMap_complex_linear, Real.zero_at_infty_vector_fourierIntegral, mdifferentiable_prod_module_iff, differentiable_finCons, ContDiff.fderiv_right, ModularForm.coe_translate, hasDerivAt_const_add_iff, LocallyCompactSpace.of_locallyCompact_manifold, continuous_posPart, ProperCone.innerDual_iUnion, ContinuousMultilinearMap.curryFinFinset_symm_apply, HasFPowerSeriesWithinOnBall.pi, VectorField.mlieBracketWithin_apply, SchwartzMap.smulLeftCLM_apply, ContDiffMapSupportedIn.withSeminorms', ContinuousAlternatingMap.opNorm_pi, NumberField.mixedEmbedding.fundamentalCone.expMap_sum, Real.uniformContinuous_mul, norm_injOn_ray_left, ContDiffMapSupportedIn.toBoundedContinuousFunctionCLM_apply, DFinsupp.inner_sum, SchwartzMap.tsum_eq_tsum_fourierIntegral, FormalMultilinearSeries.id_apply_one, MeasureTheory.integrableOn_Ioi_comp_mul_right_iff, ContinuousLinearEquiv.comp_contDiff_iff, ContMDiffSection.mdifferentiable, Orientation.kahler_rightAngleRotation_right, Real.expPartialHomeomorph_target, Real.Angle.sin_antiperiodic, TestFunctionClass.tsupport_map_subset, ContinuousLinearMap.norm_snd, ZSpan.repr_floor_apply, MeromorphicOn.divisor_def, ProbabilityTheory.cdf_paretoMeasure_eq_lintegral, Chebyshev.intervalIntegrable_one_div_log_sq, inner_matrix_row_row, MeasureTheory.condExpIndSMul_ae_eq_smul, HasFTaylorSeriesUpTo.fderiv, ExistsContDiffBumpBase.u_compact_support, ContinuousLinearMap.iteratedFDeriv_comp_right, Topology.isEmbedding_sigmoid, CFC.monotoneOn_cfcₙ_rpowIntegrand₀₁, ContDiffWithinAt.analyticOn, EuclideanGeometry.Sphere.orthRadius_parallel_orthRadius_iff, meromorphicOrderAt_add_of_top_right, MeasureTheory.Lp.simpleFunc.isDenseInducing, DiffContOnCl.differentiableOn, MeasureTheory.intervalIntegrable_charFun, MeasureTheory.Lp.dense_hasCompactSupport_contDiff, Polynomial.tendsto_div_exp_atTop, ContinuousMultilinearMap.apply_zero_uncurry0, ContinuousMap.idealOf_compl_singleton_isMaximal, Complex.arg_eq_nhds_of_re_neg_of_im_neg, SmoothPartitionOfUnity.toPartitionOfUnity_toFun, Filter.tendsto_inv₀_nhdsNE_zero, ENNReal.tendsto_toReal_iff, ProbabilityTheory.IsRatCondKernelCDFAux.tendsto_integral_of_monotone, IsUnifLocDoublingMeasure.exists_eventually_forall_measure_closedBall_le_mul, Real.tendsto_pow_log_div_mul_add_atTop, Complex.hasSum_arctan, ContDiff.continuousLinearMap_comp, ContinuousLinearMap.norm_holderL_le, fourier_add, hasFDerivWithinAt_pow, Real.borel_eq_generateFrom_Iic_rat, tendsto_smoothingFun_of_eq_zero, Path.Homotopy.symm₂_apply, PolynormableSpace.withSeminorms, lp.uniformContinuous_coe, contDiff_infty_iff_fderiv, MeasureTheory.charFun_eq_integral_innerProbChar, SchwartzMap.smulLeftCLM_compL_smulLeftCLM, coe_algEquiv_lpBCF_symm, LinearMap.polar_mem_iff, interval_average_eq, RightDerivMeasurableAux.B_mem_nhdsGT, MeasureTheory.AEEqFun.eLpNorm_compMeasurePreserving, hasDerivWithinAt_inv, ContinuousAffineMap.toConstProdContinuousLinearMap_fst, Asymptotics.isBigOTVS_prodMk_left, MeasureTheory.lpMeas.ae_fin_strongly_measurable', AffineIsometryEquiv.toHomeomorph_symm, Metric.instTietzeExtensionClosedBall, PiLp.continuousLinearEquiv_apply, hasStrictDerivAt_id, curveIntegral_sub, RCLike.nnnorm_nsmul, HasGradientAt.fderiv_apply, SchwartzMap.instFourierInvSMul, ContinuousAlternatingMap.instContinuousEval, ContinuousLinearMap.comp_analyticOnNhd, TemperedDistribution.derivCLM_apply_apply, Complex.hasDerivAt_exp, OrthonormalBasis.tensorProduct_apply, Bundle.mdifferentiable_zeroSection, HurwitzZeta.hasSum_int_completedCosZeta, TorusIntegrable.function_integrable, EuclideanGeometry.two_zsmul_oangle_orthogonalProjection_self, LinearIsometryEquiv.integrable_comp_iff, deriv_neg, AffineIsometryEquiv.toContinuousAffineEquiv_injective, ContinuousAlternatingMap.norm_compContinuousLinearMap_le, NumberField.mixedEmbedding.fundamentalCone.normAtAllPlaces_normLeOne_eq_image, Complex.hasSum_cosh, Stirling.tendsto_stirlingSeq_sqrt_pi, Asymptotics.IsLittleO.add_isEquivalent, BoundedContinuousFunction.instCompleteSpace, ContDiffWithinAt.differentiableWithinAt', MeasureTheory.Supermartingale.smul_nonneg, LeftInvariantDerivation.ext_iff, abs_signedDist_le_dist, DirichletCharacter.LFunction_isBigO_horizontal, Complex.frontier_setOf_lt_re, norm_iteratedFDeriv_zero, Orientation.norm_kahler, NumberField.mixedEmbedding.disjoint_span_commMap_ker, mfderiv_subtype_coe_Icc_one, BumpCovering.locallyFinite', VectorField.mlieBracketWithin_eq_lieBracketWithin, MeasureTheory.integral_count, Metric.continuousOn_iff, Complex.conj_tsum, cauchy_series_of_le_geometric, Polynomial.hasFDerivWithinAt, MeasureTheory.condExpIndSMul_smul', Real.hasStrictFDerivAt_rpow_of_neg, LinearMap.hasDerivAt, Rat.isEmbedding_coe_real, norm_iteratedFDeriv_eq_norm_iteratedDeriv, Real.tendsto_log_nhdsNE_zero, Complex.isometryOfOrthonormal_symm_apply, Real.hasStrictDerivAt_rpow_const, ContinuousMap.Homotopy.extend_one, egauge_smul_right, NormedSpace.exp_analytic, MeasureTheory.weightedSMul_smul_measure, unitInterval.tendsto_sigmoid_atBot, MeasureTheory.integrable_count_iff, LinearMap.hasDerivAtFilter, iteratedFDerivWithin_apply_eq_iteratedDerivWithin_mul_prod, IsStarNormal.instIsometricContinuousFunctionalCalculus, ProperCone.innerDual_toSubmodule, TangentBundle.chartAt_toPartialEquiv, PartitionOfUnity.exists_finset_nhds', Real.cosh_eq_tsum, ImplicitFunctionData.toOpenPartialHomeomorph_apply, NormedCommGroup.tendsto_nhds_one, HasFiniteFPowerSeriesOnBall.changeOrigin, tendsto_norm_zero, CurveIntegrable.sub, Real.continuousOn_arcosh, InnerProductSpace.HarmonicAt.comp_CLM, differentiableAt_inv, Metric.cauchySeq_iff', HasFiniteFPowerSeriesOnBall.fderiv_eq, NormedSpace.exp_sum_of_commute, MeasureTheory.instCompleteSpaceSubtypeAEEqFunMemAddSubgroupLpLpMeasSubgroupOfFactLeMeasurableSpace, Real.Angle.two_nsmul_coe_pi, LinearIsometryEquiv.continuous, smul_closedBall, ModularForm.coe_trace, integrable_mul_cexp_neg_mul_sq, IsLocalFrameOn.coeff_sum_eq, RCLike.ofRealCLM_coe, ProbabilityTheory.instIsGaussianMapHSub_1, ProbabilityTheory.HasCondSubgaussianMGF.integrable_exp_mul, Complex.frontier_setOf_le_im, Complex.hasDerivAt_log_sub_logTaylor, Complex.GammaIntegral_convergent, IsometricContinuousFunctionalCalculus.isometric, hasStrictDerivAt_iff_hasStrictFDerivAt, ContinuousLinearEquiv.comp_contDiffAt_iff, ContinuousAlternatingMap.hasFDerivAt, FormalMultilinearSeries.summable, HasFPowerSeriesAt.locally_zero_iff, InnerProductSpace.laplacian_CLE_comp_left, hasDerivAt_iff_tendsto_slope, MeasureTheory.tendsto_iff_forall_lipschitz_integral_tendsto, PiTensorProduct.mapL_add, ContinuousLinearMap.analyticAt_bilinear, eventually_norm_trivializationAt_lt, Complex.isOpenMap_exp, TensorProduct.congrIsometry_apply, integral_withDensity_eq_integral_smul₀, ContinuousLinearEquiv.comp_right_hasFDerivAt_iff', ConvexOn.exists_affine_le_of_lt, ProbabilityTheory.IsGaussian.charFunDual_eq', mulIndicator_thickening_eventually_eq_mulIndicator_closure, HasFPowerSeriesAt.hasStrictFDerivAt, convex_halfSpace_re_gt, MeasureTheory.integrable_const_add_iff, BumpCovering.le_one', PartitionOfUnity.exists_pos, NormedSpace.toLocallyConvexSpace', UniformSpace.Completion.instIsBoundedSMul, AnalyticOnNhd.fun_const_smul, ModelWithCorners.uniqueDiffOn_preimage_source, isConnected_setOf_sameRay, MeasureTheory.integral_prod_smul, ContinuousMap.Homotopy.curry_one, IsClosed.upperClosure_pi, ContinuousLinearMap.apply_norm_sq_eq_inner_adjoint_right, AddChar.complexBasis_apply, isBoundedLinearMap_continuousMultilinearMap_comp_linear, ImplicitFunctionData.map_implicitFunction_nhdsWithin_preimage, FormalMultilinearSeries.nnnorm_changeOriginSeriesTerm, iteratedFDerivWithin_comp_sub', MeasureTheory.integrableOn_Ioi_comp_rpow_iff, CompareReals.compare_uc, SmoothBumpFunction.nhdsWithin_range_basis, innerSL_apply_coe, differentiableOn_finCons, ContinuousLinearMap.bilinearRestrictScalars_eq_restrictScalars_restrictScalarsL_comp, Rat.instIsTopologicalAddGroup, AffineSubspace.signedInfDist_apply_of_mem, MeasureTheory.lpTrimToLpMeasSubgroup_ae_eq, ContinuousLinearMap.bound, ProbabilityTheory.analyticOnNhd_complexMGF, IsBoundedLinearMap.fderiv, HasSolidNorm.continuousSup, ContinuousLinearMap.isPositive_one, Unitary.openPartialHomeomorph_apply, ContinuousLinearMap.isPositive_sum, StrongDual.polar_singleton, DoubleCentralizer.isUniformEmbedding_toProdMulOpposite, Real.hasDerivAt_Gamma_nat, Orientation.oangle_smul_right_self_of_nonneg, MeasureTheory.L1.integral_sub, Path.truncate_one_one, MeasureTheory.L1.ofReal_norm_sub_eq_lintegral, Unitary.argSelfAdjoint_coe, ZSpan.fract_eq_fract, hasDerivAt_pi, MeasureTheory.Lp.coeFn_inf, MeasureTheory.ContinuousMap.inner_toLp, Metric.nhdsWithin_basis_ball, gradient_eq_deriv, differentiableAt_abs, ProbabilityTheory.setIntegral_stieltjesOfMeasurableRat_rat, Submodule.orthogonalProjection_comp_subtypeL_eq_zero_iff, InnerProductGeometry.continuousAt_angle, IsLowerSet.null_frontier, SlashInvariantForm.coeHom_injective, ContDiffMapSupportedIn.iteratedFDerivLM_eq_of_scalars, tendsto_const_div_pow, Asymptotics.isLittleO_pow_sub_sub, ConvexOn.real_sSup_of_nat_affine_eq, MeasureTheory.integrable_fun_norm_addHaar, NumberField.mixedEmbedding.polarCoordReal_target, SchwartzMap.toZeroAtInfty_apply, Real.continuousAt_arctan, hasFDerivAt_inv', hasSum_zeta_nat, LinearMap.toMatrix_adjoint, ProbabilityTheory.isPositive_covarianceOperator, extChartAt_target_eventuallyEq_of_mem, MeasureTheory.dominatedFinMeasAdditive_weightedSMul, Affine.Simplex.reflection_circumcenter_eq_affineCombination_of_pointsWithCircumcenter, Orientation.oangle_add_left_eq_arccos_of_oangle_eq_pi_div_two, ProbabilityTheory.IsRatCondKernelCDF.integrable, tendsto_euler_sin_prod', Matrix.exp_units_conj, hasDerivWithinAt_finCons, EisensteinSeries.eisensteinSeries_slash_apply, Metric.isPreconnected_closedBall, WeakDual.CharacterSpace.exists_apply_eq_zero, contMDiffAt_pi_space, exists_smooth_zero_one_nhds_of_isClosed, norm_iteratedFDerivWithin_eq_norm_iteratedDerivWithin, ValueDistribution.characteristic_sum_top_eventuallyLE, ZLattice.sum_piFinset_Icc_rpow_le, ContinuousMap.enorm_eq_iSup_enorm, Complex.polarCoord_target, contMDiffOn_iff_target, Circle.isCoveringMap_exp, Units.isOpenEmbedding_val, FormalMultilinearSeries.rightInv_coeff, Real.not_continuousAt_deriv_qaryEntropy_one, differentiableAt_dslope_of_ne, OpenPartialHomeomorph.univBall_target, Complex.hasDerivAt_log, Complex.arg_mul_coe_angle, Metric.instTietzeExtensionBall, ValueDistribution.logCounting_coe, HilbertBasis.tsum_inner_mul_inner, Meromorphic.smul, OpenPartialHomeomorph.unitBallBall_symm_apply, AddChar.zmod_intCast, ContinuousMap.isometryEquivBoundedOfCompact_apply, NormedSpace.exp_units_conj, hasDerivAt_zpow, TemperedDistribution.fourierTransformInv_apply, AnalyticAt.frequently_eq_iff_eventually_eq, MeasureTheory.L1.SimpleFunc.integral_L1_eq_integral, Orientation.oangle_neg_orientation_eq_neg, FormalMultilinearSeries.summable_norm_apply, tangentConeAt_eq_univ, Complex.hasSum_cos, Orientation.oangle_sign_smul_add_smul_left, ContinuousMultilinearMap.norm_constOfIsEmpty, summable_of_sum_range_norm_le, uniqueDiffOn_extChartAt_target, cfcₙHom_of_cfcHom_map_quasispectrum, contMDiffOn_vectorSpace_iff_contDiffOn, Submodule.closedComplemented_iff_isClosed_exists_isClosed_isCompl, MeromorphicOn.iterated_deriv, EuclideanGeometry.coe_orthogonalProjection_eq_iff_mem, WeakDual.CharacterSpace.compContinuousMap_id, mfderiv_neg, VectorBundle.pullback, Metric.nhds_basis_ball_inv_nat_pos, AddCircle.toCircle_nsmul, Real.Angle.sin_eq_real_sin_iff_eq_or_add_eq_pi, extChartAt_target_mem_nhds, measurable_derivWithin_Ici, DomAddAct.dist_vadd_Lp, isClosedMap_smul_left, tendsto_subseq_of_bounded, ContinuousLinearMap.isPositive_adjoint_comp_self, SchwartzMap.integral_clm_comp_laplacian_right_eq_left, hasFDerivWithinAt_iff_tendsto, FormalMultilinearSeries.compAlongOrderedFinpartition_apply, UpperHalfPlane.contMDiff_smul, Complex.isHomeomorphicTrivialFiberBundle_im, Asymptotics.isBigO_completion_left, TensorProduct.nnnorm_lid, LinearMap.im_inner_adjoint_mul_self_eq_zero, differentiableAt_iff_comp_const_add, HurwitzZeta.hasSum_int_completedSinZeta, RCLike.instTietzeExtension, ProbabilityTheory.IndepFun.charFun_map_add_eq_mul, ContinuousMultilinearMap.le_opNorm_mul_pow_of_le, ValueDistribution.log_counting_zero_sub_logCounting_top, MeasureTheory.isTightMeasureSet_iff_tendsto_measure_compl_closedBall, SeminormedCommGroup.toIsTopologicalGroup, TestFunction.coeFnAddMonoidHom_apply, HasFPowerSeriesOnBall.tendstoLocallyUniformlyOn', ClosedSubmodule.orthogonal_closure', zeta_nat_eq_tsum_of_gt_one, differentiableAt_inverse, Matrix.l2_opNorm_def, BoundedContinuousFunction.mkOfCompact_sub, ContinuousMap.uniform_continuity, fderivWithin_comp_add_right, Quaternion.hasSum_coe, Real.fourierInv_eq', tendsto_log_mul_rpow_nhdsGT_zero, UpperHalfPlane.tendsto_comap_im_ofComplex, signedDist_apply_linear, Real.differentiableAt_sin, OrthogonalFamily.linearIsometry_apply, ContinuousMultilinearMap.le_opNNNorm, HasFiniteFPowerSeriesOnBall.sub, PNat.instDiscreteTopology, MeasureTheory.Measure.toSignedMeasure_zero, ContinuousMultilinearMap.norm_compContinuousLinearMapL_le, Matrix.toEuclideanLin_toLp, Bundle.RiemannianMetric.continuousAt, contMDiffAt_iff_target, nnnorm_cfcₙ_le, ContinuousLinearMapWOT.continuous_dual_apply, continuous_stereoInvFun, Rat.instTotallyDisconnectedSpace, MellinConvergent.cpow_smul, ContDiffOn.fun_smul, ContinuousLinearMap.iteratedFDeriv_comp_left, HurwitzZeta.hasSum_nat_hurwitzZetaOdd_of_mem_Icc, closure_halfSpace, Submodule.orthogonalProjection_eq_zero_iff, ContinuousLinearMap.holderL_apply_apply, ContinuousMap.Homotopy.extend_apply_of_le_zero, MeasureTheory.Lp.instContinuousFourier, differentiableAt_comp_sub, NumberField.InfinitePlace.Completion.Rat.norm_infinitePlace_completion, hasSum_iff_tendsto_nat_of_nonneg, StrongDual.mem_polar_singleton, FormalMultilinearSeries.comp_rightInv_aux2, derivWithin_sub_const, Metric.uniformity_basis_dist_le_pow, AddChar.expect_apply_eq_ite, LeftInvariantDerivation.toFun_eq_coe, MeasureTheory.AEEqFun.eLpNorm_star, Complex.reCLM_enorm, MeasureTheory.hasFiniteIntegral_smul_iff, DomAddAct.vadd_Lp_zero, MeasureTheory.integral_fun_snd, ContinuousMultilinearMap.opNorm_prod, MeasureTheory.condExpInd_empty, UpperHalfPlane.contMDiff_denom, IsPicardLindelof.exists_forall_mem_closedBall_eq_forall_mem_Icc_hasDerivWithinAt, Asymptotics.isLittleOTVS_insert, Real.hasDerivAt_sinh, AbsoluteValue.Completion.extensionEmbedding_dist_eq_of_comp, LipschitzMul.continuousMul, isClosedEmbedding_smul_left, ContDiffMapSupportedIn.compact_supp, Polynomial.toAddCircle_C_eq_smul_fourier_zero, MeasureTheory.integrable_fun_smul_iff, MeasureTheory.condExpL1CLM_smul, isConformalMap_const_smul, tendsto_pow_atTop_nhds_zero_of_norm_lt_one, Manifold.exists_lt_of_riemannianEDist_lt, Matrix.l2_opNorm_mul, hasDerivWithinAt_iff_tendsto_slope', BoundedContinuousFunction.enorm_eq_iSup_enorm, NumberField.mixedEmbedding.fundamentalCone.expMapBasis_source, riemannZeta_eulerProduct_hasProd, InnerProductGeometry.sin_angle_add, InnerProductGeometry.angle_add_eq_arcsin_of_inner_eq_zero, norm_innerSL_le, MeromorphicAt.smul, MeasureTheory.eLpNorm'_norm_rpow, polynomialFunctions_closure_eq_top, Real.Angle.cos_antiperiodic, VectorFourier.hasFDerivAt_fourierChar_smul, DirichletCharacter.LSeries_eulerProduct, Finset.analyticWithinAt_fun_sum, integrable_cexp_quadratic', LipschitzWith.norm_compLp_le, Complex.one_div_sub_sq_sub_one_div_sq_hasFPowerSeriesOnBall_zero, SeminormedAddGroup.disjoint_nhds, Real.fourierIntegral_real_eq, ContinuousLinearMap.isLeast_opNorm, Real.circleAverage_fun_add, InformationTheory.not_differentiableAt_klFun_zero, fderiv_const_smul_of_field, writtenInExtChartAt_sumInr_eventuallyEq_id, Real.deriv_cosh, PeriodPair.lattice_eq_span_range_basis, tendsto_mulIndicator_cthickening_mulIndicator_closure, cfcₙHomSuperset_apply, Quaternion.continuous_imK, FormalMultilinearSeries.changeOriginSeriesTerm_changeOriginIndexEquiv_symm, IsSelfAdjoint.instNonUnitalIsometricContinuousFunctionalCalculus, ContinuousLinearMap.IsPositive.isSelfAdjoint, MeasureTheory.measure_unitBall_eq_integral_div_gamma, CStarAlgebra.exists_sum_four_unitary, MeasureTheory.L1.edist_def, HasLineDerivAt.smul, Metric.uniformContinuous_iff, Real.exists_extension_norm_eq, OrthonormalBasis.sum_repr', continuousMultilinearCurryRightEquiv_apply, MeasureTheory.Lp.simpleFunc.toSimpleFunc_eq_toFun, SeminormedAddGroup.tendstoUniformlyOn_zero, Submodule.coe_orthogonalProjection_apply, Submodule.starProjection_coe_eq_isCompl_projection, MeasureTheory.continuous_setIntegral, CurveIntegrable.cast, Polynomial.Chebyshev.intervalIntegrable_sqrt_one_sub_sq_inv, InnerProductGeometry.sin_angle_add_mul_norm_of_inner_eq_zero, ContDiffMapSupportedIn.structureMapLM_zero_apply, SchwartzMap.differentiableAt, ContinuousMap.idealOfSet_ofIdeal_isClosed, nnnorm_cfcₙ_nnreal_le, Complex.frontier_reProdIm, hasFDerivAtFilter_add_const_iff, CFC.sqrt_eq_real_sqrt, Units.chartAt_source, NumberField.mixedEmbedding.integral_comp_polarCoord_symm, ContinuousOn.inner_bundle, LinearMap.injective_iff_antilipschitz, AkraBazziRecurrence.growsPolynomially_deriv_rpow_p_mul_one_add_smoothingFn, OpenPartialHomeomorph.univUnitBall_symm_apply, deriv.star', Real.deriv_sin, AffineMap.deriv, SmoothBumpCovering.embeddingPiTangent_coe, ContinuousAlternatingMap.prodLIE_symm_apply, analyticOrderAt_smul_eq_top_of_right, Submodule.ClosedComplemented.of_quotient_finiteDimensional, range_mem_nhds_isInteriorPoint, AddCircle.homeomorphCircle'_apply, AnalyticOnNhd.const_smul, Real.continuous_arccos, Trivialization.isLocalFrameOn_localFrame_baseSet, ModelWithCorners.nonempty_interior', Metric.tendstoLocallyUniformly_iff, Seminorm.continuous_of_forall, EisensteinSeries.eisensteinSeriesSIF_mdifferentiable, SchwartzMap.integral_smul_deriv_right_eq_neg_left, ContinuousLinearMap.apply_apply', SmoothPartitionOfUnity.nonneg', HasFPowerSeriesWithinAt.hasFDerivWithinAt, apply_le_nnnorm_cfcₙ_nnreal, LinearIsometryEquiv.norm_iteratedFDeriv_comp_left, MeasureTheory.Martingale.stronglyMeasurable, iteratedDeriv_sum, instModuleFree_of_discrete_submodule, LinearMap.posSemidef_toMatrix_iff, tendsto_measure_thickening_of_isClosed, Affine.Triangle.orthocenter_vsub_circumcenter_eq_sum_vsub, ProbabilityTheory.IsMeasurableRatCDF.stieltjesFunction_le_one, PeriodPair.ω₁_mem_lattice, Orientation.two_zsmul_oangle_smul_smul_self, ContDiff.fderiv, instIsAddHaarMeasureUnitAddCircleVolume, Submodule.starProjection_apply_eq_zero_iff, ContMDiffSection.contMDiff_toFun, SchwartzMap.fourier_convolution, ContDiff.differentiable_one, OnePoint.isZeroAt_iff, AnalyticOnNhd.eval_continuousLinearMap', PadicInt.instIsAddTorsionFree, NumberField.mixedEmbedding.fundamentalCone.expMap_pos, UnitAddTorus.span_mFourierLp_closure_eq_top, Orientation.rotation_symm_apply, ZMod.LFunction_dft, HurwitzZeta.hasSum_nat_cosKernel₀, AbsolutelyContinuousOnInterval.integral_mul_deriv_eq_deriv_mul, TestFunction.tsupport_subset', AnalyticOnNhd.iterated_deriv, tendsto_iff_dist_tendsto_zero, Real.mem_closure_iff, Real.tendsto_logb_nhdsGT_zero, MeasureTheory.indicatorConstLp_eq_toSpanSingleton_compLp, ContinuousMapZero.continuous_toNNReal, MeasureTheory.FiniteMeasure.coe_toWeakDualBCNN, ProbabilityTheory.analyticOn_iteratedDeriv_mgf, Asymptotics.isEquivalent_const_iff_tendsto, ContinuousMultilinearMap.analyticOnNhd_uncurry_of_linear, Polynomial.div_tendsto_atTop_zero_iff_degree_lt, continuous_norm, uniformity_basis_dist_pow_of_lt_one, PeriodPair.analyticOnNhd_weierstrassP, ProbabilityTheory.poissonPMFRealSum, ContinuousLinearMap.flipₗᵢ_symm, MeasureTheory.Measure.innerRegularWRT_preimage_one_hasCompactSupport_measure_ne_top_of_addGroup, AddCircle.homeomorphCircle_apply, ImplicitFunctionData.rightDeriv_fderiv_implicitFunction, HurwitzZeta.hasSum_int_completedHurwitzZetaEven, ProbabilityTheory.integrable_gaussianPDFReal, Topology.CWComplex.continuousOn_symm, Asymptotics.IsBigOTVS.refl, expNegInvGlue.differentiable_polynomial_eval_inv_mul, Complex.differentiableAt_cos, WeakFEPair.f_modif_aux2, continuousOn_cfcₙ_nnreal_setProd, tendsto_factorial_div_pow_self_atTop, cfcHom_eq_of_isStarNormal, DoubleCentralizer.instCompleteSpace, CommCStarAlgebra.toCompleteSpace, eHolderNorm_smul, ContinuousLinearMap.bijective_iff_dense_range_and_antilipschitz, posTangentConeAt_univ, UpperHalfPlane.mdifferentiable_denom_zpow, BoundedContinuousFunction.coe_npowRec, ProbabilityTheory.stronglyMeasurable_paretoPDFReal, NormedSpace.exp_mem_unitary_of_mem_skewAdjoint, mellin_cpow_smul, HasGradientWithinAt.hasFDerivWithinAt, AlternatingMap.mkContinuousLinear_norm_le_max, continuous_nndist, ContinuousLinearMap.dist_le_opNorm, FormalMultilinearSeries.rightInv_coeff_one, Circle.exp_sub_two_pi, hasFDerivAt_exp, ContinuousAlternatingMap.opNNNorm_prod, Orientation.volumeForm_comp_linearIsometryEquiv, ContDiffWithinAt.differentiableWithinAt, Monotone.stieltjesFunction_eq, deriv_mul_const_field', RCLike.hasSum_conj', ProbabilityTheory.Kernel.HasSubgaussianMGF.aestronglyMeasurable, MeromorphicOn.eventually_analyticAt, Polynomial.hasDerivWithinAt, Path.Homotopy.refl_apply, Complex.frontier_setOf_im_le, ZSpan.mem_fundamentalDomain, IsHilbertSum.linearIsometryEquiv_apply_dfinsupp_sum_single, differentiableAt_iff_comp_sub_const, InnerProductGeometry.IsConformalMap.preserves_angle, uniqueDiffWithinAt_extChartAt_target, LinearMap.polar_mem, ApproximatesLinearOn.lipschitzOnWith, MeasureTheory.Lp.pow_mul_meas_ge_le_enorm, CFC.real_exp_eq_normedSpace_exp, CFC.norm_sqrt, LipschitzOnWith.ae_differentiableWithinAt, Orthonormal.tmul, norm_fderiv_norm_id_rpow, ContinuousLinearMap.isBigOTVS_id, ProbabilityTheory.Kernel.HasSubgaussianMGF.ae_integrable_exp_mul, MeromorphicOn.divisor_mul, LinearMap.isAdjointPair_inner, CFC.continuousOn_rpow, OpenPartialHomeomorph.extend_symm_preimage_inter_range_eventuallyEq, MeasureTheory.condExpIndL1Fin_smul', LinearMap.IsPositive.adjoint_conj, ContinuousLinearMap.norm_holder_apply_apply_le, upperHemicontinuous_spectrum, TopologicalSpace.UpgradedIsCompletelyPseudoMetrizableSpace.toCompleteSpace, LinearMap.isPositive_one, MeasureTheory.Lp.edist_dist, Orientation.tan_oangle_add_right_of_oangle_eq_pi_div_two, Real.continuous_arsinh, Circle.argPartialEquiv_symm_apply, Complex.isUniformEmbedding_equivRealProd, ProbabilityTheory.setLIntegral_stieltjesOfMeasurableRat, MeasureTheory.charFun_map_const_add, Affine.Triangle.dist_orthocenter_reflection_circumcenter_finset, Affine.Simplex.affineSpan_pair_eq_altitude_iff, NumberField.mixedEmbedding.commMap_canonical_eq_mixed, Asymptotics.IsLittleO.exists_eq_mul, SlashInvariantFormClass.slash_action_eq, Affine.Simplex.signedInfDist_apply_of_ne, tendsto_nhds_of_meromorphicOrderAt_nonneg, BoundedContinuousFunction.range_toLp, Submodule.norm_subtypeL_le, ProbabilityTheory.continuousOn_mgf, Metric.eventually_isCompact_closedBall, range_cfc, ContinuousLinearMap.hasStrictDerivAt, ContinuousLinearMap.analyticAt_uncurry_of_multilinear, AffineIsometry.coe_toContinuousAffineMap, BumpCovering.exists_isSubordinate_hasCompactSupport_of_locallyFinite_t2space, exists_contMDiffMap_one_nhds_of_subset_interior, WeakDual.CharacterSpace.instCompactSpaceElemCharacterSpaceOfProperSpace, ModularForm.summable_eta_q, hasDerivWithinAt_iff_tendsto_slope, UniformSpace.Completion.edist_eq, hasFDerivAtFilter_pi', constFormalMultilinearSeries_apply_succ, ImplicitFunctionData.hasStrictFDerivAt_rightFun, Polynomial.fourierCoeff_toAddCircle, signedDist_left_lineMap, MeasureTheory.Submartingale.integrable_stoppedValue, FormalMultilinearSeries.continuousOn, Path.uniformContinuous_extend, MeasureTheory.indicatorConstLp_disjoint_union, hasFDerivAt_inv, Complex.hasFPowerSeriesOnBall_ofScalars_mul_add_zero, continuousAt_extChartAt_symm', Affine.Simplex.direction_altitude, LinearIsometryEquiv.symm_lTensor, Complex.hasSum_iff, Real.deriv_mul_log_zero, ContinuousLinearMap.coe_ofIsClosedGraph, ProbabilityTheory.Kernel.integral_withDensity, ContinuousMultilinearMap.analyticOn_uncurry_compContinuousLinearMap, cfcHom_map_spectrum, NumberField.mixedEmbedding.norm_negAt, Orientation.oangle_sign_smul_sub_right, DoubleCentralizer.toProdHom_apply, ContinuousAlternatingMap.enorm_toContinuousMultilinearMap, AbsolutelyContinuousOnInterval.continuousOn, ModelWithCorners.isBoundaryPoint_iff, SmoothPartitionOfUnity.sum_le_one, HurwitzZeta.differentiable_completedHurwitzZetaEven₀, ModelWithCorners.mdifferentiableWithinAt_symm, ContinuousMap.isUnit_iff_forall_ne_zero, Submodule.isOrtho_bot_left, SlashInvariantForm.slash_action_eqn, CurveIntegrable.intervalIntegrable_curveIntegralFun_trans_right, BoundedContinuousFunction.dist_mkOfCompact, DoubleCentralizer.mul_snd, MonotoneOn.nnnorm_cfcₙ, ContinuousMap.linearIsometryBoundedOfCompact_toIsometryEquiv, ContinuousLinearMap.fpowerSeries_apply_one, HurwitzZeta.differentiable_completedHurwitzZetaOdd, summable_pow_mul_cexp, Real.tendsto_prod_pi_div_two, MeasureTheory.L1.integral_eq, fderiv_continuousLinearEquiv_comp', ContDiffPointwiseHolderAt.zero_order_iff, ContinuousLinearMap.smulRightL_apply_apply, MeasureTheory.indicatorConstLp_coeFn, continuousOn_clm_apply, Real.exp_sub_sum_range_isBigO_pow, Real.hasDerivAt_sqrt, GenLoop.boundary, WeakFEPair.Λ_residue_zero, IccRightChart_extend_top, GenLoop.homotopyFrom_apply, GenLoop.const_apply, ModularFormClass.hasSum_qExpansion, SchwartzMap.one_add_le_sup_seminorm_apply, ContinuousLinearMap.toSpanSingletonCLE_apply_apply, Seminorm.continuous_iff_continuous_comp, Metric.uniformCauchySeqOn_iff, PartitionOfUnity.continuous_smul, stdSimplex.instCompactSpace_coe, NumberField.mixedEmbedding.fundamentalCone.expMap_single_source, constFormalMultilinearSeries_zero, OpenPartialHomeomorph.unitBallBall_apply, ContDiffAt.exists_lipschitzOnWith, EuclideanGeometry.dist_orthogonalProjection_line_eq_iff_two_zsmul_oangle_eq, Real.fourierIntegralInv_eq, MeasureTheory.integrable_const, Real.Angle.continuous_cos, Complex.isOpenMap_re, MeasureTheory.weightedSMul_zero_measure, Asymptotics.IsBigO.isBigOTVS, taylor_within_apply, Ring.inverse_exp, HilbertBasis.hasSum_inner_mul_inner, Asymptotics.isLittleOTVS_neg_left, Real.hasDerivWithinAt_arccos_Iic, contMDiffOn_prod_module_iff, WithCStarModule.prod_inner, measurableSet_of_differentiableWithinAt_Ici, Complex.approx_Gamma_integral_tendsto_Gamma_integral, LinearIsometryEquiv.toContinuousLinearEquiv_smul, NumberField.mixedEmbedding.fundamentalCone.normLeOne_eq_preimage, ContinuousAlternatingMap.compContinuousLinearMapCLM_apply, NormedAddCommGroup.tendsto_atTop', ContinuousMultilinearMap.norm_compContinuousLinearMap_le, MeasureTheory.Lp.fourier_toTemperedDistribution_eq, ContinuousLinearMap.opNNNorm_mul_apply, CompactlySupportedContinuousMap.nnrealPart_sub_nnrealPart_neg, Real.Angle.tan_periodic, fderivInnerCLM_apply, AffineIsometry.image_intrinsicFrontier, AbsoluteValue.isEquiv_iff_isHomeomorph, eventually_norm_mfderiv_extChartAt_lt, ContinuousMultilinearMap.curryFinFinset_apply, MeasureTheory.Lp.const_val, EuclideanGeometry.orthogonalProjection_eq_iff_mem, NormedField.nhdsWithin_isUnit_neBot, PartitionOfUnity.sum_finsupport', Affine.Simplex.ninePointCircle_center, TestFunction.injective_toBoundedContinuousFunctionCLM, ConvexOn.sSup_affine_eq, unitary.mem_pathComponentOne_iff, CircleIntegrable.finsum, EuclideanGeometry.dist_orthogonalProjection_line_eq_of_two_zsmul_oangle_eq, boundary_Icc, OrderedFinpartition.applyOrderedFinpartition_update_right, properSpace_iff_isProperMap_dist, MeasureTheory.Lp.simpleFunc.coeFn_nonneg, Real.BohrMollerup.tendsto_logGammaSeq_of_le_one, tendsto_norm_sub_self_nhdsGE, MultilinearMap.mkContinuous_norm_le', BoxIntegral.HasIntegral.add, BoundedContinuousFunction.tendsto_iff_tendstoUniformly, MeasureTheory.integral_smul_measure, Real.Angle.coe_pi_add_coe_pi, deriv_sqrt_mul_log', summableLocallyUniformlyOn_iteratedDerivWithin_smul_cexp, Submodule.orthogonalProjection_coe_eq_linearProjOfIsCompl, VectorBundleCore.coordChange_comp, derivWithin_const_sub, MeasureTheory.integrable_const_iff_isFiniteMeasure, WithLp.enorm_fst_le, SchwartzMap.denseRange_toLpCLM, ConformalAt.const_smul, hasFDerivAt_fst, SchwartzMap.toZeroAtInftyCLM_apply, FormalMultilinearSeries.constFormalMultilinearSeries_radius, Asymptotics.isLittleOTVS_sup, ContDiffMapSupportedIn.coeHom_injective, SeparationQuotient.liftNormedAddGroupHomEquiv_symm_apply_coe, cfcₙHom_nonneg_iff, ContinuousMap.dist_le_iff_of_nonempty, SchwartzMap.toLp_fourier_eq, Real.differentiableAt_binEntropy_iff_ne_zero_one, MeasureTheory.tendsto_integral_meas_thickening_le, ContinuousLinearMap.toSpanSingletonCLE_symm_apply, DomMulAct.smul_Lp_val, UpperHalfPlane.continuous_coe, derivWithin_const_mul_field, MeromorphicAt.frequently_zero_iff_eventuallyEq_zero, CFC.nnnorm_nnrpow, SchwartzMap.integrable_pow_mul_iteratedFDeriv, Complex.deriv_exp, FormalMultilinearSeries.radius_eq_liminf, Trivialization.contMDiffOn, ContinuousLinearMap.norm_precompL_le, Real.fderiv_fourierChar_neg_bilinear_left_apply, Function.locallyFinsuppWithin.logCounting_even, Real.deriv_tan, Module.Basis.addHaar_self, NormedSpace.discreteTopology_zmultiples, HasFTaylorSeriesUpToOn.restrictScalars, isConformalMap_iff_is_complex_or_conj_linear, AnalyticAt.hasStrictFDerivAt, ContinuousLinearEquiv.contDiffPointwiseHolderAt_left_comp, Real.tendsto_one_add_div_rpow_exp, DomAddAct.nnnorm_vadd_Lp, Units.isOpenMap_val, tendsto_log_mul_self_nhdsLT_zero, ContinuousLinearMap.apply_apply, ContinuousLinearEquiv.comp_differentiableWithinAt_iff, intrinsicClosure_eq_closure, RCLike.span_one_I, egauge_zero_right, PeriodPair.ω₂_mem_lattice, GenLoop.fromLoop_coe, Asymptotics.isThetaTVS_iff_isTheta, hasFDerivAt_pi', MeasureTheory.eLpNorm_mono_nnnorm, DirichletCharacter.differentiable_LFunctionTrivChar₁, OrthogonalFamily.summable_iff_norm_sq_summable, ContinuousLinearMap.norm_map_removeNth_le, BoundedContinuousFunction.tendsto_integral_of_forall_limsup_integral_le_integral, ContinuousMultilinearMap.hasStrictFDerivAt_uncurry, Real.exists_measure_rpow_eq_integral, summable_partition, iteratedFDeriv_neg, tendsto_indicator_thickening_indicator_closure, summable_jacobiTheta₂'_term_iff, ContinuousMultilinearMap.compContinuousLinearMapContinuousMultilinear_apply_apply, HasGradientAtFilter.hasDerivAtFilter, Metric.uniformSpace_eq_bot, AlternatingMap.mkContinuousAlternating_apply, IsSymmSndFDerivWithinAt.eq, CurveIntegrable.add, PiTensorProduct.mapLMultilinear_opNorm, MeasureTheory.norm_condExpIndL1Fin_le, Seminorm.uniformContinuous_of_forall', Convex.instPathConnectedSpace, ContinuousMultilinearMap.norm_image_sub_le', hasFPowerSeriesAt_iff', LinearIsometryEquiv.differentiableOn, RCLike.geometric_hahn_banach_closed_compact, StieltjesFunction.right_continuous, Real.fourier_eq', ContDiff.continuous_iteratedDeriv', MeasureTheory.eLpNorm_conj, IsPicardLindelof.exists_eq_forall_mem_Icc_hasDerivWithinAt₀, MeasureTheory.charFunDual_eq_prod_iff', ContinuousLinearMapWOT.tendsto_iff_forall_dual_apply_tendsto, MeasureTheory.Measure.toSphere.instIsOpenPosMeasure, Hamming.instDiscreteTopology, SemiNormedGrp.completion_map, LinearIsometryEquiv.conjStarAlgEquiv_apply_apply, DFinsupp.sum_inner, MeasureTheory.continuous_L1_toL1, UpperHalfPlane.mdifferentiable_iff, meromorphicOrderAt_ne_top_iff_eventually_ne_zero, contMDiffOn_section_of_mem_baseSet₀, hasMellin_const_smul, Complex.isOpen_re_gt_EReal, Subgroup.IsArithmetic.discreteTopology, hasStrictDerivAt_exp_zero, deriv_const_smul_field, closure_lowerClosure_comm_pi, Submodule.orthogonalProjection_norm_le, Metric.IsCover.closure, DoubleCentralizer.intCast_toProd, ContinuousAffineMap.differentiableAt, Matrix.PosDef.posDef_sqrt, WeakFEPair.Λ_residue_k, MeasureTheory.eLpNormEssSup_le_of_ae_nnnorm_bound, Metric.hausdorffDist_closure₁, Function.HasTemperateGrowth.isBigO_uniform, integrable_cexp_neg_mul_sq, intervalIntegrable_log_sin, differentiableOn_snd, AbsoluteValue.Completion.extensionEmbedding_of_comp_coe, DiffeologicalSpace.CorePlotsOn.isPlotOn_univ, ContDiff.fun_smul, Complex.analyticAt_iff_eventually_differentiableAt, differentiableAt_comp_sub_const, iteratedFDerivWithin_zero_apply, Orientation.rightAngleRotation_neg_orientation, PositiveLinearMap.gnsNonUnitalStarAlgHom_apply, NumberField.mixedEmbedding.integral_comp_polarCoordReal_symm, Orientation.rotationAux_apply, Fourier.fourierIntegral_comp_add_right, intervalIntegrable_inv_iff, ImplicitFunctionData.left_map_implicitFunction, smooth_functions_tower, FormalMultilinearSeries.norm_mul_pow_le_of_lt_radius, BumpCovering.sum_toPOUFun_eq, MeasureTheory.indicatorConstLp_empty, NumberField.mixedEmbedding.fundamentalCone.compactSet_eq_union, fderiv_single, GenLoop.homotopicTo, RCLike.ofReal_sum, Real.tendsto_exp_atBot_nhdsGT, ContinuousMap.idealOfSet_ofIdeal_eq_closure, CircleIntegrable.add, finrank_euclideanSpace_fin, Metric.tendstoUniformly_iff, UpperHalfPlane.isOpen_upperHalfPlaneSet, mdifferentiable_iff_differentiable, Submodule.orthogonalProjection_orthogonal, Real.hasStrictDerivAt_exp, continuousFunctionalCalculus_map_id, writtenInExtChartAt_sumInl_eventuallyEq_id, CFC.norm_nnrpow, differentiableWithinAt_const_add_iff, Orientation.oangle_add_cyc3_neg_right, coe_algEquiv_lpBCF, Quaternion.continuous_normSq, UpperHalfPlane.isEmbedding_coe, HurwitzZeta.differentiable_completedSinZeta, ProbabilityTheory.stronglyMeasurable_exponentialPDFReal, HurwitzZeta.differentiable_hurwitzZetaEven_sub_hurwitzZetaEven, le_egauge_closedBall_one, hasFDerivAt_list_prod_attach', Bundle.mdifferentiableAt_zeroSection, Quaternion.continuous_re, InformationTheory.deriv_klFun, mdifferentiableOn_iff_of_mem_maximalAtlas, one_add_rpow_hasFPowerSeriesOnBall_zero, CFC.conjugate_rpow_neg_one_half, Orientation.cos_oangle_add_left_mul_norm_of_oangle_eq_pi_div_two, boundary_product, SemiNormedGrp.completion_obj_carrier, geom_series_eq_inverse, MeasureTheory.norm_condExpL2_le_one, ContinuousLinearEquiv.mdifferentiableAt, MeasureTheory.ConvolutionExists.add_distrib, differentiable_sigmoid, ContinuousMap.instNormOneClassOfNonempty, LinearMap.mem_span_iff_continuous, ProbabilityTheory.tendsto_cdf_atBot, integral_comp_pi_polarCoord_symm, BoxIntegral.Integrable.add, Real.tendsto_harmonic_sub_log_add_one, Padic.isDenseInducing_cast_withVal, ZetaAsymptotics.tendsto_riemannZeta_sub_one_div_nhds_right, UniqueMDiffOn.uniqueDiffWithinAt_range_inter, NumberField.mixedEmbedding.normAtPlace_mixedSpaceOfRealSpace, BumpCovering.coe_single, MeasureTheory.summable_measure_toReal, Asymptotics.isBigOTVS_comm, GromovHausdorff.eq_toGHSpace_iff, Real.summable_nat_rpow, GenLoop.continuous_toLoop, polarCoord_source, NumberField.mixedEmbedding.measurable_polarSpaceCoord_symm, ContinuousMap.isUniformEmbedding_equivBoundedOfCompact, mdifferentiableAt_extChartAt, MeasureTheory.condExpL2_comp_continuousLinearMap, ModularForm.is_invariant_one, LindemannWeierstrass.hasDerivAt_cexp_mul_sumIDeriv, ConvexOn.real_sSup_affine_eq, RCLike.re_extendTo𝕜'ₗ, InnerProductSpace.symm_toEuclideanLin_rankOne, MeasureTheory.Lp.coeFn_star, FormalMultilinearSeries.ofScalars_norm_eq_mul, isBoundedBilinearMap_smulRight, MeasureTheory.Measure.toSignedMeasure_restrict_sub, ProbabilityTheory.tendsto_condCDF_atTop, MeasureTheory.L2.eLpNorm_rpow_two_norm_lt_top, isOpen_setOf_linearIndependent, ZSpan.setFinite_inter, LinearIsometryEquiv.differentiableWithinAt, Trivialization.mdifferentiable, Commute.cfcₙ_real, PeriodPair.derivWeierstrassPExcept_def, Real.one_div_sub_sq_hasFPowerSeriesOnBall_zero, Complex.continuousAt_ofReal_cpow_const, Real.summable_exp_nat_mul_iff, ContinuousLinearMap.holder_add_left, differentiableOn_const_add_iff, secondCountable_of_proper, MeasureTheory.Supermartingale.add, AnalyticOnNhd.eval_continuousLinearMap, cauchySeq_finset_of_geometric_bound, hasStrictFDerivAt_pi, Real.tendsto_logb_nhdsNE_zero, Submodule.orthogonalProjection_orthogonalComplement_singleton_eq_zero, Submodule.isOrtho_sup_left, GenLoop.fromLoop_trans_toLoop, ProbabilityTheory.uncenteredCovarianceBilinDual_zero, MeasureTheory.memLp_re_im_iff, ContinuousMapZero.toNNReal_apply, AffineIsometryEquiv.coe_symm_toHomeomorph, ContinuousLinearMap.adjoint_innerSL_apply, EisensteinSeries.tsum_symmetricIco_tsum_eq_S_act, ZLattice.coe_comap, NormedAddGroupHom.completion_id, sameRay_iff_norm_smul_eq, LSeries.hasDerivAt_term, tendsto_subseq_of_frequently_bounded, MeasureTheory.eLpNorm_le_nnreal_smul_eLpNorm_of_ae_le_mul, Submodule.IsOrtho.comap, hasFDerivAt_iff_isLittleO_nhds_zero, Metric.uniformContinuous_infDist_pt, Metric.isOpen_singleton_iff, NormedAddGroupHom.continuous, continuous_circleMap_inv, fderivWithin_comp_sub, UpperHalfPlane.mdifferentiableAt_ofComplex, LSeries_eq_mul_integral', integrableOn_Ioi_deriv_norm_ofReal_cpow, ProbabilityTheory.exponentialCDFReal_eq_lintegral, ContDiffMapSupportedIn.structureMapLM_apply, CStarAlgebra.span_unitary, UniformSpace.Completion.uniformity_dist', Path.extend_trans_of_half_le, ContinuousLinearMap.circleAverage_comp_comm, EuclideanGeometry.Sphere.dist_orthogonalProjection_eq_radius_iff_isTangentAt, ProbabilityTheory.stronglyMeasurable_condVar, binomialSeries_radius_ge_one, MeasureTheory.aefinStronglyMeasurable_of_aemeasurable, writtenInExtChartAt_comp, derivWithin_const_smul', Real.fromBinary_continuous, isBoundedLinearMap_prod_multilinear, HasFiniteFPowerSeriesAt.eventually_const_of_bound_one, ContDiffAt.eventually, Submodule.orthogonalProjection_eq_linearProjOfIsCompl, Orthonormal.inner_sum, differentiableWithinAt_fst, EuclideanGeometry.reflection_apply, ContDiff.const_smul, continuousOn_coordChange, deriv_const_sub, ProbabilityTheory.IsMeasurableRatCDF.stieltjesFunction_nonneg, MeasureTheory.dist_indicatorConstLp_eq_norm, LinearIsometryEquiv.comp_fderiv', CFC.complex_exp_eq_normedSpace_exp, hasMFDerivWithinAt_iff_hasFDerivWithinAt, HasStrictDerivAt_ofNat, AbsolutelyContinuousOnInterval.intervalIntegrable_deriv, ProbabilityTheory.cdf_gammaMeasure_eq_integral, le_iff_norm_sqrt_mul_rpow, CantorScheme.VanishingDiam.map_continuous, Real.exists_seq_rat_strictMono_tendsto, ContinuousLinearMap.IsPositive.re_inner_nonneg_right, DoubleCentralizer.smul_snd, deriv_div_const, NumberField.mixedEmbedding.fundamentalCone.injective_expMap, Path.refl_extend, LipschitzWith.norm_compLp_sub_le, LeftInvariantDerivation.instLinearMapClassContMDiffMapModelWithCornersSelfSomeENatTop, summable_prod_of_nonneg, HasFiniteFPowerSeriesAt.comp, ContinuousMap.idealOfSet_isMaximal_iff, LeftInvariantDerivation.coeFnAddMonoidHom_apply, not_differentiableAt_abs_zero, BoundedContinuousFunction.toLp_denseRange, MonotoneOn.ae_differentiableWithinAt, interior_euclideanQuadrant, hasDerivWithinAt_iff_tendsto, contMDiff_snd_tangentBundle_modelSpace, MeasureTheory.condExpL2_const_inner, intervalIntegral.intervalIntegrable_log', IsUltrametricDist.isClosed_ball, Unitary.path_apply, curveIntegrable_restrictScalars_iff, SpectrumRestricts.nnreal_iff_nnnorm, WeakFEPair.differentiable_Λ₀, cyclotomicCharacter.continuous, EisensteinSeries.D2_mul, CircleDeg1Lift.tendsto_translation_number₀', IsCoercive.isClosed_range, TemperedDistribution.laplacianCLM_apply, Metric.Sigma.isOpen_iff, ZMod.toCircle_eq_circleExp, MeasureTheory.Lp.isometry_compMeasurePreserving, MeasureTheory.SignedMeasure.toJordanDecomposition_smul, continuousAt_gaussian_integral, mdifferentiableOn_iff_of_subset_source', ProperCone.innerDual_innerDual, UniformSpace.Completion.dist_self, TensorProduct.ext_iff_inner_right_threefold, ProbabilityTheory.mgf_pos_iff, mem_contMDiffFiberwiseLinear_iff, intervalIntegral.integral_deriv_of_contDiffOn_Icc, NumberField.mixedEmbedding.fundamentalCone.expMap_basis_of_ne, curveIntegralFun_def, Submodule.coe_prodEquivOfClosedCompl, Circle.exp_nsmul, BarrelledSpace.continuous_of_lowerSemicontinuous, Seminorm.continuousAt_zero, ContinuousLinearMap.norm_smulRightL_apply, ContinuousAlternatingMap.alternatizeUncurryFin_apply, hasDerivAt_finCons, Asymptotics.IsThetaTVS.rfl, Orientation.areaForm_rightAngleRotation_left, coeFn_fourierLp, Metric.nhds_basis_ball_pow, ContinuousLinearMap.contMDiffAt, MeasureTheory.Lp.simpleFunc.dense, CStarAlgebra.exists_sum_four_nonneg, Path.truncate_range, isOpen_setOf_nat_le_rank, Real.Angle.two_nsmul_eq_iff, FormalMultilinearSeries.hasFPowerSeriesOnBall_changeOrigin, CircleDeg1Lift.tendsto_translationNumber_of_dist_bounded_aux, cfcₙ_complex_eq_real, SchwartzMap.smulLeftCLM_smul, CurveIntegrable.neg, differentiableAt_iff_comp_neg, isClosed_setOf_isCompactOperator, BoundedContinuousFunction.coe_toContinuousMap, ENNReal.tsum_toReal_eq, DoubleCentralizer.coe_snd, ContinuousMultilinearMap.fin0_apply_norm, NNReal.map_coe_nhdsGE, MemHolder.smul_iff, EuclideanGeometry.dist_set_eq_iff_dist_orthogonalProjection_eq, Quaternion.exp_coe, hasFPowerSeriesAt_iff, ContinuousLinearMap.fpowerSeriesBilinear_apply_one, Metric.uniformity_basis_dist_inv_nat_pos, NumberField.mixedEmbedding.disjoint_negAt_plusPart, map_extChartAt_nhds, ContinuousMap.Homotopy.map_zero_left, MeasureTheory.Lp.instFourierAdd, unitInterval.continuous_symm, Real.hasSum_log_sub_log_of_abs_lt_one, Matrix.IsHermitian.instContinuousFunctionalCalculus, ContinuousLinearMap.le_opNorm_enorm, HasFPowerSeriesOnBall.iteratedFDeriv_eq_sum, IccLeftChart_extend_bot_mem_frontier, fderiv_norm_sq_apply, Submodule.starProjection_eq_self_iff, LipschitzWith.ae_differentiableAt_real, IsSelfAdjoint.commute_cfc, RCLike.imCLM_apply, DirichletCharacter.continuousOn_neg_logDeriv_LFunctionTrivChar₁, cfcHom_apply_mem_elemental, MeasureTheory.eLpNorm_le_of_ae_bound, hasStrictDerivAt_pow, BoxIntegral.Integrable.dist_integralSum_sum_integral_le_of_memBaseSet_of_iUnion_eq, RightDerivMeasurableAux.le_of_mem_A, OpenPartialHomeomorph.univBall_symm_apply_center, OrthonormalBasis.tensorProduct_repr_tmul_apply, contMDiffAt_iff_contDiffAt, IsContDiffImplicitAt.implicitFunctionAux_fst, Derivation.evalAt_apply, ProbabilityTheory.Kernel.tendsto_density_fst_atTop_ae_of_monotone, derivWithin_mem_iff, NormedAddCommGroup.nhds_basis_norm_lt, EuclideanGeometry.Sphere.finrank_orthRadius, DirichletCharacter.differentiable_completedLFunction, Antitone.intervalIntegrable, AffineSubspace.isConnected_setOf_sSameSide, Complex.continuousAt_tan, PositiveLinearMap.preGNS_norm_sq, ContinuousMultilinearMap.norm_curryMid, NNRat.instContinuousSMulRatReal, AlternatingMap.mkContinuous_norm_le', ConvexOn.univ_sSup_of_nat_affine_eq, differentiableOn_inv, UpperHalfPlane.IsZeroAtImInfty.of_exp_decay, ContinuousLinearEquiv.comp_right_differentiable_iff, Icc_isBoundaryPoint_top, aestronglyMeasurable_withDensity_iff, HurwitzZeta.differentiableAt_expZeta, ContinuousAlternatingMap.ratio_le_opNorm, ContinuousMultilinearMap.norm_mkPiAlgebraFin, diffContOnCl_univ, Affine.Simplex.points_vsub_eulerPoint, TensorProduct.assocIsometry_symm_apply, Orientation.oangle_add_right_eq_arccos_of_oangle_eq_pi_div_two, InnerProductGeometry.angle_smul_left_of_pos, MeasureTheory.Lp.simpleFunc.zero_toSimpleFunc, InnerProductSpace.gramSchmidt_mem_span, Real.summable_one_div_int_add_rpow, ProbabilityTheory.ofReal_cdf, Ideal.IsMaximal.closure_eq, ModelWithCorners.uniqueDiffOn, norm_iteratedFDeriv_fderiv, uniqueDiffOn_Ici, Quaternion.exp_eq, UpperHalfPlane.IsBoundedAtImInfty.slash, Real.Angle.two_nsmul_toReal_eq_two_mul, StrongDual.polar_nonempty, isClosedMap_dist, NormedSpace.dual_def, egauge_le_of_smul_mem_of_ne, TensorProduct.inner_map_map, RCLike.geometric_hahn_banach_open_open, CompactlySupportedContinuousMap.exists_add_nnrealPart_add_eq, ContinuousMap.edist_eq_iSup, Real.continuous_mulExpNegMulSq, MeasureTheory.Lp_toLp_restrict_smul, MeasureTheory.Measure.integral_comp_div, mdifferentiableWithinAt_iff_target, intervalIntegral.integral_const, Real.tendsto_atTop_csInf_of_antitoneOn_bddBelow_nat_Ici, fderiv_norm_sq, Filter.EventuallyEq.hasDerivAtFilter_iff, instProperSpaceSubtypeMemSubmoduleOfCompleteSpaceOfLocallyCompactSpace, LinearMap.IsSymmetric.orthogonalFamily_iInf_eigenspaces, differentiableWithinAtProp_self_target, MeasureTheory.Measure.toSphere_apply_univ', Complex.continuous_im, WeakDual.CharacterSpace.instStarHomClass, LightProfinite.isClosedEmbedding_natUnionInftyEmbedding, Submodule.ClosedComplemented.of_isCompl_isClosed, CircleIntegrable.fun_sum, TensorProduct.toLinearMap_mapInclIsometry, AnalyticOnNhd.differentiableOn, MeasureTheory.condExp_bot_ae_eq, Complex.equivRealProdCLM_apply, AkraBazziRecurrence.isEquivalent_deriv_rpow_p_mul_one_sub_smoothingFn, PNat.isUniformEmbedding_coe, Function.HasTemperateGrowth.isBigO, FormalMultilinearSeries.hasFPowerSeriesOnBall, ContinuousLinearMap.coe_mulₗᵢ, deriv_fun_const_smul', Filter.tendsto_inv₀_cobounded', MeasureTheory.FiniteMeasure.tendsto_iff_forall_toWeakDualBCNN_tendsto, Real.Angle.sign_antiperiodic, HasFPowerSeriesWithinOnBall.continuousWithinAt, ContinuousLinearMap.isUnit_iff_bijective, Complex.one_div_sub_hasFPowerSeriesOnBall_zero, Orientation.inner_mul_inner_add_areaForm_mul_areaForm', Real.integrableOn_rpowIntegrand₀₁_Ici, MeasureTheory.Supermartingale.stronglyAdapted, hasSum_L_function_mod_four_eval_three, DomAddAct.vadd_Lp_val, analyticOrderAt_add_of_ne, MeasureTheory.L1.SimpleFunc.coe_posPart, MeasureTheory.Integrable.of_finite, norm_cfc_lt, ProbabilityTheory.IsMeasurableRatCDF.tendsto_stieltjesFunction_atBot, ContinuousLinearMap.innerSL_apply_comp, MeasureTheory.Lp.compMeasurePreserving_val, conformalAt_iff', TensorProduct.lidIsometry_symm_apply, ContinuousLinearMap.instStarOrderedRingRCLike, surjective_stereographic, ContinuousLinearMap.mdifferentiableAt, MeasureTheory.FiniteMeasure.tendsto_iff_forall_integral_rclike_tendsto, cfc_neg_id, Real.hasDerivWithinAt_arcsin_Iic, ContinuousLinearMap.toSesqForm_apply_norm_le, PeriodPair.finrank_lattice, hasDerivAt_abs_pos, PeriodPair.derivWeierstrassP_add_coe, PiTensorProduct.injectiveSeminorm_def, ContinuousLinearMap.coeFn_holder, NumberField.mixedEmbedding.fundamentalCone.expMap_single_target, deriv_ofNat, ContDiffMapSupportedIn.structureMapLM_eq, MeasureTheory.isTightMeasureSet_of_forall_basis_tendsto, SchwartzMap.isBigO_cocompact_rpow, MeasureTheory.L1.SimpleFunc.setToL1S_smul_left, Complex.orderClosedTopology, Orientation.oangle_smul_left_of_pos, HilbertBasis.hasSum_repr_symm, MeasureTheory.Submartingale.stoppedValue_leastGE_eLpNorm_le', CStarMatrix.norm_def, ContinuousAlternatingMap.norm_image_sub_le, ProbabilityTheory.instIsGaussianMapNeg, Real.tendsto_mulExpNegMulSq, continuous_sigmoid, hasStrictFDerivAt_sub_const, ContinuousLinearMap.coe_deriv₂, AffineIsometry.continuous, IsMIntegralCurveAt.eventually_hasDerivAt, MeasureTheory.Lp.instContinuousSMulDomMulAct, OrderedFinpartition.norm_compAlongOrderedFinpartitionL_le, MeasureTheory.Lp.norm_compMeasurePreserving, hasFDerivAt_stereoInvFunAux_comp_coe, LinearIsometryEquiv.comp_hasStrictFDerivAt_iff, differentiableWithinAt_Ioi_iff_Ici, HurwitzZeta.differentiableAt_sinZeta, LinearMap.adjoint_id, ModularForm.multipliableLocallyUniformlyOn_eta, IsUltrametricDist.isClopen_ball, contDiff_succ_iff_hasFDerivAt, MeasureTheory.integrableOn_Ioi_comp_rpow_iff', MeasureTheory.Measure.ContinuousLinearMap.quasiMeasurePreserving, MeasureTheory.Lp.nnnorm_zero, InnerProductSpace.nullSubmodule_le_ker_toDualMap_right, NumberField.mixedEmbedding.fundamentalCone.expMapBasis_nonneg, BoundedContinuousFunction.continuous_comp, hasSum_geometric_of_lt_one, Unitization.continuous_inr, hasFDerivWithinAt_comp_add_left, ModularForm.SL_smul_slash, ODE.picard_apply, summable_geometric_two_encode, SeminormedAddCommGroup.to_isUniformAddGroup, MeasureTheory.condExpL2_indicator_nonneg, nhdsWithin_extChartAt_target_eq', ContinuousAlternatingMap.alternatizeUncurryFinCLM_apply, tendsto_norm_cocompact_atTop, ContinuousLinearMap.adjoint_adjoint, Path.eqOn_extend_segment, Int.isClosedEmbedding_coe_rat, Complex.isEquivalent_sin, NumberField.mixedEmbedding.convexBodyLT'_convex, differentiableOn_zpow, Seminorm.cont_normedSpace_to_withSeminorms, Submodule.coe_prodEquivOfClosedCompl_symm, selfAdjoint.expUnitary_coe, DoubleCentralizer.add_toProd, MeasureTheory.charFun_map_add_const, VectorBundleCore.toFiberBundleCore_baseSet, CFC.abs_eq_zero_iff, instIsManifoldIcc, SeminormedCommGroup.mem_closure_iff, Bundle.ContinuousRiemannianMetric.isVonNBounded, Matrix.PosSemidef.sqrt_eq_iff_eq_sq, MeasureTheory.integrable_rnDeriv_mul_log_iff, PartitionOfUnity.sum_finsupport, TemperedDistribution.smulLeftCLM_apply_apply, MeasureTheory.hasFiniteIntegral_count_iff, integrableAtFilter_rpow_atTop_iff, CFC.rpow_eq_cfc_real, ModelWithCorners.toHomeomorph_symm_apply, summable_jacobiTheta₂_term_iff, AddCircle.ergodic_zsmul_add, Real.BohrMollerup.tendsto_log_gamma, Complex.conjCLE_coe, MeasureTheory.L1.integral_neg, extChartAt_target_mem_nhds', NumberField.mixedEmbedding.mem_rat_span_latticeBasis, RCLike.restrict_toContinuousMap_eq_toContinuousMapStar_restrict, MeasureTheory.TendstoInMeasure.tendstoInDistribution_of_aemeasurable, HurwitzKernelBounds.summable_f_int, Complex.continuousOn_one_add_mul_inv, hasFDerivAt_pi, MeasureTheory.ProbabilityMeasure.tendsto_iff_forall_integral_tendsto, Real.tendsto_one_add_div_pow_exp, AnalyticAt.eventually_continuousAt, ProbabilityTheory.IsMeasurableRatCDF.tendsto_atTop_one, Real.tendsto_pow_mul_exp_neg_atTop_nhds_zero, Orientation.inner_mul_areaForm_sub, Asymptotics.IsTheta.tendsto_zero_iff, IsUltrametricDist.nnnorm_tsum_le, SmoothBumpCovering.toSmoothPartitionOfUnity_zero_of_zero, differentiableOn_fst, contDiff_one_iff_deriv, InnerProductSpace.HarmonicAt.add, inner_matrix_col_col, MeasureTheory.eLpNormEssSup_const_smul_le', hasFDerivWithinAt_snd, MeasureTheory.Measure.addHaar_closedBall', Matrix.IsHermitian.im_star_dotProduct_mulVec_self, GenLoop.instContinuousEvalConst, EisensteinSeries.eisensteinSeries_tendstoLocallyUniformly, uniformConvexOn_zero, DiscreteTopology.of_forall_le_norm', IsBoundedLinearMap.isLinearMap_and_continuous_iff_isBoundedLinearMap, deriv2_sqrt_mul_log, SmoothPartitionOfUnity.contMDiff_sum, CompletelyRegularSpace.completely_regular_isOpen, mellin_comp_mul_left, differentiableWithinAt_finCons, Real.hasStrictDerivAt_log_of_pos, FormalMultilinearSeries.ofScalars_norm, MeasureTheory.Measure.zero_le_toSignedMeasure, derivWithin_comp_neg, ContinuousMultilinearMap.norm_ofSubsingleton_id, DeltaGeneratedSpace.continuous_iff, Hyperreal.isSt_ofSeq_iff_tendsto, hasFTaylorSeriesUpToOn_pi, ZSpan.fundamentalDomain_ae_parallelepiped, Real.sinhHomeomorph_apply, ContinuousMap.dist_eq_iSup, contMDiffOn_projIcc, IsBoundedBilinearMap.differentiableWithinAt, MeasureTheory.SignedMeasure.im_toComplexMeasure, MeasureTheory.memLp_top_const, differentiableAt_jacobiTheta, TangentBundle.mem_chart_source_iff, NumberField.mixedEmbedding.fundamentalCone.logMap_normAtAllPlaces, DiffeologicalSpace.isOpen_iff_preimages_plots, ContinuousLinearMap.orthogonal_ker, ContDiffBump.continuous_normed, NumberField.mixedEmbedding.fundamentalCone.normAtAllPlaces_normLeOne, InnerProductGeometry.angle_eq_angle_add_add_angle_add, MeasureTheory.pdf.hasFiniteIntegral_mul, AnalyticAt.hasStrictDerivAt, ProbabilityTheory.IsCondKernelCDF.toKernel_apply, Metric.exists_contMDiffMap_forall_closedEBall_subset, signedDist_vadd_vadd, iter_deriv_pow, Asymptotics.IsThetaTVS.refl, ContinuousLinearMap.continuousAt_uncurry_of_multilinear, MeasureTheory.Lp.mul_meas_ge_le_pow_enorm, ContDiffMapSupportedIn.norm_toBoundedContinuousFunction, contMDiff_circleExp, pi_mul_cot_pi_q_exp, ContDiffMapSupportedInClass.map_zero_on_compl, contDiffWithinAt_succ_iff_hasFDerivWithinAt, ProbabilityTheory.instIsProbabilityMeasurecdf, Stirling.tendsto_self_div_two_mul_self_add_one, BoundedContinuousFunction.probCharDual_apply, PeriodPair.weierstrassPExcept_add, hasFDerivWithinAt_apply, Real.deriv2_negMulLog, intervalIntegral.inv_smul_integral_comp_add_div, InnerProductSpace.norm_rankOne, SchwartzMap.tsum_eq_tsum_fourier, NumberField.mixedEmbedding.normAtAllPlaces_normAtAllPlaces, ZLattice.exists_finsetSum_norm_rpow_le_tsum, Stirling.stirlingSeq_has_pos_limit_a, Real.Angle.nsmul_eq_iff, DomMulAct.smul_Lp_add, Complex.hasDerivAt_Gamma_nat, MeasureTheory.Measure.integrable_pow_neg_integrablePower, TangentBundle.trivializationAt_target, Rat.uniformContinuous_coe_real, ContMDiffMap.coeFnLinearMap_apply, Submodule.isHilbertSumOrthogonal, GromovHausdorff.HD_below_aux1, IsClosed.reProdIm, DoubleCentralizer.neg_fst, ContDiffMapSupportedIn.iteratedFDerivWithOrderLM_apply_of_le, Units.chartAt_apply, PiTensorProduct.mapLMultilinear_toFun_apply, extChartAt_target_subset_closure_interior, ZLattice.abs_repr_le, CStarMatrix.inner_toCLM_conjTranspose_right, norm_jacobiTheta₂_term_fderiv_le, CFC.isUnit_sqrt_iff, EisensteinSeries.isBoundedAtImInfty_eisensteinSeriesSIF, HasFiniteFPowerSeriesOnBall.fderiv, ContinuousLinearEquiv.norm_pos, isProperMap_nndist, SeparationQuotient.liftNormedAddGroupHom_norm_le, Cardinal.summable_cantor_function, AnalyticWithinAt.smul, Matrix.PosDef.re_dotProduct_pos, ContinuousAffineMap.toConstProdContinuousLinearMap_snd, ContDiffBump.sub, mellin_comp_mul_right, NonUnitalStarAlgHom.instContinuousLinearMapClassComplex, GaussianFourier.integral_rexp_neg_mul_sq_norm, ContinuousLinearEquiv.comp_hasStrictFDerivAt_iff, lp.tsum_mul_le_mul_norm, ContinuousMultilinearMap.curryMidEquiv_symm_apply, FormalMultilinearSeries.comp_summable_nnreal, bernsteinApproximation.apply, ampleSet_univ, TensorProduct.edist_tmul_le, MeasureTheory.SignedMeasure.rnDeriv_add, quasispectrum.instCompactSpace, Real.tendsto_Icc_vitaliFamily_right, HurwitzZeta.hasSum_int_evenKernel₀, Metric.NonemptyCompacts.dist_eq, tendsto_iff_norm_sub_tendsto_zero, fderiv_eq_smul_deriv, integrableOn_rpow_mul_exp_neg_mul_rpow, MeasureTheory.Lp.continuous_posPart, unitary.inner_map_map, CStarMatrix.toCLM_apply_single_apply, MeasureTheory.Measure.integrable_toReal_rnDeriv, LinearMap.IsPositive.conj_adjoint, ContinuousMultilinearMap.uncurryRight_norm, ContinuousLinearMap.flipAlternating_apply_apply, Real.isEquivalent_sinh, LinearMap.ker_toContinuousLinearMap, isometry_cfcHom, ApproximatesLinearOn.continuous, MeasureTheory.Measure.addHaar_real_closedBall, MeasureTheory.Lp.norm_def, EuclideanGeometry.angle_const_vadd, ContinuousMap.Homotopy.curry_zero, tangentBundleCore_coordChange_achart, Metric.sphere.instIsTopologicalGroup, Orthonormal.tsum_inner_products_le, rieszContentAux_le, ZLattice.comap_refl, ContinuousAlternatingMap.le_opNorm_mul_prod_of_le, Complex.tendsto_exp_comap_re_atBot_nhdsNE, MeasureTheory.eLpNorm_nsmul, differentiable_circleMap, Complex.arg_neg_coe_angle, UpperHalfPlane.mdifferentiable_smul, hasFDerivAt_prodMk_right, BoundedContinuousFunction.isInducing_coeFn, DoubleCentralizer.toProdMulOppositeHom_apply, Function.locallyFinsuppWithin.toClosedBall_eval_within, ContinuousLinearMap.coeFn_compLp', BumpCovering.support_toPartitionOfUnity_subset, ModularForm.slash_apply, HurwitzZeta.tendsto_hurwitzZetaEven_sub_one_div_nhds_one, Metric.PiNatEmbed.exists_embedding_to_hilbert_cube, selfAdjoint.joined_one_expUnitary, integrableOn_exp_mul_complex_Ioi, NormedSpace.exp_add, Unitization.cfcₙ_eq_cfc_inr, summable_indicator_mod_iff, MeasureTheory.average_eq, Metric.isUniformEmbedding_iff', EuclideanGeometry.orthogonalProjection_mem_subspace_eq_self, curveIntegralFun_zero, deriv_comp_sub_const, AnalyticWithinAt.exists_hasFTaylorSeriesUpToOn, iteratedFDeriv_add_apply', Complex.isClosed_range_intCast, polynomialFunctions.comap_compRightAlgHom_iccHomeoI, AffineMap.continuous_of_finiteDimensional, tendsto_rpow_atBot_of_base_gt_one, OpenPartialHomeomorph.univBall_source, Real.instTietzeExtension, ProbabilityTheory.indepFun_iff_charFunDual_prod, iteratedFDeriv_succ_apply_left, IsSymmSndFDerivAt.eq, Metric.mk_uniformity_basis, le_iff_norm_sqrt_mul_sqrt_inv, Submodule.orthogonalProjectionFn_mem, LinearMap.IsPositive.re_inner_nonneg_left, ProbabilityTheory.IsGaussian.exists_integrable_exp_sq, iteratedFDeriv_const_of_ne, continuous_iff_continuous_dist, hasDerivWithinAt_sub_const_iff, MeasureTheory.MemLp.toLp_const, HurwitzZeta.differentiable_completedCosZeta₀, intervalIntegral.smul_integral_comp_add_mul, Real.continuousOn_tan_Ioo, ContDiffPointwiseHolderAt.continuousAt, ProbabilityTheory.integrable_stieltjesOfMeasurableRat, Homeomorph.unitBall_symm_apply, Complex.restrictScalars_toSpanSingleton', Metric.ball_contractible, Real.differentiableAt_negMulLog_iff, QuadraticMap.hasLineDerivAt, LinearIsometryEquiv.submoduleMap_apply_coe, Polynomial.fourierCoeff_toAddCircle_eq_zero_of_lt_zero, fderiv_inv', MeasureTheory.Measure.integral_comp_inv_mul_right, ContinuousLinearEquiv.contDiff, ModelWithCorners.mdifferentiableWithinAt, ContinuousLinearMapWOT.ext_inner_iff, Besicovitch.SatelliteConfig.exists_normalized_aux3, MeasureTheory.memLp_const, BoundedContinuousFunction.integrable_of_nnreal, ContinuousLinearMap.coeFn_ofIsClosedGraph, Complex.differentiable_iteratedDeriv_cosh, unitary.continuousOn_argSelfAdjoint, MeasureTheory.charFunDual_conv, AffineSubspace.isPreconnected_setOf_sSameSide, Complex.closedEmbedding_intCast, NNReal.instCompleteSpace, Complex.rectangle_eq_convexHull, NumberField.mixedEmbedding.mixedSpaceOfRealSpace_apply, HurwitzZeta.hurwitzZetaEven_residue_one, NumberField.mixedEmbedding.fundamentalCone.closure_paramSet_ae_interior, EisensteinSeries.G2_T_transform, norm_inner_div_norm_mul_norm_eq_one_iff, ProbabilityTheory.IsGaussian.integrable_id, MeasureTheory.lpMeas.aestronglyMeasurable, tendsto_zero_geometric_tsum_pnat, RCLike.geometric_hahn_banach_open_point, Real.deriv2_mul_log, ProbabilityTheory.analyticOnNhd_iteratedDeriv_mgf, CFC.rpow_sqrt, FormalMultilinearSeries.comp_assoc, InnerProductGeometry.norm_div_cos_angle_add_of_inner_eq_zero, MeasureTheory.SignedMeasure.rnDeriv_sub, PiTensorProduct.tprodL_coe, ModelWithCorners.extChartAt_transContinuousLinearEquiv_target, egauge_smul_left, MeasureTheory.Measure.addHaar_smul, HasFPowerSeriesWithinAt.comp, Submodule.mem_iff_norm_starProjection, differentiable_neg_iff, Complex.reCLM_apply, Metric.dist_mem_uniformity, PartitionOfUnity.mem_finsupport, Real.hasDerivAt_negMulLog, continuousAt_dslope_of_ne, AffineIsometryEquiv.coe_toContinuousAffineEquiv, Complex.closure_setOf_im_lt, NumberField.mixedEmbedding.lintegral_comp_polarSpaceCoord_symm, Orientation.abs_volumeForm_apply_le, PeriodPair.differentiableOn_derivWeierstrassPExcept, continuousMultilinearCurryFin1_apply, MeasureTheory.exists_continuous_eLpNorm_sub_le_of_closed, IsCoercive.antilipschitz, PiLp.hasStrictFDerivAt_toLp, LeftInvariantDerivation.evalAt_apply, hasStrictDerivAt_neg, UpperHalfPlane.petersson_slash, deriv_id', Bornology.IsBounded.closure, hasStrictFDerivAt_euclidean, unitInterval.instConnectedSpaceElemReal, EisensteinSeries.tsum_symmetricIco_tsum_sub_eq, SemiNormedGrp.completion_completeSpace, Real.tendsto_logb_nat_add_one_sub_logb, hasFDerivAt_finset_prod, fourierCoeff_fourier, Asymptotics.superpolynomialDecay_iff_superpolynomialDecay_norm, exists_mem_frontier_infDist_compl_eq_dist, NNReal.instContinuousStar, unitary.linearIsometryEquiv_coe_apply, Affine.Simplex.signedInfDist_incenter, ProbabilityTheory.Kernel.stronglyAdapted_densityProcess, Urysohns.CU.tendsto_approx_atTop, HilbertBasis.finite_spans_dense, nnnorm_cfcₙ_lt, toMeromorphicNFOn_eqOn_codiscrete, aemeasurable_derivWithin_Ioi, MeasureTheory.L1.norm_eq_integral_norm, MeasureTheory.Measure.addHaar_image_homothety, MeasureTheory.setIntegral_const, IsCoveringMap.liftPath_trans, SeminormedGroup.tendstoUniformlyOn_one, LipschitzAdd.continuousAdd, norm_combo_lt_of_ne, ProbabilityTheory.Kernel.tendsto_densityProcess_atTop_of_antitone, StieltjesFunction.right_continuous', isSimplyConnected_iff_exists_homotopy_refl_forall_mem, MeasureTheory.levyProkhorov_eq_convergenceInDistribution, Orientation.oangle_add_oangle_rev_neg_right, UpperHalfPlane.continuous_re bridge: BoxIntegral.hasIntegralIndicatorConst

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
cobounded_sets 📖	mathematical	—	Filter.sets Bornology.cobounded toBornology setOf Set Real	—	—
dist_comm 📖	mathematical	—	Dist.dist toDist	—	—
dist_eq_of_dist_zero 📖	—	Dist.dist toDist Real Real.instZero	—	—	sub_eq_zero abs_nonpos_iff IsOrderedAddMonoid.toAddLeftMono Real.instIsOrderedAddMonoid covariant_swap_add_of_covariant_add abs_dist_sub_le dist_comm
dist_self 📖	mathematical	—	Dist.dist toDist Real Real.instZero	—	—
dist_triangle 📖	mathematical	—	Real Real.instLE Dist.dist toDist Real.instAdd	—	—
edist_dist 📖	mathematical	—	edist ENNReal.ofReal Dist.dist toDist	—	—
ext 📖	—	toDist	—	—	UniformSpace.ext Bornology.ext Filter.ext Filter.mem_sets
ext_iff 📖	mathematical	—	toDist	—	ext
replaceBornology_eq 📖	mathematical	Bornology.IsBounded toBornology	replaceBornology	—	ext Dist.ext
replaceTopology_eq 📖	mathematical	UniformSpace.toTopologicalSpace toUniformSpace	replaceTopology	—	ext Dist.ext
replaceUniformity_eq 📖	mathematical	uniformity PseudoEMetricSpace.toUniformSpace toPseudoEMetricSpace	replaceUniformity	—	ext Dist.ext
uniformity_dist 📖	mathematical	—	uniformity toUniformSpace iInf Filter Real Filter.instInfSet Real.instLT Real.instZero Filter.principal setOf Dist.dist toDist	—	—

Real

Definitions

Name	Category	Theorems
pseudoMetricSpace 📖	CompOp	2753 math math: MeasureTheory.Measure.exists_innerRegular_eq_of_isCompact, IsLocalMaxOn.fderivWithin_nonpos, MeasureTheory.tendstoInMeasure_iff_measureReal_norm, geometric_hahn_banach_open, ZLattice.summable_norm_zpow, differentiableOn_arcosh, NumberField.mixedEmbedding.integral_comp_polarSpaceCoord_symm, hasDerivAt_arccos, hasDerivAt_fourier, ArithmeticFunction.vonMangoldt.summable_residueClass_non_primes_div, NumberField.mixedEmbedding.fundamentalCone.expMapBasis_apply', BoundedContinuousFunction.tietze_extension_step, aux_hasSum_of_le_geometric, InformationTheory.integrable_klFun_rnDeriv_iff, Circle.periodic_exp, MeasureTheory.Integrable.integral_norm_prod_right, TendstoUniformly.im, continuousOn_rpowIntegrand₀₁_uncurry, Bundle.ContMDiffRiemannianMetric.isVonNBounded, ProbabilityTheory.tendsto_defaultRatCDF_atBot, ProbabilityTheory.stieltjesOfMeasurableRat_ae_eq, NNReal.summable_coe, uniqueDiffOn_Icc, isCompact_stdSimplex, ProbabilityTheory.Kernel.tendsto_m_density, exists_continuous_sum_one_of_isOpen_isCompact, ProbabilityTheory.paretoCDFReal_eq_lintegral, SpectrumRestricts.nnreal_of_nonneg, integrableOn_rpowIntegrand₀₁_Ioi, Bundle.ContMDiffRiemannianMetric.contMDiff, SmoothBumpCovering.toSmoothPartitionOfUnity_eq_mul_prod, completelyRegularSpace_iff_isOpen, summable_sigma_of_nonneg, ProbabilityTheory.condCDF_ae_eq, ProbabilityTheory.isGaussian_iff_gaussian_charFun, differentiable_arctan, map_exp_nhds, exists_contMDiffMap_zero_one_of_isClosed, differentiableAt_mulExpNegMulSq, NumberField.mixedEmbedding.normAtComplexPlaces_mixedSpaceOfRealSpace, Complex.restrictScalars_one_smulRight', not_continuousAt_inv_log_neg_one, ProbabilityTheory.lintegral_condCDF, IsSelfAdjoint.quasispectrumRestricts, eventually_residual_irrational, BumpCovering.eventuallyEq_one, bernsteinApproximation.apply_zero, Asymptotics.IsBigO.rpow_rpow_nhdsGE_zero_of_le, NumberField.mixedEmbedding.lintegral_comp_polarCoord_symm, Matrix.IsHermitian.isClosedEmbedding_cfcAux, RCLike.ofRealCLM_apply, tendsto_norm_sub_self_nhdsNE, hasFDerivAt_fourierChar_neg_bilinear_left, instIsManifoldRealEuclideanSpaceFinModelWithCornersSelfTopWithTopENatElemHAddNatOfNatSphere, differentiableAt_arcsin, geometric_hahn_banach_point_point, tendsto_smoothingFun_of_ne_zero, NumberField.mixedEmbedding.fundamentalCone.interior_paramSet, NumberField.mixedEmbedding.measurable_polarCoordReal_symm, intervalIntegral.continuousOn_primitive_interval, ProbabilityTheory.condCDF_nonneg, RCLike.reCLM_apply, unitInterval.symmHomeomorph_apply, ZLattice.summable_norm_sub_inv_pow, ConvexOn.continuousOn_tfae, intervalIntegral.intervalIntegrable_one_div_one_add_sq, ProbabilityTheory.tendsto_defaultRatCDF_atTop, ProbabilityTheory.IsCondKernelCDF.toKernel_Iic, Path.continuousMapClass, ContinuousMap.abs_mem_subalgebra_closure, ContinuousMap.HomotopyWith.coe_toContinuousMap, hasDerivAt_sqrt_mul_log, Manifold.pathELength_eq_lintegral_mfderiv_Ioo, Complex.isOpenMap_im, ProbabilityTheory.aemeasurable_exp_mul, Complex.ofRealCLM_coe, Complex.norm_polarCoord_symm, MeasureTheory.SimpleFunc.setToSimpleFunc_smul_left, ProbabilityTheory.eqOn_complexMGF_of_mgf', ProbabilityTheory.IsCondKernelCDF.le_one, RightDerivMeasurableAux.D_subset_differentiable_set, Metric.exists_continuous_real_forall_closedEBall_subset, deriv_negMulLog, hasDerivAt_sigmoid, ProbabilityTheory.analyticOn_mgf, summable_riemannZetaSummand, ContinuousMap.Homotopy.extend_apply_of_one_le, deriv_abs, EuclideanSpace.closedBall_zero_eq, curveIntegrable_segment, StieltjesFunction.rightLim_eq, AkraBazziRecurrence.tendsto_zero_sumCoeffsExp, ProbabilityTheory.covarianceBilinDual_apply', Circle.exp_arg, nnnorm_deriv_mulExpNegMulSq_le_one, deriv_binEntropy, MeasureTheory.charFunDual_apply, uniqueDiffWithinAt_Iic, expNegInvGlue.hasDerivAt_polynomial_eval_inv_mul, rpow_eq_nhds_of_neg, isLittleO_exp_neg_mul_sq_cocompact, BoundedContinuousFunction.integral_eq_integral_nnrealPart_sub, ProbabilityTheory.hasGaussianLaw_iff_charFunDual_map_eq, Complex.integral_comp_pi_polarCoord_symm, summable_ofDigitsTerm, CFC.tendsto_cfc_rpow_sub_one_log, integrableOn_exp_mul_Iic, ProbabilityTheory.IsGaussian.integrable_dual, dist_mulExpNegMulSq_le_two_mul_sqrt, SchwartzMap.pairing_apply_apply, BumpCovering.toPartitionOfUnity_apply, ProbabilityTheory.HasSubgaussianMGF.integrable_exp_mul, AddCircle.homeomorphCircle'_apply_mk, hasStrictDerivAt_rpow_const_of_ne, geometric_hahn_banach_open_point, ContinuousMap.attachBound_apply_coe, frontier_halfSpace, binEntropy_continuous, Metric.PiNatEmbed.continuous_distDenseSeq_inv, Complex.continuousWithinAt_arg_of_re_neg_of_im_zero, ProbabilityTheory.unitInterval.cdf_eq_real, Rat.continuous_coe_real, MeasureTheory.Measure.toJordanDecomposition_toSignedMeasure_sub, span_fourier_closure_eq_top, Path.extend_extends, ProbabilityTheory.gammaCDFReal_eq_lintegral, GenLoop.fromLoop_apply, HasDerivWithinAt.complexToReal_fderiv', Nat.isUniformEmbedding_coe_real, ContDiffBump.integrable, ContinuousLinearMap.integral_apply, ODE.FunSpace.isUniformInducing_toContinuousMap, ProbabilityTheory.covarianceBilinDual_apply, SchwartzMap.integral_clm_comp_lineDerivOp_right_eq_neg_left, ProbabilityTheory.IsGaussian.map_eq_gaussianReal, ProbabilityTheory.IsRatCondKernelCDFAux.tendsto_one_of_monotone, fderiv_fourierChar_neg_bilinear_right_apply, stdSimplexHomeomorphUnitInterval_symm_apply_coe, Nat.dist_cast_real, LipschitzWith.memLp_lineDeriv, WeakFEPair.hf_modif_int, Quaternion.continuous_imI, intervalIntegrable_bernoulliFun, SmoothPartitionOfUnity.contMDiffAt_finsum, differentiableWithinAt_abs_pos, MeasureTheory.Integrable.continuous_primitive, Complex.uniformlyContinuous_im, Circle.exp_natCast_mul, ProbabilityTheory.tendsto_condCDF_atBot, ProbabilityTheory.integrable_preCDF, SchwartzMap.lineDerivOp_fourier_eq, Seminorm.uniformContinuous_of_forall, DifferentiableWithinAt.norm, det_fderivPolarCoordSymm, AddCircle.coe_real_preimage_closedBall_eq_iUnion, tendsto_rpow_mul_exp_neg_mul_atTop_nhds_zero, Ioo_eq_ball, SmoothPartitionOfUnity.locallyFinite, Topology.RelCWComplex.continuousOn_symm, SeminormFamily.filter_eq_iInf, MeasureTheory.Integrable.norm_integral_condExpKernel, exists_smooth_one_nhds_of_subset_interior, differentiable_sinh, MeasureTheory.mem_L1_toReal_of_lintegral_ne_top, MeasureTheory.Measure.toSphere_apply_aux, AkraBazziRecurrence.isLittleO_deriv_one_add_smoothingFn, unitInterval.toNNReal_continuous, Topology.CWComplex.continuousOn, ProbabilityTheory.covarianceBilin_apply_eq_cov, ProbabilityTheory.covarianceBilin_self, NumberField.mixedEmbedding.normAtPlace_polarCoord_symm_of_isComplex, continuous_rpow_const, DiffeologicalSpace.CorePlotsOn.isOpen_iff_preimages_plots, Complex.continuousOn_arg, NumberField.mixedEmbedding.fundamentalCone.abs_det_completeBasis_equivFunL_symm, AkraBazziRecurrence.differentiableAt_one_add_smoothingFn, SmoothPartitionOfUnity.nonneg, ContinuousMap.Homotopy.apply_zero_path, hasDerivAt_bernoulliFun, BoxIntegral.Box.isBounded, QuasispectrumRestricts.nnreal_iff, HomotopyGroup.symmAt_indep, hasSum_one_div_nat_pow_mul_fourier, continuous_mul_log, AddCircle.toCircle_add, ContDiffBump.integrable_normed, ProbabilityTheory.uncenteredCovarianceBilin_apply, deriv_log, Complex.ofRealCLM_norm, HasDerivAt.comp_ofReal, dense_liouville, CircleDeg1Lift.tendsto_translationNumber_aux, not_differentiableAt_norm_zero, uniqueDiffOn_Iic, continuous_arcsin, LipschitzWith.ae_exists_fderiv_of_countable, BumpCovering.point_finite, Besicovitch.ae_tendsto_measure_inter_div_of_measurableSet, deltaGenerated_eq_coinduced, ContinuousMap.HomotopyWith.prop', cauchySeq_iff_tendsto_dist_atTop_0, SchwartzMap.bilinLeftCLM_apply, Set.Countable.exists_pos_hasSum_le, ODE.FunSpace.range_toContinuousMap, tendsto_cos_pi_div_two, NumberField.mixedEmbedding.fundamentalCone.completeBasis_apply_of_ne, HasGradientAt.hasDerivAt', SmoothBumpCovering.exists_immersion_euclidean, IsOpen.exists_msmooth_support_eq, SmoothPartitionOfUnity.locallyFinite', ProbabilityTheory.integrable_toReal_condExpKernel, Bundle.RiemannianMetric.isVonNBounded, BoundedContinuousFunction.indicator_apply, ProbabilityTheory.setIntegral_condCDF, tendsto_norm_nhdsNE_one, one_mem_posTangentConeAt_iff_frequently, hasDerivAt_sin, Seminorm.continuous_of_forall', NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_apply_comp_toReal, Path.Homotopy.map_apply, ProbabilityTheory.IsCondKernelCDF.tendsto_atTop_one, Complex.closure_preimage_im, summable_one_div_nat_add_rpow, MeasureTheory.Measure.jordanDecompositionOfToSignedMeasureSub_toSignedMeasure, not_IntegrableOn_Ioi_inv, NNReal.tendsto_dist_agmSequences_atTop_zero, continuousAt_tan, hasSum_log_one_add_inv, differentiableOn_log, ProbabilityTheory.integral_continuousLinearMap_gaussianReal, Differentiable.fderiv_norm_rpow, Behrend.sphere_subset_preimage_metric_sphere, lintegral_fderiv_lineMap_eq_edist, UnitAddTorus.mFourierSubalgebra_coe, Path.ofLine_extend, signedDist_right_congr, MeasureTheory.Measure.toSignedMeasure_le_toSignedMeasure_iff, Seminorm.continuous', BoundedContinuousFunction.coe_normComp, ContinuousMap.toNNReal_neg_algebraMap, summable_one_div_int_pow, differentiableOn_arcsin, ContinuousMap.Homotopy.evalAt_eq, MeasureTheory.SignedMeasure.exists_compl_positive_negative, MeasureTheory.MemLp.integrable_norm_rpow', summable_norm_mul_geometric_of_norm_lt_one, AkraBazziRecurrence.isTheta_deriv_rpow_p_mul_one_sub_smoothingFn, EReal.nhds_coe, MeasureTheory.ComplexMeasure.HaveLebesgueDecomposition.imPart, Topology.RelCWComplex.pairwiseDisjoint', Affine.Simplex.sign_signedInfDist_lineMap_incenter_touchpoint, uniqueDiffOn_Ioc, NumberField.mixedEmbedding.instIsAddHaarMeasureMixedSpaceVolume, SchwartzMap.laplacianCLM_eq, monomial_has_deriv_aux, StieltjesFunction.measure_Ioo, NumberField.mixedEmbedding.fundamentalCone.compactSet_eq_union_aux₁, ContinuousMap.coeNNRealReal_apply, CompactlySupportedContinuousMap.nnrealPart_smul_neg, MeasureTheory.MemLp.norm_rpow, UnitAddTorus.mFourierSubalgebra_closure_eq_top, hasDerivAt_mul_log, Filter.tendsto_ofReal_iff', NumberField.mixedEmbedding.polarCoordReal_apply, ProbabilityTheory.cdf_paretoMeasure_eq_integral, differentiableWithinAt_abs, tendsto_sigmoid_atTop, continuous_sinc, deriv_arccos, ProbabilityTheory.setLIntegral_stieltjesOfMeasurableRat_rat, hasStrictDerivAt_sinh, AddCircle.homeomorphCircle'_symm_apply, isSelfAdjoint_iff_isStarNormal_and_spectrumRestricts, LocallyBoundedVariationOn.ae_differentiableWithinAt, hasFPowerSeriesOnBall_ofScalars_mul_add_zero, integrableOn_exp_Iic, RCLike.hasSum_ofReal, cfcₙHom_nnreal_eq_restrict, CircleDeg1Lift.dist_map_zero_translationNumber_le, instIsManifoldRealEuclideanSpaceFinOfNatNatEuclideanHalfSpaceModelWithCornersEuclideanHalfSpaceElemIcc, RCLike.continuous_normSq, ProbabilityTheory.IsCondKernelCDF.nonneg, summable_norm_mul_geometric_of_norm_lt_one', hasStrictDerivAt_abs_pos, deriv_sqrt_mul_log, ProbabilityTheory.cdf_expMeasure_eq, volume_closedBall, hasDerivWithinAt_abs_pos, ContinuousLinearMap.norm_extendTo𝕜, IsLocalMax.fderiv_eq_zero, MeasureTheory.Measure.sub_toSignedMeasure_eq_toSignedMeasure_sub, Seminorm.continuousAt_zero_of_forall', HasFDerivAt.norm_sq, tendsto_norm_div_self, Circle.isAddQuotientCoveringMap_exp, antideriv_bernoulliFun, hasStrictFDerivAt_rpow_of_pos, differentiableAt_sigmoid, exists_dist_slope_lt_pairwiseDisjoint_hasSum, BumpCovering.support_toPOUFun_subset, SpectrumRestricts.nnreal_iff, geometric_hahn_banach_compact_closed, ProbabilityTheory.IsCondKernelCDF.integral, integrable_prod_sub, WeakFEPair.hf_zero', Icc_isBoundaryPoint_bot, volume_val, borel_eq_generateFrom_Iio_rat, deriv_abs_neg, Tactic.ComputeAsymptotics.Majorized.tendsto_zero_of_neg, PartitionOfUnity.nonneg', differentiableWithinAt_arccos_Ici, ContDiffAt.exists_forall_mem_closedBall_exists_eq_forall_mem_Ioo_hasDerivAt₀, summable_condensed_iff_of_eventually_nonneg, summable_nat_rpow_inv, ball_eq_Ioo, HarmonicAt.analyticAt_complex_partial, ProbabilityTheory.stronglyMeasurable_geometricPMFReal, integrableOn_Ioi_rpow_of_lt, volume_pi_ball, Multipliable.norm, stereographic'_source, intervalIntegral.continuousOn_primitive, aestronglyMeasurable_rpowIntegrand₀₁, signedDist_left_congr, stdSimplexHomeomorphUnitInterval_zero, comap_norm_nhdsGT_zero, integrableOn_Ioi_norm_cpow_of_lt, IsClosed.lowerClosure_pi, InformationTheory.leftDeriv_klFun_one, curveIntegralFun_segment, ProbabilityTheory.stieltjesOfMeasurableRat_nonneg, Circle.exp_eq_exp, RCLike.reCLM_norm, GenLoop.homotopyTo_apply, signedDist_triangle, hasDerivAt_arcosh, PartitionOfUnity.locallyFinite, ProbabilityTheory.gammaCDFReal_eq_integral, MeasureTheory.SignedMeasure.toComplexMeasure_apply, Path.Homotopy.continuous_transAssocReparamAux, ConvexOn.monotoneOn_rightDeriv, tendsto_self_mul_const_pow_of_lt_one, UniformSpace.Completion.uniformContinuous_dist, Polynomial.Chebyshev.isLocalMin_T_real, expPartialHomeomorph_apply, enorm_fderiv_norm_rpow_le, Path.extend_symm_apply, LocallyBoundedVariationOn.ae_differentiableAt, Polynomial.toAddCircle_X_pow_eq_fourier, MonotoneOn.intervalIntegrable_deriv, MeasureTheory.AEStronglyMeasurable.ae_integrable_condKernel_iff, Icc_mem_vitaliFamily_at_left, Path.Homotopy.target, signedDist_linear_apply_apply, intervalIntegral.intervalIntegrable_zpow, Circle.exp_two_pi_mul_int, NumberField.mixedEmbedding.polarSpaceCoord_target, AddCircle.scaled_exp_map_periodic, Topology.RelCWComplex.source_eq, NumberField.mixedEmbedding.negAt_apply_snd, GammaIntegral_convergent, tendsto_atTop_csSup_of_monotoneOn_bddAbove_nat_Ici, EReal.isOpenEmbedding_coe, borel_eq_generateFrom_Ioo_rat, hasSum_sinh, tendsto_eulerMascheroniSeq', one_add_rpow_hasFPowerSeriesOnBall_zero, ProbabilityTheory.monotone_cdf, intervalIntegral.continuousOn_primitive_interval_left, VectorFourier.fourierPowSMulRight_eq_comp, MeasureTheory.charFunDual_eq_charFun_map_one, fourier_norm, Metric.continuousAt_inv_infDist_pt, Complex.uniformContinuous_im, MeasureTheory.memLp_two_iff_integrable_sq_norm, mfderivWithin_projIcc_one, StieltjesFunction.measure_singleton, Complex.frontier_preimage_re, ProbabilityTheory.Kernel.HasSubgaussianMGF.integrable_exp_add_compProd, indicator_thickening_eventually_eq_indicator_closure, comap_norm_nhds_zero, SmoothBumpFunction.continuous, comap_exp_nhds_zero, HomotopyGroup.isUnital_auxGroup, hasStrictDerivAt_arccos, MeasureTheory.integrable_norm_rpow_iff, Stirling.log_stirlingSeq_diff_hasSum, ProbabilityTheory.integral_stieltjesOfMeasurableRat, Complex.reCLM_nnnorm, Complex.nndist_of_im_eq, Rat.dist_cast, MeasureTheory.SignedMeasure.toJordanDecomposition_zero, intervalIntegral.intervalIntegrable_inv_one_add_sq, ENNReal.hasSum_toReal, Topology.RelCWComplex.continuousOn, Euclidean.closedBall_eq_image, NumberField.mixedEmbedding.fundamentalCone.expMap_target, continuousOn_log, NumberField.mixedEmbedding.negAt_preimage, InformationTheory.not_differentiableWithinAt_klFun_Iio_zero, ProbabilityTheory.Kernel.HasSubgaussianMGF.memLp_exp_mul, exists_continuous_zero_one_of_isClosed, Wallis.tendsto_W_nhds_pi_div_two, isOpenEmbedding_exp, NumberField.mixedEmbedding.fundamentalCone.volume_frontier_normLeOne, MeasureTheory.charFunDual_pi', MeasureTheory.L1.setToL1_smul_left, stdSimplex_subset_closedBall, NumberField.mixedEmbedding.iUnion_negAt_plusPart_ae, Rat.isDenseEmbedding_coe_real, BoxIntegral.unitPartition.integralSum_eq_tsum_div, instPathConnectedSpace, norm_deriv_mulExpNegMulSq_le_one, MeasureTheory.SignedMeasure.singularPart_smul, uniformContinuous_norm, Topology.RelCWComplex.union', lp.norm_rpow_eq_tsum, norm_curveIntegral_segment_le, Icc_isInteriorPoint_interior, signedDist_le_dist, not_continuousAt_deriv_mul_log_zero, integrable_one_add_norm, ProbabilityTheory.integrable_condCDF, Complex.continuousAt_arg, integrableOn_add_rpow_Ioi_of_lt, InformationTheory.klDiv_eq_top_iff, SchwartzMap.fourier_lineDerivOp_eq, TemperedDistribution.instLineDerivLeftSMulReal, ProbabilityTheory.IsRatCondKernelCDFAux.tendsto_atBot_zero, closedBall_eq_Icc, hasSum_cosh, ProbabilityTheory.tendsto_stieltjesOfMeasurableRat_atTop, isMIntegralCurveAt_eventuallyEq_of_contMDiffAt_boundaryless, ENNReal.tendsto_toReal, SchwartzMap.smulLeftCLM_compCLMOfContinuousLinearEquiv, Filter.tendsto_ofReal_iff, Monotone.ae_differentiableAt, ExistsContDiffBumpBase.u_continuous, mfderivWithin_comp_projIcc_one, NumberField.mixedEmbedding.fundamentalCone.isCompact_compactSet, IsMIntegralCurveOn.hasDerivWithinAt, PartitionOfUnity.sum_eq_one', NumberField.mixedEmbedding.negAt_signSet_apply_isComplex, NumberField.mixedEmbedding.fundamentalCone.volume_interior_eq_volume_closure, SmoothPartitionOfUnity.sum_finsupport', SchwartzMap.smulLeftCLM_real_smul, not_summable_indicator_one_div_natCast, BoundedContinuousFunction.integral_const_sub, ContinuousMap.Homotopy.ulift_apply, continuous_tan, ZLattice.tsum_norm_rpow_le, Complex.integral_comp_polarCoord_symm, Complex.uniformContinuous_re, signedDist_apply_apply, GenLoop.loopHomeo_apply, differentiableAt_rpow_const_of_ne, UnitAddTorus.mFourierCoeff_toLp, ProbabilityTheory.gaussianReal_map_continuousLinearMap, Manifold.pathELength_def, ODE.FunSpace.continuousOn_comp_compProj, exp_sub_sum_range_succ_isLittleO_pow, EuclideanSpace.volume_closedBall_fin_three, BoxIntegral.Box.isCompact_Icc, IccLeftChart_extend_interior_pos, hasDerivAt_arsinh, MeasureTheory.SignedMeasure.mutuallySingular_ennreal_iff, hasSum_zeta_four, taylor_tendsto, NumberField.mixedEmbedding.euclidean.stdOrthonormalBasis_map_eq, MeasureTheory.SignedMeasure.exists_isCompl_positive_negative, uniformContinuous_const_mul, HasFDerivAt.curveIntegral_segment_source, Bundle.ContinuousRiemannianMetric.symm, summable_abs_int_rpow, CompactlySupportedContinuousMap.toRealLinearMap_apply_apply, ProbabilityTheory.Kernel.tendsto_density_atTop_ae_of_antitone, InformationTheory.tendsto_rightDeriv_klFun_atTop, deriv_norm_ofReal_cpow, MeasureTheory.Integrable.integral_norm_condDistrib_map, NumberField.mixedEmbedding.normAtComplexPlaces_polarSpaceCoord_symm, Path.truncate_self, ProbabilityTheory.stieltjesOfMeasurableRat_le_one, hasDerivAt_abs_neg, IsUnifLocDoublingMeasure.exists_measure_closedBall_le_mul'', Metric.PiNatEmbed.dist_def, NumberField.tendsto_sub_one_mul_dedekindZeta_nhdsGT, StieltjesFunction.id_leftLim, deriv_sqrt_aux, UpperHalfPlane.dist_log_im_le, MeasureTheory.SignedMeasure.mutuallySingular_singularPart, uniformContinuous_dist, HasStrictDerivAt.real_of_complex, AddCircle.instIsAddHaarMeasureRealVolume, ProbabilityTheory.cdf_eq_real, deriv_rpow_const, comap_exp_nhds_exp, tendsto_norm_sub_self, DifferentiableWithinAt.dist, MeasureTheory.integrable_thickenedIndicator, tendsto_exp_neg_atTop_nhds_zero, hasDerivWithinAt_abs, Path.continuous_extend, tendsto_smoothingFun_comp, PartitionOfUnity.exists_finset_nhds, ProbabilityTheory.IsRatCondKernelCDFAux.tendsto_integral_of_antitone, NumberField.mixedEmbedding.fundamentalCone.logMap_expMapBasis, Hyperreal.tendsto_iff_forall, Path.extend_trans_of_le_half, instPathConnectedSpaceElemForallRealStdSimplexOfNonempty, BoundedVariationOn.intervalIntegrable_deriv, AkraBazziRecurrence.eventually_deriv_one_add_smoothingFn, CircleDeg1Lift.dist_map_map_zero_lt, AbsolutelyContinuousOnInterval.tendsto_volume_totalLengthFilter_nhds_zero, Complex.reCLM_coe, BoundedContinuousFunction.exists_extension_norm_eq_of_isClosedEmbedding, Complex.continuous_re, deriv_sinh, not_summable_of_antitone_of_neg, continuousAt_rpow_const, PartitionOfUnity.IsSubordinate.continuous_finsum_smul, MeasureTheory.convolution_precompR_apply, ProbabilityTheory.IsMeasurableRatCDF.instIsProbabilityMeasure_stieltjesFunction, VectorFourier.fourierIntegral_iteratedFDeriv, InformationTheory.hasDerivAt_klFun, ContinuousMap.toNNReal_algebraMap, integrableOn_Ioi_norm_cpow_iff, tsum_exp_neg_mul_int_sq, Seminorm.closedBall_zero_eq_preimage_closedBall, diam_stdSimplex, intervalIntegral.intervalIntegrable_sin, StarAlgHom.continuous_realContinuousMapOfNNReal, LiouvilleNumber.summable, ae_differentiableAt_norm, hasSum_cos, IsOpen.exists_contMDiff_support_eq_aux, sinhHomeomorph_symm_apply, Icc_chartedSpaceChartAt_of_le_top, Manifold.pathELength_eq_lintegral_mfderivWithin_Icc, continuous_log, Path.extend_apply, AddCircle.ergodic_nsmul_add, lp.summable_mul, NumberField.mixedEmbedding.convexBodySum_compact, ContinuousMap.continuous_toNNReal, continuous_sqrt, ContinuousMap.Homotopy.pathExtend_evalAt, ProbabilityTheory.uncenteredCovarianceBilinDual_of_not_memLp, AddCircle.dense_addSubgroup_iff_ne_zmultiples, Bundle.ContinuousRiemannianMetric.continuous, AddSubgroup.tendsto_zmultiples_subtype_cofinite, Nat.preimage_closedBall, NormedSpace.norm_expSeries_summable, volume_eq_stieltjes_id, LSeries.summable_real_of_abscissaOfAbsConv_lt, MeasureTheory.AEStronglyMeasurable.dist, MeasureTheory.charFunDual_prod, GammaSeq_tendsto_Gamma, ProbabilityTheory.Kernel.integrable_densityProcess, SmoothBumpCovering.toSmoothPartitionOfUnity_apply, VectorFourier.norm_iteratedFDeriv_fourierPowSMulRight, MeasureTheory.tendstoInMeasure_iff_measureReal_dist, Complex.equivRealProdCLM_symm_apply, hasSum_log_one_add, HasGradientAtFilter.hasDerivAtFilter', NNReal.continuous_coe, CompactlySupportedContinuousMap.coe_toRealLinearMap, Complex.interior_preimage_re, tendsto_of_bddAbove_monotone, IsLocalExtr.fderiv_eq_zero, SmoothPartitionOfUnity.contDiffAt_finsum, memℓp_gen_iff, MeasureTheory.Submartingale.bddAbove_iff_exists_tendsto, fourier_one, totallyBounded_ball, differentiableOn_rpow_const, Path.uniformContinuous_extend_left, MeasureTheory.MemLp.integrable_norm_pow, continuousMap_mem_polynomialFunctions_closure, BoxIntegral.Box.nndist_le_distortion_mul, lintegral_comp_pi_polarCoord_symm, SimplexCategory.toTop_obj, NumberField.mixedEmbedding.fundamentalCone.subset_interior_normLeOne, polarCoord_target, BoxIntegral.TaggedPrepartition.isSubordinate_single, HomotopyGroup.transAt_indep, SchwartzMap.smulLeftCLM_sum, NNReal.isEmbedding_coe, MeasureTheory.SignedMeasure.absolutelyContinuous_iff_withDensityᵥ_rnDeriv_eq, AddCircle.denseRange_zsmul_iff, MeasureTheory.Integrable.norm_integral_condDistrib, has_fderiv_at_filter_real_equiv, NumberField.mixedEmbedding.negAt_signSet_apply_isReal, hasDerivWithinAt_arccos_Ici, RightDerivMeasurableAux.differentiable_set_subset_D, continuousAt_rpow_of_pos, continuous_dist, InformationTheory.leftDeriv_klFun, tendsto_integral_exp_smul_cocompact, LinearMap.IsSymmetric.hasStrictFDerivAt_reApplyInnerSelf, ProbabilityTheory.eqOn_complexMGF_of_mgf, StarAlgHom.realContinuousMapOfNNReal_apply, curveIntegral_segment, tendsto_norm_div_self_nhdsNE, MeasureTheory.SignedMeasure.totalVariation_zero, ProbabilityTheory.IsMeasurableRatCDF.tendsto_atBot_zero, summable_schlomilch_iff_of_nonneg, MeasureTheory.Integrable.integral_norm_comp, intervalIntegral.FTCFilter.nhdsWithinSingleton, tendsto_exp_comp_nhds_zero, Complex.uniformlyContinuous_re, continuousAt_const_rpow', ZLattice.tsumNormRPowBound_spec, RCLike.summable_ofReal, tendsto_norm_div_self_nhdsGE, WithSeminorms.uniformEquicontinuous_iff_exists_continuous_seminorm, SimplexCategory.toTop_map, EisensteinSeries.summable_norm_eisSummand, Seminorm.ball_zero_eq_preimage_ball, Polynomial.toAddCircle.integrable, intervalIntegral.FTCFilter.le_nhds, Besicovitch.ae_tendsto_rnDeriv, fourier_zero, fourier_neg', differentiable_cos, PartitionOfUnity.coe_finsupport, Affine.Simplex.ExcenterExists.sign_signedInfDist_touchpoint, Path.continuous_delayReflRight, qaryEntropy_continuous, IsUnifLocDoublingMeasure.exists_measure_closedBall_le_mul, one_div_one_sub_sq_hasFPowerSeriesOnBall_zero, hasFDerivAt_norm_rpow, ProbabilityTheory.cdf_nonneg, volume_ball, intervalIntegral.integrableOn_Ioo_rpow_iff, GenLoop.instContinuousEval, Path.Homotopy.hcomp_half, StieltjesFunction.iInf_rat_gt_eq, ProbabilityTheory.IsMeasurableRatCDF.stronglyMeasurable_stieltjesFunction, Metric.exists_smooth_forall_closedBall_subset, dist_right_le_of_mem_uIcc, CompactlySupportedContinuousMap.nnrealPart_add_le_add_nnrealPart, Path.Homotopy.hcomp_apply, UpperHalfPlane.dist_of_re_eq, PartitionOfUnity.exists_finset_nhds_support_subset, MeasureTheory.SignedMeasure.toJordanDecomposition_smul_real, ProbabilityTheory.ofReal_condCDF_ae_eq, Path.continuous_delayReflLeft, ProbabilityTheory.IsMeasurableRatCDF.measure_stieltjesFunction_univ, intervalIntegral.intervalIntegrable_log, Path.Homotopy.symm_apply, IsPicardLindelof.continuousOn, hasDerivAt_abs_rpow, hasSum_ofDigitsTerm_digits, signedDist_eq_zero_of_orthogonal, Path.instContinuousEvalElemRealUnitInterval, ProbabilityTheory.covarianceBilin_zero, NumberField.mixedEmbedding.instDiscreteTopologySubtypeMixedSpaceMemSubmoduleIntIdealLattice, dimH_ball_pi, ZetaAsymptotics.term_tsum_of_lt, AddCircle.ergodic_add_left, Polynomial.Chebyshev.isLocalMax_T_real, SchwartzMap.smulLeftCLM_fun_neg, ContinuousOn.norm', tendsto_cos_neg_pi_div_two, Complex.continuous_circleTransform, Path.Homotopy.eval_apply, deriv_Gamma_nat, MeasureTheory.Measure.innerRegularWRT_preimage_one_hasCompactSupport_measure_ne_top_of_group, MeasureTheory.Measure.HasTemperateGrowth.exists_integrable, Circle.exp_two_pi, Complex.polarCoord_apply, HurwitzZeta.continuousOn_cosKernel, fourierIntegral_convergent_iff', Seminorm.continuous, instIsTopologicalDivisionRingReal, MeasureTheory.SignedMeasure.absolutelyContinuous_ennreal_iff, ContinuousMap.Homotopy.apply_one_path, integrable_rpow_neg_one_add_norm_sq, hasDerivAt_binEntropy, hasDerivAt_gronwallBound_shift, PartitionOfUnity.sum_le_one', Bundle.ContMDiffRiemannianMetric.symm, MeasureTheory.charFunDual_eq_prod_iff, SchwartzMap.pairing_apply, continuous_cosh, UnitAddTorus.mFourier_add, continuous_polarCoord_symm, hasDerivAt_qaryEntropy, IsCoveringMap.liftPath_const, intervalIntegral.FTCFilter.nhdsUIcc, ProbabilityTheory.analyticOnNhd_cgf, SmoothPartitionOfUnity.le_one, Monotone.ae_hasDerivAt, StrongFEPair.hf_zero', SimplexCategory.toTop₀_map, ProbabilityTheory.IsCondKernelCDF.setIntegral, AffineSubspace.signedInfDist_eq_signedDist_of_mem, borel_eq_generateFrom_Ioi_rat, one_mem_posTangentConeAt_iff_mem_closure, BumpCovering.le_one, integrable_sinc, Continuous.dist, MeasureTheory.FiniteMeasure.tendsto_iff_forall_integral_tendsto, coe_tanPartialHomeomorph, EuclideanSpace.volume_closedBall_fin_two, NormedSpace.norm_expSeries_summable_of_mem_ball', ProbabilityTheory.stronglyMeasurable_poissonPMFReal, Continuous.norm', NumberField.mixedEmbedding.polarCoordReal_source, MeasureTheory.tendsto_of_uncrossing_lt_top, not_IntegrableOn_Ici_inv, stereographic'_target, curveIntegral_segment_const, Irrational.instOrderTopologySubtypeReal, tendsto_measure_cthickening, Affine.Simplex.signedInfDist_apply_self, Quaternion.continuous_imJ, differentiableAt_rpow_of_ne, exists_contMDiffMap_zero_one_nhds_of_isClosed, Circle.exp_sub, Convex.uniformContinuous_gauge, one_div_one_sub_hasFPowerSeriesOnBall_zero, RCLike.reCLM_coe, Metric.uniformContinuous_infDist_Hausdorff_dist, AddCircle.ergodic_add_right, differentiableAt_log, MeasureTheory.ComplexMeasure.equivSignedMeasure_apply, Complex.tendsto_arg_nhdsWithin_im_nonneg_of_re_neg_of_im_zero, exists_seq_rat_strictAnti_tendsto, tendsto_sin_neg_pi_div_two, intervalIntegral.intervalIntegrable_cos, tendsto_measure_Icc, HarmonicAt.differentiableAt_complex_partial, NumberField.mixedEmbedding.fundamentalCone.prod_deriv_expMap_single, uniformContinuous_inv, UnitAddTorus.mFourier_zero, ContinuousMap.HomotopyLike.toContinuousMapClass, tendsto_exp_nhds_zero_nhds_one, MeasureTheory.hasFDerivAt_convolution_right_with_param, ProbabilityTheory.IsGaussian.charFun_eq', deriv_inv_log, ProbabilityTheory.covarianceBilinDual_eq_covariance, signedDist_zero, ProbabilityTheory.Kernel.HasSubgaussianMGF.integrable_exp_mul, ConcaveOn.continuousOn, AffineSubspace.signedInfDist_eq_signedDist_orthogonalProjection, CircleDeg1Lift.transnumAuxSeq_dist_lt, RCLike.isUniformEmbedding_ofReal, CompactlySupportedContinuousMap.toRealLinearMap_apply, intervalIntegral.continuousOn_primitive_Icc, NumberField.mixedEmbedding.fundamentalCone.norm_expMapBasis, PartitionOfUnity.sum_eq_one, AkraBazziRecurrence.differentiableAt_one_sub_smoothingFn, exists_bounded_zero_one_of_closed, MeasureTheory.Integrable.integral_norm_prod_left, HasCompactSupport.hasFDerivAt_convolution_right, frontier_range_modelWithCornersEuclideanHalfSpace, NNReal.map_coe_nhdsGT, intervalIntegral.intervalIntegrable_rpow, AkraBazziRecurrence.eventually_deriv_rpow_p_mul_one_sub_smoothingFn, HurwitzZeta.hasSum_nat_sinKernel, SchwartzMap.integral_bilinear_deriv_right_eq_neg_left, ProbabilityTheory.covarianceBilinDual_zero, Irrational.eventually_forall_le_dist_cast_div_of_denom_le, RealRMK.integral_rieszMeasure, dense_irrational, bernstein.variance, tsum_geometric_of_lt_one, continuous_probChar, diam_Ioo, bernstein_apply, isEquivalent_sin, tendsto_rpow_atTop_of_base_gt_one, tendsto_sigmoid_atBot, geometric_hahn_banach_point_closed, LiouvilleNumber.remainder_summable, Complex.interior_preimage_im, Orthonormal.inner_products_summable, tendsto_harmonic_sub_log, IsUnifLocDoublingMeasure.exists_measure_closedBall_le_mul', differentiable_exp, ProbabilityTheory.differentiableOn_mgf, abs_mulExpNegMulSq_comp_le_norm, Int.isClosedEmbedding_coe_real, hasStrictDerivAt_arcosh, UnitAddTorus.coeFn_mFourierLp, MeasureTheory.Integrable.integral_norm_condExpKernel, differentiableAt_cos, isClosed_preCantorSet, CompactlySupportedContinuousMap.nnrealPart_neg_toReal_eq, ContinuousWithinAt.norm, GenLoop.ext_iff, SmoothBumpFunction.contMDiffAt, CircleDeg1Lift.tendsto_translation_number', NumberField.mixedEmbedding.polarCoord_symm_apply, Polynomial.intervalIntegrable_mahlerMeasure, exists_continuous_one_zero_of_isCompact, volume_real_closedBall, ball_eq_openSegment, MeasureTheory.ProbabilityMeasure.continuous_iff_forall_continuousMap_continuous_integral, deriv_log', Circle.exp_neg, ProbabilityTheory.IsCondKernelCDF.setLIntegral, BumpCovering.toPartitionOfUnity_eq_mul_prod, Filter.Tendsto.norm, intervalIntegrable_sub_inv_iff, one_div_sub_hasFPowerSeriesOnBall_zero, ProbabilityTheory.integrable_condVar, Metric.PiNatEmbed.separation, unitInterval.continuous_sigmoid, ContDiff.euclidean_dist, measurableSet_pi_polarCoord_target, instIsTopologicalRingReal, isMIntegralCurveAt_iff, Path.truncate_zero_zero, Bundle.ContMDiffRiemannianMetric.pos, signedDist_triangle_left, IsContMDiffRiemannianBundle.exists_contMDiff, MeasureTheory.SignedMeasure.singularPart_add, Complex.nhdsWithin_lt_le_nhdsWithin_stolzSet, Complex.hasSum_ofReal, Complex.ofRealCLM_nnnorm, Complex.imCLM_norm, deriv2_binEntropy, isClosed_stdSimplex, SmoothBumpCovering.sum_toSmoothPartitionOfUnity_eq, UnitAddTorus.mFourier_neg, interior_halfSpace, SimplexCategory.toTop₀_obj, Complex.continuousOn_norm_circleTransformBoundingFunction, exists_continuous_nonneg_pos, ContinuousMap.sup_mem_closed_subalgebra, contMDiff_subtype_coe_Icc, hasDerivAt_arcsin, integral_comp_polarCoord_symm, CompactlySupportedContinuousMap.toRealPositiveLinear_apply, Matrix.SpecialLinearGroup.isClosedEmbedding_mapGLInt, ProperCone.innerDual_singleton, VitaliFamily.ae_tendsto_average_norm_sub, hasDerivAt_tan, intervalIntegral.FTCFilter.nhdsIcc, Icc_chartedSpaceChartAt, deriv_tan_sub_id, instIsOrderBornology, leftDeriv_mul_log, differentiableAt_Gamma, comap_norm_nhdsGT_zero', ContinuousMap.Homotopy.extend_apply_coe, hasStrictDerivAt_cosh, ConvexOn.real_univ_sSup_of_countable_affine_eq, CircleDeg1Lift.continuous_iff_surjective, ProbabilityTheory.analyticOn_cgf, BoundedContinuousFunction.exists_norm_eq_restrict_eq_of_closed, zero_at_infty_fourierIntegral, closure_upperClosure_comm_pi, diam_stdSimplex_of_subsingleton, ProbabilityTheory.covarianceBilin_comm, ProbabilityTheory.Kernel.tendsto_integral_density_of_monotone, ProbabilityTheory.Kernel.memL1_limitProcess_densityProcess, ProbabilityTheory.cdf_le_one, BoundedContinuousFunction.neg_norm_le_apply, isTopologicalBasis_Ioo_rat, gradient_eq_deriv', ZetaAsymptotics.continuousOn_term, Chebyshev.integrableOn_theta_div_id_mul_log_sq, hasStrictDerivAt_log, MonotoneOn.intervalIntegrable_slope, sin_eq_tsum, tendsto_rpow_div_mul_add, BoxIntegral.Box.dist_le_distortion_mul, tendsto_rpow_atTop_of_base_lt_one, NumberField.mixedEmbedding.euclidean.volumePreserving_toMixed, ArithmeticFunction.vonMangoldt.not_summable_residueClass_prime_div, SchwartzMap.smulRightCLM_apply_apply, differentiableOn_Gamma_Ioi, NormedSpace.norm_expSeries_summable_of_mem_ball, differentiableOn_mul_log, MeasureTheory.Submartingale.bddAbove_iff_exists_tendsto_aux, MeasureTheory.setToFun_smul_left, InformationTheory.klDiv_def, HasDerivAt.complexToReal_fderiv', PartitionOfUnity.exists_isSubordinate_of_locallyFinite_t2space, MeasureTheory.Integrable.norm_integral_condKernel, MeasureTheory.condExp_stronglyMeasurable_simpleFunc_bilin, ProbabilityTheory.Kernel.tendsto_densityProcess_atTop_empty_of_antitone, Path.source', NumberField.mixedEmbedding.negAt_apply_isReal_and_notMem, MeasureTheory.JordanDecomposition.exists_compl_positive_negative, ProbabilityTheory.IsRatCondKernelCDF.tendsto_atTop_one, ProbabilityTheory.memLp_id_gaussianReal', Complex.tendsto_arg_nhdsWithin_im_neg_of_re_neg_of_im_zero, fderiv_norm_smul_neg, Seminorm.continuousAt_zero', continuousOn_cos, CompactlySupportedContinuousMap.toReal_apply, deriv_mulExpNegMulSq, EuclideanHalfSpace.convex, fourier_coe_apply, NNReal.continuousAt_rpow, Nat.Primes.not_summable_one_div, periodizedBernoulli.continuous, GenLoop.continuous_fromLoop, fourierSubalgebra_separatesPoints, dense_differentiableAt_norm, MeasureTheory.SignedMeasure.re_toComplexMeasure, HurwitzZeta.continuousOn_evenKernel, NumberField.mixedEmbedding.fundamentalCone.expMap_basis_of_eq, Complex.continuous_circleTransformDeriv, AkraBazziRecurrence.eventually_deriv_rpow_p_mul_one_add_smoothingFn, MonotoneOn.intervalIntegral_deriv_mem_uIcc, MeasureTheory.SignedMeasure.mutuallySingular_iff, NumberField.mixedEmbedding.volume_preserving_negAt, EuclideanSpace.sphere_zero_eq, StarAlgHom.realContinuousMapOfNNReal_apply_comp_toReal, Affine.Simplex.ExcenterExists.sign_signedInfDist_lineMap_excenter_touchpoint, deriv_qaryEntropy, closure_of_rat_image_lt, deriv_arctan, monotoneOn_deriv_descPochhammer_eval, SchwartzMap.smulLeftCLM_const, ProbabilityTheory.HasSubgaussianMGF.memLp_exp_mul, SmoothPartitionOfUnity.sum_eq_one', Circle.exp_inj, sinh_eq_tsum, BumpCovering.locallyFinite, Path.reparam_id, cos_eq_tsum, BoundedContinuousFunction.abs_self_eq_nnrealPart_add_nnrealPart_neg, continuous_sin, ProperCone.hyperplane_separation_point, NumberField.mixedEmbedding.fundamentalCone.prod_expMapBasis_pow, StieltjesFunction.countable_leftLim_ne, NumberField.mixedEmbedding.negAt_apply_isComplex, continuousOn_logb, MeasureTheory.Measure.toSignedMeasure_toMeasureOfZeroLE, Filter.Tendsto.norm', NumberField.mixedEmbedding.fundamentalCone.expMapBasis_closure_subset_compactSet, MeasureTheory.Measure.toSignedMeasure_smul, Topology.CWComplex.union', Path.uniformContinuous, Quaternion.re_exp, Path.extend_of_one_le, NumberField.mixedEmbedding.fundamentalCone.continuous_expMap, continuous_circleMap, CircleDeg1Lift.dist_map_zero_lt_of_semiconj, summable_nat_pow_inv, intervalIntegral.FTCFilter.nhdsRight, not_integrableOn_Ioi_rpow, continuousAt_logb_iff, AbsolutelyContinuousOnInterval.uniformContinuousOn, tendsto_measure_thickening, NormedSpace.ofReal_exp_ℝ_ℝ, ProbabilityTheory.setIntegral_stieltjesOfMeasurableRat, Circle.exp_add_two_pi, Path.image_extend_of_subset, tendsto_rpow_sub_one_log, SmoothPartitionOfUnity.mem_finsupport, Continuous.inner_bundle, continuous_negMulLog, MeasureTheory.Measure.integrable_measure_prodMk_left, has_antideriv_at_fourier_neg, ZLattice.summable_norm_rpow, differentiableAt_log_iff, IsOpen.exists_contMDiff_support_eq, uniformContinuous_neg, ProbabilityTheory.cdf_gammaMeasure_eq_lintegral, UnitAddTorus.mFourier_norm, IsPicardLindelof.continuousOn_uncurry, WithSeminorms.uniformEquicontinuous_iff_bddAbove_and_continuous_iSup, hasFDerivAt_iff_tendsto, GenLoop.toLoop_apply, NumberField.mixedEmbedding.normAtComplexPlaces_normAtAllPlaces, DifferentiableAt.norm_sq, BoundedContinuousFunction.nnrealPart_coeFn_eq, tsum_geometric_two, FormalMultilinearSeries.not_summable_norm_of_radius_lt_nnnorm, Orientation.areaForm'_apply, NumberField.mixedEmbedding.fundamentalCone.expMap_smul, continuous_const_rpow, IsGδ.setOf_irrational, ENNReal.continuous_ofReal, PiCountable.dist_summable, HurwitzZeta.hasSum_int_evenKernel, summable_exp_neg_nat, ODE.FunSpace.toContinuousMap_apply_eq_apply, hasSum_one_div_nat_pow_mul_cos, signedDist_smul_of_pos, MeasureTheory.BorelCantelli.integrable_process, Distribution.mapCLM_apply, continuous_gauge, MeasureTheory.SignedMeasure.singularPart_zero, hasStrictDerivAt_const_rpow_of_neg, tendsto_pow_const_mul_const_pow_of_abs_lt_one, IsContinuousRiemannianBundle.exists_continuous, Set.OrdConnected.null_frontier, AkraBazziRecurrence.isTheta_deriv_rpow_p_mul_one_add_smoothingFn, MeasureTheory.Submartingale.ae_tendsto_limitProcess_of_uniformIntegrable, Complex.frontier_preimage_im, MeasureTheory.MemLp.integrable_norm_rpow, Circle.invOn_arg_exp, isLittleO_log_rpow_nhdsGT_zero, tendsto_comp_exp_atBot, instSeparatingDualRealOfIsTopologicalAddGroupOfContinuousSMulOfLocallyConvexSpaceOfT1Space, intervalIntegral.intervalIntegrable_id, signedDist_lineMap_lineMap, Complex.ofRealCLM_apply, MeasureTheory.IntegrableAtFilter.norm, AkraBazziRecurrence.differentiableOn_one_add_smoothingFn, BoundedContinuousFunction.exists_extension_forall_exists_le_ge_of_isClosedEmbedding, PartitionOfUnity.finsum_smul_mem_convex, exists_continuous_zero_one_of_isCompact', cfcHom_real_eq_restrict, NumberField.mixedEmbedding.mem_negAt_plusPart_of_mem, IsUnifLocDoublingMeasure.eventually_measure_le_doublingConstant_mul, nonneg_iff_isSelfAdjoint_and_spectrumRestricts, NNReal.ContinuousMap.canLift, Filter.Tendsto.dist, dist_le_of_mem_Icc, HomotopyGroup.mul_spec, BoundedContinuousFunction.probCharDual_zero, tendsto_integral_mul_one_add_inv_smul_sq_pow, expNegInvGlue.tendsto_polynomial_inv_mul_zero, AffineSubspace.abs_signedInfDist_eq_dist_of_mem_affineSpan_insert, NumberField.InfinitePlace.Completion.isClosed_image_extensionEmbeddingOfIsReal, tendsto_rpow_abs_mul_exp_neg_mul_sq_cocompact, continuous_bernoulliFun, measurableSet_of_differentiableWithinAt_Ici_of_isComplete, signedDist_vadd_left_swap, IsSelfAdjoint.spectrumRestricts, diam_stdSimplex_le, HurwitzZeta.continuousOn_oddKernel, NumberField.mixedEmbedding.fundamentalCone.closure_normLeOne_subset, borel_eq_generateFrom_Ici_rat, intervalIntegral.FTCFilter.nhdsUniv, Seminorm.preimage_metric_closedBall, MeasureTheory.integrable_prod_iff, HasFDerivWithinAt.norm_sq, PartitionOfUnity.nonneg, differentiableAt_abs_neg, Complex.summable_ofReal, BoundedContinuousFunction.apply_le_norm, hasDerivAt_fourier_neg, ProbabilityTheory.isGaussian_gaussianReal, norm_fderiv_norm_rpow_le, deriv_abs_zero, bounded_stdSimplex, Metric.exists_continuous_real_forall_closedBall_subset, MeasureTheory.integral_posConvolution, hasStrictDerivAt_abs, fourier_eval_zero, Matrix.IsHermitian.cfcAux_apply, SchwartzMap.fourierInv_lineDerivOp_eq, EulerProduct.summable_and_hasSum_smoothNumbers_prod_primesBelow_geometric, Bundle.RiemannianMetric.symm, ContinuousMap.toNNReal_one, ProbabilityTheory.Kernel.tendsto_integral_density_of_antitone, closure_open_halfSpace, Path.extend_range, Angle.toCircle_coe, Complex.dist_of_im_eq, hasDerivAt_cos, GenLoop.fromLoop_symm_toLoop, Topology.CWComplex.source_eq, NumberField.mixedEmbedding.convexBodySumFun_continuous, Topology.CWComplex.pairwiseDisjoint', AffineSubspace.signedInfDist_eq_const_of_mem, summable_pow_div_add, HurwitzZeta.continuousOn_sinKernel, ProbabilityTheory.HasSubgaussianMGF.integrable, disjoint_residual_ae, ContinuousMap.sup_mem_subalgebra_closure, RCLike.continuous_re, nhds_comap_dist, DifferentiableOn.norm_sq, ContDiffMapSupportedIn.locallyConvexSpace, tsum_geometric_of_abs_lt_one, NumberField.mixedEmbedding.fundamentalCone.normAtAllPlaces_mem_fundamentalCone_iff, fourierCoeff_toLp, continuous_logb, EReal.continuousOn_toReal, Differentiable.norm_rpow, ProbabilityTheory.IsGaussian.charFunDual_eq, hasDerivAt_half_log_one_add_div_one_sub_sub_sum_range, ProbabilityTheory.variance_continuousLinearMap_gaussianReal, tendsto_measure_Icc_nhdsWithin_right, differentiableWithinAt_arcsin_Ici, ProbabilityTheory.covarianceBilin_eq_covarianceBilinDual, ProbabilityTheory.Kernel.density_ae_eq_limitProcess, BumpCovering.continuous_toPOUFun, InformationTheory.klDiv_ne_top_iff, MeasureTheory.integrable_conv_iff, ProbabilityTheory.Kernel.IsFiniteKernel.integrable, hasDerivWithinAt_arcsin_Ici, signedDist_vadd_right, NumberField.Ideal.tendsto_norm_le_div_atTop₀, InnerProductSpace.instIsContPerfPairRealInnerₗOfCompleteSpace, hasSum_sq_fourierCoeffOn, hasDerivAt_taylorWithinEval_succ, IsMIntegralCurveAt.hasMFDerivAt, polarCoord_symm_apply, SpectrumRestricts.real_iff, hasSum_geometric_two, ContinuousAt.norm', tsum_le_of_sum_range_le, dist_le_of_mem_uIcc, RCLike.tendsto_ofReal_cobounded_cobounded, NumberField.mixedEmbedding.volume_preserving_mixedSpaceToRealMixedSpace_symm, tendsto_integral_mulExpNegMulSq_comp, SmoothBumpCovering.embeddingPiTangent_injective_mfderiv, NNReal.coe_tsum_of_nonneg, continuous_logb', deriv_abs_pos, PartitionOfUnity.locallyFinite', SchwartzMap.smulLeftCLM_smulLeftCLM_apply, exists_polynomial_near_continuousMap, iInter_halfSpaces_eq, Subadditive.tendsto_lim, NumberField.mixedEmbedding.fundamentalCone.hasFDerivAt_expMap, MeasureTheory.Measure.integrable_compProd_iff, Complex.interior_reProdIm, geometric_hahn_banach_closed_compact, Path.isUniformEmbedding_coe, ContinuousMap.inf_mem_subalgebra_closure, unitInterval.symmHomeomorph_symm_apply, tendsto_mul_log_one_add_div_atTop, differentiableAt_cosh, MeasureTheory.Measure.toSignedMeasure_apply, homeomorphUnitSphereProd_symm_apply_coe, ProbabilityTheory.covarianceBilin_self_nonneg, unitInterval.continuous_qRight, MeasureTheory.SignedMeasure.toJordanDecomposition_neg, ZLattice.covolume.tendsto_card_le_div', exists_msmooth_support_eq_eq_one_iff, EuclideanQuadrant.convex, instOrderTopologyReal, Complex.closure_preimage_re, ContinuousMap.inf_mem_closed_subalgebra, Complex.nndist_of_re_eq, continuousAt_arcsin, closedBall_zero_eq_Icc, Polynomial.hermite_eq_deriv_gaussian', ProbabilityTheory.indepFun_iff_charFunDual_prod', AddCircle.continuous_toCircle, MeasureTheory.integrable_of_integral_eq_one, MeasureTheory.integrable_norm_iff, MeasureTheory.integrable_toReal_of_lintegral_ne_top, uniqueDiffWithinAt_Ioo, ProbabilityTheory.covarianceBilinDual_self_eq_variance, CompactlySupportedContinuousMap.integralLinearMap_apply, Circle.exp_add, Path.Homotopy.trans_apply, geometric_hahn_banach_open_open, ProbabilityTheory.measurable_measure_stieltjesOfMeasurableRat, hasStrictFDerivAt_norm_sq, ProbabilityTheory.exists_integrable_exp_sq_of_map_rotation_eq_self', SmoothPartitionOfUnity.coe_finsupport, ProbabilityTheory.stronglyMeasurable_stieltjesOfMeasurableRat, tendsto_log_nhdsGT_zero, Emetric.exists_contMDiffMap_forall_closedBall_subset, Metric.PiNatEmbed.exists_closed_embedding_to_hilbert_cube, isLittleO_abs_log_rpow_rpow_nhdsGT_zero, EisensteinSeries.norm_le_tsum_norm, BumpCovering.nonneg', deriv_exp, IsMIntegralCurveAt.continuousAt, ENNReal.continuousAt_toReal, QuasispectrumRestricts.real_iff, unitInterval.instTietzeExtension, TemperedDistribution.instLineDerivSMulReal, ball_zero_eq_Ioo, EisensteinSeries.summable_one_div_norm_rpow, Topology.CWComplex.mapsTo', isClosed_cantorSet, IsSelfAdjoint.sq_spectrumRestricts, Multipliable.norm_tprod, MDifferentiableOn.inner_bundle, dist_mono_left_pi, tendsto_integral_exp_smul_cocompact_of_inner_product, hasDerivAt_rpow_const, exists_bounded_mem_Icc_of_closed_of_le, tendsto_log_nhdsLT_zero, MeasureTheory.Integrable.re_im_iff, Path.Homotopy.continuous_reflTransSymmAux, differentiableAt_norm_smul, AbsolutelyContinuousOnInterval.tendsto_volume_restrict_totalLengthFilter_disjWithin_nhds_zero, MeasureTheory.SignedMeasure.singularPart_neg, continuous_coe_real_ereal, MeasureTheory.AEStronglyMeasurable.norm, iter_deriv_exp, Metric.exists_contMDiffMap_forall_closedBall_subset, summable_dirichletSummand, differentiable_iteratedDeriv_cos, Differentiable.norm_sq, exists_msmooth_zero_iff_one_iff_of_isClosed, PartitionOfUnity.sum_finsupport_smul_eq_finsum, continuous_sinh, ProbabilityTheory.IsGaussian.memLp_dual, MeasureTheory.SignedMeasure.haveLebesgueDecomposition_smul_real, continuousOn_exp, ZetaAsymptotics.term_tsum_one, Complex.continuous_normSq, isTheta_deriv_rpow_const_atTop, ProbabilityTheory.covarianceBilinDual_self_nonneg, IccLeftChart_extend_bot, BoxIntegral.Box.isBounded_Icc, NumberField.mixedEmbedding.fundamentalCone.continuous_expMapBasis, isOpen_deltaGenerated_iff, MeasureTheory.charFunDual_map_const_add, tendsto_smoothingFun_of_map_one_le_one, SmoothPartitionOfUnity.finsum_smul_mem_convex, MeasureTheory.charFunDual_map_add_const, Continuous.norm, Polynomial.deriv_gaussian_eq_hermite_mul_gaussian, uniqueDiffWithinAt_Ioi, Path.continuous_uncurry_iff, MeasureTheory.Measure.toSignedMeasure_add, signedDist_lineMap_left, ProbabilityTheory.covarianceBilin_real_self, tendsto_rightDeriv_mul_log_atTop, hasStrictDerivAt_arsinh, circleMap_preimage_codiscrete, bernsteinApproximation.apply_one, EulerProduct.summable_and_hasSum_factoredNumbers_prod_filter_prime_geometric, tendsto_self_mul_const_pow_of_abs_lt_one, MeasureTheory.Integrable.integral_norm_compProd, Complex.lintegral_comp_polarCoord_symm, SmoothPartitionOfUnity.sum_le_one', Int.tendsto_zmultiplesHom_cofinite, integrable_rpow_mul_exp_neg_mul_sq, tsum_geometric_two', SchwartzMap.integral_pow_mul_iteratedFDeriv_le, WeakFEPair.hf_zero, HurwitzKernelBounds.summable_f_nat, ProbabilityTheory.IsCondKernelCDF.measurable, Circle.leftInverse_exp_arg, Seminorm.uniformContinuous, Complex.continuousAt_ofReal_cpow, InformationTheory.klDiv_eq_integral_klFun, CircleDeg1Lift.dist_pow_map_zero_mul_translationNumber_le, EuclideanGeometry.continuousAt_angle, integrable_mul_exp_neg_mul_sq, bernstein_nonneg, VectorFourier.fourierSMulRight_apply, tendsto_fib_div_fib_succ_atTop, RCLike.continuous_ofReal, continuousAt_gauge_zero, ProbabilityTheory.tendsto_stieltjesOfMeasurableRat_atBot, MeasureTheory.tendsto_ae_condExp, BumpCovering.exists_finset_toPartitionOfUnity_eventuallyEq, closedBall_eq_segment, MeasureTheory.condExpL2_indicator_eq_toSpanSingleton_comp, NumberField.mixedEmbedding.fundamentalCone.expMap_symm_apply, PartitionOfUnity.locallyFinite_tsupport, stronglyMeasurable_sinc, NumberField.Units.dirichletUnitTheorem.unitLattice_inter_ball_finite, NumberField.mixedEmbedding.polarCoord_source, SmoothBumpCovering.embeddingPiTangent_ker_mfderiv, isSelfAdjoint_iff_isStarNormal_and_quasispectrumRestricts, continuous_log', ContMDiffOn.inner_bundle, SmoothPartitionOfUnity.sum_nonneg, ProbabilityTheory.Kernel.tendsto_densityProcess_fst_atTop_univ_of_monotone, Manifold.riemannianEDist_def, hasDerivAt_circleMap, ProbabilityTheory.IsRatCondKernelCDFAux.tendsto_zero_of_antitone, one_div_one_sub_rpow_hasFPowerSeriesOnBall_zero, MeasureTheory.ProbabilityMeasure.continuous_integral_boundedContinuousFunction, signedDist_anticomm, BumpCovering.locallyFinite_tsupport, IsOpen.measure_eq_biSup_integral_continuous, PartitionOfUnity.continuous_finsum_smul, continuousAt_gauge, SchwartzMap.smulLeftCLM_add, continuousAt_rpow_of_ne, taylor_tendsto, tendsto_uniformity_iff_dist_tendsto_zero, curveIntegralFun_def', NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_apply, NumberField.mixedEmbedding.continuous_norm, IsMIntegralCurve.continuous, uniqueDiffOn_Icc_zero_one, intervalIntegral.continuousWithinAt_primitive, MeasureTheory.ComplexMeasure.HaveLebesgueDecomposition.rePart, instProperSpaceReal, tendsto_log_div_rpow_nhdsGT_zero, tendsto_logb_nhdsNE_zero_of_base_lt_one, not_summable_indicator_mod_of_antitone_of_neg, ZetaAsymptotics.zeta_limit_aux1, ContinuousLinearMap.norm_extendTo𝕜'_bound, ProbabilityTheory.measurable_stieltjesOfMeasurableRat, Quaternion.normSq_exp, MeasureTheory.AEStronglyMeasurable.re, differentiableAt_arctan, ContinuousMultilinearMap.integral_apply, uniqueDiffWithinAt_Iio, ProbabilityTheory.exponentialCDFReal_eq_integral, differentiableWithinAt_abs_neg, ProbabilityTheory.stieltjesOfMeasurableRat_eq, differentiableOn_negMulLog, convex_iff_isPreconnected, ProbabilityTheory.integrable_exp_mul_gaussianReal, hasGradientAt_iff_tendsto, hasDerivAt_fourier, ProbabilityTheory.cdf_expMeasure_eq_integral, ProbabilityTheory.instIsProbabilityMeasureCondCDF, NumberField.mixedEmbedding.polarSpaceCoord_symm_apply, stdSimplexHomeomorphUnitInterval_apply_coe, Complex.measurableEquivRealProd_symm_polarCoord_symm_apply, Besicovitch.ae_tendsto_measure_inter_div, summable_one_div_nat_rpow, NumberField.mixedEmbedding.fundamentalCone.norm_normAtAllPlaces, rightDeriv_mul_log, ProbabilityTheory.Kernel.integrable_density, ZLattice.summable_norm_pow_inv, continuousOn_sin, homeomorphSphereProd_symm_apply_coe, ContinuousMap.HomotopyWith.extendProp, MeasureTheory.L1.SimpleFunc.setToL1SCLM_smul_left, fourier_apply, ProbabilityTheory.isGaussian_iff_gaussian_charFunDual, Seminorm.continuous_iff, ContinuousMap.Homotopy.curry_apply, DeltaGeneratedSpace.isOpen_iff, hasStrictDerivAt_abs_neg, MDifferentiableWithinAt.inner_bundle, WithSeminorms.continuous_seminorm, ProbabilityTheory.iIndepFun_iff_charFunDual_pi, NumberField.InfinitePlace.Completion.isClosed_image_extensionEmbedding_of_isReal, ProbabilityTheory.norm_uncenteredCovarianceBilinDual_le, MeasureTheory.stronglyMeasurable_llr, MeasureTheory.Measure.measurePreserving_homeomorphUnitSphereProd, ProbabilityTheory.paretoCDFReal_eq_integral, isPathConnected_stdSimplex, Polynomial.Chebyshev.isLocalExtr_T_real_iff, Quaternion.im_exp, ProbabilityTheory.IsRatCondKernelCDF.tendsto_atBot_zero, SmoothBumpCovering.exists_finset_toSmoothPartitionOfUnity_eventuallyEq, ProbabilityTheory.exp_neg_integrableOn_Ioc, SchwartzMap.integral_bilinear_laplacian_right_eq_left, Circle.argEquiv_symm_apply, MeasureTheory.Integrable.norm_integral_condDistrib_map, tendsto_exp_atBot, AddCircle.toCircle_apply_mk, homeomorphUnitSphereProd_apply_fst_coe, tendsto_rpow_neg_nhdsGT_zero, differentiableWithinAt_arcsin_Iic, signedDist_triangle_right, Polynomial.hermite_eq_deriv_gaussian, EReal.tendsto_coe, Path.Homotopy.cast_apply, HasStrictDerivAt.complexToReal_fderiv', contMDiffWithinAt_comp_projIcc_iff, hasFDerivAt_polarCoord_symm, NormedSpace.norm_expSeries_summable', continuous_norm', continuous_exp, NumberField.mixedEmbedding.mixedSpaceToRealMixedSpace_apply, NormedSpace.norm_expSeries_div_summable_of_mem_ball, ContinuousMap.Homotopy.extend_apply_of_mem_I, intervalIntegral.intervalIntegrable_exp, IntervalIntegrable.norm, Complex.hasSum_re, ConvexOn.real_univ_sSup_affine_eq, MeasureTheory.SignedMeasure.toComplexMeasure_apply_re, ProbabilityTheory.hasDerivAt_neg_exp_mul_exp, deriv_arcsin, gronwallBound_continuous_ε, abs_signedDist_eq_dist_iff_vsub_mem_span, cexp_neg_quadratic_isLittleO_abs_rpow_cocompact, ProbabilityTheory.Kernel.tendsto_eLpNorm_one_densityProcess_limitProcess, BumpCovering.toFun_eq_coe, ConvexOn.monotoneOn_leftDeriv, ContinuousMap.toNNReal_mul_add_neg_mul_add_mul_neg_eq, summable_exp_nat_mul_of_ge, tendsto_pow_atTop_nhds_zero_of_abs_lt_one, GenLoop.toLoop_apply_coe, tendsto_gauge_nhds_zero_nhdsGE, NumberField.Units.instDiscrete_unitLattice, summable_one_div_pow_of_le, NumberField.mixedEmbedding.fundamentalCone.closure_paramSet, differentiable_sin, RCLike.hasSum_re, NumberField.mixedEmbedding.euclidean.instDiscreteTopologySubtypeMixedSpaceMemSubmoduleIntIntegerLattice, continuous_arctan, ContinuousLinearMap.extendTo𝕜_apply, integrableOn_Ioi_rpow_iff, eulerMascheroniConstant_eq_neg_deriv, Metric.PiNatEmbed.continuous_distDenseSeq, EuclideanSpace.volume_ball_fin_three, not_differentiableAt_inv_log_zero, ProbabilityTheory.IsGaussian.integral_dual, instNoncompactSpaceReal, deriv_mul_log, IsOpen.exists_msmooth_support_eq_aux, NumberField.mixedEmbedding.polarCoord_target, AddCircle.denseRange_zsmul_coe_iff, ContinuousMapZero.toNNReal_mul_add_neg_mul_add_mul_neg_eq, ContinuousLinearMap.norm_extendTo𝕜', Int.dist_cast_real, integrableOn_rpow_mul_exp_neg_rpow, NumberField.mixedEmbedding.fundamentalCone.hasFDerivAt_expMapBasis, ContinuousMapZero.toContinuousMapHom_toNNReal, Path.Homotopy.coeFn_injective, cauchySeq_iff_le_tendsto_0, NumberField.mixedEmbedding.normAtPlace_polarCoord_symm_of_isReal, tendsto_abs_tan_of_cos_eq_zero, Quaternion.summable_coe, MeasureTheory.Integrable.integral_norm_condDistrib, summable_iff_not_tendsto_nat_atTop_of_nonneg, signedDist_neg, ProbabilityTheory.IsRatCondKernelCDFAux.integrable, exists_contMDiff_zero_iff_one_iff_of_isClosed, hasSum_geometric_two', integrableOn_exp_mul_Ioi, ProbabilityTheory.measure_cdf, ProbabilityTheory.IsCondKernelCDF.integrable, tendsto_norm_one, ProbabilityTheory.integrable_of_mem_integrableExpSet, ProbabilityTheory.IndepFun.charFunDual_map_add_eq_mul, NumberField.mixedEmbedding.fundamentalCone.hasDerivAt_expMap_single, tendsto_iff_norm_div_tendsto_zero, ProbabilityTheory.HasCondSubgaussianMGF.memLp_exp_mul, eventually_ball_subset, differentiableAt_tan, ConvexOn.locallyLipschitzOn_iff_continuousOn, differentiable_cosh, NumberField.mixedEmbedding.negAt_symm, fourierSubalgebra_coe, ProbabilityTheory.integrable_compProd_iff, Polynomial.toAddCircle_monomial_eq_smul_fourier, CompletelyRegularSpace.completely_regular, cfcHom_nnreal_eq_restrict, GenLoop.loopHomeo_symm_apply, Complex.polarCoord_source, isProperMap_dist, EMetric.exists_continuous_real_forall_closedBall_subset, BoundedContinuousFunction.lintegral_of_real_lt_top, intervalIntegral.intervalIntegrable_const, MeasureTheory.MemLp.norm_rpow_div, NumberField.mixedEmbedding.polarCoord_symm_eq, tsum_geometric_inv_two_ge, tendsto_tan_pi_div_two, signedDist_vsub_self_rev, BumpCovering.ind_apply, probChar_apply', ProperCone.relative_hyperplane_separation, tendsto_log_comp_add_sub_log, Complex.continuousOn_prod_circle_transform_function, BoxIntegral.Box.exists_seq_mono_tendsto, Icc_chartedSpaceChartAt_of_top_le, signedDist_linear_apply, isBoundedSMul, NumberField.mixedEmbedding.negAt_apply_isReal_and_mem, hasDerivAt_log, MeasureTheory.addHaarMeasure_eq_volume_pi, oneTangentSpaceIcc_def, Complex.isHomeomorphicTrivialFiberBundle_re, continuous_inv, Path.continuous, MeasureTheory.tendstoInMeasure_iff_measureReal_enorm, NumberField.mixedEmbedding.polarSpaceCoord_target', IccRightChart_extend_top_mem_frontier, nndist_eq, CompactlySupportedContinuousMap.toReal_add, ProbabilityTheory.IsMeasurableRatCDF.stieltjesFunction_eq, NumberField.mixedEmbedding.volume_negAt_plusPart, ProbabilityTheory.IsMeasurableRatCDF.measure_stieltjesFunction_Iic, continuousOn_rpowIntegrand₀₁_Ici, ProbabilityTheory.IsCondKernelCDF.tendsto_atBot_zero, Module.Basis.parallelepiped_eq_map, ZLattice.covolume.tendsto_card_div_pow', SmoothPartitionOfUnity.sum_eq_one, Complex.isBigO_comp_ofReal_nhds_ne, SchwartzMap.hasDerivAt, exists_continuous_zero_one_of_isCompact, ContDiffBump.continuous, signedDist_self, MeasureTheory.MemLp.norm, comap_norm_nhds_one, hasDerivAtFilter_iff_tendsto, ProperCone.dual_flip_dual, ProbabilityTheory.measure_stieltjesOfMeasurableRat_univ, RCLike.ofRealCLM_norm, unitInterval.tendsto_sigmoid_atTop, integrable_inv_one_add_sq, ENNReal.tsum_coe_ne_top_iff_summable_coe, ProbabilityTheory.exponentialCDFReal_eq, signedDist_vsub_self, MeasureTheory.SignedMeasure.rnDeriv_smul, ContinuousMap.realToNNReal_apply, Affine.Simplex.exists_forall_signedInfDist_eq_iff_eq_incenter, IsPicardLindelof.exists_forall_mem_closedBall_eq_hasDerivWithinAt_continuousOn, instIsUniformAddGroupReal, signedDist_smul, ENNReal.tendsto_toReal_zero_iff, RCLike.im_tsum, StieltjesFunction.measure_Icc, continuous_cos, geometric_hahn_banach_point_open, hasStrictDerivAt_arctan, Quaternion.tsum_coe, intervalIntegrable_posLog_norm_meromorphicOn, taylor_isLittleO, MeasureTheory.SignedMeasure.haveLebesgueDecomposition_smul, ConcaveOn.continuousOn_interior, Circle.exp_zero, BoxIntegral.Box.diam_Icc_le_of_distortion_le, isConformalMap_complex_linear_conj, TendstoUniformlyOn.im, RightDerivMeasurableAux.A_mem_nhdsGT, Euclidean.closedBall_eq_preimage, tendsto_norm', NumberField.mixedEmbedding.iUnion_negAt_plusPart_union, uniqueDiffOn_Iio, ProbabilityTheory.IsMeasurableRatCDF.measurable_stieltjesFunction, ProbabilityTheory.memLp_id_gaussianReal, LipschitzWith.locallyIntegrable_lineDeriv, NumberField.mixedEmbedding.homeoRealMixedSpacePolarSpace_apply_fst_ofIsReal, SmoothBumpCovering.embeddingPiTangent_injOn, MeasureTheory.memLp_norm_rpow_iff, Angle.continuous_coe, AddCircle.compactSpace, MeasureTheory.measureReal_abs_dual_gt_le_integral_charFunDual, MeasureTheory.SignedMeasure.totalVariation_neg, ContinuousMapZero.toNNReal_add_add_neg_add_neg_eq, hasDerivAt_mulExpNegMulSq, tendstoLocallyUniformlyOn_rpow_sub_one_log, SchwartzMap.tsupport_smulLeftCLM_subset, AkraBazziRecurrence.eventually_deriv_one_sub_smoothingFn, separate_convex_open_set, cfcₙHom_real_eq_restrict, MeasureTheory.ComplexMeasure.im_apply, smoothTransition.continuousAt, UnitAddTorus.mFourierSubalgebra_separatesPoints, differentiableOn_arccos, tendsto_zero_iff_norm_tendsto_zero, hasDerivAt_cosh, tendsto_deriv_mul_log_atTop, dist_eq, ProbabilityTheory.Kernel.tendsto_setIntegral_densityProcess, LipschitzOnWith.ae_differentiableWithinAt_real, MeasureTheory.AEStronglyMeasurable.ae_integrable_condDistrib_map_iff, lp.hasSum_norm, indicator_cthickening_eventually_eq_indicator_closure, ProbabilityTheory.Kernel.stronglyMeasurable_countableFiltration_densityProcess, tendsto_gauge_nhds_zero, Path.subpathAux_continuous, fourierCoeff_eq_intervalIntegral, map_exp_atBot, NumberField.mixedEmbedding.continuous_normAtPlace, uniformContinuous_norm', UpperHalfPlane.continuous_im, tendsto_mod_div_atTop_nhds_zero_nat, Complex.closure_reProdIm, ContinuousOn.ofReal_map_toNNReal, CompactlySupportedContinuousMap.toNNRealLinear_apply, hasDerivAt_fourierChar, numDerangements_tendsto_inv_e, ContinuousLinearMap.intervalIntegral_apply, tendsto_of_bddBelow_antitone, GromovHausdorff.HD_below_aux2, SchwartzMap.smulLeftCLM_neg, Complex.isUniformEmbedding_ofReal, differentiableWithinAt_arccos_Iic, MeasureTheory.charFunDual_eq_pi_iff, mdifferentiableWithinAt_comp_projIcc_iff, zero_at_infty_fourier, Complex.re_tsum, TendstoUniformlyOn.re, signedDist_smul_of_neg, HomotopyGroup.one_def, Diffeology.isOpen_iff_preimages_plots, MeasureTheory.SignedMeasure.singularPart_sub, lp.tsum_mul_le_mul_norm', nnnorm_fderiv_norm_rpow_le, hasFPowerSeriesOnBall_linear_zero, differentiableAt_abs_pos, integrableOn_exp_neg_Ioi, Path.target', NumberField.mixedEmbedding.fundamentalCone.expMap_single_symm_apply, Asymptotics.superpolynomialDecay_iff_norm_tendsto_zero, ProbabilityTheory.IsMeasurableRatCDF.continuousWithinAt_stieltjesFunctionAux_Ici, hasDerivAt_Gamma_one_half, ProbabilityTheory.isPosSemidef_covarianceBilinDual, fderiv_norm_smul, MeasureTheory.Measure.integrable_integral_norm_of_integrable_comp, dist_le_of_mem_Icc_01, expNegInvGlue.continuous_polynomial_eval_inv_mul, NumberField.mixedEmbedding.injective_mixedSpaceOfRealSpace, MeasureTheory.MemLp.re, EuclideanSpace.ball_zero_eq, instCompleteSpace, HurwitzZeta.hasSum_int_oddKernel, NumberField.mixedEmbedding.fundamentalCone.expMapBasis_pos, MeasureTheory.AEStronglyMeasurable.im, MeasureTheory.Integrable.re, Diffeology.IsPlot.continuous, ContinuousMap.Homotopy.extend_of_mem_I, HasFDerivWithinAt.curveIntegral_segment_source, MeasureTheory.integrable_prod_iff', ZLattice.summable_norm_sub_rpow, TopologicalSpace.exists_isInducing_l_infty, summable_geometric_of_abs_lt_one, ProbabilityTheory.Kernel.IsMarkovKernel.integrable, Affine.Simplex.sign_signedInfDist_touchpoint_empty, Irrational.eventually_forall_le_dist_cast_div, MeasureTheory.SignedMeasure.singularPart_add_withDensity_rnDeriv_eq, intervalIntegrable_log_cos, SchwartzMap.pairing_continuous_left, ContinuousMap.toNNReal_apply, one_add_rpow_hasFPowerSeriesAt_zero, signedDist_vadd_right_swap, ProbabilityTheory.integral_condCDF, ProbabilityTheory.IsRatStieltjesPoint.tendsto_atTop_one, SchwartzMap.integralCLM_apply, PolynormableSpace.withSeminorms', differentiable_mulExpNegMulSq, ContinuousMap.neg_norm_le_apply, ProbabilityTheory.condCDF_le_one, AddCircle.coe_real_preimage_closedBall_period_zero, NumberField.mixedEmbedding.volume_preserving_homeoRealMixedSpacePolarSpace, EuclideanSpace.volume_ball_fin_two, Polynomial.fourierCoeff_toAddCircle_natCast, differentiableAt_arccos, ConvexOn.real_univ_sSup_of_nat_affine_eq, summable_pow_div_factorial, ArithmeticFunction.vonMangoldt.LSeries_residueClass_lower_bound, SimpleGraph.tendsto_turanDensity, dist_0_eq_abs, summable_condensed_iff_of_nonneg, not_DifferentiableAt_log_mul_zero, EReal.continuous_coe_iff, NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_injective, iccLeftChart_extend_zero, SmoothBumpCovering.comp_embeddingPiTangent_mfderiv, MeasureTheory.Submartingale.tendsto_eLpNorm_one_limitProcess, dist_le_dist_of_le_pi, ProbabilityTheory.Kernel.tendsto_densityProcess_limitProcess, CircleDeg1Lift.tendsto_translation_number₀, MeasureTheory.SignedMeasure.singularPart_smul_nnreal, ProbabilityTheory.covarianceBilin_real, tendsto_tan_neg_pi_div_two, tsum_geometric_inv_two, Euclidean.ball_eq_preimage, MeasureTheory.Measure.exists_regular_eq_of_compactSpace, not_summable_one_div_natCast, NumberField.Ideal.tendsto_norm_le_div_atTop, NumberField.mixedEmbedding.fundamentalCone.expMap_apply, SchwartzMap.lineDerivOp_fourierInv_eq, InformationTheory.rightDeriv_klFun_one, hasDerivAt_abs, Path.truncate_zero_one, EuclideanSpace.volume_ball, BumpCovering.sum_toPartitionOfUnity_eq, intervalIntegral.integral_hasFDerivWithinAt_of_tendsto_ae, ProbabilityTheory.covarianceBilin_of_not_memLp, InformationTheory.rightDeriv_klFun, dense_addSubgroupClosure_pair_iff, IsUnifLocDoublingMeasure.eventually_measure_le_scaling_constant_mul', Path.extend_one, IsMIntegralCurveOn.continuousWithinAt, interior_range_modelWithCornersEuclideanHalfSpace, BoxIntegral.TaggedPrepartition.IsSubordinate.diam_le, AkraBazziRecurrence.differentiableOn_one_sub_smoothingFn, ConvexOn.real_sSup_of_countable_affine_eq, NumberField.mixedEmbedding.instDiscreteTopologySubtypeMixedSpaceMemSubmoduleIntIntegerLattice, dimH_ball_pi_fin, tendsto_logb_comp_add_sub_logb, ProbabilityTheory.differentiableOn_complexMGF, PartitionOfUnity.sum_le_one, closure_ordConnected_inter_rat, dist_le_of_mem_pi_Icc, hasDerivAt_Gamma_one, hasStrictDerivAt_cos, MeasureTheory.ComplexMeasure.equivSignedMeasureₗ_symm_apply, continuousAt_log_iff, ODE.FunSpace.continuous_compProj, Circle.exp_int_mul_two_pi, AkraBazziRecurrence.deriv_smoothingFn, not_differentiableAt_rpow_const_zero, stdSimplexHomeomorphUnitInterval_one, Seminorm.continuousAt_zero_of_forall, RCLike.hasSum_iff, Differentiable.dist, SeminormFamily.withSeminorms_iff_nhds_eq_iInf, EulerSine.antideriv_cos_comp_const_mul, ProbabilityTheory.condVar_of_sigmaFinite, curveIntegral_eq_intervalIntegral_deriv, tendsto_norm, ContinuousMap.Homotopy.continuous, MeasureTheory.JordanDecomposition.toSignedMeasure_smul, RightDerivMeasurableAux.differentiable_set_eq_D, ZetaAsymptotics.continuousOn_term_tsum, StarAlgHom.realContinuousMapOfNNReal_injective, tendsto_integral_exp_smul_cocompact, mellin_convergent_iff_norm, tendsto_closedBall_smallSets, ProbabilityTheory.iIndepFun_iff_charFunDual_pi', tsum_sq_fourierCoeffOn, Complex.continuous_ofReal_cpow_const, ProbabilityTheory.eq_condKernel_of_measure_eq_compProd_real, HasDerivAt.real_of_complex, ProbabilityTheory.covarianceBilinDual_comm, uniformContinuous_abs, ProbabilityTheory.isGaussian_iff_charFunDual_eq, tendsto_arctan_atTop, tendsto_rpow_div, measurableSet_of_differentiableWithinAt_Ioi, differentiable_iteratedDeriv_sin, SmoothPartitionOfUnity.exists_pos_of_mem, fourier_neg, AkraBazziRecurrence.isEquivalent_deriv_rpow_p_mul_one_add_smoothingFn, deriv_sigmoid, ProperCone.dual_dual_flip, Topology.RelCWComplex.mapsTo, MeasureTheory.LocallyIntegrableOn.norm, one_add_rpow_hasFPowerSeriesAt_zero, HomotopyGroup.inv_spec, Complex.integrable_pow_mul_norm_one_add_mul_inv, exists_smooth_zero_one_of_isClosed, tendsto_measure_cthickening_of_isClosed, ProbabilityTheory.IsRatStieltjesPoint.tendsto_atBot_zero, Path.range_coe, separatesPoints_continuous_of_t35Space_Icc, ContMDiff.inner_bundle, seminormFromConst_isLimit, EulerSine.antideriv_sin_comp_const_mul, IntervalIntegrable.intervalIntegrable_norm_iff, signedDist_vadd_left, Asymptotics.IsBigO.rpow_rpow_nhdsGE_zero_of_le_of_imp, ModularGroup.tendsto_lcRow0, ProbabilityTheory.integrable_kernel_prodMk_left, comap_exp_nhdsGT_zero, Complex.imCLM_coe, Complex.isQuotientMap_im, tendsto_mul_add_inv_atTop_nhds_zero, intervalIntegral.integral_hasFDerivWithinAt, SmoothBumpCovering.embeddingPiTangent_injective, MeasureTheory.charFunDual_prod', summable_pow_mul_exp_neg_nat_mul, ProbabilityTheory.covarianceBilin_apply, exists_contMDiff_support_eq_eq_one_iff, ProbabilityTheory.measure_stieltjesOfMeasurableRat_Iic, Quaternion.norm_exp, ProbabilityTheory.IsRatCondKernelCDFAux.integrable_iInf_rat_gt, hasDerivAt_gronwallBound, Quaternion.continuous_coe, uniformContinuous_add, Complex.continuous_ofReal, ContinuousMap.comp_attachBound_mem_closure, EuclideanGeometry.hasFDerivAt_inversion, InformationTheory.continuous_klFun, InformationTheory.stronglyMeasurable_klFun, NNReal.isUniformEmbedding_coe, MeasureTheory.JordanDecomposition.toSignedMeasure_neg, NumberField.mixedEmbedding.fundamentalCone.injective_expMapBasis, hasDerivAt_ofReal_cpow_const, hasDerivAt_norm_rpow, NumberField.mixedEmbedding.homeoRealMixedSpacePolarSpace_apply_fst_ofIsComplex, differentiableAt_tan_of_mem_Ioo, not_continuousAt_deriv_qaryEntropy_zero, ContMDiffAt.inner_bundle, ContinuousMap.Homotopy.coe_toContinuousMap, SmoothPartitionOfUnity.sum_finsupport_smul_eq_finsum, tendsto_rpow_neg_div, ProbabilityTheory.uncenteredCovarianceBilin_of_not_memLp, signedDist_apply_linear_apply, Matrix.IsHermitian.cfcAux_id, ProbabilityTheory.HasGaussianLaw.charFunDual_map_eq_fun, Path.extend_symm, MonotoneOn.exists_tendsto_deriv_liminf_lintegral_enorm_le, NumberField.mixedEmbedding.lintegral_comp_polarCoordReal_symm, ProbabilityTheory.covarianceBilin_map, BoundedContinuousFunction.integral_add_const, ENNReal.continuous_truncateToReal, Path.subpath_continuous_family, HasFDerivAt.curveIntegral_segment_source', AffineSubspace.signedInfDist_singleton, volume_real_ball, NumberField.mixedEmbedding.measurable_polarCoord_symm, Circle.surjOn_exp_neg_pi_pi, tendsto_rpow_neg_atTop, ContinuousMap.apply_le_norm, continuous_real_toNNReal, hasSum_one_div_nat_pow_mul_sin, ProbabilityTheory.Kernel.tendsto_densityProcess_fst_atTop_ae_of_monotone, AkraBazziRecurrence.differentiableAt_smoothingFn, NumberField.mixedEmbedding.fundamentalCone.expMap_source, tendsto_arctan_atBot, SchwartzMap.fderivCLM_fourier_eq, Bundle.ContinuousRiemannianMetric.pos, ContDiffAt.exists_forall_mem_closedBall_exists_eq_forall_mem_Ioo_hasDerivAt, SchwartzMap.derivCLM_apply, NumberField.mixedEmbedding.fundamentalCone.expMapBasis_apply'', deriv_cos, IsCoercive.continuousLinearEquivOfBilin_apply, Circle.exp_intCast_mul, integrableOn_Ioi_exp_neg_mul_sq_iff, SmoothPartitionOfUnity.contMDiff_finsum_smul, BoundedContinuousFunction.nnnorm_coeFn_eq, continuousAt_const_rpow, differentiableAt_binEntropy, smoothTransition.continuous, tendsto_mulIndicator_thickening_mulIndicator_closure, SmoothPartitionOfUnity.sum_finsupport, hasDerivAt_arctan', instIsAddHaarMeasureProdRealVolume, ProbabilityTheory.stronglyMeasurable_gaussianPDFReal, deriv_bernoulliFun, det_fderivPiPolarCoordSymm, tsum_le_of_sum_le, injOn_pi_polarCoord_symm, Path.Homotopy.continuous_transReflReparamAux, cantorToHilbert_continuous, deriv2_qaryEntropy, differentiableAt_exp, Topology.RelCWComplex.disjointBase', locallyFinite_volume, hasStrictDerivAt_arcsin, Metric.continuous_infDist_pt, SchwartzMap.integral_clm_comp_deriv_right_eq_neg_left, ENNReal.tsum_coe_eq_top_iff_not_summable_coe, ENNReal.summable_toReal, comap_gauge_nhds_zero, LipschitzWith.ae_differentiableAt_of_real, MeasureTheory.Submartingale.ae_tendsto_limitProcess, BumpCovering.eventuallyEq_one', NormedSpace.of_real_exp_ℝ_ℝ, MeasureTheory.Measure.integrable_comp_iff, Angle.continuous_sin, Metric.eventually_notMem_cthickening_of_infEdist_pos, Bundle.RiemannianMetric.pos, NumberField.mixedEmbedding.polarCoord_apply, tendsto_sub_mul_tsum_nat_rpow, hasSum_zeta_two, NumberField.mixedEmbedding.hasFDerivAt_polarCoordReal_symm, exists_continuousMap_one_of_isCompact_subset_isOpen, IsGδ.setOf_liouville, ProbabilityTheory.analyticOnNhd_mgf, differentiable_iteratedDeriv_cosh, hasStrictDerivAt_sin, BoundedContinuousFunction.add_norm_nonneg, tendsto_indicator_cthickening_indicator_closure, Complex.equivRealProdCLM_symm_apply_re, MeasureTheory.ProbabilityMeasure.continuous_iff_forall_continuous_integral, Manifold.pathELength_eq_lintegral_mfderiv_Icc, ProbabilityTheory.tendsto_cdf_atTop, ContinuousMap.HomotopyWith.prop, NumberField.mixedEmbedding.continuous_normAtAllPlaces, QuasispectrumRestricts.nnreal_of_nonneg, MeasureTheory.charFunDual_eq_pi_iff', uniqueDiffOn_Ioi, MeasureTheory.exists_null_frontiers_thickening, intervalIntegral.intervalIntegrable_pow, AbsolutelyContinuousOnInterval.uniformlyContinuousOn, BohrMollerup.tendsto_logGammaSeq, Path.id_apply, Nat.preimage_ball, CompactlySupportedContinuousMap.toReal_smul, hasFDerivAt_pi_polarCoord_symm, Int.instDiscreteTopologySubtypeRealMemAddSubgroupZmultiples, tendsto_sum_pi_div_four, IsPicardLindelof.exists_eq_forall_mem_Icc_hasDerivWithinAt, BoundedContinuousFunction.norm_sub_nonneg, MeromorphicOn.intervalIntegrable_log, summable_of_sum_le, UniformContinuous.dist, MeasureTheory.MemLp.im, InformationTheory.not_differentiableWithinAt_klFun_Ioi_zero, fourierChar_apply', DifferentiableWithinAt.norm_sq, MeasureTheory.StronglyMeasurable.norm, fourierIntegral_continuousLinearMap_apply', ODE.FunSpace.continuous, PartitionOfUnity.le_one, MeasureTheory.SignedMeasure.haveLebesgueDecomposition_neg, signedDist_right_lineMap, ProbabilityTheory.uncenteredCovarianceBilin_zero, Nat.isClosedEmbedding_coe_real, tendsto_div_pow_mul_exp_add_atTop, IsUpperSet.null_frontier, differentiable_fourierChar, Path.extend_zero, lintegral_comp_polarCoord_symm, Metric.eventually_notMem_thickening_of_infEdist_pos, ContinuousMap.Homotopy.extend_zero, tendsto_pow_const_mul_const_pow_of_lt_one, VectorFourier.fourierPowSMulRight_apply, TendstoUniformly.re, uniqueDiffOn_Ico, BumpCovering.nonneg, Nat.Primes.summable_rpow, dist_norm_norm_le', MeasureTheory.FiniteMeasure.continuous_integral_boundedContinuousFunction, dist_anti_right_pi, MeasureTheory.Submartingale.exists_ae_tendsto_of_bdd, RCLike.ofReal_tsum, deriv_cos', Path.coe_toContinuousMap, SmoothBumpCovering.support_toSmoothPartitionOfUnity_subset, isBigO_deriv_rpow_const_atTop, bernsteinApproximation_uniform, polarCoord_apply, not_summable_natCast_inv, ContinuousMap.Homotopy.map_one_left, DifferentiableOn.dist, dist_dist_dist_le, deriv_rpow_const', continuous_fourierChar, MeasureTheory.isAddHaarMeasure_volume_pi, cobounded_eq, NumberField.mixedEmbedding.normAtPlace_negAt, differentiableAt_arcosh, Module.Basis.parallelepiped_map, IsLocalMaxOn.fderivWithin_eq_zero, MeasureTheory.Integrable.of_mem_Icc, ContinuousAt.norm, MeasureTheory.charFunDual_dirac, tendsto_one_iff_norm_tendsto_zero, Metric.uniformity_eq_comap_nhds_zero, WeakFEPair.hg_int, ProbabilityTheory.cdf_expMeasure_eq_lintegral, tendsto_Icc_vitaliFamily_left, tendsto_measure_Icc_nhdsWithin_right', hasStrictDerivAt_sqrt, tendsto_eulerMascheroniSeq, NumberField.mixedEmbedding.homeoRealMixedSpacePolarSpace_apply, Metric.eventually_notMem_cthickening_of_infEDist_pos, continuousOn_tan, Complex.HadamardThreeLines.eventuallyle, BumpCovering.exists_finset_toPOUFun_eventuallyEq, GenLoop.Homotopic.equiv, NumberField.mixedEmbedding.fundamentalCone.isBounded_normLeOne, Seminorm.continuous_of_lowerSemicontinuous, eventually_closedBall_subset, hasDerivAt_tan_of_mem_Ioo, contMDiffOn_comp_projIcc_iff, iter_deriv_rpow_const, ZLattice.summable_norm_sub_zpow, Complex.imCLM_nnnorm, SmoothBumpFunction.contMDiff, Path.truncate_const_continuous_family, NumberField.mixedEmbedding.polarCoordReal_symm_target_ae_eq_univ, exists_continuous_one_zero_of_isCompact_of_isGδ, Affine.Simplex.abs_signedInfDist_eq_dist_of_mem_affineSpan_range, NNReal.summable_mk, hasDerivAt_exp, fourierSubalgebra_closure_eq_top, Summable.norm, summable_norm_iff, ProbabilityTheory.HasSubgaussianMGF.memLp, NumberField.mixedEmbedding.convexBodySum_isBounded, Affine.Simplex.ExcenterExists.signedInfDist_excenter, hasSum_sin, NumberField.mixedEmbedding.polarSpaceCoord_apply, BoxIntegral.Box.volume_apply, MeasureTheory.BorelCantelli.stronglyAdapted_process, SmoothPartitionOfUnity.finite_tsupport, ProbabilityTheory.analyticOn_complexMGF, WeakFEPair.hf_int, ContDiffAt.exists_eventually_eq_hasDerivAt, polarCoord_source_ae_eq_univ, NumberField.mixedEmbedding.negAt_apply_norm_isReal, Hyperreal.isSt_iff_tendsto, hasSum_geometric_of_abs_lt_one, Complex.hasSum_im, hasFDerivAtFilter_iff_tendsto, SchwartzMap.integral_bilinear_lineDerivOp_right_eq_neg_left, ConvexOn.continuousOn_interior, sub_le_dist, intervalIntegral.FTCFilter.nhds, ProbabilityTheory.stronglyMeasurable_condCDF, Metric.exists_subseq_summable_dist_of_cauchySeq, IsCompact.measure_eq_biInf_integral_hasCompactSupport, CompactlySupportedContinuousMap.nnrealPart_apply, ContinuousOn.norm, MeasureTheory.Measure.toSignedMeasure_apply_measurable, tendsto_pow_logb_div_mul_add_atTop, NumberField.mixedEmbedding.fundamentalCone.expMap_add, CompactlySupportedContinuousMap.eq_toRealPositiveLinear_toReal, ContinuousLinearMap.IsPositive.spectrumRestricts, homeomorphSphereProd_apply_snd_coe, TemperedDistribution.derivCLM_toTemperedDistributionCLM_eq, not_summable_iff_tendsto_nat_atTop_of_nonneg, hasDerivWithinAt_abs_neg, TestFunction.instLocallyConvexSpaceReal, StieltjesFunction.ae_hasDerivAt, rpow_eq_nhds_of_pos, hasSum_sq_fourierCoeff, PartitionOfUnity.sum_nonneg, EReal.tendsto_toReal, ProbabilityTheory.measure_condCDF_Iic, diam_Ico, polynomialFunctions.topologicalClosure, differentiableAt_negMulLog, ProbabilityTheory.HasSubgaussianMGF.aestronglyMeasurable, Metric.eventually_notMem_thickening_of_infEDist_pos, Besicovitch.tendsto_filterAt, RCLike.imCLM_coe, StieltjesFunction.id_apply, CompactlySupportedContinuousMap.toReal_nonneg, separatesPoints_continuous_of_t35Space, Path.extend_extends', tendsto_logb_nhdsGT_zero_of_base_lt_one, exists_embedding_euclidean_of_compact, nonneg_iff_isSelfAdjoint_and_quasispectrumRestricts, continuousAt_rpow, hasDerivAt_ofReal_cpow_const', ProbabilityTheory.measurable_measure_condCDF, MeasureTheory.ComplexMeasure.absolutelyContinuous_ennreal_iff, summable_of_sum_range_le, differentiable_fourierChar_neg_bilinear_right, MeasureTheory.SignedMeasure.rnDeriv_neg, ProbabilityTheory.stronglyMeasurable_gammaPDFReal, MeasureTheory.SignedMeasure.integrable_rnDeriv, AffineSubspace.signedInfDist_def, NNReal.coeNNRealReal_zero, NumberField.mixedEmbedding.fundamentalCone.expMapBasis_apply, Path.truncate_continuous_family, isMIntegralCurveAt_eventuallyEq_of_contMDiffAt, Complex.isQuotientMap_re, ProbabilityTheory.integrable_exp_mul_of_le, instSecondCountableTopologyReal, instIsTopologicalAddGroupReal, tendsto_fib_succ_div_fib_atTop, tendsto_measure_cthickening_of_isCompact, ProbabilityTheory.instIsProbabilityMeasure_stieltjesOfMeasurableRat, ProbabilityTheory.IsGaussian.integral_dual_conv_map_neg_eq_zero, UnitAddTorus.span_mFourier_closure_eq_top, signedDist_lineMap_right, expPartialHomeomorph_symm_apply, AkraBazziRecurrence.isLittleO_deriv_one_sub_smoothingFn, Complex.imCLM_enorm, SchwartzMap.tsupport_derivCLM_subset, setOf_liouville_eq_iInter_iUnion, isLocalHomeomorph_circleExp, MeasureTheory.Measure.toSignedMeasure_sub_apply, hasSum_arctan, instContinuousStarReal, NumberField.mixedEmbedding.homeoRealMixedSpacePolarSpace_apply_snd, ContinuousLinearMap.reApplyInnerSelf_continuous, tendsto_abs_tan_atTop, Manifold.lintegral_norm_mfderiv_Icc_eq_pathELength_projIcc, TopologicalSpace.exists_embedding_l_infty, tendsto_norm_nhdsNE_zero, differentiable_norm_rpow, Int.preimage_ball, CompactlySupportedContinuousMap.nnrealPart_smul_pos, Affine.Simplex.sign_signedInfDist_incenter, ConcaveOn.continuousOn_tfae, Affine.Simplex.ExcenterExists.sign_signedInfDist_excenter, ContinuousMap.polynomial_comp_attachBound, VectorFourier.norm_fourierSMulRight_le, BoundedContinuousFunction.norm_normComp, Seminorm.preimage_metric_ball, summable_norm_geometric_of_norm_lt_one, CompareReals.compare_uc_symm, IsMIntegralCurveOn.continuousOn, MeasureTheory.charFunDual_map, summable_geometric_two', Memℓp.summable, Complex.ofRealCLM_enorm, uniqueDiffWithinAt_Ici, DirichletCharacter.LFunctionTrivChar_isBigO_near_one_horizontal, ZSpan.discreteTopology_pi_basisFun, isMIntegralCurveAt_iff', NNReal.tendsto_coe, Affine.Simplex.signedInfDist_affineCombination, CompactlySupportedContinuousMap.integralPositiveLinearMap_toFun, MeasureTheory.ComplexMeasure.re_apply, one_div_sub_pow_hasFPowerSeriesOnBall_zero, signedDist_apply, ContinuousMap.HomotopyWith.continuous, coe_tanPartialHomeomorph_symm, NumberField.mixedEmbedding.polarSpaceCoord_source, UnitAddTorus.hasSum_sq_mFourierCoeff, not_integrableOn_Ici_inv, fourierCoeffOn_eq_integral, ProbabilityTheory.IsGaussian.charFunDual_eq_of_integral_eq_zero, ContinuousMap.toNNReal_neg_one, Circle.expHom_apply, homeomorphUnitSphereProd_apply_snd_coe, ProbabilityTheory.variance_dual_prod, ProbabilityTheory.IsRatCondKernelCDFAux.tendsto_atTop_one, tendsto_pow_const_div_const_pow_of_one_lt, intervalIntegral.intervalIntegrable_rpow', differentiableAt_sinh, MeasureTheory.addHaarMeasure_eq_volume, signedDist_eq_dist_iff_vsub_mem_span, continuous_ofDigits, uniqueDiffOn_Ioo, continuousAt_logb, differentiable_iteratedDeriv_sinh, Complex.lintegral_comp_pi_polarCoord_symm, NumberField.mixedEmbedding.fundamentalCone.setLIntegral_expMapBasis_image, NumberField.mixedEmbedding.fundamentalCone.expMap_single_apply, ProbabilityTheory.setLIntegral_condCDF, ZetaAsymptotics.term_welldef, exp_neg_integrableOn_Ioi, ContinuousLinearMap.extendTo𝕜'_apply, ContinuousAt.inner_bundle, AddCircle.instProperlyDiscontinuousVAddSubtypeAddOppositeRealMemAddSubgroupOpZmultiples, VectorFourier.norm_fourierPowSMulRight_le, NormedSpace.norm_expSeries_div_summable, Complex.equivRealProdCLM_symm_apply_im, summable_pow_mul_jacobiTheta₂_term_bound, integrable_exp_neg_mul_sq_iff, Complex.polarCoord_symm_apply, SmoothPartitionOfUnity.mem_fintsupport_iff, MeasureTheory.Measure.integrableOn_toReal_rnDeriv, not_integrableOn_Ioi_inv, Emetric.exists_smooth_forall_closedBall_subset, ProbabilityTheory.norm_uncenteredCovarianceBilin_le, UnitAddTorus.mFourier_single, hasFDerivAt_fourierChar_neg_bilinear_right, ContinuousWithinAt.inner_bundle, ProbabilityTheory.IsMeasurableRatCDF.measurable_measure_stieltjesFunction, ProbabilityTheory.measure_condCDF_univ, lp.norm_eq_tsum_rpow, not_summable_one_div_on_primes, Cube.insertAt_boundary, intervalIntegrable_log_norm_meromorphicOn, ProbabilityTheory.lintegral_stieltjesOfMeasurableRat, Seminorm.uniformContinuous', VectorFourier.norm_fourierSMulRight, stereographic'_symm_apply, Asymptotics.IsBigO.id_rpow_of_le_one, differentiableOn_abs, Probability.stronglyMeasurable_cauchyPDFReal, NumberField.mixedEmbedding.polarCoord_target_eq_polarCoordReal_target, homeomorphSphereProd_apply_fst_coe, MeasureTheory.ProbabilityMeasure.continuous_integral_continuousMap, ProbabilityTheory.integrable_toReal_condDistrib, Circle.arg_exp, SchwartzMap.smulLeftCLM_sub, summable_geometric_two, MeasureTheory.Martingale.ae_eq_condExp_limitProcess, SchwartzMap.smulLeftCLM_apply_apply, Probability.integrable_cauchyPDFReal, MeasureTheory.integrable_toReal_iff, not_continuousAt_inv_log_one, MeasureTheory.charFunDual_pi, SchwartzMap.fourier_fderivCLM_eq, SpectrumRestricts.nnreal_iff_spectralRadius_le, PartitionOfUnity.finite_tsupport, integrable_mulExpNegMulSq_comp_restrict_of_isCompact, FormalMultilinearSeries.radius_eq_top_iff_summable_norm, CircleDeg1Lift.tendsto_translationNumber, integrableOn_rpow_mul_exp_neg_mul_sq, Filter.Tendsto.pathExtend, summable_one_div_nat_pow, hasStrictDerivAt_tan, borelSpace, ENNReal.continuousOn_toReal, NumberField.mixedEmbedding.fundamentalCone.compactSet_ae, StieltjesFunction.measure_Ico, tendsto_euler_sin_prod, NumberField.mixedEmbedding.fundamentalCone.abs_det_fderiv_expMapBasis, eventually_residual_liouville, MeasureTheory.FiniteMeasure.continuous_iff_forall_continuousMap_continuous_integral, MeasureTheory.JordanDecomposition.toSignedMeasure_zero, NumberField.mixedEmbedding.instIsAddHaarMeasureRealMixedSpaceVolume, dist_mono_right_pi, Int.isUniformEmbedding_coe_real, DifferentiableAt.norm, pi_polarCoord_symm_target_ae_eq_univ, differentiable_fourierChar_neg_bilinear_left, NNReal.tendsto_coe', EReal.isEmbedding_coe, Urysohns.CU.continuous_lim, fderiv_norm_smul_pos, hasDerivAt_arctan, dist_dist_dist_le_left, NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_expMap_symm, Path.Homotopy.source, intervalIntegral.FTCFilter.nhdsLeft, Affine.Simplex.ExcenterExists.signedInfDist_excenter_eq_mul_sum_inv, ProbabilityTheory.geometricPMFRealSum, tendsto_seminormFromConst_seq_atTop, geometric_hahn_banach_closed_point, hasSum_one_div_pow_mul_fourier_mul_bernoulliFun, polynomialFunctions_closure_eq_top', NumberField.mixedEmbedding.measurableSet_negAt_plusPart, BoundedContinuousFunction.coe_le_coe_add_dist, MeasureTheory.SignedMeasure.toComplexMeasure_apply_im, ProbabilityTheory.measurable_condCDF, NumberField.mixedEmbedding.homeoRealMixedSpacePolarSpace_symm_apply, bernstein.probability, TestFunction.instContinuousSMulReal, IsLocalMinOn.fderivWithin_nonneg, AkraBazziRecurrence.growsPolynomially_deriv_rpow_p_mul_one_sub_smoothingFn, Complex.reCLM_norm, completelyRegularSpace_iff, IsUnifLocDoublingMeasure.eventually_measure_le_scaling_constant_mul, ContinuousMapZero.toNNReal_neg_smul, FormalMultilinearSeries.summable_norm_mul_pow, Rat.isUniformEmbedding_coe_real, NumberField.mixedEmbedding.euclidean.volumePreserving_toMixed_symm, ContinuousMap.polynomial_comp_attachBound_mem, Matrix.SpecialLinearGroup.discreteSpecialLinearGroupIntRange, Circle.coe_exp, Polynomial.Chebyshev.isLocalExtr_T_real, setOf_liouville_eq_irrational_inter_iInter_iUnion, NumberField.Ideal.tendsto_norm_le_and_mk_eq_div_atTop, MeasureTheory.ComplexMeasure.toComplexMeasure_to_signedMeasure, ProbabilityTheory.stronglyMeasurable_betaPDFReal, hasGradientWithinAt_iff_tendsto, ProbabilityTheory.IsMeasurableRatCDF.tendsto_stieltjesFunction_atTop, HasFDerivWithinAt.curveIntegral_segment_source', CStarAlgebra.nonneg_TFAE, MDifferentiableAt.inner_bundle, deriv_arcsin_aux, fourier_add', RCLike.continuous_im, IsLocalMin.fderiv_eq_zero, ProperCone.hyperplane_separation, Circle.exp_zsmul, ProbabilityTheory.IsCondKernelCDF.lintegral, MeasureTheory.Integrable.fourier_smul, unitInterval.eq_closedBall, intervalIntegral.continuousOn_primitive_interval', differentiableAt_qaryEntropy, NNReal.hasSum_coe, Complex.isBigO_comp_ofReal_nhds, ProbabilityTheory.Kernel.HasSubgaussianMGF.ae_aestronglyMeasurable, MeasureTheory.condExp_aestronglyMeasurable_bilin_of_bound, tendsto_sin_pi_div_two, Affine.Simplex.exists_forall_signedInfDist_eq_iff_excenterExists_and_eq_excenter, tsum_sq_fourierCoeff, hasDerivAt_iff_tendsto, exp_eq_exp_ℝ, AkraBazziRecurrence.isLittleO_deriv_smoothingFn, differentiable_arsinh, NumberField.mixedEmbedding.fundamentalCone.sum_expMap_symm_apply, SchwartzMap.smulLeftCLM_ofReal, Circle.exp_eq_one, Complex.ofReal_tsum, MeasureTheory.ComplexMeasure.equivSignedMeasureₗ_apply, PiCountable.dist_eq_tsum, integrable_exp_neg_mul_sq, fderiv_norm_rpow, PartitionOfUnity.mem_fintsupport_iff, Polynomial.toAddCircle_X_eq_fourier_one, hasStrictDerivAt_const_rpow, MeasureTheory.FiniteMeasure.continuous_integral_continuousMap, hasSum_pow_div_log_of_abs_lt_one, IsPicardLindelof.exists_forall_mem_closedBall_eq_hasDerivWithinAt_lipschitzOnWith, summable_norm_pow_mul_geometric_of_norm_lt_one, ProbabilityTheory.Kernel.tendsto_eLpNorm_one_restrict_densityProcess_limitProcess, Irrational.eventually_forall_le_dist_cast_rat_of_den_le, NumberField.mixedEmbedding.fundamentalCone.normAtAllPlaces_image_preimage_expMapBasis, SchwartzMap.integrable_pow_mul, Icc_mem_vitaliFamily_at_right, BumpCovering.toPOUFun_eq_mul_prod, expPartialHomeomorph_source, MeasureTheory.SignedMeasure.null_of_totalVariation_zero, AkraBazziRecurrence.continuous_sumCoeffsExp, ContinuousMap.toNNReal_add_add_neg_add_neg_eq, hasDerivAt_fourierIntegral, mulIndicator_cthickening_eventually_eq_mulIndicator_closure, fourier_add_half_inv_index, MeasureTheory.Submartingale.memLp_limitProcess, isCompact_cantorSet, Path.extend_of_le_zero, EReal.nhds_coe_coe, ContinuousMapZero.toNNReal_smul, continuousAt_log, integrable_mulExpNegMulSq_comp, MeasureTheory.Measure.toSignedMeasure_restrict_eq_restrict_toSignedMeasure, AffineSubspace.signedInfDist_apply_self, ProbabilityTheory.covarianceBilinDual_of_not_memLp, ProbabilityTheory.exists_integrable_exp_sq_of_map_rotation_eq_self_of_isProbabilityMeasure, MeasureTheory.FiniteMeasure.continuous_iff_forall_continuous_integral, Complex.imCLM_apply, MeasureTheory.charFun_map_eq_charFunDual_smul, Int.tendsto_coe_cofinite, tendsto_log_nat_add_one_sub_log, MeasureTheory.integrable_withDensity_iff, summable_geometric_of_lt_one, exists_tsupport_one_of_isOpen_isClosed, NumberField.mixedEmbedding.normAtAllPlaces_mixedSpaceOfRealSpace, NNReal.coe_tsum, NumberField.mixedEmbedding.det_fderivPolarCoordRealSymm, abs_integral_sub_setIntegral_mulExpNegMulSq_comp_lt, AddCircle.pathConnectedSpace, continuousOn_rpowIntegrand₀₁, differentiable_rpow_const, ProbabilityTheory.integrable_exp_mul_of_mem_Icc, isConformalMap_complex_linear, zero_at_infty_vector_fourierIntegral, SchwartzMap.smulLeftCLM_apply, MeasureTheory.Integrable.norm, ProbabilityTheory.exists_integrable_exp_sq_of_map_rotation_eq_self, NumberField.mixedEmbedding.fundamentalCone.expMap_sum, uniformContinuous_mul, SchwartzMap.tsum_eq_tsum_fourierIntegral, ProbabilityTheory.uncenteredCovarianceBilinDual_apply, expPartialHomeomorph_target, ProbabilityTheory.cdf_paretoMeasure_eq_lintegral, Chebyshev.intervalIntegrable_one_div_log_sq, Topology.isEmbedding_sigmoid, Polynomial.tendsto_div_exp_atTop, SmoothPartitionOfUnity.toPartitionOfUnity_toFun, ENNReal.tendsto_toReal_iff, ProbabilityTheory.IsRatCondKernelCDFAux.tendsto_integral_of_monotone, IsUnifLocDoublingMeasure.exists_eventually_forall_measure_closedBall_le_mul, tendsto_pow_log_div_mul_add_atTop, fourier_add, SmoothPartitionOfUnity.contMDiff_smul, borel_eq_generateFrom_Iic_rat, tendsto_smoothingFun_of_eq_zero, Path.Homotopy.symm₂_apply, PolynormableSpace.withSeminorms, Topology.CWComplex.mapsTo, SchwartzMap.smulLeftCLM_compL_smulLeftCLM, RightDerivMeasurableAux.B_mem_nhdsGT, TemperedDistribution.derivCLM_apply_apply, NumberField.mixedEmbedding.fundamentalCone.normAtAllPlaces_normLeOne_eq_image, Stirling.tendsto_stirlingSeq_sqrt_pi, abs_signedDist_le_dist, DirichletCharacter.LFunction_isBigO_horizontal, mfderiv_subtype_coe_Icc_one, BumpCovering.locallyFinite', hasStrictFDerivAt_rpow_of_neg, Rat.isEmbedding_coe_real, tendsto_log_nhdsNE_zero, hasStrictDerivAt_rpow_const, ContinuousMap.Homotopy.extend_one, MeasureTheory.weightedSMul_smul_measure, unitInterval.tendsto_sigmoid_atBot, MeasureTheory.integrable_count_iff, MeasureTheory.memLp_norm_iff, PartitionOfUnity.exists_finset_nhds', cosh_eq_tsum, tendsto_norm_zero, continuousOn_arcosh, MeasureTheory.Submartingale.exists_ae_trim_tendsto_of_bdd, MeasureTheory.condExp_stronglyMeasurable_bilin_of_bound, RCLike.ofRealCLM_coe, ProbabilityTheory.HasCondSubgaussianMGF.integrable_exp_mul, Icc_eq_closedBall, MeasureTheory.tendsto_iff_forall_lipschitz_integral_tendsto, ProbabilityTheory.IsGaussian.charFunDual_eq', mulIndicator_thickening_eventually_eq_mulIndicator_closure, BumpCovering.le_one', PartitionOfUnity.exists_pos, ContinuousMap.Homotopy.curry_one, IsClosed.upperClosure_pi, CompareReals.compare_uc, AffineSubspace.signedInfDist_apply_of_mem, ProbabilityTheory.analyticOnNhd_complexMGF, hasDerivAt_Gamma_nat, Path.truncate_one_one, differentiableAt_abs, ProbabilityTheory.setIntegral_stieltjesOfMeasurableRat_rat, InnerProductGeometry.continuousAt_angle, IsLowerSet.null_frontier, tendsto_const_div_pow, ConvexOn.real_sSup_of_nat_affine_eq, NumberField.mixedEmbedding.polarCoordReal_target, continuousAt_arctan, hasSum_zeta_nat, dist_dist_dist_le_right, ProbabilityTheory.IsRatCondKernelCDF.integrable, exists_smooth_zero_one_nhds_of_isClosed, ZLattice.sum_piFinset_Icc_rpow_le, Complex.polarCoord_target, Circle.isCoveringMap_exp, not_continuousAt_deriv_qaryEntropy_one, DifferentiableOn.norm, AddChar.zmod_intCast, BoxIntegral.unitPartition.diam_boxIcc, FormalMultilinearSeries.summable_norm_apply, diam_Ioc, intervalIntegral.continuous_primitive, SchwartzMap.integral_clm_comp_laplacian_right_eq_left, hasFDerivWithinAt_iff_tendsto, Complex.isHomeomorphicTrivialFiberBundle_im, MeasureTheory.MemLp.integrable_norm_pow', dist_inf_sup_pi, Quaternion.hasSum_coe, tendsto_log_mul_rpow_nhdsGT_zero, signedDist_apply_linear, differentiableAt_sin, MeasureTheory.Measure.toSignedMeasure_zero, Bundle.RiemannianMetric.continuousAt, closure_halfSpace, ContinuousMap.Homotopy.extend_apply_of_le_zero, hasSum_iff_tendsto_nat_of_nonneg, MeasureTheory.tendsto_integral_norm_approxOn_sub, Complex.reCLM_enorm, MeasureTheory.integrable_mconv_iff, IsPicardLindelof.exists_forall_mem_closedBall_eq_forall_mem_Icc_hasDerivWithinAt, hasDerivAt_sinh, Polynomial.toAddCircle_C_eq_smul_fourier_zero, Manifold.exists_lt_of_riemannianEDist_lt, NumberField.mixedEmbedding.fundamentalCone.expMapBasis_source, Subalgebra.SeparatesPoints.rclike_to_real, polynomialFunctions_closure_eq_top, VectorFourier.hasFDerivAt_fourierChar_smul, InformationTheory.not_differentiableAt_klFun_zero, deriv_cosh, tendsto_mulIndicator_cthickening_mulIndicator_closure, Quaternion.continuous_imK, exists_extension_norm_eq, Polynomial.Chebyshev.intervalIntegrable_sqrt_one_sub_sq_inv, Complex.frontier_reProdIm, NumberField.mixedEmbedding.integral_comp_polarCoord_symm, ContinuousOn.inner_bundle, AkraBazziRecurrence.growsPolynomially_deriv_rpow_p_mul_one_add_smoothingFn, deriv_sin, SmoothBumpCovering.embeddingPiTangent_coe, AddCircle.homeomorphCircle'_apply, continuous_arccos, volume_pi_closedBall, nndist_eq', Seminorm.continuous_of_forall, dist_norm_norm_le, SmoothPartitionOfUnity.nonneg', dist_mulExpNegMulSq_le_dist, ProbabilityTheory.covarianceBilinDual_of_not_memLp', tendsto_measure_thickening_of_isClosed, ProbabilityTheory.IsMeasurableRatCDF.stieltjesFunction_le_one, instIsAddHaarMeasureUnitAddCircleVolume, SchwartzMap.fourier_convolution, NumberField.mixedEmbedding.fundamentalCone.expMap_pos, SmoothPartitionOfUnity.IsSubordinate.contMDiff_finsum_smul, RCLike.hasSum_im, HurwitzZeta.hasSum_nat_cosKernel₀, tendsto_iff_dist_tendsto_zero, mem_closure_iff, tendsto_logb_nhdsGT_zero, MeasureTheory.indicatorConstLp_eq_toSpanSingleton_compLp, ContinuousWithinAt.norm', ContinuousMapZero.continuous_toNNReal, ProbabilityTheory.analyticOn_iteratedDeriv_mgf, MeasureTheory.Integrable.integral_norm_condKernel, continuous_norm, ProbabilityTheory.poissonPMFRealSum, MeasureTheory.Measure.innerRegularWRT_preimage_one_hasCompactSupport_measure_ne_top_of_addGroup, AddCircle.homeomorphCircle_apply, ProbabilityTheory.integrable_gaussianPDFReal, Topology.CWComplex.continuousOn_symm, expNegInvGlue.differentiable_polynomial_eval_inv_mul, tendsto_factorial_div_pow_self_atTop, MeasureTheory.StronglyMeasurable.dist, ProbabilityTheory.stronglyMeasurable_paretoPDFReal, Circle.exp_sub_two_pi, Monotone.stieltjesFunction_eq, ProbabilityTheory.Kernel.HasSubgaussianMGF.aestronglyMeasurable, Path.Homotopy.refl_apply, norm_fderiv_norm_id_rpow, ProbabilityTheory.Kernel.HasSubgaussianMGF.ae_integrable_exp_mul, Complex.dist_of_re_eq, continuous_arsinh, Circle.argPartialEquiv_symm_apply, Complex.isUniformEmbedding_equivRealProd, ProbabilityTheory.setLIntegral_stieltjesOfMeasurableRat, Affine.Simplex.signedInfDist_apply_of_ne, ProbabilityTheory.continuousOn_mgf, Metric.eventually_isCompact_closedBall, BumpCovering.exists_isSubordinate_hasCompactSupport_of_locallyFinite_t2space, exists_contMDiffMap_one_nhds_of_subset_interior, ModularForm.summable_eta_q, Polynomial.fourierCoeff_toAddCircle, signedDist_left_lineMap, Path.uniformContinuous_extend, Complex.hasSum_iff, deriv_mul_log_zero, NumberField.mixedEmbedding.norm_negAt, AbsolutelyContinuousOnInterval.continuousOn, SmoothPartitionOfUnity.sum_le_one, VectorFourier.fourierIntegral_fderiv, tendsto_prod_pi_div_two, exp_sub_sum_range_isBigO_pow, hasDerivAt_sqrt, GenLoop.boundary, hasLipschitzAdd, IccRightChart_extend_top, GenLoop.homotopyFrom_apply, GenLoop.const_apply, Seminorm.continuous_iff_continuous_comp, PartitionOfUnity.continuous_smul, stdSimplex.instCompactSpace_coe, NumberField.mixedEmbedding.fundamentalCone.expMap_single_source, Angle.continuous_cos, Complex.isOpenMap_re, hasDerivWithinAt_arccos_Iic, measurableSet_of_differentiableWithinAt_Ici, NumberField.mixedEmbedding.fundamentalCone.normLeOne_eq_preimage, CompactlySupportedContinuousMap.nnrealPart_sub_nnrealPart_neg, ContMDiffWithinAt.inner_bundle, ProbabilityTheory.HasGaussianLaw.charFunDual_map_eq, PartitionOfUnity.sum_finsupport', boundary_Icc, properSpace_iff_isProperMap_dist, BohrMollerup.tendsto_logGammaSeq_of_le_one, tendsto_norm_sub_self_nhdsGE, HasProd.norm, deriv_sqrt_mul_log', differentiableAt_binEntropy_iff_ne_zero_one, MeasureTheory.tendsto_integral_meas_thickening_le, SchwartzMap.integrable_pow_mul_iteratedFDeriv, fderiv_fourierChar_neg_bilinear_left_apply, deriv_tan, CircleDeg1Lift.dist_map_zero_lt_of_semiconjBy, tendsto_one_add_div_rpow_exp, tendsto_log_mul_self_nhdsLT_zero, GenLoop.fromLoop_coe, OrthogonalFamily.summable_iff_norm_sq_summable, exists_measure_rpow_eq_integral, summable_partition, tendsto_indicator_thickening_indicator_closure, fourierIntegral_continuousMultilinearMap_apply', BoundedContinuousFunction.self_eq_nnrealPart_sub_nnrealPart_neg, Seminorm.uniformContinuous_of_forall', StieltjesFunction.right_continuous, IsPicardLindelof.exists_eq_forall_mem_Icc_hasDerivWithinAt₀, MeasureTheory.charFunDual_eq_prod_iff', ProbabilityTheory.integrable_comp_iff, Subgroup.IsArithmetic.discreteTopology, closure_lowerClosure_comm_pi, intervalIntegrable_log_sin, DiffeologicalSpace.CorePlotsOn.isPlotOn_univ, EuclideanSpace.volume_closedBall, NumberField.mixedEmbedding.integral_comp_polarCoordReal_symm, intervalIntegrable_inv_iff, BumpCovering.sum_toPOUFun_eq, NumberField.mixedEmbedding.fundamentalCone.compactSet_eq_union, GenLoop.homotopicTo, tendsto_exp_atBot_nhdsGT, hasStrictDerivAt_exp, Quaternion.continuous_normSq, ProbabilityTheory.stronglyMeasurable_exponentialPDFReal, Quaternion.continuous_re, InformationTheory.deriv_klFun, one_add_rpow_hasFPowerSeriesOnBall_zero, boundary_product, Manifold.exists_lt_locally_constant_of_riemannianEDist_lt, differentiable_sigmoid, ProbabilityTheory.tendsto_cdf_atBot, integral_comp_pi_polarCoord_symm, tendsto_harmonic_sub_log_add_one, ZetaAsymptotics.tendsto_riemannZeta_sub_one_div_nhds_right, NumberField.mixedEmbedding.normAtPlace_mixedSpaceOfRealSpace, BumpCovering.coe_single, MeasureTheory.summable_measure_toReal, summable_nat_rpow, GenLoop.continuous_toLoop, polarCoord_source, NumberField.mixedEmbedding.measurable_polarSpaceCoord_symm, LindemannWeierstrass.hasDerivAt_cexp_mul_sumIDeriv, ConvexOn.real_sSup_affine_eq, RCLike.re_extendTo𝕜'ₗ, MeasureTheory.Measure.toSignedMeasure_restrict_sub, ProbabilityTheory.tendsto_condCDF_atTop, one_div_sub_sq_hasFPowerSeriesOnBall_zero, Complex.continuousAt_ofReal_cpow_const, summable_exp_nat_mul_iff, tendsto_logb_nhdsNE_zero, GenLoop.fromLoop_trans_toLoop, ProbabilityTheory.uncenteredCovarianceBilinDual_zero, MeasureTheory.memLp_re_im_iff, ContinuousMapZero.toNNReal_apply, Metric.uniformContinuous_infDist_pt, continuous_circleMap_inv, integrableOn_Ioi_deriv_norm_ofReal_cpow, ProbabilityTheory.exponentialCDFReal_eq_lintegral, Path.extend_trans_of_half_le, ProbabilityTheory.stronglyMeasurable_condVar, fromBinary_continuous, integrable_of_le_of_pow_mul_le, ProbabilityTheory.IsMeasurableRatCDF.stieltjesFunction_nonneg, ProbabilityTheory.cdf_gammaMeasure_eq_integral, RCLike.re_tsum, exists_seq_rat_strictMono_tendsto, NumberField.mixedEmbedding.fundamentalCone.injective_expMap, Path.refl_extend, summable_prod_of_nonneg, not_differentiableAt_abs_zero, MonotoneOn.ae_differentiableWithinAt, interior_euclideanQuadrant, hasDerivWithinAt_iff_tendsto, intervalIntegral.intervalIntegrable_log', SpectrumRestricts.nnreal_iff_nnnorm, CircleDeg1Lift.tendsto_translation_number₀', ZMod.toCircle_eq_circleExp, MeasureTheory.SignedMeasure.toJordanDecomposition_smul, ProbabilityTheory.mgf_pos_iff, NumberField.mixedEmbedding.fundamentalCone.expMap_basis_of_ne, curveIntegralFun_def, Circle.exp_nsmul, BarrelledSpace.continuous_of_lowerSemicontinuous, Seminorm.continuousAt_zero, Complex.im_tsum, coeFn_fourierLp, Differentiable.norm, Path.truncate_range, SchwartzMap.smulLeftCLM_smul, Int.preimage_closedBall, ENNReal.tsum_toReal_eq, NNReal.map_coe_nhdsGE, Quaternion.exp_coe, NumberField.mixedEmbedding.disjoint_negAt_plusPart, ContinuousMap.Homotopy.map_zero_left, unitInterval.continuous_symm, hasSum_log_sub_log_of_abs_lt_one, NonUnitalStarAlgHom.continuous_realContinuousMapZeroOfNNReal, DifferentiableAt.dist, IccLeftChart_extend_bot_mem_frontier, fderiv_norm_sq_apply, LipschitzWith.ae_differentiableAt_real, RCLike.imCLM_apply, ProbabilityTheory.Kernel.tendsto_density_fst_atTop_ae_of_monotone, ConcaveOn.locallyLipschitzOn_iff_continuousOn, NNRat.instContinuousSMulRatReal, Icc_isBoundaryPoint_top, summable_one_div_int_add_rpow, ProbabilityTheory.ofReal_cdf, uniqueDiffOn_Ici, Quaternion.exp_eq, isClosedMap_dist, CompactlySupportedContinuousMap.exists_add_nnrealPart_add_eq, LSeries_tendsto_sub_mul_nhds_one_of_tendsto_sum_div, continuous_mulExpNegMulSq, tendsto_atTop_csInf_of_antitoneOn_bddBelow_nat_Ici, fderiv_norm_sq, Complex.continuous_im, LightProfinite.isClosedEmbedding_natUnionInftyEmbedding, Complex.equivRealProdCLM_apply, AkraBazziRecurrence.isEquivalent_deriv_rpow_p_mul_one_sub_smoothingFn, ConvexOn.continuousOn, integrableOn_rpowIntegrand₀₁_Ici, hasSum_L_function_mod_four_eval_three, MDifferentiable.inner_bundle, ProbabilityTheory.IsMeasurableRatCDF.tendsto_stieltjesFunction_atBot, Complex.tendsto_tsum_powerSeries_nhdsWithin_lt, hasDerivWithinAt_arcsin_Iic, hasDerivAt_abs_pos, NumberField.mixedEmbedding.fundamentalCone.expMap_single_target, dist_left_le_of_mem_uIcc, MeasureTheory.L1.SimpleFunc.setToL1S_smul_left, tendsto_mulExpNegMulSq, continuous_sigmoid, IsMIntegralCurveAt.eventually_hasDerivAt, NumberField.mixedEmbedding.fundamentalCone.expMapBasis_nonneg, hasSum_geometric_of_lt_one, summable_geometric_two_encode, Path.eqOn_extend_segment, HasCompactSupport.hasFDerivAt_convolution_left, instIsManifoldIcc, Bundle.ContinuousRiemannianMetric.isVonNBounded, MeasureTheory.integrable_rnDeriv_mul_log_iff, PartitionOfUnity.sum_finsupport, TemperedDistribution.smulLeftCLM_apply_apply, MeasureTheory.hasFiniteIntegral_count_iff, integrableAtFilter_rpow_atTop_iff, AddCircle.ergodic_zsmul_add, BohrMollerup.tendsto_log_gamma, RCLike.restrict_toContinuousMap_eq_toContinuousMapStar_restrict, HurwitzKernelBounds.summable_f_int, Complex.continuousOn_one_add_mul_inv, MeasureTheory.ProbabilityMeasure.tendsto_iff_forall_integral_tendsto, tendsto_one_add_div_pow_exp, ProbabilityTheory.IsMeasurableRatCDF.tendsto_atTop_one, tendsto_pow_mul_exp_neg_atTop_nhds_zero, SmoothBumpCovering.toSmoothPartitionOfUnity_zero_of_zero, dist_anti_left_pi, GenLoop.instContinuousEvalConst, deriv2_sqrt_mul_log, SmoothPartitionOfUnity.contMDiff_sum, CompletelyRegularSpace.completely_regular_isOpen, hasStrictDerivAt_log_of_pos, MeasureTheory.Measure.zero_le_toSignedMeasure, DeltaGeneratedSpace.continuous_iff, Hyperreal.isSt_ofSeq_iff_tendsto, sinhHomeomorph_apply, contMDiffOn_projIcc, diam_Icc, MeasureTheory.SignedMeasure.im_toComplexMeasure, NumberField.mixedEmbedding.fundamentalCone.logMap_normAtAllPlaces, DiffeologicalSpace.isOpen_iff_preimages_plots, ContDiffBump.continuous_normed, NumberField.mixedEmbedding.fundamentalCone.normAtAllPlaces_normLeOne, ProbabilityTheory.IsCondKernelCDF.toKernel_apply, Metric.exists_contMDiffMap_forall_closedEBall_subset, signedDist_vadd_vadd, UniformSpace.Completion.continuous_dist, contMDiff_circleExp, ProbabilityTheory.instIsProbabilityMeasurecdf, Stirling.tendsto_self_div_two_mul_self_add_one, BoundedContinuousFunction.probCharDual_apply, deriv2_negMulLog, SchwartzMap.tsum_eq_tsum_fourier, NumberField.mixedEmbedding.normAtAllPlaces_normAtAllPlaces, ZLattice.exists_finsetSum_norm_rpow_le_tsum, Stirling.stirlingSeq_has_pos_limit_a, MeasureTheory.Measure.integrable_pow_neg_integrablePower, Rat.uniformContinuous_coe_real, GromovHausdorff.HD_below_aux1, Cardinal.summable_cantor_function, lp.tsum_mul_le_mul_norm, bernsteinApproximation.apply, MeasureTheory.SignedMeasure.rnDeriv_add, tendsto_Icc_vitaliFamily_right, HurwitzZeta.hasSum_int_evenKernel₀, tendsto_iff_norm_sub_tendsto_zero, integrableOn_rpow_mul_exp_neg_mul_rpow, MeasureTheory.Measure.integrable_toReal_rnDeriv, isEquivalent_sinh, ContinuousMap.Homotopy.curry_zero, Orthonormal.tsum_inner_products_le, differentiable_circleMap, BumpCovering.support_toPartitionOfUnity_subset, Metric.PiNatEmbed.exists_embedding_to_hilbert_cube, summable_indicator_mod_iff, MeasureTheory.Integrable.im, polynomialFunctions.comap_compRightAlgHom_iccHomeoI, tendsto_rpow_atBot_of_base_gt_one, instTietzeExtension, ProbabilityTheory.indepFun_iff_charFunDual_prod, ProbabilityTheory.IsGaussian.exists_integrable_exp_sq, continuous_iff_continuous_dist, continuousOn_tan_Ioo, ProbabilityTheory.integrable_stieltjesOfMeasurableRat, Complex.restrictScalars_toSpanSingleton', differentiableAt_negMulLog_iff, Polynomial.fourierCoeff_toAddCircle_eq_zero_of_lt_zero, BoundedContinuousFunction.integrable_of_nnreal, NumberField.mixedEmbedding.mixedSpaceOfRealSpace_apply, NumberField.mixedEmbedding.fundamentalCone.closure_paramSet_ae_interior, IsLocalMinOn.fderivWithin_eq_zero, deriv2_mul_log, ProbabilityTheory.analyticOnNhd_iteratedDeriv_mgf, MeasureTheory.SignedMeasure.rnDeriv_sub, Complex.reCLM_apply, PartitionOfUnity.mem_finsupport, hasDerivAt_negMulLog, NumberField.mixedEmbedding.lintegral_comp_polarSpaceCoord_symm, BoundedContinuousFunction.exists_extension_norm_eq_of_isClosedEmbedding', unitInterval.instConnectedSpaceElemReal, tendsto_logb_nat_add_one_sub_logb, fourierCoeff_fourier, Asymptotics.superpolynomialDecay_iff_superpolynomialDecay_norm, Affine.Simplex.signedInfDist_incenter, ProbabilityTheory.Kernel.stronglyAdapted_densityProcess, Urysohns.CU.tendsto_approx_atTop, IsCoveringMap.liftPath_trans, ProbabilityTheory.Kernel.tendsto_densityProcess_atTop_of_antitone, StieltjesFunction.right_continuous', isSimplyConnected_iff_exists_homotopy_refl_forall_mem, UpperHalfPlane.continuous_re

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
Icc_eq_closedBall 📖	mathematical	—	Set.Icc Real instPreorder Metric.closedBall pseudoMetricSpace DivInvMonoid.toDiv instDivInvMonoid instAdd instOfNatAtLeastTwo instNatCast Nat.instAtLeastTwoHAddOfNat instSub	—	Nat.instAtLeastTwoHAddOfNat closedBall_eq_Icc sub_div add_comm sub_add add_sub_cancel_left add_self_div_two ZeroLEOneClass.neZero.two instZeroLEOneClass NeZero.charZero_one IsStrictOrderedRing.toCharZero instIsStrictOrderedRing IsOrderedAddMonoid.toAddLeftMono instIsOrderedAddMonoid add_div add_assoc add_sub_cancel
Ioo_eq_ball 📖	mathematical	—	Set.Ioo Real instPreorder Metric.ball pseudoMetricSpace DivInvMonoid.toDiv instDivInvMonoid instAdd instOfNatAtLeastTwo instNatCast Nat.instAtLeastTwoHAddOfNat instSub	—	Nat.instAtLeastTwoHAddOfNat ball_eq_Ioo sub_div add_comm sub_add add_sub_cancel_left add_self_div_two ZeroLEOneClass.neZero.two instZeroLEOneClass NeZero.charZero_one IsStrictOrderedRing.toCharZero instIsStrictOrderedRing IsOrderedAddMonoid.toAddLeftMono instIsOrderedAddMonoid add_div add_assoc add_sub_cancel
ball_eq_Ioo 📖	mathematical	—	Metric.ball Real pseudoMetricSpace Set.Ioo instPreorder instSub instAdd	—	Set.ext Metric.mem_ball dist_comm dist_eq abs_sub_lt_iff instIsOrderedAddMonoid Set.mem_Ioo sub_lt_iff_lt_add' IsLeftCancelAdd.addLeftStrictMono_of_addLeftMono AddLeftCancelSemigroup.toIsLeftCancelAdd IsOrderedAddMonoid.toAddLeftMono sub_lt_comm
ball_zero_eq_Ioo 📖	mathematical	—	Metric.ball Real pseudoMetricSpace instZero Set.Ioo instPreorder instNeg	—	ball_eq_Ioo zero_sub zero_add
closedBall_eq_Icc 📖	mathematical	—	Metric.closedBall Real pseudoMetricSpace Set.Icc instPreorder instSub instAdd	—	Set.ext Metric.mem_closedBall dist_comm dist_eq abs_sub_le_iff instIsOrderedAddMonoid Set.mem_Icc sub_le_iff_le_add' IsOrderedAddMonoid.toAddLeftMono sub_le_comm
closedBall_zero_eq_Icc 📖	mathematical	—	Metric.closedBall Real pseudoMetricSpace instZero Set.Icc instPreorder instNeg	—	closedBall_eq_Icc zero_sub zero_add
dist_0_eq_abs 📖	mathematical	—	Dist.dist Real PseudoMetricSpace.toDist pseudoMetricSpace instZero abs lattice instAddGroup	—	sub_zero
dist_eq 📖	mathematical	—	Dist.dist Real PseudoMetricSpace.toDist pseudoMetricSpace abs lattice instAddGroup instSub	—	—
nndist_eq 📖	mathematical	—	NNDist.nndist Real PseudoMetricSpace.toNNDist pseudoMetricSpace DFunLike.coe MonoidWithZeroHom NNReal NonAssocSemiring.toMulZeroOneClass Semiring.toNonAssocSemiring semiring instSemiringNNReal MonoidWithZeroHom.funLike nnabs instSub	—	—
nndist_eq' 📖	mathematical	—	NNDist.nndist Real PseudoMetricSpace.toNNDist pseudoMetricSpace DFunLike.coe MonoidWithZeroHom NNReal NonAssocSemiring.toMulZeroOneClass Semiring.toNonAssocSemiring semiring instSemiringNNReal MonoidWithZeroHom.funLike nnabs instSub	—	nndist_comm
sub_le_dist 📖	mathematical	—	Real instLE instSub Dist.dist PseudoMetricSpace.toDist pseudoMetricSpace	—	dist_eq le_abs le_refl

UniformSpace

Definitions

Name	Category	Theorems
ofDist 📖	CompOp	1 math math: Metric.toUniformSpace_eq

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
ofDist_aux 📖	mathematical	Real Real.instLT Real.instZero	Real.instAdd	—	Nat.instAtLeastTwoHAddOfNat half_pos PosMulReflectLE.toPosMulReflectLT PosMulStrictMono.toPosMulReflectLE IsStrictOrderedRing.toPosMulStrictMono Real.instIsStrictOrderedRing add_lt_add IsLeftCancelAdd.addLeftStrictMono_of_addLeftMono AddLeftCancelSemigroup.toIsLeftCancelAdd IsOrderedAddMonoid.toAddLeftMono Real.instIsOrderedAddMonoid IsRightCancelAdd.addRightStrictMono_of_addRightMono AddRightCancelSemigroup.toIsRightCancelAdd covariant_swap_add_of_covariant_add add_halves ZeroLEOneClass.neZero.two Real.instZeroLEOneClass NeZero.charZero_one IsStrictOrderedRing.toCharZero

(root)

Definitions

Name	Category	Theorems
NNDist 📖	CompData	—
PseudoMetricSpace 📖	CompData	1 math math: WithAbs.pseudoMetricSpace_induced_of_comp
instPseudoMetricSpaceAdditive 📖	CompOp	4 math math: nndist_ofMul, nndist_toMul, instProperSpaceAdditive, instLipschitzAddAdditiveOfLipschitzMul
instPseudoMetricSpaceMultiplicative 📖	CompOp	4 math math: nndist_ofAdd, instLipschitzMulMultiplicativeOfLipschitzAdd, instProperSpaceMultiplicative, nndist_toAdd
instPseudoMetricSpaceOrderDual 📖	CompOp	5 math math: nndist_toDual, instLipschitzAddOrderDual, instLipschitzMulOrderDual, instProperSpaceOrderDual, nndist_ofDual

Theorems

Name	Kind	Assumes	Proves	Validates	Depends On
abs_dist 📖	mathematical	—	abs Real Real.lattice Real.instAddGroup Dist.dist PseudoMetricSpace.toDist	—	abs_of_nonneg IsOrderedAddMonoid.toAddLeftMono Real.instIsOrderedAddMonoid dist_nonneg
abs_dist_sub_le 📖	mathematical	—	Real Real.instLE abs Real.lattice Real.instAddGroup Real.instSub Dist.dist PseudoMetricSpace.toDist	—	abs_sub_le_iff Real.instIsOrderedAddMonoid sub_le_iff_le_add covariant_swap_add_of_covariant_add IsOrderedAddMonoid.toAddLeftMono dist_triangle dist_triangle_left
coe_nndist 📖	mathematical	—	NNReal.toReal NNDist.nndist PseudoMetricSpace.toNNDist Dist.dist PseudoMetricSpace.toDist	—	—
coe_nnreal_ennreal_nndist 📖	mathematical	—	ENNReal.ofNNReal NNDist.nndist PseudoMetricSpace.toNNDist EDist.edist PseudoMetricSpace.toEDist	—	edist_nndist
dist_comm 📖	mathematical	—	Dist.dist PseudoMetricSpace.toDist	—	PseudoMetricSpace.dist_comm
dist_dist_dist_le 📖	mathematical	—	Real Real.instLE Dist.dist PseudoMetricSpace.toDist Real.pseudoMetricSpace Real.instAdd	—	LE.le.trans dist_triangle add_le_add IsOrderedAddMonoid.toAddLeftMono Real.instIsOrderedAddMonoid covariant_swap_add_of_covariant_add dist_dist_dist_le_left dist_dist_dist_le_right
dist_dist_dist_le_left 📖	mathematical	—	Real Real.instLE Dist.dist PseudoMetricSpace.toDist Real.pseudoMetricSpace	—	abs_dist_sub_le
dist_dist_dist_le_right 📖	mathematical	—	Real Real.instLE Dist.dist PseudoMetricSpace.toDist Real.pseudoMetricSpace	—	dist_comm dist_dist_dist_le_left
dist_edist 📖	mathematical	—	Dist.dist PseudoMetricSpace.toDist ENNReal.toReal EDist.edist PseudoMetricSpace.toEDist	—	edist_dist ENNReal.toReal_ofReal dist_nonneg
dist_le_coe 📖	mathematical	—	Real Real.instLE Dist.dist PseudoMetricSpace.toDist NNReal.toReal NNReal Preorder.toLE PartialOrder.toPreorder instPartialOrderNNReal NNDist.nndist PseudoMetricSpace.toNNDist	—	—
dist_lt_coe 📖	mathematical	—	Real Real.instLT Dist.dist PseudoMetricSpace.toDist NNReal.toReal NNReal Preorder.toLT PartialOrder.toPreorder instPartialOrderNNReal NNDist.nndist PseudoMetricSpace.toNNDist	—	—
dist_nndist 📖	mathematical	—	Dist.dist PseudoMetricSpace.toDist NNReal.toReal NNDist.nndist PseudoMetricSpace.toNNDist	—	—
dist_nonneg 📖	mathematical	—	Real Real.instLE Real.instZero Dist.dist PseudoMetricSpace.toDist	—	dist_self dist_comm dist_triangle
dist_self 📖	mathematical	—	Dist.dist PseudoMetricSpace.toDist Real Real.instZero	—	PseudoMetricSpace.dist_self
dist_triangle 📖	mathematical	—	Real Real.instLE Dist.dist PseudoMetricSpace.toDist Real.instAdd	—	PseudoMetricSpace.dist_triangle
dist_triangle4 📖	mathematical	—	Real Real.instLE Dist.dist PseudoMetricSpace.toDist Real.instAdd	—	dist_triangle add_le_add_left covariant_swap_add_of_covariant_add IsOrderedAddMonoid.toAddLeftMono Real.instIsOrderedAddMonoid
dist_triangle4_left 📖	mathematical	—	Real Real.instLE Dist.dist PseudoMetricSpace.toDist Real.instAdd	—	add_left_comm dist_comm add_assoc dist_triangle4
dist_triangle4_right 📖	mathematical	—	Real Real.instLE Dist.dist PseudoMetricSpace.toDist Real.instAdd	—	add_right_comm dist_comm dist_triangle4
dist_triangle8 📖	mathematical	—	Real Real.instLE Dist.dist PseudoMetricSpace.toDist Real.instAdd	—	le_trans dist_triangle4 add_le_add_left covariant_swap_add_of_covariant_add IsOrderedAddMonoid.toAddLeftMono Real.instIsOrderedAddMonoid
dist_triangle_left 📖	mathematical	—	Real Real.instLE Dist.dist PseudoMetricSpace.toDist Real.instAdd	—	dist_comm dist_triangle
dist_triangle_right 📖	mathematical	—	Real Real.instLE Dist.dist PseudoMetricSpace.toDist Real.instAdd	—	dist_comm dist_triangle
edist_dist 📖	mathematical	—	EDist.edist PseudoMetricSpace.toEDist ENNReal.ofReal Dist.dist PseudoMetricSpace.toDist	—	PseudoMetricSpace.edist_dist
edist_le_coe 📖	mathematical	—	ENNReal Preorder.toLE PartialOrder.toPreorder ENNReal.instPartialOrder EDist.edist PseudoMetricSpace.toEDist ENNReal.ofNNReal NNReal instPartialOrderNNReal NNDist.nndist PseudoMetricSpace.toNNDist	—	edist_nndist ENNReal.coe_le_coe
edist_le_ofReal 📖	mathematical	Real Real.instLE Real.instZero	ENNReal Preorder.toLE PartialOrder.toPreorder ENNReal.instPartialOrder EDist.edist PseudoMetricSpace.toEDist ENNReal.ofReal Dist.dist PseudoMetricSpace.toDist	—	edist_dist ENNReal.ofReal_le_ofReal_iff
edist_lt_coe 📖	mathematical	—	ENNReal Preorder.toLT PartialOrder.toPreorder ENNReal.instPartialOrder EDist.edist PseudoMetricSpace.toEDist ENNReal.ofNNReal NNReal instPartialOrderNNReal NNDist.nndist PseudoMetricSpace.toNNDist	—	edist_nndist ENNReal.coe_lt_coe
edist_lt_ofReal 📖	mathematical	—	ENNReal Preorder.toLT PartialOrder.toPreorder ENNReal.instPartialOrder EDist.edist PseudoMetricSpace.toEDist ENNReal.ofReal Real Real.instLT Dist.dist PseudoMetricSpace.toDist	—	edist_dist ENNReal.ofReal_lt_ofReal_iff_of_nonneg dist_nonneg
edist_lt_top 📖	mathematical	—	ENNReal Preorder.toLT PartialOrder.toPreorder ENNReal.instPartialOrder EDist.edist PseudoMetricSpace.toEDist Top.top instTopENNReal	—	ENNReal.ofReal_lt_top edist_dist
edist_ne_top 📖	—	—	—	—	LT.lt.ne edist_lt_top
edist_nndist 📖	mathematical	—	EDist.edist PseudoMetricSpace.toEDist ENNReal.ofNNReal NNDist.nndist PseudoMetricSpace.toNNDist	—	edist_dist dist_nndist ENNReal.ofReal_coe_nnreal
nhds_comap_dist 📖	mathematical	—	Filter.comap Real Dist.dist PseudoMetricSpace.toDist nhds UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace Real.pseudoMetricSpace Real.instZero	—	dist_comm nhds_eq_comap_uniformity Metric.uniformity_eq_comap_nhds_zero Filter.comap_comap
nndist_comm 📖	mathematical	—	NNDist.nndist PseudoMetricSpace.toNNDist	—	NNReal.eq dist_comm
nndist_dist 📖	mathematical	—	NNDist.nndist PseudoMetricSpace.toNNDist Real.toNNReal Dist.dist PseudoMetricSpace.toDist	—	dist_nndist Real.toNNReal_coe
nndist_edist 📖	mathematical	—	NNDist.nndist PseudoMetricSpace.toNNDist ENNReal.toNNReal EDist.edist PseudoMetricSpace.toEDist	—	edist_nndist
nndist_ofAdd 📖	mathematical	—	NNDist.nndist Multiplicative PseudoMetricSpace.toNNDist instPseudoMetricSpaceMultiplicative DFunLike.coe Equiv EquivLike.toFunLike Equiv.instEquivLike Multiplicative.ofAdd	—	—
nndist_ofDual 📖	mathematical	—	NNDist.nndist PseudoMetricSpace.toNNDist DFunLike.coe Equiv OrderDual EquivLike.toFunLike Equiv.instEquivLike OrderDual.ofDual instPseudoMetricSpaceOrderDual	—	—
nndist_ofMul 📖	mathematical	—	NNDist.nndist Additive PseudoMetricSpace.toNNDist instPseudoMetricSpaceAdditive DFunLike.coe Equiv EquivLike.toFunLike Equiv.instEquivLike Additive.ofMul	—	—
nndist_self 📖	mathematical	—	NNDist.nndist PseudoMetricSpace.toNNDist NNReal instZeroNNReal	—	NNReal.coe_eq_zero dist_self
nndist_toAdd 📖	mathematical	—	NNDist.nndist PseudoMetricSpace.toNNDist DFunLike.coe Equiv Multiplicative EquivLike.toFunLike Equiv.instEquivLike Multiplicative.toAdd instPseudoMetricSpaceMultiplicative	—	—
nndist_toDual 📖	mathematical	—	NNDist.nndist OrderDual PseudoMetricSpace.toNNDist instPseudoMetricSpaceOrderDual DFunLike.coe Equiv EquivLike.toFunLike Equiv.instEquivLike OrderDual.toDual	—	—
nndist_toMul 📖	mathematical	—	NNDist.nndist PseudoMetricSpace.toNNDist DFunLike.coe Equiv Additive EquivLike.toFunLike Equiv.instEquivLike Additive.toMul instPseudoMetricSpaceAdditive	—	—
nndist_triangle 📖	mathematical	—	NNReal Preorder.toLE PartialOrder.toPreorder instPartialOrderNNReal NNDist.nndist PseudoMetricSpace.toNNDist Distrib.toAdd NonUnitalNonAssocSemiring.toDistrib NonAssocSemiring.toNonUnitalNonAssocSemiring Semiring.toNonAssocSemiring instSemiringNNReal	—	dist_triangle
nndist_triangle_left 📖	mathematical	—	NNReal Preorder.toLE PartialOrder.toPreorder instPartialOrderNNReal NNDist.nndist PseudoMetricSpace.toNNDist Distrib.toAdd NonUnitalNonAssocSemiring.toDistrib NonAssocSemiring.toNonUnitalNonAssocSemiring Semiring.toNonAssocSemiring instSemiringNNReal	—	dist_triangle_left
nndist_triangle_right 📖	mathematical	—	NNReal Preorder.toLE PartialOrder.toPreorder instPartialOrderNNReal NNDist.nndist PseudoMetricSpace.toNNDist Distrib.toAdd NonUnitalNonAssocSemiring.toDistrib NonAssocSemiring.toNonUnitalNonAssocSemiring Semiring.toNonAssocSemiring instSemiringNNReal	—	dist_triangle_right
swap_dist 📖	mathematical	—	Function.swap Real Dist.dist PseudoMetricSpace.toDist	—	dist_comm
tendsto_iff_dist_tendsto_zero 📖	mathematical	—	Filter.Tendsto nhds UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace Real Dist.dist PseudoMetricSpace.toDist Real.pseudoMetricSpace Real.instZero	—	nhds_comap_dist Filter.tendsto_comap_iff
tendsto_iff_of_dist 📖	—	Filter.Tendsto Real Dist.dist PseudoMetricSpace.toDist nhds UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace Real.pseudoMetricSpace Real.instZero	—	—	Uniform.tendsto_congr tendsto_uniformity_iff_dist_tendsto_zero
tendsto_of_tendsto_of_dist 📖	—	Filter.Tendsto nhds UniformSpace.toTopologicalSpace PseudoMetricSpace.toUniformSpace Real Dist.dist PseudoMetricSpace.toDist Real.pseudoMetricSpace Real.instZero	—	—	Filter.Tendsto.congr_dist
tendsto_uniformity_iff_dist_tendsto_zero 📖	mathematical	—	Filter.Tendsto uniformity PseudoMetricSpace.toUniformSpace Real Dist.dist PseudoMetricSpace.toDist nhds UniformSpace.toTopologicalSpace Real.pseudoMetricSpace Real.instZero	—	Metric.uniformity_eq_comap_nhds_zero Filter.tendsto_comap_iff

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