toPseudoMetricSpace 📖 | CompOp | 1010 mathmath: Affine.Simplex.isTangentAt_insphere_iff_eq_touchpoint, closure_diff_intrinsicFrontier, integrableOn_cfcₙ', cfcₙ_def, EuclideanGeometry.dist_smul_vadd_sq, GromovHausdorff.hausdorffDist_optimal, EuclideanGeometry.subset_sphere, EuclideanGeometry.sin_oangle_right_mul_dist_of_oangle_eq_pi_div_two, continuous_cfcₙHomSuperset_left, cfcₙL_integral, AffineIsometry.image_intrinsicClosure, norm_cfcₙHom, IsStarNormal.instNonUnitalContinuousFunctionalCalculus, Affine.Simplex.orthogonalProjectionSpan_map, EuclideanGeometry.vsub_orthogonalProjection_mem_direction_orthogonal, IsSelfAdjoint.commute_cfcHom, cfcₙ_norm_nonneg, ContinuousWithinAt.cfcₙ, NonUnitalIsometricContinuousFunctionalCalculus.isometric, Isometry.preimage_perpBisector, cfcₙHom_apply_mem_elemental, Affine.Simplex.ExcenterExists.excenter_notMem_affineSpan_face, Affine.Simplex.smul_mongePoint_vsub_circumcenter_eq_sum_vsub, CFC.abs_eq_cfc_norm, inner_vsub_right_eq_zero_symm, Affine.Simplex.sSameSide_excenter_singleton_point, CFC.sqrt_eq_one_iff', Filter.Tendsto.cfc, CFC.posPart_one, Affine.Simplex.neg_mul_lt_inner_vsub_altitudeFoot, EuclideanGeometry.Sphere.isExtTangent_iff_dist_center, EuclideanGeometry.sin_oangle_right_of_oangle_eq_pi_div_two, nnnorm_cfcₙ_nnreal_le_iff, ContractingWith.dist_fixedPoint_le, nnnorm_cfc_lt, EuclideanGeometry.Sphere.isDiameter_iff_right_mem_and_midpoint_eq_center, Matrix.IsHermitian.det_abs, EuclideanGeometry.dist_inversion_inversion, Affine.Simplex.finiteDimensional_direction_altitude, NormedAddGroup.dist_eq, AffineSubspace.mem_perpBisector_iff_inner_eq_zero', CFC.posPart_natCast, Affine.Simplex.circumcenter_map, CFC.tendsto_cfc_rpow_sub_one_log, EuclideanGeometry.dist_eq_of_angle_eq_angle_of_angle_ne_pi, Matrix.IsHermitian.cfc_eq, UpperHalfPlane.image_coe_sphere, Affine.Simplex.inv_height_eq_sum_mul_inv_dist, CFC.sq_sqrt, Affine.Simplex.ExcenterExists.excenter_notMem_affineSpan_faceOpposite, EuclideanGeometry.Cospherical.affineIndependent_of_mem_of_ne, Metric.PiNatEmbed.continuous_distDenseSeq_inv, Rat.continuous_coe_real, Int.instProperSpace, AffineSpace.cobounded_eq_iSup_sphere_asymptoticNhds, Affine.Simplex.circumcenter_mem_affineSpan, Affine.Simplex.affineSpan_pair_altitudeFoot_eq_altitude, integrableOn_cfc', Affine.Simplex.excenter_singleton_mem_affineSpan_range, EuclideanGeometry.law_sin, not_bounded_iff_exists_ne_zero_mem_asymptoticCone, ODE.FunSpace.isUniformInducing_toContinuousMap, unique_topology_of_t2, ContinuousFunctionalCalculus.compactSpace_spectrum, EuclideanGeometry.orthogonalProjection_congr, Unitization.real_cfcₙ_eq_cfc_inr, norm_cfc_lt_iff, EuclideanGeometry.dist_div_tan_oangle_right_of_oangle_eq_pi_div_two, Affine.Simplex.dist_point_faceOppositeCentroid, EuclideanGeometry.Sphere.secondInter_dist, EuclideanGeometry.Sphere.IsExtTangent.dist_center, CFC.abs_eq_cfcₙ_coe_norm, EuclideanGeometry.Sphere.mem_orthRadius_iff_inner_right, Affine.Simplex.incenter_map, AffineSubspace.left_mem_perpBisector, nnnorm_cfcₙ_lt_iff, EuclideanGeometry.preimage_inversion_perpBisector_inversion, Affine.Triangle.sSameSide_affineSpan_pair_point_incenter, CFC.nnnorm_sqrt, Tactic.ComputeAsymptotics.Seq.dist_cons_nil, ContinuousMap.isUltrametricDist, Int.isUniformEmbedding_coe_rat, nndist_eq_zero, Metric.sphere_zero, Isometry.coe_affineIsometryOfStrictConvexSpace, LipschitzWith.completion_extension, ContinuousOn.cfcₙ', Besicovitch.ae_tendsto_measure_inter_div_of_measurableSet, TopologicalSpace.Opens.CompleteCopy.dist_eq, Affine.Triangle.sbtw_touchpoint_singleton, Affine.Triangle.dist_point_faceOppositeCentroid, toIsCompletelyMetrizableSpace, EuclideanGeometry.reflection_symm, Affine.Simplex.mem_circumsphere, IsGreatest.nnnorm_cfcₙ, ContinuousAt.cfc, NNRat.dist_eq, EuclideanGeometry.orthogonalProjection_contLinear, CFC.sqrt_rpow, EuclideanGeometry.inversion_dist_center, Nat.isUniformEmbedding_coe_rat, EuclideanGeometry.Sphere.mem_commonExtTangents_iff, Matrix.PosSemidef.sqrt_eq_zero_iff, EuclideanGeometry.oangle_sign_eq_zero_iff_collinear, EuclideanGeometry.dist_eq_add_dist_iff_angle_eq_pi, Besicovitch.SatelliteConfig.hlast, PNat.dist_eq, EuclideanGeometry.reflection_map, AffineEquiv.continuous_of_finiteDimensional, Affine.Simplex.sign_signedInfDist_lineMap_incenter_touchpoint, EuclideanGeometry.angle_eq_arctan_of_angle_eq_pi_div_two, Affine.Simplex.ExcenterExists.affineCombination_eq_excenter_iff, cfc_complex_eq_real, EuclideanGeometry.Sphere.mem_tangentsFrom_iff, norm_cfc_le_iff, Rat.not_countably_generated_cocompact, Tactic.ComputeAsymptotics.Seq.instBoundedSpaceSeq, EuclideanGeometry.Sphere.IsDiameter.dist_left_right, CFC.negPart_algebraMap, cfcₙHom_nnreal_eq_restrict, Besicovitch.exists_closedBall_covering_tsum_measure_le, Rat.uniformContinuous_neg, Rat.dist_eq, EuclideanGeometry.Sphere.mem_commonTangents_iff, cfcHom_continuous, cfcL_apply, Affine.Simplex.excenterWeightsUnnorm_reindex, IsometryEquiv.midpoint_fixed, ContinuousMapZero.isometry_toContinuousMap, Besicovitch.exist_disjoint_covering_families, cfcHom_nonneg_iff, Continuous.cfc', RCLike.nonUnitalContinuousFunctionalCalculus, EuclideanGeometry.dist_eq_abs_sub_dist_of_angle_eq_zero, cfc_apply_mkD, Rat.borelSpace, Affine.Triangle.orthocenter_eq_smul_vsub_vadd_circumcenter, EuclideanGeometry.inter_eq_singleton_orthogonalProjection, EuclideanGeometry.inversion_mem_perpBisector_inversion_iff', cfcₙ_eq_cfcₙL_mkD, TopologicalSpace.Opens.CompleteCopy.instCompleteSpace, Affine.Simplex.ExcenterExists.touchpoint_map, cfcₙ_integral, EuclideanGeometry.angle_eq_iff_oangle_eq_or_wbtw, signedDist_triangle, Besicovitch.SatelliteConfig.h, cfcₙ_setIntegral, EuclideanGeometry.dist_eq_iff_eq_smul_rotation_pi_div_two_vadd_midpoint, Affine.Simplex.orthogonalProjectionSpan_eq_point, Continuous.cfc_nnreal', EuclideanGeometry.angle_vadd_const, signedDist_linear_apply_apply, EuclideanGeometry.Sphere.isDiameter_iff_right_mem_and_pointReflection_center_right, Affine.Simplex.sSameSide_incenter_point, EuclideanGeometry.collinear_iff_of_two_zsmul_oangle_eq, EuclideanGeometry.oangle_midpoint_right, Affine.Simplex.ExcenterExists.excenter_map, EuclideanGeometry.orthogonalProjection_map, cfcHom_isClosedEmbedding, ODE.FunSpace.dist_next_next, Affine.Simplex.ExcenterExists.touchpoint_notMem_affineSpan_of_ne, Affine.Simplex.abs_inner_vsub_altitudeFoot_div_lt_one, Rat.dist_cast, IsUnit.cfcSqrt, CFC.continuousOn_log, EuclideanGeometry.angle_eq_zero_iff_eq_and_ne_or_sbtw, Affine.Simplex.touchpoint_singleton_mem_interior_faceOpposite, Affine.Simplex.excenterExists_reindex, cfcL_integrable, EuclideanGeometry.Sphere.secondInter_collinear, ContinuousOn.cfc_nnreal', IsGreatest.nnnorm_cfc_nnreal, Rat.isDenseEmbedding_coe_real, EuclideanGeometry.Sphere.dist_div_sin_oangle_div_two_eq_radius, ContinuousFunctionalCalculus.isCompact_spectrum, Affine.Simplex.ninePointCircle_eq_circumsphere_medial, EuclideanGeometry.tan_oangle_right_of_oangle_eq_pi_div_two, signedDist_le_dist, EuclideanGeometry.Sphere.IsTangentAt.mem_space, Affine.Simplex.circumcenter_reindex, cfcₙ_apply_mkD, ContinuousOn.cfc, cfcₙHom_id, EuclideanGeometry.affineSpan_of_orthocentricSystem, AffineSubspace.mem_perpBisector_iff_inner_eq_zero, EuclideanGeometry.inversion_vsub_center, CFC.continuousOn_sqrt, Affine.Simplex.excenter_eq_affineCombination, Affine.Triangle.dist_div_sin_angle_eq_two_mul_circumradius, EuclideanGeometry.oangle_right_eq_arcsin_of_oangle_eq_pi_div_two, WithAbs.uniformSpace_comap_eq_of_comp, EuclideanGeometry.Sphere.nonempty_iff, EuclideanGeometry.Sphere.commonIntTangents_union_commonExtTangents, AffineSubspace.perpBisector_nonempty, signedDist_apply_apply, Affine.Simplex.altitudeFoot_mem_affineSpan_image_compl, EuclideanGeometry.oangle_right_eq_arctan_of_oangle_eq_pi_div_two, NormedAddCommGroup.dist_eq, Affine.Simplex.finrank_direction_altitude, EuclideanGeometry.angle_vsub_const, EuclideanGeometry.Sphere.IsDiameter.wbtw, Metric.measure_closedBall_pos_iff, Affine.Simplex.mongePoint_mem_mongePlane, cfcHom_le_iff, cfcHom_id, Affine.Simplex.isTangentAt_insphere_touchpoint, Affine.Simplex.excenterWeightsUnnorm_map, EuclideanGeometry.Sphere.IsExtTangentAt.wbtw, Matrix.PosSemidef.det_sqrt, Nat.closedBall_eq_Icc, range_cfcₙHom, Affine.Simplex.ExcenterExists.affineSpan_faceOpposite_eq_orthRadius, Affine.Simplex.inner_mongePoint_vsub_face_centroid_vsub, EuclideanGeometry.tan_oangle_left_mul_dist_of_oangle_eq_pi_div_two, Affine.Simplex.ExcenterExists.dist_excenter, norm_cfcₙ_lt, ext_iff, EuclideanGeometry.oangle_eq_pi_iff_sbtw, Commute.cfc_real, Affine.Simplex.circumcenter_eq_affineCombination_of_pointsWithCircumcenter, Affine.Simplex.affineSpan_faceOpposite_eq_orthRadius_insphere, Matrix.IsHermitian.charpoly_cfc_eq, Nat.preimage_closedBall, IsGreatest.norm_cfcₙ, EuclideanGeometry.Sphere.orthRadius_center, nnnorm_cfcₙ_nnreal_lt, CFC.sqrt_eq_rpow, cfcₙ_comp_norm, cfcₙ_neg, zero_eq_dist, ContractingWith.aposteriori_dist_iterate_fixedPoint_le, EuclideanGeometry.orthogonalProjection_apply', Continuous.cfcₙ_of_mem_nhdsSet, EuclideanGeometry.Sphere.coe_secondInter, Rat.not_firstCountableTopology_opc, EuclideanGeometry.dist_sq_eq_dist_sq_add_dist_sq_sub_two_mul_dist_mul_dist_mul_cos_angle, lipschitzOnWith_cfc_fun_of_subset, UpperHalfPlane.image_coe_ball, cfc_real_eq_nnreal, Matrix.PosSemidef.posSemidef_sqrt, EuclideanGeometry.Sphere.power_pos_iff_radius_lt_dist_center, cfcₙHom_integral, Continuous.cfcₙ, continuousOn_cfc_setProd, EuclideanGeometry.oangle_midpoint_rev_left, Affine.Triangle.touchpoint_singleton_sbtw, EuclideanGeometry.Sphere.isTangent_iff_isTangentAt_orthogonalProjection, IsGreatest.norm_cfc, exists_nat_nat_continuous_surjective_of_completeSpace, Affine.Simplex.exradius_map, PNat.instProperSpace, ODE.FunSpace.dist_iterate_iterate_next_le_of_lipschitzWith, EuclideanGeometry.mul_dist_eq_mul_dist_of_cospherical_of_angle_eq_zero, Affine.Triangle.dist_circumcenter_reflection_orthocenter, IsometryEquiv.coe_toRealAffineIsometryEquiv, NormedDivisionRing.dist_eq, Besicovitch.ae_tendsto_rnDeriv, Affine.Simplex.ExcenterExists.sign_signedInfDist_touchpoint, continuousOn_cfcₙ, Affine.Simplex.ExcenterExists.dist_excenter_eq_dist_excenter, Metric.dense_iUnion_range_toInductiveLimit, Affine.Simplex.abs_inner_vsub_altitudeFoot_lt_mul, Affine.Simplex.excenterWeights_reindex, EuclideanGeometry.collinear_of_angle_eq_zero, EuclideanGeometry.Sphere.tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center, dist_le_zero, RCLike.instContinuousMapUniqueHom, Affine.Simplex.ExcenterExists.isTangentAt_touchpoint, Affine.Simplex.inradius_reindex, Tactic.ComputeAsymptotics.Seq.dist_cons_cons_eq_one, EuclideanGeometry.preimage_inversion_perpBisector, CFC.posPart_algebraMap_nnreal, Affine.Simplex.incenter_mem_interior, Affine.Simplex.mongePoint_eq_affineCombination_of_pointsWithCircumcenter, Affine.Simplex.altitudeFoot_map, range_cfcₙ, Matrix.PosSemidef.sqrt_eq_one_iff, NNRat.instContinuousSub, EuclideanGeometry.dist_div_tan_angle_of_angle_eq_pi_div_two, Isometry.mapsTo_perpBisector, EuclideanGeometry.Cospherical.affineIndependent_of_ne, CStarAlgebra.toCompleteSpace, IsGreatest.nnnorm_cfc, Affine.Simplex.circumcenter_eq_point, EuclideanGeometry.dist_eq_add_dist_of_angle_eq_pi, Matrix.PosSemidef.sqrt_sq, ContractingWith.apriori_dist_iterate_fixedPoint_le, Rat.instOrderTopology, UpperHalfPlane.image_coe_closedBall, EuclideanGeometry.oangle_eq_zero_iff_wbtw, Tactic.ComputeAsymptotics.Seq.dist_eq_one_of_head, AffineSubspace.isometryEquivMap.toAffineMap_eq, Rat.cocompact_inf_nhds_neBot, Int.ball_eq_Ioo, instIsBoundedSMulSeparationQuotient, Affine.Simplex.signedInfDist_apply_self, CFC.sqrt_eq_one_iff, NormedCommGroup.dist_eq, Metric.uniformContinuous_infDist_Hausdorff_dist, CStarAlgebra.norm_posPart_le, EuclideanGeometry.Sphere.dist_div_sin_oangle_eq_two_mul_radius, EuclideanGeometry.Sphere.IsDiameter.pointReflection_center_left, AffineIsometry.image_intrinsicInterior, IsGreatest.nnnorm_cfcₙ_nnreal, Matrix.PosSemidef.eq_sqrt_iff_sq_eq, signedDist_zero, AffineSubspace.signedInfDist_eq_signedDist_orthogonalProjection, isometry_cfcₙHom, MeasureTheory.Measure.pi_ball, EuclideanGeometry.reflection_reflection, Affine.Simplex.ExcenterExists.sOppSide_excenter_point_iff, Affine.Simplex.incenter_notMem_affineSpan_face, GromovHausdorff.rep_gHSpace_compactSpace, Besicovitch.exist_finset_disjoint_balls_large_measure, CFC.continuous_abs, Affine.Triangle.affineSpan_pair_eq_orthRadius, continuousOn_cfc_nnreal, cfcHom_integral, EuclideanGeometry.image_inversion_perpBisector, Affine.Simplex.mongePlane_def, Affine.Triangle.acuteAngled_iff_angle_lt, cfcₙHom_predicate, cfc_nnreal_eq_real, nnnorm_apply_le_nnnorm_cfcₙ, RCLike.uniqueNonUnitalContinuousFunctionalCalculus, Besicovitch.exists_disjoint_closedBall_covering_ae_of_finiteMeasure_aux, cfcₙ_real_eq_complex, signedDist_triangle_left, Affine.Simplex.excenterExists_map, isBounded_iff_asymptoticCone_subset_singleton, IsometricContinuousFunctionalCalculus.toNonUnital, Affine.Simplex.vectorSpan_isOrtho_altitude_direction, ContinuousFunctionalCalculus.exists_cfc_of_predicate, Affine.Simplex.exsphere_reindex, Int.dist_cast_rat, EuclideanGeometry.reflection_eq_self_iff, exists_locallyFinite_iUnion_eq_ball_radius_lt, CFC.exp_eq_normedSpace_exp, CFC.abs_natCast, CStarAlgebra.isStrictlyPositive_iff_isStrictlyPositive_sqrt_and_eq_sqrt_mul_sqrt, Affine.Simplex.altitudeFoot_mem_affineSpan, TopologicalSpace.Opens.CompleteCopy.dist_val_le_dist, IsometryEquiv.map_midpoint, integrable_cfcₙ, IsSelfAdjoint.cfc_arg, Affine.Triangle.circumsphere_eq_of_dist_of_oangle, NNRat.instContinuousInv₀, EuclideanGeometry.image_inversion_sphere_dist_center, EuclideanGeometry.orthogonalProjection_subtype, EuclideanGeometry.dist_div_sin_oangle_left_of_oangle_eq_pi_div_two, cfc_def, norm_cfcₙ_lt_iff, GromovHausdorff.ghDist_le_hausdorffDist, Affine.Triangle.sOppSide_affineSpan_pair_excenter_singleton_point, cfcₙ_neg_id, Commute.cfcₙHom, AffineSubspace.closed_of_finiteDimensional, ContractingWith.dist_le_mul, Affine.Simplex.ExcenterExists.sign_signedInfDist_lineMap_excenter_touchpoint, TopologicalSpace.UpgradedIsCompletelyMetrizableSpace.toCompleteSpace, Tactic.ComputeAsymptotics.Seq.dist_cons_cons, EuclideanGeometry.oangle_midpoint_left, PadicInt.completeSpace, lipschitzOnWith_cfc_fun, Affine.Simplex.circumsphere_unique_dist_eq, EuclideanGeometry.dist_center_eq_dist_center_of_mem_sphere', PiNat.boundedSpace, Continuous.cfc_nnreal_of_mem_nhdsSet, IsSelfAdjoint.instNonUnitalContinuousFunctionalCalculus, EuclideanGeometry.preimage_inversion_sphere_dist_center, MeasureTheory.hausdorffMeasure_lineMap_image, Continuous.cfcₙ_nnreal, AffineMap.lipschitzWith_of_finiteDimensional, NNRat.tendsto_inv_atTop_nhds_zero_nat, Affine.Triangle.dist_orthocenter_reflection_circumcenter, signedDist_smul_of_pos, EuclideanGeometry.cospherical_def, Besicovitch.SatelliteConfig.inter', IsometricContinuousFunctionalCalculus.toContinuousFunctionalCalculus, EuclideanGeometry.cos_oangle_left_mul_dist_of_oangle_eq_pi_div_two, Affine.Simplex.exradius_reindex, Affine.Simplex.ninePointCircle_reindex, PNat.dist_coe, signedDist_lineMap_lineMap, NNRat.instContinuousSMulOfIsScalarTowerOfRat, cfcHom_real_eq_restrict, Affine.Triangle.dist_div_sin_oangle_eq_two_mul_circumradius, ContinuousAt.cfcₙ_nnreal, NormedField.dist_eq, Rat.uniformContinuous_add, EuclideanGeometry.Sphere.dist_div_cos_oangle_center_div_two_eq_radius, GromovHausdorff.toGHSpace_continuous, range_cfcₙ_eq_range_cfcₙHom, EuclideanGeometry.dist_eq_abs_sub_dist_iff_angle_eq_zero, SimpleGraph.UnitDistEmbedding.unit_dist, EuclideanGeometry.sin_angle_div_dist_eq_sin_angle_div_dist, signedDist_vadd_left_swap, EuclideanGeometry.Sphere.power_neg_iff_dist_center_lt_radius, ContinuousOn.cfc_nnreal_of_mem_nhdsSet, Metric.subsingleton_sphere, CFC.abs_algebraMap, Tactic.ComputeAsymptotics.Seq.dist_eq_two_inv_pow, Tactic.ComputeAsymptotics.Seq.Stream'.dist_le_one, EuclideanGeometry.OrthocentricSystem.affineIndependent, Affine.Simplex.touchpointWeights_reindex, Affine.Simplex.height_map, RCLike.toCompleteSpace, Affine.Simplex.dist_incenter_eq_dist_incenter, Affine.Simplex.orthogonalProjection_circumcenter, IsStrictlyPositive.nnrpow, exists_nat_bool_continuous_surjective_of_compact, Filter.Tendsto.cfcₙ, Tactic.ComputeAsymptotics.Seq.dist_nil_cons, NonUnitalCommCStarAlgebra.toCompleteSpace, signedDist_vadd_right, PiNat.completeSpace, AffineIsometry.coe_toAffineIsometryEquiv, inr_comp_cfcₙHom_eq_cfcₙAux, CFC.monotoneOn_one_sub_one_add_inv_real, Rat.uniformContinuous_abs, EuclideanGeometry.dist_div_sin_angle_of_angle_eq_pi_div_two, ContinuousWithinAt.cfcₙ_nnreal, nnnorm_cfc_le_iff, Metric.closedBall_zero, Affine.Simplex.touchpoint_mem_affineSpan, EuclideanGeometry.Sphere.inv_tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center, EuclideanGeometry.oangle_eq_zero_or_eq_pi_iff_collinear, CFC.continuousOn_nnrpow, inner_vsub_vsub_right_eq_dist_sq_left_iff, Affine.Simplex.direction_mongePlane, cfc_neg, Affine.Simplex.dist_point_centroid, Affine.Simplex.altitudeFoot_reindex, Affine.Simplex.affineCombination_eq_touchpoint_iff, Metric.PiNatEmbed.exists_closed_embedding_to_hilbert_cube, range_cfcₙ_nnreal_eq_image_cfcₙ_real, Affine.Simplex.altitudeFoot_mem_altitude, AffineIsometry.map_eq_iff, Affine.Triangle.inv_tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_circumcenter, Filter.Tendsto.cfcₙ_nnreal, lipschitzOnWith_cfcₙ_fun, EuclideanGeometry.oangle_ne_zero_and_ne_pi_iff_affineIndependent, Affine.Triangle.affineSpan_orthocenter_point_le_altitude, Nat.dist_cast_rat, Nat.instIsOrderBornology, EuclideanGeometry.Cospherical.affineIndependent, continuous_cfcHomSuperset_left, EuclideanGeometry.orthogonalProjection_affineSpan_singleton, IsUnit.cfcNNRpow, Continuous.cfc_of_mem_nhdsSet, cfcₙHom_isClosedEmbedding, EuclideanGeometry.Sphere.IsTangentAt_of_angle_eq_pi_div_two, signedDist_lineMap_left, ContinuousOn.cfc_nnreal, nnnorm_cfcₙ_nnreal_lt_iff, EuclideanGeometry.cos_oangle_left_of_oangle_eq_pi_div_two, cfc_integral, Nat.isClosedEmbedding_coe_rat, AffineSubspace.isometryEquivMap.coe_apply, EuclideanGeometry.continuousAt_angle, cfcₙHom_le_iff, Affine.Simplex.sOppSide_excenter_singleton_point, nnnorm_cfc_nnreal_lt, EuclideanGeometry.oangle_homothety, Affine.Simplex.ExcenterExists.sOppSide_point_excenter_iff, EuclideanGeometry.Sphere.cospherical, signedDist_anticomm, EuclideanGeometry.oangle_left_eq_arccos_of_oangle_eq_pi_div_two, Affine.Simplex.dist_circumcenter_eq_circumradius, IsStrictlyPositive.sqrt, EuclideanGeometry.cos_angle_of_angle_eq_pi_div_two, MeasureTheory.hausdorffMeasure_homothety_image, Matrix.PosSemidef.isUnit_sqrt_iff, cfc_eq_cfcL_mkD, cfcₙ_real_eq_nnreal, EuclideanGeometry.sin_angle_of_angle_eq_pi_div_two, Besicovitch.ae_tendsto_measure_inter_div, EuclideanGeometry.Sphere.direction_orthRadius_le_iff, dist_add_dist_eq_iff, nnnorm_cfc_nnreal_le, IsSelfAdjoint.norm_eq_max_norm_posPart_negPart, ContinuousOn.cfcₙ_nnreal_of_mem_nhdsSet, EuclideanGeometry.Sphere.IsTangentAt.mem_and_mem_iff_eq, EuclideanGeometry.collinear_iff_eq_or_eq_or_sin_eq_zero, EuclideanGeometry.continuousAt_oangle, EuclideanGeometry.Sphere.IsDiameter.sbtw, Continuous.cfc_nnreal, AffineSubspace.mem_perpBisector_iff_inner_eq_inner, ContinuousOn.cfc_of_mem_nhdsSet, cfcHomSuperset_apply, GromovHausdorff.instCompleteSpaceGHSpace, nnnorm_cfc_nnreal_le_iff, EuclideanGeometry.Sphere.IsTangent.infDist_eq_radius, CFC.sqrt_sq, ContractingWith.tendsto_iterate_fixedPoint, cfcₙHom_eq_cfcₙ_extend, EuclideanGeometry.inversion_def, range_cfc_eq_range_cfcHom, Affine.Simplex.inner_vsub_altitudeFoot_vsub_altitudeFoot_eq_zero, EuclideanGeometry.oangle_left_eq_arcsin_of_oangle_eq_pi_div_two, GromovHausdorff.ghDist_le_nonemptyCompacts_dist, Rat.totallyBounded_Icc, CFC.rpow_sqrt_nnreal, Affine.Simplex.dist_circumcenter_eq_circumradius', signedDist_triangle_right, Affine.Simplex.orthogonalProjectionSpan_faceOpposite_eq_point_rev, EuclideanGeometry.Sphere.IsIntTangentAt.wbtw, EuclideanGeometry.Sphere.IsTangentAt.le_orthRadius, EuclideanGeometry.dist_orthogonalProjection_eq_infNndist, 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, NonUnitalIsometricContinuousFunctionalCalculus.toNonUnitalContinuousFunctionalCalculus, EuclideanGeometry.Concyclic.Coplanar, Affine.Simplex.ExcenterExists.isTangentAt_exsphere_iff_eq_touchpoint, EuclideanGeometry.dist_div_tan_oangle_left_of_oangle_eq_pi_div_two, Affine.Simplex.ExcenterExists.excenter_notMem_affineSpan_pair, Affine.Simplex.pointsWithCircumcenter_point, EuclideanGeometry.tan_angle_of_angle_eq_pi_div_two, Metric.PiNatEmbed.continuous_distDenseSeq, Affine.Simplex.mongePoint_reindex, Affine.Triangle.affineSpan_pair_eq_orthRadius_insphere, EuclideanGeometry.cospherical_or_collinear_of_two_zsmul_oangle_eq, Affine.Simplex.mongePoint_eq_smul_vsub_vadd_circumcenter, EuclideanGeometry.Sphere.dist_div_cos_oangle_center_eq_two_mul_radius, EuclideanGeometry.angle_homothety, PadicInt.instIsUltrametricDist, Affine.Simplex.altitude_reindex, signedDist_neg, Delone.DeloneSet.packingRadius_lt_dist_of_mem_ne, cfcₙHom_map_quasispectrum, GromovHausdorff.hausdorffDist_optimal_le_HD, IsSelfAdjoint.instIsometricContinuousFunctionalCalculus, EuclideanGeometry.mul_dist_add_mul_dist_eq_mul_dist_of_cospherical, instT0Space, ODE.FunSpace.exists_forall_closedBall_funSpace_dist_le_mul, MeasureTheory.Measure.pi_closedBall, cfcHom_nnreal_eq_restrict, ContractingWith.dist_inequality, integrableOn_cfcₙ, norm_cfcₙ_le, Matrix.PosSemidef.sq_sqrt, continuous_barycentric_coord, signedDist_vsub_self_rev, EuclideanGeometry.Sphere.dist_orthogonalProjection_eq_radius_iff_isTangent, EuclideanGeometry.mem_sphere, EuclideanGeometry.angle_eq_arccos_of_angle_eq_pi_div_two, ContinuousOn.cfcₙ_nnreal', EuclideanGeometry.dist_reflection, signedDist_linear_apply, EuclideanGeometry.mul_dist_le_mul_dist_add_mul_dist, cfcHom_eq_cfc_extend, integrable_cfcₙ', EuclideanGeometry.orthogonalProjection_eq_orthogonalProjection_iff_vsub_mem, EuclideanGeometry.tan_oangle_right_mul_dist_of_oangle_eq_pi_div_two, nnnorm_cfc_le, EuclideanGeometry.Sphere.IsDiameter.pointReflection_center_right, Affine.Simplex.incenter_eq_affineCombination, signedDist_self, signedDist_vsub_self, EuclideanGeometry.inversion_mul, integrable_cfc', signedDist_smul, Rat.not_countably_generated_nhds_infty_opc, CFC.abs_ofNat, EuclideanGeometry.Sphere.power_nonneg_iff_radius_le_dist_center, nnnorm_apply_le_nnnorm_cfc, Metric.isCompact_closure_iff_exists_finite_isCover, CFC.negPart_one, Affine.Simplex.sOppSide_point_excenter_singleton, Rat.not_secondCountableTopology_opc, cfcₙHomSuperset_id, Continuous.cfc, AffineSubspace.mem_perpBisector_iff_dist_eq', Matrix.PosSemidef.inv_sqrt, EuclideanGeometry.cos_angle_mul_dist_of_angle_eq_pi_div_two, Affine.Simplex.ninePointCircle_center_mem_affineSpan, cfcₙHom_real_eq_restrict, CFC.abs_algebraMap_nnreal, EuclideanGeometry.Sphere.power_nonpos_iff_dist_center_le_radius, AffineSubspace.perpBisector_eq_top, EuclideanGeometry.dist_orthogonalProjection_eq_infDist, EuclideanGeometry.orthogonalProjection_mem, EuclideanGeometry.tan_angle_mul_dist_of_angle_eq_pi_div_two, Commute.cfcHom, EuclideanGeometry.mem_sphere', Isometry.affineIsometryOfStrictConvexSpace_apply, Tactic.ComputeAsymptotics.Seq.instCompleteSpaceStream', EuclideanGeometry.sin_angle_mul_dist_of_angle_eq_pi_div_two, cfc_apply_mem_elemental, AffineSubspace.midpoint_mem_perpBisector, Tactic.ComputeAsymptotics.Seq.instCompleteSpaceSeq, dist_pos, Affine.Simplex.touchpoint_reindex, TopologicalSpace.complete_completelyMetrizableMetric, EuclideanGeometry.inner_weightedVSub, GromovHausdorff.HD_below_aux2, nnnorm_cfcₙHom, EuclideanGeometry.Sphere.mem_coe, EuclideanGeometry.Sphere.center_mem_orthRadius_iff, Besicovitch.exists_disjoint_closedBall_covering_ae, CFC.nnnorm_rpow, EuclideanGeometry.collinear_of_sin_eq_zero, MeasureTheory.volume_pi_ball, Affine.Simplex.ExcenterExists.excenter_mem_affineSpan_range, Continuous.cfcₙ_nnreal_of_mem_nhdsSet, ContinuousOn.cfcₙ, EuclideanGeometry.dist_eq_of_two_zsmul_oangle_eq, signedDist_smul_of_neg, ContractingWith.dist_le_of_fixedPoint, IsStarNormal.instContinuousFunctionalCalculus, Affine.Triangle.orthocenter_mem_altitude, ODE.FunSpace.dist_iterate_next_le, Tactic.ComputeAsymptotics.Seq.instBoundedSpaceStream', EuclideanGeometry.dist_orthogonalProjection_eq_zero_iff, CStarAlgebra.isStrictlyPositive_iff_isUnit_sqrt_and_eq_sqrt_mul_sqrt, cfc_comp_norm, CFC.abs_intCast, Rat.uniformSpace_eq, apply_le_nnnorm_cfc_nnreal, EuclideanGeometry.Sphere.isDiameter_iff_mem_and_mem_and_dist, Affine.Triangle.eulerPoint_eq_midpoint, Commute.cfc, Affine.Simplex.sign_signedInfDist_touchpoint_empty, lipschitzOnWith_cfcₙ_fun_of_subset, range_cfc_nnreal_eq_image_cfc_real, signedDist_vadd_right_swap, ContinuousOn.cfcₙ_of_mem_nhdsSet, Affine.Simplex.midpoint_faceOppositeCentroid_eulerPoint, isClosedEmbedding_cfcₙHom_of_cfcHom, EuclideanGeometry.Sphere.IsTangentAt.eq_orthogonalProjection, EuclideanGeometry.angle_eq_arcsin_of_angle_eq_pi_div_two, EuclideanGeometry.Sphere.IsDiameter.midpoint_eq_center, Affine.Triangle.dist_circumcenter_reflection_orthocenter_finset, IsSelfAdjoint.commute_cfcₙHom, ODE.FunSpace.dist_iterate_next_iterate_next_le, EuclideanGeometry.Sphere.secondInter_vsub_mem_affineSpan, cfcL_integral, Affine.Simplex.point_eq_affineCombination_of_pointsWithCircumcenter, AffineSubspace.perpBisector_self, AffineIsometry.toAffineIsometryEquiv_apply, EuclideanGeometry.triangle_congruent_iff_dist_eq, NonUnitalContinuousFunctionalCalculus.exists_cfc_of_predicate, GromovHausdorff.compactSpace_optimalGHCoupling, inner_vsub_vsub_left_eq_dist_sq_right_iff, EuclideanGeometry.reflection_eq_iff_orthogonalProjection_eq, EuclideanGeometry.Sphere.isDiameter_iff_mem_and_mem_and_wbtw, MeasureTheory.volume_pi_closedBall, EuclideanGeometry.oangle_midpoint_rev_right, EuclideanGeometry.dist_div_cos_oangle_right_of_oangle_eq_pi_div_two, cfcHom_isStrictlyPositive_iff, Affine.Simplex.incenter_mem_affineSpan_range, norm_cfc_le, EuclideanGeometry.orthogonalProjection_orthogonalProjection, Affine.Simplex.eulerPoint_reindex, EuclideanGeometry.Sphere.coe_mk, Metric.Sum.dist_eq, CFC.exists_measure_nnrpow_eq_integral_cfcₙ_rpowIntegrand₀₁, NonUnitalNormedRing.dist_eq, CFC.spectrum_abs, Affine.Simplex.excenterWeights_map, Set.Countable.isTotallyDisconnected, Affine.Simplex.sum_inv_height_sq_smul_vsub_eq_zero, signedDist_vadd_left, AffineSpace.asymptoticNhds_le_cobounded, Affine.Simplex.incenter_notMem_affineSpan_pair, Int.closedBall_eq_Icc, cfc_apply_pi, Real.instContinuousMapUniqueHom, AffineSubspace.mem_perpBisector_iff_inner_pointReflection_vsub_eq_zero, Affine.Simplex.touchpoint_eq_point_rev, Continuous.cfcₙ', Affine.Simplex.signedInfDist_reindex, GromovHausdorff.instSecondCountableTopologyGHSpace, EuclideanGeometry.angle_const_vsub, signedDist_apply_linear_apply, ContinuousOn.cfc', EuclideanGeometry.dist_div_cos_oangle_left_of_oangle_eq_pi_div_two, EuclideanGeometry.inversion_mem_perpBisector_inversion_iff, Affine.Simplex.neg_one_lt_inner_vsub_altitudeFoot_div, Affine.Simplex.ExcenterExists.touchpointWeights_map, EuclideanGeometry.collinear_of_angle_eq_pi, Affine.Simplex.mongePoint_map, Affine.Simplex.eulerPoint_map, cfcₙ_norm_sq_nonneg, Affine.Triangle.sOppSide_affineSpan_pair_point_excenter_singleton, AffineSubspace.signedInfDist_singleton, EuclideanGeometry.dist_div_cos_angle_of_angle_eq_pi_div_two, EuclideanGeometry.angle_midpoint_eq_pi, NonUnitalContinuousFunctionalCalculus.isCompact_quasispectrum, Affine.Simplex.affineCombination_touchpointWeights, NNRat.nndist_eq, Affine.Triangle.orthocenter_mem_affineSpan, EuclideanGeometry.oangle_ne_zero_and_ne_pi_iff_not_collinear, cfcHomSuperset_id, Affine.Simplex.faceOppositeCentroid_mem_ninePointCircle, Affine.Simplex.mongePoint_mem_affineSpan, GromovHausdorff.toGHSpace_lipschitz, Commute.cfcₙ, NNRat.instContinuousSMulNNReal, EuclideanGeometry.Sphere.IsTangent.isTangentAt, EuclideanGeometry.Sphere.orthRadius_le_orthRadius_iff, IsometryEquiv.coeFn_toRealAffineIsometryEquiv, CFC.sqrt_eq_cfc, ContinuousAt.cfcₙ, EuclideanGeometry.collinear_iff_eq_or_eq_or_angle_eq_zero_or_angle_eq_pi, Affine.Simplex.incenter_reindex, exists_locallyFinite_subset_iUnion_ball_radius_lt, AffineSubspace.mem_perpBisector_iff_dist_eq, NNRat.instOrderTopology, nnnorm_cfcₙ_le_iff, WithAbs.pseudoMetricSpace_induced_of_comp, Metric.inductiveLimitDist_eq_dist, Filter.Tendsto.cfc_nnreal, Nat.preimage_ball, dist_eq_zero, IsSelfAdjoint.instContinuousFunctionalCalculus, zero_eq_nndist, CFC.abs_eq_cfcₙ_norm, Affine.Simplex.mongePoint_vsub_face_centroid_eq_weightedVSub_of_pointsWithCircumcenter, continuousOn_cfcₙ_nnreal, EuclideanGeometry.mul_dist_eq_mul_dist_of_cospherical_of_angle_eq_pi, EuclideanGeometry.reflection_apply', cfcₙHom_continuous, CFC.abs_sq, IsStarNormal.instNonUnitalIsometricContinuousFunctionalCalculus, signedDist_right_lineMap, NonUnitalCStarAlgebra.toCompleteSpace, Rat.instIsTopologicalRing, EuclideanGeometry.Sphere.mem_tangentSet_iff, cfcₙHomSuperset_continuous, instTotallySeparatedSpaceOfIsUltrametricDist, nnnorm_cfc_lt_iff, Affine.Simplex.altitude_map, cfcₙ_apply_pi, Rat.instIsUniformAddGroup, Complex.instContinuousMapUniqueHom, EuclideanGeometry.Sphere.isTangentAt_center_iff, ODE.FunSpace.instCompleteSpace, Rat.instNoncompactSpace, CStarAlgebra.isStrictlyPositive_TFAE, continuousOn_cfcₙ_setProd, EuclideanGeometry.sin_oangle_left_of_oangle_eq_pi_div_two, Unitization.complex_cfcₙ_eq_cfc_inr, Affine.Simplex.ExcenterExists.signedInfDist_excenter, Metric.lipschitz_infDist, CStarAlgebra.norm_negPart_le, cfcₙ_nnreal_eq_real, Affine.Simplex.orthogonalProjectionSpan_reindex, CFC.sqrt_algebraMap, CFC.posPart_algebraMap, CFC.sqrt_one, NonUnitalContinuousFunctionalCalculus.compactSpace_quasispectrum, MeasureTheory.hausdorffMeasure_affineSegment, Affine.Triangle.sbtw_touchpoint_empty, EuclideanGeometry.Sphere.isIntTangent_iff_dist_center, CFC.nnrpow_eq_cfcₙ_real, dist_lt_dist_add_dist_iff, Affine.Simplex.touchpoint_empty_notMem_affineSpan_of_ne, EuclideanGeometry.Sphere.IsTangentAt_iff_angle_eq_pi_div_two, EuclideanGeometry.Sphere.mem_coe', Besicovitch.tendsto_filterAt, UpperHalfPlane.instProperSpace, EuclideanGeometry.orthogonalProjection_linear, Affine.Simplex.sSameSide_point_excenter_singleton, norm_apply_le_norm_cfc, cfcHom_predicate, AffineSubspace.signedInfDist_def, Affine.Simplex.acuteAngled_reindex_iff, CFC.negPart_def, TopologicalSpace.IsCompletelyMetrizableSpace.complete, EuclideanGeometry.oangle_right_eq_arccos_of_oangle_eq_pi_div_two, integrable_cfc, Affine.Simplex.mem_altitude, Affine.Simplex.isDiameter_ninePointCircle, signedDist_lineMap_right, Affine.Triangle.sSameSide_affineSpan_pair_point_excenter_singleton, Affine.Triangle.dist_div_sin_angle_div_two_eq_circumradius, CFC.sqrt_rpow_nnreal, Affine.Simplex.orthogonalProjectionSpan_eulerPoint_mem_ninePointCircle, Affine.Simplex.mongePlane_reindex, nnnorm_cfc_nnreal_lt_iff, EuclideanGeometry.reflection_involutive, Int.preimage_ball, Affine.Simplex.sign_signedInfDist_incenter, Affine.Simplex.ExcenterExists.sign_signedInfDist_excenter, EuclideanGeometry.Sphere.isTangentAt_iff_dist_sq_eq_power, norm_cfcHom, KuratowskiEmbedding.embeddingOfSubset_dist_le, EuclideanGeometry.law_cos, isOpenMap_barycentric_coord, Affine.Simplex.signedInfDist_affineCombination, EuclideanGeometry.sin_oangle_left_mul_dist_of_oangle_eq_pi_div_two, signedDist_apply, Metric.lipschitz_infDist_set, cfc_real_eq_complex, CFC.norm_rpow, AffineEquiv.coe_toHomeomorphOfFiniteDimensional_symm, Tactic.ComputeAsymptotics.Seq.FriendlyOperation.dist_le, EuclideanGeometry.dist_affineCombination, signedDist_eq_dist_iff_vsub_mem_span, EuclideanGeometry.Sphere.mem_commonIntTangents_iff, AffineSubspace.direction_perpBisector, AffineSubspace.angle_coe, Affine.Simplex.ninePointCircle_map, EuclideanGeometry.dist_smul_vadd_eq_dist, EuclideanGeometry.orthogonalProjection_eq_self_iff, AffineSubspace.mem_perpBisector_iff_inner_eq, EuclideanGeometry.reflection_subtype, MonotoneOn.nnnorm_cfc, Tactic.ComputeAsymptotics.Seq.dist_eq_half_of_head, PNat.instNoncompactSpace, cfc_setIntegral', EuclideanGeometry.dist_sq_mul_dist_add_dist_sq_mul_dist, cfcₙ_setIntegral', cfcₙL_apply, ContinuousOn.cfcₙ_nnreal, cfcHomSuperset_continuous, cfcₙ_apply_mem_elemental, NormedRing.dist_eq, CFC.posPart_def, CFC.nnrpow_eq_rpow, AffineSubspace.isometryEquivMap.apply_symm_apply, EuclideanGeometry.cos_oangle_right_mul_dist_of_oangle_eq_pi_div_two, CFC.cfcₙ_rpowIntegrand₀₁_eq_cfcₙ_rpowIntegrand₀₁_one, AffineEquiv.coe_toHomeomorphOfFiniteDimensional, IsSelfAdjoint.commute_cfcₙ, EuclideanGeometry.concyclic_or_collinear_of_two_zsmul_oangle_eq, Affine.Simplex.ExcenterExists.signedInfDist_excenter_eq_mul_sum_inv, EuclideanGeometry.dist_inversion_mul_dist_center_eq, norm_apply_le_norm_cfcₙ, EuclideanGeometry.dist_div_sin_oangle_right_of_oangle_eq_pi_div_two, continuousOn_cfc_nnreal_setProd, Rat.isUniformEmbedding_coe_real, Tactic.ComputeAsymptotics.Seq.dist_le_one, range_cfcHom, CFC.abs_one, nnnorm_cfcHom, integrableOn_cfc, Matrix.PosSemidef.sqrt_mul_self, continuousOn_cfc, EuclideanGeometry.orthogonalProjection_vsub_mem_direction_orthogonal, Affine.Simplex.touchpoint_mem_affineSpan_simplex, closure_diff_intrinsicInterior, EuclideanGeometry.angle_eq_zero_iff_ne_and_wbtw, Metric.Sum.mem_uniformity_iff_glueDist, EuclideanGeometry.dist_center_inversion, Affine.Simplex.circumsphere_reindex, InnerProductSpace.Core.topology_eq, Besicovitch.exists_disjoint_closedBall_covering_ae_aux, EuclideanGeometry.eq_orthogonalProjection_of_eq_subspace, EuclideanGeometry.orthogonalProjection_apply, EuclideanGeometry.Sphere.direction_orthRadius, Besicovitch.SatelliteConfig.inter, EuclideanGeometry.eq_reflection_of_eq_subspace, EuclideanGeometry.dist_sq_add_dist_sq_eq_two_mul_dist_midpoint_sq_add_half_dist_sq, Affine.Simplex.circumradius_reindex, AffineSubspace.signedInfDist_apply_self, EuclideanGeometry.orthogonalProjection_vsub_orthogonalProjection, EuclideanGeometry.Sphere.IsIntTangent.dist_center, EuclideanGeometry.orthogonalProjection_mem_orthogonal, KuratowskiEmbedding.embeddingOfSubset_coe, inner_vsub_vsub_left_eq_dist_sq_left_iff, NNRat.instIsTopologicalSemiring, CFC.isUnit_nnrpow_iff, CFC.monotoneOn_cfcₙ_rpowIntegrand₀₁, EuclideanGeometry.Sphere.orthRadius_parallel_orthRadius_iff, EuclideanGeometry.inner_vsub_vsub_of_mem_sphere_of_mem_sphere, Affine.Triangle.sSameSide_affineSpan_pair_excenter_singleton_point, cfcₙL_integrable, abs_signedDist_le_dist, EuclideanGeometry.tan_oangle_left_of_oangle_eq_pi_div_two, Rat.isEmbedding_coe_real, IsStarNormal.instIsometricContinuousFunctionalCalculus, AffineIsometry.injective, IsometricContinuousFunctionalCalculus.isometric, MeasureTheory.hausdorffMeasure_homothety_preimage, Affine.Triangle.dist_div_sin_oangle_div_two_eq_circumradius, Int.instIsOrderBornology, EuclideanGeometry.affineIndependent_iff_of_two_zsmul_oangle_eq, UniformSpace.Completion.instIsBoundedSMul, ContinuousAt.cfc_nnreal, Rat.instIsTopologicalAddGroup, EuclideanGeometry.dist_inversion_center, ContinuousWithinAt.cfc, Affine.Simplex.reflection_circumcenter_eq_affineCombination_of_pointsWithCircumcenter, Affine.Simplex.height_reindex, Affine.Simplex.dist_incenter, Affine.Simplex.inradius_map, EuclideanGeometry.inversion_dist_center', cfcₙHom_of_cfcHom_map_quasispectrum, EuclideanGeometry.coe_orthogonalProjection_eq_iff_mem, EuclideanGeometry.Sphere.secondInter_eq_lineMap, signedDist_apply_linear, EuclideanGeometry.Sphere.secondInter_map, PNat.instDiscreteTopology, nnnorm_cfcₙ_le, Rat.instTotallyDisconnectedSpace, EuclideanGeometry.Sphere.isDiameter_iff_left_mem_and_midpoint_eq_center, EuclideanGeometry.cospherical_iff_exists_sphere, ContinuousWithinAt.cfc_nnreal, cfcₙHomSuperset_apply, IsSelfAdjoint.instNonUnitalIsometricContinuousFunctionalCalculus, antilipschitzWith_lineMap, nnnorm_cfcₙ_nnreal_le, CFC.sqrt_eq_real_sqrt, AffineSubspace.mem_perpBisector_pointReflection_iff_inner_eq_zero, apply_le_nnnorm_cfcₙ_nnreal, Affine.Triangle.orthocenter_vsub_circumcenter_eq_sum_vsub, EuclideanGeometry.Sphere.isDiameter_iff_left_mem_and_pointReflection_center_left, Affine.Simplex.altitudeFoot_mem_affineSpan_faceOpposite, continuousOn_cfcₙ_nnreal_setProd, cfcHom_eq_of_isStarNormal, CommCStarAlgebra.toCompleteSpace, EuclideanGeometry.inversion_eq_lineMap, CFC.real_exp_eq_normedSpace_exp, CFC.norm_sqrt, CFC.continuousOn_rpow, Affine.Triangle.dist_orthocenter_reflection_circumcenter_finset, Affine.Simplex.affineSpan_pair_eq_altitude_iff, AffineIsometry.angle_map, Affine.Simplex.signedInfDist_apply_of_ne, range_cfc, signedDist_left_lineMap, Affine.Simplex.direction_altitude, cfcHom_map_spectrum, MonotoneOn.nnnorm_cfcₙ, Affine.Simplex.circumcenter_eq_centroid, Affine.Simplex.excenter_reindex, AffineIsometry.image_intrinsicFrontier, EuclideanGeometry.orthogonalProjection_eq_iff_mem, EuclideanGeometry.cos_oangle_right_of_oangle_eq_pi_div_two, Affine.Simplex.ninePointCircle_center, EuclideanGeometry.dist_orthogonalProjection_line_eq_of_two_zsmul_oangle_eq, cfcₙHom_nonneg_iff, CFC.nnnorm_nnrpow, intrinsicClosure_eq_closure, Affine.Triangle.sSameSide_affineSpan_pair_incenter_point, Matrix.PosDef.posDef_sqrt, norm_cfcₙ_le_iff, CFC.norm_nnrpow, Affine.Simplex.centroid_eq_affineCombination_of_pointsWithCircumcenter, Affine.Simplex.incenter_notMem_affineSpan_faceOpposite, Affine.Simplex.touchpoint_empty_mem_interior_faceOpposite, ODE.FunSpace.dist_iterate_next_apply_le, Metric.subsingleton_closedBall, Nat.instProperSpace, Commute.cfcₙ_real, AffineSubspace.right_mem_perpBisector, EuclideanGeometry.Sphere.dist_orthogonalProjection_eq_radius_iff_isTangentAt, EuclideanGeometry.dist_sq_eq_dist_sq_add_dist_sq_iff_angle_eq_pi_div_two, EuclideanGeometry.reflection_apply, CFC.complex_exp_eq_normedSpace_exp, EuclideanGeometry.Sphere.mem_orthRadius_iff_inner_left, Metric.Sigma.isOpen_iff, EuclideanGeometry.Sphere.secondInter_eq_self_iff, cfcₙ_complex_eq_real, Int.preimage_closedBall, Matrix.IsHermitian.instContinuousFunctionalCalculus, IsSelfAdjoint.commute_cfc, cfcHom_apply_mem_elemental, EuclideanGeometry.Sphere.finrank_orthRadius, NNRat.instContinuousSMulRatReal, cfc_setIntegral, NormedGroup.dist_eq, Affine.Simplex.points_vsub_eulerPoint, Affine.Simplex.ExcenterExists.sSameSide_excenter_point_iff, inner_vsub_vsub_right_eq_dist_sq_right_iff, PNat.isUniformEmbedding_coe, EuclideanGeometry.angle_eq_pi_iff_sbtw, norm_cfc_lt, inner_vsub_left_eq_zero_symm, cfc_neg_id, EuclideanGeometry.Sphere.IsDiameter.dist_left_right_div_two, Affine.Triangle.dist_point_centroid, cfc_integral', Affine.Triangle.orthocenter_reindex, Int.isClosedEmbedding_coe_rat, Affine.Simplex.circumradius_map, Matrix.PosSemidef.sqrt_eq_iff_eq_sq, CFC.rpow_eq_cfc_real, Delone.DeloneSet.exists_dist_le_coveringRadius, EuclideanGeometry.Sphere.infDist_eq_radius_iff_isTangent, Affine.Simplex.altitude_def, signedDist_vadd_vadd, Continuous.cfcₙ_nnreal', Rat.uniformContinuous_coe_real, GromovHausdorff.HD_below_aux1, EuclideanGeometry.Sphere.self_mem_orthRadius, CFC.isUnit_sqrt_iff, Affine.Simplex.insphere_reindex, Metric.NonemptyCompacts.dist_eq, isometry_cfcHom, EuclideanGeometry.angle_const_vadd, Metric.Sigma.dist_ne, Metric.PiNatEmbed.exists_embedding_to_hilbert_cube, Metric.isUniformEmbedding_iff', EuclideanGeometry.orthogonalProjection_mem_subspace_eq_self, Affine.Simplex.sSameSide_point_incenter, AffineMap.continuous_of_finiteDimensional, EuclideanGeometry.dist_center_eq_dist_center_of_mem_sphere, cfcₙ_integral', GromovHausdorff.HD_candidatesBDist_le, Int.cobounded_eq, Metric.Sigma.dist_same, CFC.rpow_sqrt, Affine.Simplex.ExcenterExists.sSameSide_point_excenter_iff, Affine.Simplex.signedInfDist_incenter, nnnorm_cfcₙ_lt, Affine.Simplex.inner_vsub_vsub_altitudeFoot_eq_height_sq
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