toInner 📖 | CompOp | 596 mathmath: norm_sub_sq_real, WithLp.prod_inner_apply, ContinuousLinearMap.inner_map_map_of_mem_unitary, ContinuousAt.inner, inner_lt_one_iff_real_of_norm_eq_one, EuclideanGeometry.dist_smul_vadd_sq, real_inner_div_norm_mul_norm_eq_neg_one_iff, TensorProduct.inner_tmul, Orthonormal.inner_left_finsupp, ProbabilityTheory.isGaussian_iff_gaussian_charFun, OrthonormalBasis.orthogonalProjection_eq_sum, LinearMap.IsSymmetric.inner_map_polarization, MeasureTheory.charFun_eq_fourierIntegral', real_inner_div_norm_mul_norm_eq_neg_one_of_ne_zero_of_neg_mul, Function.hasTemperateGrowth_inner_right, Orientation.inner_rotation_pi_div_two_right_smul, inner_vsub_right_eq_zero_symm, Affine.Simplex.neg_mul_lt_inner_vsub_altitudeFoot, norm_eq_iInf_iff_real_inner_le_zero, MeasureTheory.L2.inner_indicatorConstLp_eq_inner_setIntegral, Real.fourierIntegralInv_eq', LinearMap.IsPositive.ne_zero_iff, ContinuousLinearMapWOT.le_nhds_iff_forall_inner_apply_le_nhds, AffineSubspace.mem_perpBisector_iff_inner_eq_zero', ContinuousLinearMap.IsPositive.inner_left_eq_inner_right, conformalAt_iff, lp.inner_eq_tsum, ContinuousLinearMapWOT.tendsto_iff_forall_inner_apply_tendsto, Affine.Simplex.inv_height_eq_sum_mul_inv_dist, OrthonormalBasis.sum_inner_mul_inner, Real.fourierIntegral_eq, Submodule.re_inner_starProjection_eq_normSq, inner_self_eq_one_of_norm_eq_one, RCLike.inner_apply', MeasureTheory.MemLp.const_inner, LinearMap.IsPositive.re_inner_nonneg_right, real_inner_smul_self_left, LinearMap.IsSymmetric.im_inner_self_apply, SchwartzMap.lineDerivOp_fourier_eq, Orientation.inner_mul_inner_add_areaForm_mul_areaForm, MeasureTheory.isTightMeasureSet_iff_inner_tendsto, innerSL_apply_apply, InnerProductGeometry.sin_angle, EuclideanGeometry.Sphere.mem_orthRadius_iff_inner_right, inner_sum, EuclideanSpace.inner_single_left, Submodule.orthogonalProjectionFn_inner_eq_zero, Measurable.inner, inner_eq_norm_mul_iff, ProbabilityTheory.covarianceBilin_apply_eq_cov, ProbabilityTheory.covarianceBilin_self, ContinuousLinearMap.IsPositive.inner_nonneg_right, GaussianFourier.integral_cexp_neg_mul_sq_norm_add_of_euclideanSpace, TemperedDistribution.lineDerivOp_fourier_eq, MeasureTheory.charFun_neg, Submodule.mem_orthogonal_singleton_iff_inner_right, toDual_symm_apply, Submodule.starProjection_singleton, Submodule.isOrtho_iff_inner_eq, ClosedSubmodule.mem_orthogonal', fourierIntegral_gaussian_innerProductSpace', MeasureTheory.charFun_toDual_symm_eq_charFunDual, MeasureTheory.charFun_eq_fourierIntegral, norm_add_pow_two_real, ProbabilityTheory.hasGaussianLaw_iff_charFun_map_eq, GaussianFourier.integral_cexp_neg_mul_sq_norm_add, ContDiffOn.inner, inner_gradientWithin_right, smul_left, norm_sub_mul_self, inner_smul_left_eq_star_smul, ProbabilityTheory.covarianceOperator_apply, inner_lt_norm_mul_iff_real, im_inner_eq_norm_sub_i_smul_mul_self_sub_norm_add_i_smul_mul_self_div_four, inner_left_rankOne_apply, tendsto_integral_exp_inner_smul_cocompact_of_continuous_compact_support, innerₛₗ_apply_apply, ContinuousLinearMap.eq_adjoint_iff, MeasureTheory.L2.inner_def, OrthonormalBasis.sum_sq_inner_right, rankOne_apply, Submodule.reflection_singleton_apply, Orientation.inner_rightAngleRotation_swap', MeasureTheory.AEStronglyMeasurable.inner_const, SchwartzMap.inner_toL2_toL2_eq, Submodule.starProjection_inner_eq_zero, signedDist_linear_apply_apply, inner_self_eq_norm_sq_to_K, MeasureTheory.charFunDual_eq_charFun_map_one, inner_mul_inner_self_le, norm_sub_pow_two_real, Affine.Simplex.abs_inner_vsub_altitudeFoot_div_lt_one, Orthonormal.inner_left_fintype, RCLike.wInner_cWeight_eq_expect, norm_sub_sq, LinearIsometryEquiv.inner_map_eq_flip, LinearMap.toMatrixOrthonormal_apply_apply, MeasureTheory.charFun_apply_real, LDL.lowerInv_orthogonal, GaussianFourier.integrable_cexp_neg_mul_sq_norm_add_of_euclideanSpace, LinearMap.IsSymmetric.coe_re_inner_self_apply, SchwartzMap.fourier_lineDerivOp_eq, AffineSubspace.mem_perpBisector_iff_inner_eq_zero, Finsupp.sum_inner, TemperedDistribution.fourierInv_lineDerivOp_eq, re_inner_eq_norm_add_mul_self_sub_norm_mul_self_sub_norm_mul_self_div_two, abs_real_inner_le_norm, toDualMap_apply_apply, LinearMap.eq_adjoint_iff_basis_left, signedDist_apply_apply, norm_add_eq_sqrt_iff_real_inner_eq_zero, re_inner_eq_norm_mul_self_add_norm_mul_self_sub_norm_sub_mul_self_div_two, ProperCone.hyperplane_separation', real_inner_mul_inner_self_le, ext_inner_map, MeasureTheory.MemLp.inner_const, coe_innerSL_apply, inner_eq_zero_of_right, LinearMap.IsSymmetric.inner_map_self_eq_zero, norm_sub_sq_eq_norm_sq_add_norm_sq_iff_real_inner_eq_zero, inner_re_zero_right, MeasureTheory.StronglyMeasurable.inner, Affine.Simplex.inner_mongePoint_vsub_face_centroid_vsub, LinearMap.IsPositive.inner_nonneg_left, hasGradientAtFilter_iff_isLittleO, hasGradientAt_iff_isLittleO, OrthonormalBasis.orthogonalProjection_apply_eq_sum, LinearMap.trace_eq_sum_inner, Matrix.gram_zero, Submodule.norm_eq_iInf_iff_inner_eq_zero, ProbabilityTheory.complexMGF_mul_I, norm_inner_eq_norm_iff, ContinuousLinearMap.apply_norm_sq_eq_inner_adjoint_left, inner_eq_norm_mul_iff_div, HasDerivWithinAt.norm_sq, MeasureTheory.charFun_eq_prod_iff, LinearMap.IsSymmetric.hasEigenvalue_iSup_of_finiteDimensional, inner_self_im, inner_re_zero_left, inner_self_ofReal_re, trace_rankOne, Affine.Simplex.abs_inner_vsub_altitudeFoot_lt_mul, LinearIsometry.inner_map_map, sum_inner, fourier_gaussian_innerProductSpace', InnerProductGeometry.cos_angle, Matrix.posDef_gram_of_linearIndependent, hasGradientAt_iff_isLittleO_nhds_zero, real_inner_eq_norm_mul_self_add_norm_mul_self_sub_norm_sub_mul_self_div_two, HilbertBasis.hasSum_orthogonalProjection, LinearMap.adjoint_inner_right, InnerProductGeometry.cos_angle_mul_norm_mul_norm, inner_map_polarization', inner_right_rankOne_apply, PositiveLinearMap.preGNS_inner_def, real_inner_div_norm_mul_norm_eq_one_iff, TensorProduct.inner_lid_lid, EuclideanGeometry.Sphere.IsTangentAt.inner_right_eq_zero_of_mem, toDual_apply, norm_sub_eq_sqrt_iff_real_inner_eq_zero, HasDerivWithinAt.inner, DifferentiableAt.inner, ProbabilityTheory.IsGaussian.charFun_eq', OrthonormalBasis.sum_sq_norm_inner_right, lp.inner_single_right, Orthonormal.inner_left_right_finset, Finsupp.inner_sum, HasFDerivWithinAt.inner, toDualMap_apply, Orthonormal.inner_products_summable, gramSchmidt_orthogonal, ContinuousLinearMap.adjoint_inner_left, gramSchmidt_pairwise_orthogonal, AEMeasurable.const_inner, ContinuousLinearMap.apply_norm_eq_sqrt_inner_adjoint_right, innerₗ_apply, ProbabilityTheory.complexMGF_id_mul_I, Submodule.norm_eq_iInf_iff_real_inner_eq_zero, inner_neg_right, Orthonormal.isHilbertSum, inner_eq_sum_norm_sq_div_four, IsContMDiffRiemannianBundle.exists_contMDiff, toDual_apply_apply, Orientation.inner_rotation_pi_div_two_right, ContinuousLinearMap.inner_map_map_iff_adjoint_comp_self, real_inner_eq_re_inner, differentiable_inner, MeasureTheory.charFun_pi, ContinuousLinearMap.adjointAux_inner_left, inner_self_conj, BoundedContinuousFunction.innerProbChar_apply, OrthonormalBasis.repr_apply_apply, Orientation.inner_rotation_pi_div_two_left, EuclideanGeometry.inner_pos_or_eq_of_dist_le_radius, MeasureTheory.L2.integral_inner_eq_sq_eLpNorm, real_inner_self_nonneg, MeasureTheory.L2.inner_indicatorConstLp_indicatorConstLp, ConvexCone.hyperplane_separation_of_nonempty_of_isClosed_of_notMem, InnerProductGeometry.inner_eq_neg_mul_norm_of_angle_eq_pi, inner_smul_real_right, Orientation.inner_eq_norm_mul_norm_mul_cos_oangle, EuclideanGeometry.Sphere.IsTangentAt.inner_left_eq_zero_of_mem, Submodule.mem_orthogonal', Matrix.posDef_gram_iff_linearIndependent, OrthonormalBasis.sum_sq_inner_left, RCLike.wInner_one_eq_inner, ProbabilityTheory.isGaussian_iff_charFun_eq, Orientation.inner_rotation_pi_div_two_left_smul, inner_zero_left, InnerProductGeometry.inner_eq_neg_mul_norm_iff_angle_eq_pi, fourierIntegral_eq_half_sub_half_period_translate, Continuous.inner_bundle, inner_neg_neg, inner_eq_norm_sq_left_iff, innerSLFlip_apply_apply, IsContinuousRiemannianBundle.exists_continuous, inner_add_left, Submodule.smul_starProjection_singleton, Orientation.inner_comp_rightAngleRotation, Orthonormal.inner_finsupp_eq_sum_right, inner_re_symm, inner_map_complex, MeasureTheory.charFun_conv, MeasureTheory.AEStronglyMeasurable.inner, Submodule.inner_orthogonalProjection_eq_of_mem_right, real_inner_self_abs, Matrix.isHermitian_gram, integral_inner, Orthonormal.linearIsometryEquiv_symm_apply_single_one, SchwartzMap.fourierInv_lineDerivOp_eq, MeasureTheory.integral_charFun_Icc, real_inner_add_sub_eq_zero_iff, norm_inner_eq_norm_tfae, AEMeasurable.inner, signedDist_vadd_right, RCLike.inner_tmul_eq, LinearPMap.adjointDomainMkCLM_apply, ContDiff.inner, HasDerivAt.norm_sq, Real.fourier_eq, Measurable.const_inner, inner_vsub_vsub_right_eq_dist_sq_left_iff, ContinuousLinearMap.reApplyInnerSelf_apply, LinearMap.IsSymmetric.coe_reApplyInnerSelf_apply, inner_self_eq_norm_mul_norm, Submodule.starProjection_unit_singleton, norm_add_sq_eq_norm_sq_add_norm_sq_iff_real_inner_eq_zero, RCLike.inner_apply, ClosedSubmodule.mem_orthogonal, MDifferentiableOn.inner_bundle, LinearMap.re_inner_adjoint_mul_self_nonneg, real_inner_le_norm, orthonormal_subtype_iff_ite, conformalFactorAt_inner_eq_mul_inner', TemperedDistribution.fourier_lineDerivOp_eq, Submodule.coe_inner, Orientation.inner_eq_zero_of_oangle_eq_neg_pi_div_two, ext_iff_inner_left, inner_lt_one_iff_real_of_norm_one, UniformSpace.Completion.Continuous.inner, inner_zero_right, LinearMap.eq_adjoint_iff, inner_self_eq_zero, MeasureTheory.AEStronglyMeasurable.const_inner, Orthonormal.inner_right_finsupp, AEMeasurable.inner_const, real_inner_le_one_of_norm_eq_one, ProbabilityTheory.indepFun_iff_charFun_prod, inner_product_apply_eigenvector, real_inner_smul_right, gramSchmidtOrthonormalBasis_det, Orientation.nonneg_inner_and_areaForm_eq_zero_iff_sameRay, OrthonormalBasis.sum_sq_norm_inner_left, abs_real_inner_div_norm_mul_norm_le_one, LinearMap.isPositive_iff_complex, inner_self_eq_norm_sq, ContMDiffOn.inner_bundle, MeasureTheory.norm_charFun_le_one, real_inner_self_eq_norm_sq, OrthonormalBasis.inner_eq_zero, Submodule.isOrtho_span, HasGradientWithinAt.fderivWithin_apply, inner_add_add_self, hasGradientAt_iff_tendsto, ContinuousLinearMap.IsPositive.re_inner_nonneg_left, inner_add_right, continuous_inner, nnnorm_inner_le_nnnorm, LinearMap.norm_map_iff_inner_map_map, ProbabilityTheory.covarianceOperator_inner, real_inner_self_nonpos, MDifferentiableWithinAt.inner_bundle, Orientation.inner_rightAngleRotation_left, AffineSubspace.mem_perpBisector_iff_inner_eq_inner, ContinuousLinearMap.IsPositive.inner_nonneg_left, Real.fourierIntegral_eq', ContinuousLinearMap.apply_norm_eq_sqrt_inner_adjoint_left, HasFDerivAt.inner, MeasureTheory.L2.eLpNorm_inner_lt_top, norm_inner_div_norm_mul_norm_eq_one_of_ne_zero_of_ne_zero_mul, OrthogonalFamily.inner_sum, Affine.Simplex.inner_vsub_altitudeFoot_vsub_altitudeFoot_eq_zero, EuclideanSpace.inner_eq_star_dotProduct, norm_sq_eq_re_inner, Orthonormal.inner_left_sum, Orientation.inner_smul_rotation_pi_div_two_right, Orientation.inner_eq_zero_of_oangle_eq_pi_div_two, Orientation.inner_mul_areaForm_sub', inner_sub_left, Matrix.posSemidef_gram, ProbabilityTheory.HasGaussianLaw.charFun_map_eq, Submodule.inner_orthogonalProjection_eq_of_mem_left, Submodule.inner_left_of_mem_orthogonal, MeasureTheory.L2.inner_indicatorConstLp_eq_setIntegral_inner, SeparationQuotient.inner_mk_mk, inner_eq_zero_of_left, neg_one_le_real_inner_of_norm_eq_one, HilbertBasis.repr_apply_apply, Complex.inner, Orthonormal.inner_finsupp_eq_sum_left, LinearIsometryEquiv.inner_map_map, ProperCone.relative_hyperplane_separation, contDiffAt_inner, lp.summable_inner, MeasureTheory.measureReal_abs_gt_le_integral_charFun, DifferentiableOn.inner, Submodule.inner_right_of_mem_orthogonal, Differentiable.inner, signedDist_linear_apply, Orientation.inner_rightAngleRotation_swap, inner_self_ofReal_norm, rankOne_comp_rankOne, Orientation.inner_smul_rotation_pi_div_two_left, parallelogram_law, Submodule.orthogonal_closure', re_inner_self_pos, inner_eq_neg_one_iff_of_norm_eq_one, Submodule.mem_orthogonal, EuclideanSpace.basisFun_inner, inner_smul_right, lp.inner_single_left, Real.fourierIntegral_convergent_iff, inner_eq_one_iff_of_norm_eq_one, innerₗ_apply_apply, LinearMap.eq_adjoint_iff_basis, Function.hasTemperateGrowth_inner_left, MeasureTheory.Integrable.inner_const, inner_sum_smul_sum_smul_of_sum_eq_zero, gramSchmidt_def'', MeasureTheory.norm_one_sub_charFun_le_two, EuclideanGeometry.inner_weightedVSub, inner_map_self_eq_zero, OrthogonalFamily.eq_ite, Orientation.inner_sq_add_areaForm_sq, Continuous.inner, norm_add_sq_real, inner_smul_real_left, ext_iff_inner_right, norm_add_sq, EuclideanSpace.inner_basisFun_real, innerSLFlip_apply, inner_eq_ofReal_norm_sq_left_iff, norm_add_mul_self, SchwartzMap.lineDerivOp_fourierInv_eq, EuclideanGeometry.inner_nonneg_of_dist_le_radius, Orientation.inner_eq_zero_iff_eq_zero_or_eq_smul_rotation_pi_div_two, contDiff_inner, Real.fourier_bilin_convolution_eq_integral, LinearMap.adjoint_inner_left, inner_vsub_vsub_left_eq_dist_sq_right_iff, Matrix.star_dotProduct_gram_mulVec, LinearMap.IsSymmetric.hasEigenvalue_iInf_of_finiteDimensional, MeasureTheory.charFun_eq_charFunDual_toDualMap, real_inner_sub_sub_self, Submodule.IsOrtho.inner_eq, ContMDiff.inner_bundle, real_inner_self_eq_norm_mul_norm, signedDist_vadd_left, MeasureTheory.charFun_zero_measure, lp.hasSum_inner, isBoundedBilinearMap_inner, OrthonormalBasis.norm_le_card_mul_iSup_norm_inner, ContinuousLinearMap.isPositive_iff_complex, ProbabilityTheory.covarianceBilin_apply, instSymmEqInnerOfNat, fourierIntegral_half_period_translate, MeasureTheory.stronglyMeasurable_charFun, AffineSubspace.mem_perpBisector_iff_inner_pointReflection_vsub_eq_zero, Orientation.eq_zero_or_oangle_eq_iff_inner_eq_zero, Orthonormal.inner_finsupp_eq_zero, ContMDiffAt.inner_bundle, inner_sub_right, ContinuousLinearMap.isPositive_iff, signedDist_apply_linear_apply, Affine.Simplex.neg_one_lt_inner_vsub_altitudeFoot_div, MeasureTheory.measureReal_abs_inner_gt_le_integral_charFun, ProbabilityTheory.iIndepFun_iff_charFun_pi, MeasureTheory.L2.mem_L1_inner, IsCoercive.continuousLinearEquivOfBilin_apply, Unitary.inner_map_map, inner_gradientWithin_left, isConformalMap_iff, real_inner_eq_norm_add_mul_self_sub_norm_mul_self_sub_norm_mul_self_div_two, ProperCone.mem_innerDual, ContinuousLinearMap.adjointAux_inner_right, InnerProductGeometry.inner_eq_mul_norm_of_angle_eq_zero, GaussianFourier.integrable_cexp_neg_mul_sq_norm_add, MeasureTheory.L2.integrable_inner, LinearPMap.adjointDomainMkCLMExtend_apply, MeasureTheory.charFun_map_mul, inner_mul_symm_re_eq_norm, Orientation.inner_rightAngleRotationAux₁_right, Submodule.re_inner_starProjection_nonneg, ContDiffWithinAt.inner, LinearMap.IsPositive.inner_nonneg_right, inner_gramSchmidtOrthonormalBasis_eq_zero, inner_eq_norm_mul_iff_real, Submodule.mem_orthogonal_singleton_iff_inner_left, Submodule.mem_adjoint_iff, inner_eq_zero_symm, Orthonormal.orthogonalFamily, Inseparable.inner_eq_inner, gramSchmidtOrthonormalBasis_inv_triangular, conformalFactorAt_inner_eq_mul_inner, HilbertBasis.summable_inner_mul_inner, ContinuousLinearMap.isPositive_iff', Orientation.inner_rightAngleRotation_right, ProperCone.hyperplane_separation_of_notMem, OrthonormalBasis.inner_eq_one, re_inner_self_nonpos, LinearMap.IsSymmetric.im_inner_apply_self, innerₛₗ_apply, deriv_inner_apply, innerSL_apply, abs_real_inner_div_norm_mul_norm_eq_one_of_ne_zero_of_ne_zero_mul, stereographic_apply, inner_map_polarization, Submodule.inner_starProjection_left_eq_right, inner_smul_left_eq_smul, Orientation.kahler_apply_apply, Orientation.inner_rightAngleRotationAux₁_left, Matrix.submatrix_gram, HasDerivAt.inner, ContinuousLinearMap.adjoint_inner_right, LinearMap.isPositive_iff, tendsto_integral_exp_inner_smul_cocompact, inner_smul_right_eq_smul, orthonormal_iff_ite, ContinuousOn.inner, RCLike.wInner_one_eq_sum, inner_self_eq_one_of_norm_one, MeasureTheory.charFun_dirac, UniformSpace.Completion.inner_coe, EuclideanSpace.inner_toLp_toLp, TemperedDistribution.lineDerivOp_fourierInv_eq, sphere_ext_iff, inner_self_re_eq_norm, LinearMap.IsSymmetric.conj_inner_sym, Filter.Tendsto.inner, MeasureTheory.Integrable.const_inner, ProbabilityTheory.IsGaussian.charFun_eq, ContinuousAt.inner_bundle, EuclideanGeometry.dist_smul_vadd_eq_dist, ContinuousWithinAt.inner_bundle, AffineSubspace.mem_perpBisector_iff_inner_eq, SchwartzMap.integral_inner_fourier_fourier, ContDiffAt.inner, real_inner_smul_left, norm_add_mul_self_real, LinearMap.eq_adjoint_iff_basis_right, innerₛₗ_apply_coe, PiLp.inner_apply, norm_add_pow_two, hasGradientWithinAt_iff_tendsto, add_left, EuclideanSpace.inner_single_right, real_inner_add_add_self, norm_eq_sqrt_re_inner, inner_self_nonneg, Orientation.areaForm_rightAngleRotation_right, MDifferentiableAt.inner_bundle, Orientation.inner_smul_rotation_pi_div_two_smul_left, real_inner_div_norm_mul_norm_eq_one_of_ne_zero_of_pos_mul, abs_real_inner_div_norm_mul_norm_eq_one_iff, Orientation.inner_smul_rotation_pi_div_two_smul_right, UniformSpace.Completion.continuous_inner, re_inner_eq_norm_add_mul_self_sub_norm_sub_mul_self_div_four, EuclideanGeometry.inner_pos_of_dist_lt_radius, coe_innerₛₗ_apply, ContinuousWithinAt.inner, MeasureTheory.charFun_map_eq_charFunDual_smul, inner_vsub_vsub_left_eq_dist_sq_left_iff, continuousLinearMapOfBilin_apply, hasGradientWithinAt_iff_isLittleO, norm_sub_pow_two, Real.fourierInv_eq, DFinsupp.inner_sum, inner_matrix_row_row, MeasureTheory.intervalIntegrable_charFun, InnerProductGeometry.inner_eq_cos_angle_of_norm_eq_one, EuclideanGeometry.inner_vsub_vsub_of_mem_sphere_of_mem_sphere, MeasureTheory.charFun_eq_integral_innerProbChar, HasGradientAt.fderiv_apply, Orientation.inner_rightAngleRotation_self, inner_gradient_left, inner_sub_sub_self, ContinuousLinearMap.apply_norm_sq_eq_inner_adjoint_right, innerSL_apply_coe, HasStrictFDerivAt.inner, re_inner_le_norm, Orientation.inner_rev_eq_zero_of_oangle_eq_pi_div_two, inner_eq_one_iff_of_norm_one, ProbabilityTheory.charFun_gaussianReal, HilbertBasis.tsum_inner_mul_inner, LinearMap.isSymmetric_iff_inner_map_self_real, EuclideanGeometry.Sphere.secondInter_eq_lineMap, LinearMap.im_inner_adjoint_mul_self_eq_zero, ProbabilityTheory.IndepFun.charFun_map_add_eq_mul, Real.fourierInv_eq', MeasureTheory.charFun_zero, norm_sub_mul_self_real, Orientation.inner_rev_eq_zero_of_oangle_eq_neg_pi_div_two, real_inner_smul_self_right, InnerProductGeometry.sin_angle_add, MeasureTheory.norm_charFun_le, norm_inner_symm, MeasureTheory.measurable_charFun, OrthonormalBasis.sum_repr', ContinuousOn.inner_bundle, orthonormal_vecCons_iff, AffineSubspace.mem_perpBisector_pointReflection_iff_inner_eq_zero, real_inner_comm, InnerProductGeometry.inner_eq_zero_iff_angle_eq_pi_div_two, Orthonormal.inner_right_fintype, conj_inner_symm, inner_eq_norm_sq_right_iff, MeasureTheory.charFun_map_const_add, MeasureTheory.charFun_eq_pi_iff, DifferentiableWithinAt.inner, Real.fourierIntegralInv_eq, LinearPMap.adjointAux_inner, HilbertBasis.hasSum_inner_mul_inner, fderivInnerCLM_apply, Orthonormal.sum_inner_products_le, ContMDiffWithinAt.inner_bundle, MeasureTheory.charFun_prod, EuclideanGeometry.inner_vsub_vsub_of_dist_eq_of_dist_eq, LinearMap.IsSymmetric.coe_re_inner_apply_self, InnerProductGeometry.sin_angle_mul_norm_mul_norm, Real.fourier_eq', inner_gradient_right, DFinsupp.sum_inner, inner_conj_symm, Orientation.cos_oangle_eq_inner_div_norm_mul_norm, inner_im_symm, MeasureTheory.charFun_map_smul, real_inner_self_pos, OrthogonalFamily.inner_right_fintype, Orthonormal.inner_sum, ContinuousLinearMap.IsPositive.re_inner_nonneg_right, EuclideanGeometry.Sphere.mem_orthRadius_iff_inner_left, MeasureTheory.condExpL2_const_inner, EuclideanGeometry.Sphere.secondInter_eq_self_iff, inner_eq_ofReal_norm_sq_right_iff, Orientation.areaForm_rightAngleRotation_left, InnerProductGeometry.inner_eq_mul_norm_iff_angle_eq_zero, RCLike.inner_eq_wInner_one, inner_vsub_vsub_right_eq_dist_sq_right_iff, real_inner_mem_Icc_of_norm_eq_one, MeasureTheory.charFun_eq_integral_probChar, OrthogonalFamily.inner_right_dfinsupp, Orientation.inner_mul_inner_add_areaForm_mul_areaForm', MDifferentiable.inner_bundle, conformalAt_iff', inner_vsub_left_eq_zero_symm, inner_neg_left, inner_smul_left, MeasureTheory.charFun_map_add_const, Orientation.inner_mul_areaForm_sub, fderiv_inner_apply, norm_inner_le_norm, inner_matrix_col_col, OrthonormalBasis.inner_eq_ite, Orthonormal.inner_right_sum, Measurable.inner_const, unitary.inner_map_map, Orthonormal.tsum_inner_products_le, Matrix.gram_single, norm_eq_sqrt_real_inner, Orthonormal.inner_eq_zero, LinearMap.IsPositive.re_inner_nonneg_left, ContinuousLinearMapWOT.ext_inner_iff, norm_inner_div_norm_mul_norm_eq_one_iff, gramSchmidt_inv_triangular, LinearMap.IsSymmetric.apply_clm, Affine.Simplex.inner_vsub_vsub_altitudeFoot_eq_height_sq
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toNormedSpace 📖 | CompOp | 2845 mathmath: Matrix.l2_opNorm_toEuclideanCLM, OrthonormalBasis.singleton_repr, Pi.comul_eq_adjoint, Orientation.rightAngleRotationAux₁_rightAngleRotationAux₁, TensorProduct.mapInclIsometry_apply, ContinuousLinearMap.rayleigh_smul, Affine.Simplex.isTangentAt_insphere_iff_eq_touchpoint, ProbabilityTheory.variance_eq_integral, TemperedDistribution.lineDerivOpCLM_eq, NumberField.mixedEmbedding.fundamentalDomain_integerLattice, Submodule.starProjection_apply_eq_isComplProjection, Orientation.oangle_sign_smul_add_right, MeasureTheory.Lp.toTemperedDistributionCLM_apply, UpperHalfPlane.mdifferentiable_num, Orientation.oangle_eq_zero_or_eq_pi_iff_right_eq_smul, TemperedDistribution.fourierInv_toTemperedDistributionCLM_eq, hasSum_mellin_pi_mul_sq', MeasureTheory.Integrable.integral_norm_prod_right, Orthonormal.linearIndependent, MeasureTheory.mulEquivHaarChar_smul_integral_map, EuclideanGeometry.dist_smul_vadd_sq, Bundle.ContMDiffRiemannianMetric.isVonNBounded, real_inner_div_norm_mul_norm_eq_neg_one_iff, TensorProduct.enorm_lid, Orientation.oangle_ne_zero_and_ne_pi_iff_linearIndependent, Polynomial.mahlerMeasure_def_of_ne_zero, EulerSine.integral_cos_mul_cos_pow, TensorProduct.inner_tmul, ContinuousLinearMap.isPositive_iff_eq_sum_rankOne, Bundle.ContMDiffRiemannianMetric.contMDiff, continuousOn_stereoToFun, isPositive_rankOne_self, SmoothBumpCovering.toSmoothPartitionOfUnity_eq_mul_prod, ContDiffBump.ae_convolution_tendsto_right_of_locallyIntegrable, MonotoneOn.intervalIntegral_slope_le, Orthonormal.inner_left_finsupp, ProbabilityTheory.condIndepFun_iff_condExp_inter_preimage_eq_mul, ProbabilityTheory.isGaussian_iff_gaussian_charFun, ProperCone.innerDual_le_innerDual, exists_contMDiffMap_zero_one_of_isClosed, InformationTheory.integral_llr_add_mul_log_nonneg, NumberField.mixedEmbedding.normAtComplexPlaces_mixedSpaceOfRealSpace, OrthonormalBasis.orthogonalProjection_eq_sum, MeasureTheory.eLpNorm_condExp_le, LinearMap.IsSymmetric.inner_map_polarization, CuspFormClass.holo, LinearMap.adjoint_adjoint, Affine.Simplex.orthogonalProjectionSpan_map, TensorProduct.ext_iff_inner_left, EuclideanGeometry.vsub_orthogonalProjection_mem_direction_orthogonal, toLinearIsometry_toDual, integral_cos, SchwartzMap.integral_sesq_fourier_fourier, ProbabilityTheory.condDistrib_ae_eq_condExp, MeasureTheory.charFun_eq_fourierIntegral', PeriodPair.hasFPowerSeriesAt_weierstrassPExcept, Real.hasFDerivAt_fourierChar_neg_bilinear_left, span_gramSchmidtNormed, instIsManifoldRealEuclideanSpaceFinModelWithCornersSelfTopWithTopENatElemHAddNatOfNatSphere, real_inner_div_norm_mul_norm_eq_neg_one_of_ne_zero_of_neg_mul, hasFDerivAt_iff_hasGradientAt, Function.hasTemperateGrowth_inner_right, Isometry.preimage_perpBisector, NumberField.Units.finrank_eq_rank, IsHilbertSum.surjective_isometry, ValueDistribution.proximity_zero, Affine.Simplex.ExcenterExists.excenter_notMem_affineSpan_face, Affine.Simplex.smul_mongePoint_vsub_circumcenter_eq_sum_vsub, ContinuousLinearMap.isSelfAdjoint_iff_isSymmetric, Submodule.reflection_trans_reflection, Real.fourierCoeff_tsum_comp_add, ModularFormClass.qExpansionFormalMultilinearSeries_apply_norm, Orientation.inner_rotation_pi_div_two_right_smul, ModularFormClass.hasFPowerSeries_cuspFunction, tendsto_tsum_div_pow_atTop_integral, Orientation.oangle_add_left_smul_rotation_pi_div_two, Real.fourierIntegral_comp_linearIsometry, Real.fderiv_fourierIntegral, Submodule.orthogonalDecomposition_symm_apply, Affine.Simplex.sSameSide_excenter_singleton_point, ModularFormClass.qExpansionFormalMultilinearSeries_radius, OrthogonalFamily.linearIsometry_apply_single, ContinuousLinearMap.isStarProjection_iff_isSymmetricProjection, rankOne_one_left_eq_innerSL, Submodule.IsOrtho.starProjection_comp_starProjection, Affine.Simplex.neg_mul_lt_inner_vsub_altitudeFoot, Manifold.pathELength_eq_lintegral_mfderiv_Ioo, LinearMap.IsSymmetric.restrictScalars, ZSpan.volume_real_fundamentalDomain, Complex.kahler, ClosedSubmodule.toSubmodule_orthogonal_eq, SchwartzMap.inner_fourier_toL2_eq, Complex.areaForm, SchwartzMap.toLp_fourierTransformInv_eq, finrank_real_complex_fact', Real.hasDerivAt_sigmoid, PeriodPair.coeff_weierstrassPExceptSeries, ProbabilityTheory.analyticOn_mgf, MeasureTheory.lintegral_comp_eq_lintegral_meas_le_mul_of_measurable_of_sigmaFinite, Matrix.IsHermitian.det_abs, LinearMap.IsPositive.ne_zero_iff, OpenPartialHomeomorph.contDiff_unitBallBall_symm, ContinuousLinearMapWOT.le_nhds_iff_forall_inner_apply_le_nhds, ProbabilityTheory.condIndep_iff, deriv_abs, Complex.meromorphic_digamma, integral_sin_mul_cos₂, Affine.Simplex.finiteDimensional_direction_altitude, LinearMap.isPositive_adjoint_comp_self, ProbabilityTheory.covarianceBilinDual_apply', Submodule.toLinearEquiv_orthogonalDecomposition_symm, OrthonormalBasis.repr_injective, LinearMap.IsSymmetric.isFinitelySemisimple, AffineSubspace.mem_perpBisector_iff_inner_eq_zero', MeasureTheory.charFunDual_apply, ContinuousLinearMap.IsPositive.inner_left_eq_inner_right, PeriodPair.iteratedDeriv_weierstrassPExcept_self, Affine.Simplex.circumcenter_map, Complex.GammaIntegral_eq_mellin, ProbabilityTheory.hasGaussianLaw_iff_charFunDual_map_eq, norm_jacobiTheta₂_term_fderiv_ge, Matrix.spectrum_toEuclideanLin, norm_add_eq_iff_real, MeasureTheory.norm_condExpL2_le, contDiffAt_norm_smul_iff, NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_completeFamily_of_ne, intervalIntegral.mul_integral_comp_mul_sub, isIdempotentElem_rankOne_self, Matrix.cstar_nnnorm_def, AbsolutelyContinuousOnInterval.integral_deriv_eq_sub, intervalIntegral.integral_hasFDerivAt_of_tendsto_ae, Polynomial.Chebyshev.integral_measureT_eq_integral_cos, Orientation.linearEquiv_det_rotation, ContinuousLinearMapWOT.tendsto_iff_forall_inner_apply_tendsto, EuclideanGeometry.Sphere.wbtw_secondInter, Orientation.tan_oangle_add_left_smul_rotation_pi_div_two, Affine.Simplex.inv_height_eq_sum_mul_inv_dist, Affine.Simplex.ExcenterExists.excenter_notMem_affineSpan_faceOpposite, Matrix.l2_opNorm_mulVec, EuclideanGeometry.Cospherical.affineIndependent_of_mem_of_ne, PeriodPair.basis_one, Submodule.re_inner_starProjection_eq_normSq, ProperCone.innerDual_univ, Affine.Simplex.circumcenter_mem_affineSpan, Affine.Simplex.affineSpan_pair_altitudeFoot_eq_altitude, Orientation.kahler_comp_rightAngleRotation', dist_sq_lineMap_lineMap_of_inner_eq_zero, integral_const_on_unit_interval, circleIntegral_def_Icc, integral_exp_mul_Iic, MeasureTheory.submartingale_iff_expected_stoppedValue_mono, MeasureTheory.inner_condExpL2_left_eq_right, Orientation.rotation_eq_self_iff, Affine.Simplex.excenter_singleton_mem_affineSpan_range, ZLattice.covolume_eq_det_inv, one_add_cpow_hasFPowerSeriesAt_zero, Orientation.two_zsmul_oangle_smul_left_of_ne_zero, circleIntegrable_iff, ProbabilityTheory.covarianceBilinDual_apply, Submodule.reflection_orthogonal_apply, InnerProductGeometry.angle_normalize_left, hasFDerivAt_stereoInvFunAux, SchwartzMap.integral_clm_comp_lineDerivOp_right_eq_neg_left, ProbabilityTheory.IsGaussian.map_eq_gaussianReal, MeasureTheory.integral_fintype_prod_volume_eq_pow, Real.fderiv_fourierChar_neg_bilinear_right_apply, LinearMap.IsSymmetric.diagonalization_apply_self_apply, EuclideanGeometry.orthogonalProjection_congr, LinearMap.IsPositive.re_inner_nonneg_right, ConvexOn.map_set_average_le, real_inner_smul_self_left, intervalIntegral.fderiv_integral_of_tendsto_ae, flip_innerSL_real, LipschitzWith.memLp_lineDeriv, Orientation.volumeForm_robust_neg, Submodule.starProjection_orthogonal', RCLike.linearIndependent_of_ne_zero_of_wInner_one_eq_zero, SmoothPartitionOfUnity.contMDiffAt_finsum, LinearMap.IsSymmetric.im_inner_self_apply, ContinuousLinearMap.IsPositive.toLinearMap, Submodule.toLinearEquiv_orthogonalDecomposition, Affine.Simplex.dist_point_faceOppositeCentroid, differentiableWithinAt_abs_pos, OrthonormalBasis.toBasis_tensorProduct, TensorProduct.congrIsometry_refl_refl, eventually_enorm_mfderivWithin_symm_extChartAt_lt, MeasureTheory.condExpL2_ae_eq_zero_of_ae_eq_zero, LipschitzWith.ae_lineDeriv_sum_eq, SchwartzMap.lineDerivOp_fourier_eq, Orientation.inner_mul_inner_add_areaForm_mul_areaForm, intervalIntegral.measure_integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae_right, Orientation.areaForm_le, DifferentiableWithinAt.norm, det_fderivPolarCoordSymm, TensorProduct.enorm_comm, innerSL_apply_apply, Submodule.isOrtho_sup_right, SmoothPartitionOfUnity.locallyFinite, LinearIsometry.rTensor_def, EuclideanGeometry.Sphere.mem_orthRadius_iff_inner_right, Affine.Simplex.incenter_map, SchwartzMap.integral_bilin_fourierInv_eq, LinearMap.adjoint_innerₛₗ_apply, exists_smooth_one_nhds_of_subset_interior, Orientation.neg_rotation, Unitary.conjStarAlgEquiv_unitaryLinearIsometryEquiv, GaussianFourier.integral_cexp_neg_mul_sq_norm, inner_eq_norm_mul_iff, ProbabilityTheory.covarianceBilin_apply_eq_cov, ProbabilityTheory.covarianceBilin_self, LinearMap.adjoint_eq_toCLM_adjoint, ClosedSubmodule.orthogonal_gc, LinearMap.isPositive_id, AffineSubspace.left_mem_perpBisector, NumberField.mixedEmbedding.fundamentalCone.abs_det_completeBasis_equivFunL_symm, EuclideanGeometry.preimage_inversion_perpBisector_inversion, Submodule.orthogonalProjection_mem_subspace_eq_self, Affine.Triangle.sSameSide_affineSpan_pair_point_incenter, ContinuousLinearMap.IsPositive.inner_nonneg_right, SmoothPartitionOfUnity.nonneg, circleIntegral.integral_sub_inv_of_mem_ball, Orientation.eq_rotation_self_iff_angle_eq_zero, hasDerivAt_bernoulliFun, Orientation.volumeForm_neg_orientation, ProbabilityTheory.sum_prob_mem_Ioc_le, Complex.betaIntegral_scaled, MeasureTheory.pdf.integral_mul_eq_integral, GaussianFourier.integral_cexp_neg_mul_sq_norm_add_of_euclideanSpace, fourierCoeffOn.const_mul, span_gramSchmidtNormed_range, mellin_div_const, ProbabilityTheory.uncenteredCovarianceBilin_apply, Submodule.orthogonal_disjoint, InnerProductGeometry.angle_smul_right_of_pos, TemperedDistribution.lineDerivOp_fourier_eq, LinearMap.isSelfAdjoint_toContinuousLinearMap_iff, VonNeumannAlgebra.ext_iff, Submodule.starProjection_add_starProjection_orthogonal, Matrix.spectrum_toLpLin, contMDiff_neg_sphere, not_differentiableAt_norm_zero, ProbabilityTheory.hasDerivAt_integral_pow_mul_exp, OrthonormalBasis.orthogonalProjection_eq_sum_rankOne, Submodule.mem_orthogonal_singleton_iff_inner_right, circleAverage_log_norm_sub_const₁, BoxIntegral.unitPartition.mem_smul_span_iff, exists_eq_const_mul_intervalIntegral_of_nonneg, ContDiffBump.integral_normed, toDual_symm_apply, MeasureTheory.integral_fintype_prod_eq_prod, NumberField.mixedEmbedding.fundamentalCone.completeBasis_apply_of_ne, HasGradientAt.hasDerivAt', IsHilbertSum.linearIsometryEquiv_symm_apply, SmoothBumpCovering.exists_immersion_euclidean, IsOpen.exists_msmooth_support_eq, Affine.Triangle.sbtw_touchpoint_singleton, Affine.Triangle.dist_point_faceOppositeCentroid, Submodule.starProjection_singleton, IsOpen.exists_smooth_support_eq, SmoothPartitionOfUnity.locallyFinite', Real.rpow_eq_const_mul_integral, EuclideanGeometry.reflection_symm, interval_average_eq_div, Bundle.RiemannianMetric.isVonNBounded, Orientation.tan_oangle_add_right_smul_rotation_pi_div_two, Affine.Simplex.mem_circumsphere, ProbabilityTheory.setIntegral_condCDF, EuclideanGeometry.orthogonalProjection_contLinear, ClosedSubmodule.mem_orthogonal', integral_pow, fourierIntegral_gaussian_innerProductSpace', MeasureTheory.charFun_toDual_symm_eq_charFunDual, EuclideanGeometry.Sphere.mem_commonExtTangents_iff, OrthogonalFamily.orthonormal_sigma_orthonormal, canonicalCovariantTensor_eq_sum, fourier_gaussian_pi', MeasureTheory.charFun_eq_fourierIntegral, Matrix.PosSemidef.sqrt_eq_zero_iff, ProbabilityTheory.integral_continuousLinearMap_gaussianReal, integral_log_sin_zero_pi_div_two, lintegral_fderiv_lineMap_eq_edist, EuclideanGeometry.oangle_sign_eq_zero_iff_collinear, exists_eq_interval_average_of_noAtoms, MeasureTheory.Measure.addHaarScalarFactor_eq_integral_div, ConvexOn.set_average_mem_epigraph, Submodule.reflection_symm, PeriodPair.iteratedDeriv_derivWeierstrassPExcept_self, OrthonormalBasis.det_eq_neg_det_of_opposite_orientation, LinearMap.IsSymmetric.orthogonalFamily_eigenspaces, TensorProduct.ext_iff_inner_right_threefold', signedDist_right_congr, StrictConcaveOn.ae_eq_const_or_lt_map_average, intervalIntegral.integral_ofReal, ProbabilityTheory.hasGaussianLaw_iff_charFun_map_eq, MeasureTheory.lintegral_comp_eq_lintegral_meas_le_mul, OrthonormalBasis.det_to_matrix_orthonormalBasis_of_opposite_orientation, TensorProduct.toLinearEquiv_lidIsometry, GaussianFourier.integral_cexp_neg_mul_sq_norm_add, ContDiffOn.inner, EuclideanGeometry.reflection_map, ContinuousLinearMap.adjoint_id, smul_left, integral_exp, ClosedSubmodule.inf_orthogonal, integral_inv_of_pos, ContinuousLinearMap.isPositive_natCast, ContinuousLinearMap.isStarNormal_iff_norm_eq_adjoint, Submodule.starProjection_comp_starProjection_eq_zero_iff, Affine.Simplex.sign_signedInfDist_lineMap_incenter_touchpoint, Module.Basis.parallelepiped_basisFun, SchwartzMap.laplacianCLM_eq, LinearIsometryEquiv.conjStarAlgEquiv_apply, MeasureTheory.hasFiniteIntegral_prod_iff', Affine.Simplex.ExcenterExists.affineCombination_eq_excenter_iff, Real.vector_fourierIntegral_eq_integral_exp_smul, LinearMap.toMatrixOrthonormal_reindex, EuclideanGeometry.Sphere.mem_tangentsFrom_iff, ProbabilityTheory.covarianceOperator_apply, InnerProductGeometry.angle_smul_left_of_neg, ProbabilityTheory.cdf_paretoMeasure_eq_integral, InnerProductGeometry.angle_normalize_right, differentiableWithinAt_abs, im_inner_eq_norm_sub_i_smul_mul_self_sub_norm_add_i_smul_mul_self_div_four, LocallyBoundedVariationOn.ae_differentiableWithinAt, integral_sin_pow_three, LinearMap.IsSymmetricProjection.ext_iff, Real.hasFPowerSeriesOnBall_ofScalars_mul_add_zero, inner_left_rankOne_apply, instIsManifoldRealEuclideanSpaceFinOfNatNatEuclideanHalfSpaceModelWithCornersEuclideanHalfSpaceElemIcc, circleAverage_log_norm_sub_const_of_mem_closedBall, MeasureTheory.Lp.instFourierInvSMul, ClosedSubmodule.orthogonal_injective, hasStrictDerivAt_abs_pos, hasDerivWithinAt_abs_pos, Submodule.norm_starProjection_apply_le, EuclideanGeometry.Sphere.mem_commonTangents_iff, ProbabilityTheory.IsRatCondKernelCDF.setIntegral, LinearIsometry.map_starProjection', analyticOnNhd_circleMap, antideriv_bernoulliFun, NumberField.mixedEmbedding.commMap_apply_of_isComplex, innerₛₗ_apply_apply, differentiableAt_sigmoid, Affine.Simplex.excenterWeightsUnnorm_reindex, OrthonormalBasis.repr_self, Submodule.symmetric_isOrtho, differentiableOn_iteratedDerivWithin_cotTerm, ProbabilityTheory.IsCondKernelCDF.integral, intervalIntegral.integral_mono_on, Orientation.oangle_smul_left_of_neg, OrthogonalFamily.norm_sq_diff_sum, ContinuousLinearMap.eq_adjoint_iff, abs_setIntegral_mulExpNegMulSq_comp_sub_le_mul_measure, MeasureTheory.L2.inner_def, Orientation.volumeForm_map, Icc_isBoundaryPoint_bot, LinearMap.IsSymmetric.directSum_decompose_apply, Polynomial.Chebyshev.integral_T_real_mul_self_measureT_of_ne_zero, deriv_abs_neg, ProbabilityTheory.moment_one, integral_exp_neg_mul_rpow, MeasureTheory.BorelCantelli.martingalePart_process_ae_eq, Homeomorph.contDiff_unitBall, ContinuousLinearMap.IsPositive.smul_of_nonneg, rankOne_apply, Unitary.coe_linearIsometryEquiv_apply, OrthonormalBasis.toBasis_adjustToOrientation, Submodule.reflection_singleton_apply, Polynomial.Chebyshev.integral_measureT, intervalIntegral.integral_div, integral_sin_pow_pos, Affine.Triangle.orthocenter_eq_smul_vsub_vadd_circumcenter, EuclideanGeometry.inter_eq_singleton_orthogonalProjection, EuclideanGeometry.inversion_mem_perpBisector_inversion_iff', signedDist_left_congr, Affine.Simplex.ExcenterExists.touchpoint_map, Orientation.inner_rightAngleRotation_swap', EuclideanGeometry.angle_eq_iff_oangle_eq_or_wbtw, Complex.integral_rpow_mul_exp_neg_rpow, OrthonormalBasis.measurePreserving_repr, InformationTheory.leftDeriv_klFun_one, Submodule.reflection_apply, integral_Ioi_rpow_of_lt, SchwartzMap.integral_fourierInv_smul_eq, exists_smooth_tsupport_subset, MeasureTheory.withDensityᵥ_eq_withDensity_pos_part_sub_withDensity_neg_part, signedDist_triangle, Submodule.orthogonal_eq_bot_iff, TensorProduct.adjoint_map, PeriodPair.analyticAt_weierstrassPExcept, summableLocallyUniformlyOn_iteratedDerivWithin_cotTerm, SchwartzMap.inner_toL2_toL2_eq, tendsto_setIntegral_pow_smul_of_unique_maximum_of_isCompact_of_integrableOn, LinearIsometryEquiv.lTensor_apply, EuclideanGeometry.dist_eq_iff_eq_smul_rotation_pi_div_two_vadd_midpoint, ProbabilityTheory.gammaCDFReal_eq_integral, integral_bernoulliFun, gramSchmidt_def, ContinuousLinearMap.isPositive_self_comp_adjoint, LinearMap.adjoint_toContinuousLinearMap, Affine.Simplex.orthogonalProjectionSpan_eq_point, LocallyBoundedVariationOn.ae_differentiableAt, MeasurableEquiv.withDensity_ofReal_map_symm_apply_eq_integral_abs_det_fderiv_mul, MonotoneOn.intervalIntegrable_deriv, MeasureTheory.AEStronglyMeasurable.ae_integrable_condKernel_iff, Real.Icc_mem_vitaliFamily_at_left, Unitary.linearIsometryEquiv_coe_apply, LDL.lowerInv_eq_gramSchmidtBasis, MeasureTheory.MemLp.condExpL2_ae_eq_condExp, Orientation.abs_volumeForm_apply_of_orthonormal, ContDiffBump.normed_def, ContinuousLinearMap.toSesqForm_apply_coe, signedDist_linear_apply_apply, Affine.Simplex.sSameSide_incenter_point, EuclideanGeometry.collinear_iff_of_two_zsmul_oangle_eq, setIntegral_Ioi_zero_rpow, SchwartzMap.integral_bilin_fourierIntegral_eq, fourier_gaussian_innerProductSpace, EuclideanGeometry.oangle_midpoint_right, Affine.Simplex.ExcenterExists.excenter_map, integral_rpow_mul_exp_neg_rpow, LinearIsometryEquiv.adjoint_eq_symm, SchwartzMap.toLp_fourierInv_eq, NumberField.mixedEmbedding.negAt_apply_snd, TensorProduct.mapIsometry_id_id, MeasureTheory.measure_lt_one_eq_integral_div_gamma, MeasureTheory.setIntegral_prod_mul, Orientation.neg_rotation_neg_pi_div_two, Matrix.toEuclideanLin_apply, Real.one_add_rpow_hasFPowerSeriesOnBall_zero, Submodule.IsOrtho.orthogonalProjection_comp_subtypeL, LinearMap.IsPositive.isPositive_smul_iff, Polynomial.Chebyshev.integral_measureT_eq_integral_cos_of_continuous, VectorFourier.fourierPowSMulRight_eq_comp, EuclideanGeometry.orthogonalProjection_map, IsHilbertSum.hasSum_linearIsometryEquiv_symm, Submodule.IsOrtho.map_iff, MeasureTheory.integral_fintype_prod_eq_pow, MeasureTheory.charFun_apply, mfderivWithin_projIcc_one, intervalIntegral.integral_pos_iff_support_of_nonneg_ae', integral_cos_pow, Orientation.oangle_sign_sub_smul_left, ProbabilityTheory.integral_stieltjesOfMeasurableRat, Affine.Simplex.ExcenterExists.touchpoint_notMem_affineSpan_of_ne, EuclideanGeometry.Sphere.isTangentAt_of_dist_sq_eq_power, Affine.Simplex.abs_inner_vsub_altitudeFoot_div_lt_one, MeasureTheory.Measure.integral_isAddLeftInvariant_eq_smul_of_hasCompactSupport, Orientation.rightAngleRotation_def, EuclideanGeometry.angle_eq_zero_iff_eq_and_ne_or_sbtw, ProbabilityTheory.IndepFun.integral_comp_mul_comp, Function.HasTemperateGrowth.toTemperedDistribution_apply, Euclidean.closedBall_eq_image, Affine.Simplex.touchpoint_singleton_mem_interior_faceOpposite, MeasureTheory.Measure.integral_isMulLeftInvariant_isMulRightInvariant_combo, Orthonormal.inner_left_fintype, NumberField.mixedEmbedding.negAt_preimage, InformationTheory.not_differentiableWithinAt_klFun_Iio_zero, Complex.hasDerivAt_GammaIntegral, Submodule.coe_orthogonalDecomposition_symm, Affine.Simplex.excenterExists_reindex, LSeries_iteratedDeriv, Complex.analyticOnNhd_univ_iff_differentiable, SchwartzMap.integral_sesq_fourier_eq, MeasureTheory.aestronglyMeasurable_condExpL2, EuclideanGeometry.Sphere.secondInter_collinear, Submodule.orthogonalProjection_bot, Real.fderiv_fourier, intervalIntegral.integral_mono_ae_restrict, ContinuousLinearMap.adjointAux_norm, NumberField.mixedEmbedding.iUnion_negAt_plusPart_ae, Submodule.range_starProjection, BoxIntegral.unitPartition.integralSum_eq_tsum_div, InformationTheory.toReal_klDiv_eq_integral_klFun, LinearIsometryEquiv.inner_map_eq_flip, Quaternion.linearIsometryEquivTuple_symm_apply, Affine.Simplex.ninePointCircle_eq_circumsphere_medial, Probability.integral_cauchyPDFReal, intervalIntegral.hasFDerivAt_integral_of_dominated_loc_of_lip, MeasureTheory.SignedMeasure.singularPart_smul, Pi.counit_eq_adjoint, ProbabilityTheory.covarianceBilin_apply_basisFun_self, LinearMap.toMatrixOrthonormal_apply_apply, MeasureTheory.charFun_apply_real, Complex.taylorSeries_eq_on_ball', Orientation.areaForm_to_volumeForm, stereoInvFunAux_apply, Icc_isInteriorPoint_interior, fourierCoeff_bernoulli_eq, Submodule.exists_add_mem_mem_orthogonal, circleAverage_log_norm_sub_const_eq_log_radius_add_posLog, signedDist_le_dist, EuclideanGeometry.Sphere.IsTangentAt.mem_space, Affine.Simplex.circumcenter_reindex, OpenPartialHomeomorph.contDiff_univUnitBall, LinearMap.IsSymmetric.coe_re_inner_self_apply, EulerSine.integral_cos_mul_cos_pow_aux, SchwartzMap.fourier_lineDerivOp_eq, EuclideanGeometry.affineSpan_of_orthocentricSystem, TemperedDistribution.instLineDerivLeftSMulReal, AffineSubspace.mem_perpBisector_iff_inner_eq_zero, Orientation.areaForm_neg_orientation, EuclideanGeometry.inversion_vsub_center, Orientation.rightAngleRotation_trans_rightAngleRotation, Module.Basis.mulOpposite_is_orthonormal_iff, Function.Periodic.sInf_add_zsmul_le_integral_of_pos, EuclideanSpace.instFactEqNatFinrankFin, differentiable_euclidean, NumberField.mixedEmbedding.stdBasis_apply_isComplex_snd, Monotone.ae_differentiableAt, ProbabilityTheory.iCondIndep_iff, ProbabilityTheory.centralMoment_one', MeasureTheory.integral_fin_nat_prod_volume_eq_prod, TemperedDistribution.fourierInv_lineDerivOp_eq, MeasureTheory.condExpL2_indicator_ae_eq_smul, Affine.Simplex.excenter_eq_affineCombination, mfderivWithin_comp_projIcc_one, ProbabilityTheory.iCondIndepFun_iff_condExp_inter_preimage_eq_mul, UpperHalfPlane.mdifferentiable_inv_denom, Affine.Triangle.dist_div_sin_angle_eq_two_mul_circumradius, ClosedSubmodule.orthogonal_closure'', contDiffWithinAt_euclidean, SimpleGraph.lapMatrix_toLinearMap₂'_apply'_eq_zero_iff_forall_reachable, NumberField.mixedEmbedding.negAt_signSet_apply_isComplex, LinearIsometryEquiv.adjoint_toLinearMap_eq_symm, SmoothPartitionOfUnity.sum_finsupport', ProbabilityTheory.variance_le_sub_mul_sub, toDualMap_apply_apply, EuclideanGeometry.Sphere.commonIntTangents_union_commonExtTangents, Submodule.le_orthogonal_orthogonal, ContDiffBump.measure_closedBall_div_le_integral, Orientation.kahler_eq_zero_iff, LinearMap.eq_adjoint_iff_basis_left, Orientation.oangle_sign_sub_smul_right, ProperCone.innerDual_sUnion, AffineSubspace.perpBisector_nonempty, signedDist_apply_apply, LinearMap.IsSymmetricProjection.isIdempotentElem, integral_sin_sq, SchwartzMap.integral_norm_sq_fourier, Orientation.oangle_smul_left_self_of_nonneg, Affine.Simplex.altitudeFoot_mem_affineSpan_image_compl, UnitAddTorus.mFourierCoeff_toLp, ProbabilityTheory.gaussianReal_map_continuousLinearMap, Manifold.pathELength_def, IccLeftChart_extend_interior_pos, Orientation.areaForm_swap, NumberField.mixedEmbedding.euclidean.stdOrthonormalBasis_map_eq, ext_inner_map, ProbabilityTheory.covarianceOperator_zero, Bundle.ContinuousRiemannianMetric.symm, integral_exp_mul_complex_Ioi, LinearIsometryEquiv.measurePreserving, MeasureTheory.SignedMeasure.withDensityᵥ_rnDeriv_eq, setIntegral_Ioi_zero_cpow, Submodule.instHasOrthogonalProjectionOfCompleteSpace, Affine.Simplex.finrank_direction_altitude, OrthogonalFamily.linearIsometry_apply_dfinsupp_sum_single, InformationTheory.tendsto_rightDeriv_klFun_atTop, TemperedDistribution.instFourierAdd, intervalIntegral.integral_mono, Complex.sameRay_of_arg_eq, MeasureTheory.Integrable.integral_norm_condDistrib_map, NumberField.mixedEmbedding.normAtComplexPlaces_polarSpaceCoord_symm, MeasureTheory.ComplexMeasure.singularPart_add_withDensity_rnDeriv_eq, LinearMap.nonneg_iff_isPositive, hasDerivAt_abs_neg, Affine.Simplex.mongePoint_mem_mongePlane, Orientation.kahler_swap, coe_innerSL_apply, Orientation.det_rotation, Orientation.rotation_pi_apply, LinearMap.IsSymmetric.inner_map_self_eq_zero, OrthonormalBasis.prod_apply, intervalIntegral.integral_mono_interval, PeriodPair.hasFPowerSeriesAt_derivWeierstrassPExcept, Affine.Simplex.isTangentAt_insphere_touchpoint, Orientation.rotation_rotation, MeasureTheory.condExp_smul_of_aestronglyMeasurable_right, Affine.Simplex.excenterWeightsUnnorm_map, LSeries_analyticOnNhd, EuclideanGeometry.Sphere.IsExtTangentAt.wbtw, Matrix.PosSemidef.det_sqrt, MeasureTheory.integral_condExpL2_eq, ContinuousLinearMap.instStarOrderedRing, TemperedDistribution.instFourierSMul, instIsContinuousRiemannianBundleTrivial, DifferentiableWithinAt.dist, hasDerivWithinAt_abs, contDiff_circleMap, Affine.Simplex.ExcenterExists.affineSpan_faceOpposite_eq_orthRadius, TensorProduct.lidIsometry_apply, intervalIntegral.integral_mono_on_of_le_Ioo, eventually_norm_mfderivWithin_symm_extChartAt_lt, ProbabilityTheory.IsRatCondKernelCDFAux.tendsto_integral_of_antitone, NumberField.mixedEmbedding.fundamentalCone.logMap_expMapBasis, Affine.Simplex.inner_mongePoint_vsub_face_centroid_vsub, BoundedVariationOn.intervalIntegrable_deriv, Orientation.volumeForm_def, ProbabilityTheory.Kernel.setIntegral_densityProcess_of_mem, VectorFourier.hasFDerivAt_fourierIntegral, MeasureTheory.Integrable.tendsto_eLpNorm_condExp, LinearMap.IsPositive.inner_nonneg_left, MeasureTheory.convolution_precompR_apply, ContinuousLinearMap.instCStarRingId, ProbabilityTheory.condIndepSets_singleton_iff, VectorFourier.fourierIntegral_iteratedFDeriv, MonotoneOn.sum_le_integral, UpperHalfPlane.contMDiff_coe, InformationTheory.hasDerivAt_klFun, MeasureTheory.setIntegral_condExpL2_indicator, CuspForm.holo', contMDiff_coe_sphere, integral_cos_pow_aux, nnnorm_rankOne, Differentiable.hasFPowerSeriesOnBall, ProbabilityTheory.isPosSemidef_covarianceBilin, stereographic_apply_neg, intervalIntegral.abs_intervalIntegral_eq, OrthonormalBasis.orthogonalProjection_apply_eq_sum, Orientation.kahler_comp_rightAngleRotation, InformationTheory.toReal_klDiv, TemperedDistribution.instFourierPairInv, EuclideanGeometry.oangle_eq_pi_iff_sbtw, TemperedDistribution.instFourierPair, ae_differentiableAt_norm, IsOpen.exists_contMDiff_support_eq_aux, HasGradientWithinAt.differentiableWithinAt, LinearMap.trace_eq_sum_inner, TemperedDistribution.delta_apply, NumberField.Units.instZLattice_unitLattice, Manifold.pathELength_eq_lintegral_mfderivWithin_Icc, Affine.Simplex.circumcenter_eq_affineCombination_of_pointsWithCircumcenter, PeriodPair.analyticOnNhd_derivWeierstrassPExcept, MeasureTheory.BorelCantelli.predictablePart_process_ae_eq, ProbabilityTheory.iIndepSet.condExp_indicator_filtrationOfSet_ae_eq, isSymmetricProjection_rankOne_self, PositiveLinearMap.gnsNonUnitalStarAlgHom_apply_coe, ProbabilityTheory.tendsto_integral_truncation, Orientation.volumeForm_zero_pos, ProbabilityTheory.tilted_mul_apply_eq_ofReal_integral_mgf', fourierIntegral_gaussian_pi, ProbabilityTheory.uncenteredCovarianceBilinDual_of_not_memLp, Bundle.ContinuousRiemannianMetric.continuous, hasSum_mellin, Affine.Simplex.affineSpan_faceOpposite_eq_orthRadius_insphere, iteratedDerivWithin_cot_pi_mul_eq_mul_tsum_div_pow, SchwartzMap.laplacianCLM_eq', hasGradientWithinAt_iff_hasFDerivWithinAt, norm_inner_eq_norm_iff, MeasureTheory.condExp_mul_of_aestronglyMeasurable_right, integral_exp_mul_complex, ContinuousLinearMap.apply_norm_sq_eq_inner_adjoint_left, DifferentiableOn.contDiffOn, EuclideanGeometry.Sphere.orthRadius_center, NumberField.Units.span_basisOfIsMaxRank, inner_eq_norm_mul_iff_div, Submodule.topologicalClosure_eq_self, instIsManifoldRealEuclideanSpaceFinOfNatNatModelWithCornersSelfTopWithTopENatCircle, SmoothBumpCovering.toSmoothPartitionOfUnity_apply, VectorFourier.norm_iteratedFDeriv_fourierPowSMulRight, ProbabilityTheory.Kernel.martingale_densityProcess, range_stereographic_symm, Complex.GammaIntegral_ofReal, TemperedDistribution.instContinuousFourier, HasGradientAtFilter.hasDerivAtFilter', MonotoneOn.integral_le_sum_Ico, EuclideanGeometry.orthogonalProjection_apply', SmoothPartitionOfUnity.contDiffAt_finsum, intervalIntegral.intervalIntegral_pos_of_pos, isOpenEmbedding_stereographic_symm, Chebyshev.integral_one_div_log_sq_isBigO, LinearMap.IsSymmetric.hasEigenvalue_iSup_of_finiteDimensional, MeasureTheory.lintegral_nnnorm_condExpL2_indicator_le, NumberField.Units.basisOfIsMaxRank_apply, EuclideanGeometry.Sphere.coe_secondInter, Orientation.measure_eq_volume, Complex.integral_exp_neg_rpow, MeasureTheory.SignedMeasure.absolutelyContinuous_iff_withDensityᵥ_rnDeriv_eq, PeriodPair.basis_zero, ProbabilityTheory.analyticAt_mgf, NumberField.mixedEmbedding.negAt_signSet_apply_isReal, Matrix.PosSemidef.posSemidef_sqrt, unitary.linearIsometryEquiv_coe_symm_apply, ContinuousLinearMap.isPositive_def, integral_le_sum_mul_Ico_of_antitone_monotone, LipschitzWith.ae_lineDifferentiableAt, EuclideanGeometry.oangle_midpoint_rev_left, InformationTheory.leftDeriv_klFun, integral_bernoulliFun_eq_zero, Affine.Triangle.touchpoint_singleton_sbtw, OrthonormalBasis.coe_ofRepr, Submodule.starProjection_top', MeasureTheory.Integrable.tendsto_ae_condExp, Orientation.rotation_symm, EuclideanGeometry.Sphere.isTangent_iff_isTangentAt_orthogonalProjection, OrthonormalBasis.toBasis_mulOpposite, Submodule.adjoint_subtypeL, NumberField.mixedEmbedding.fundamentalDomain_idealLattice, Affine.Simplex.exradius_map, MeasureTheory.Integrable.integral_norm_comp, LinearMap.isSymmetric_adjoint_mul_self, ProbabilityTheory.differentiableAt_mgf, UpperHalfPlane.contMDiff_inv_denom, Orientation.oangle_eq_zero_iff_sameRay, Submodule.reflection_orthogonalComplement_singleton_eq_neg, Complex.orthonormalBasisOneI_repr_apply, NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_completeFamily_of_eq, analyticOn_log, Affine.Triangle.dist_circumcenter_reflection_orthocenter, MeasureTheory.norm_condExpL2_coe_le, MeasureTheory.setLIntegral_nnnorm_condExpL2_indicator_le, trace_rankOne, analyticOnNhd_log, Orientation.angle_eq_iff_oangle_eq_or_sameRay, Real.fourierIntegralInv_comp_linearIsometry, Affine.Simplex.ExcenterExists.sign_signedInfDist_touchpoint, ProbabilityTheory.iteratedDeriv_mgf, SchwartzMap.delta_apply, InnerProductGeometry.angle_eq_zero_iff, Affine.Simplex.abs_inner_vsub_altitudeFoot_lt_mul, ProbabilityTheory.tilted_mul_apply_eq_ofReal_integral_mgf, SchwartzMap.norm_fourier_toL2_eq, Submodule.isIdempotentElem_starProjection, norm_cauchyPowerSeries_le, Orientation.rotation_map, ProbabilityTheory.Kernel.setIntegral_densityProcess_of_le, Orientation.oangle_rotation_left, Real.one_div_one_sub_sq_hasFPowerSeriesOnBall_zero, SchwartzMap.instFourierPair, hasFDerivAt_norm_rpow, ProperCone.innerDual_zero, LinearIsometry.inner_map_map, Affine.Simplex.excenterWeights_reindex, EuclideanGeometry.collinear_of_angle_eq_zero, Metric.exists_smooth_forall_closedBall_subset, EuclideanGeometry.Sphere.tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center, instLieGroupRealEuclideanSpaceFinOfNatNatModelWithCornersSelfTopWithTopENatCircle, fourier_gaussian_innerProductSpace', ContDiffBump.convolution_tendsto_right, Affine.Simplex.ExcenterExists.isTangentAt_touchpoint, intervalIntegral.integral_lt_integral_of_continuousOn_of_le_of_exists_lt, Affine.Simplex.inradius_reindex, hasDerivAt_abs_rpow, ContinuousLinearMap.IsPositive.conj_adjoint, Matrix.toEuclideanCLM_toLp, signedDist_eq_zero_of_orthogonal, EuclideanGeometry.preimage_inversion_perpBisector, hasSum_fourier_series_L2, NumberField.mixedEmbedding.mem_span_fractionalIdealLatticeBasis, integral_cpow, ContinuousLinearMap.isPositive_id, ZSpan.volume_fundamentalDomain, ProbabilityTheory.iteratedDeriv_complexMGF, ProbabilityTheory.covarianceBilin_zero, Real.tendsto_integral_gaussian_smul', contDiffOn_stereoToFun, Real.hasFDerivAt_fourier, VectorFourier.differentiable_fourierIntegral, Affine.Simplex.incenter_mem_interior, Affine.Simplex.mongePoint_eq_affineCombination_of_pointsWithCircumcenter, MeasureTheory.condExp_mul_of_stronglyMeasurable_right, Unitary.coe_symm_linearIsometryEquiv_apply, Affine.Simplex.altitudeFoot_map, analyticOnNhd_sigmoid, LinearMap.adjoint_rTensor, Matrix.PosSemidef.sqrt_eq_one_iff, LinearMap.IsPositive.add, ProbabilityTheory.integral_truncation_eq_intervalIntegral, ProbabilityTheory.condExpKernel_ae_eq_condExp', Real.deriv_Gamma_nat, HilbertBasis.hasSum_orthogonalProjection, LinearMap.adjoint_inner_right, adjoint_rankOne, stereoInvFun_apply, Isometry.mapsTo_perpBisector, EuclideanGeometry.Cospherical.affineIndependent_of_ne, rankOne_eq_zero, Affine.Simplex.circumcenter_eq_point, Real.fourierIntegral_convergent_iff', Matrix.PosSemidef.sqrt_sq, RCLike.mul_wInner_left, TensorProduct.ext_iff_inner_left_threefold', Submodule.isOrtho_sSup_right, LinearIsometry.lTensor_apply, ClosedSubmodule.bot_orthogonal_eq_top, Submodule.norm_sq_eq_add_norm_sq_starProjection, inner_map_polarization', Bundle.ContMDiffRiemannianMetric.symm, inner_right_rankOne_apply, HilbertBasis.hasSum_repr, Real.fourier_comp_linearIsometry, MeasureTheory.integral_comap_eq_addEquivAddHaarChar_smul, innerSL_inj, LSeries_eq_mul_integral_of_nonneg, ProbabilityTheory.analyticOnNhd_cgf, real_inner_div_norm_mul_norm_eq_one_iff, TensorProduct.ext_iff_inner_left_threefold, MeasureTheory.lintegral_nnnorm_condExpL2_le, SmoothPartitionOfUnity.le_one, EuclideanGeometry.oangle_eq_zero_iff_wbtw, Monotone.ae_hasDerivAt, StrongDual.toLp_of_not_memLp, ProbabilityTheory.IsCondKernelCDF.setIntegral, LinearMap.IsSymmetric.coe_toSelfAdjoint, SchwartzMap.norm_fourierTransformCLM_toL2_eq, TensorProduct.inner_lid_lid, OrthonormalBasis.toBasis_map, Matrix.piLp_ofLp_toEuclideanLin, LinearMap.IsSymmetric.diagonalization_symm_apply, maximal_orthonormal_iff_basis_of_finiteDimensional, TensorProduct.norm_comm, LinearIsometryEquiv.coe_toMeasurableEquiv, ContinuousLinearMap.isPositive_toLinearMap_iff, Affine.Simplex.signedInfDist_apply_self, VectorFourier.iteratedFDeriv_fourierIntegral, exists_contMDiffMap_zero_one_nhds_of_isClosed, ProbabilityTheory.HasCondSubgaussianMGF.ae_condExp_le, Real.one_div_one_sub_hasFPowerSeriesOnBall_zero, ContDiffBump.normed_convolution_eq_right, ProbabilityTheory.gaussianReal_map_linearMap, rankOne_eq_rankOne_iff_comm, toDual_apply, OrthonormalBasis.tensorProduct_repr_tmul_apply', HasDerivWithinAt.inner, AbsolutelyContinuousOnInterval.integral_deriv_mul_eq_sub, BoxIntegral.integral_nonneg, DifferentiableAt.inner, Real.differentiable_fourierIntegral, IntervalIntegrable.absolutelyContinuousOnInterval_intervalIntegral, NumberField.mixedEmbedding.fundamentalCone.prod_deriv_expMap_single, Real.fourierInv_comp_linearIsometry, MeasureTheory.hasFDerivAt_convolution_right_with_param, ProbabilityTheory.IsGaussian.charFun_eq', ProbabilityTheory.covarianceBilinDual_eq_covariance, Matrix.PosSemidef.eq_sqrt_iff_sq_eq, signedDist_zero, LinearIsometryEquiv.reflections_generate, AffineSubspace.signedInfDist_eq_signedDist_orthogonalProjection, EulerSine.sin_pi_mul_eq, Submodule.map_orthogonal_equiv, integral_exp_Iic, Chebyshev.primeCounting_eq_theta_div_log_add_integral, integral_mul_cexp_neg_mul_sq, Matrix.l2_opNNNorm_mulVec, MeasureTheory.integrable_comp, NumberField.mixedEmbedding.span_idealLatticeBasis, NumberField.mixedEmbedding.fundamentalCone.norm_expMapBasis, InformationTheory.integral_llr_add_sub_measure_univ_nonneg, MeasureTheory.Integrable.integral_norm_prod_left, HasCompactSupport.hasFDerivAt_convolution_right, frontier_range_modelWithCornersEuclideanHalfSpace, ClosedSubmodule.top_orthogonal_eq_bot, VonNeumannAlgebra.centralizer_centralizer', SchwartzMap.integral_bilinear_deriv_right_eq_neg_left, MeasureTheory.condExp_stronglyMeasurable_simpleFunc_mul, ProbabilityTheory.covarianceBilinDual_zero, EuclideanGeometry.reflection_reflection, Submodule.norm_orthogonalProjection_apply_le, Affine.Simplex.ExcenterExists.sOppSide_excenter_point_iff, contDiff_bernoulliFun, Affine.Simplex.incenter_notMem_affineSpan_face, HasFDerivWithinAt.inner, TensorProduct.norm_assoc, EuclideanSpace.instIsManifoldSphere, TensorProduct.nnnorm_tmul, Affine.Triangle.affineSpan_pair_eq_orthRadius, comp_rankOne, OrthonormalBasis.starProjection_eq_sum_rankOne, MeasureTheory.tendsto_sum_indicator_atTop_iff, Orientation.abs_volumeForm_apply_of_pairwise_orthogonal, toDualMap_apply, ContinuousLinearMap.adjoint_inner_left, TensorProduct.inner_mapIncl_mapIncl, circleAverage_log_norm_sub_const₀, Orientation.oangle_rotation_oangle_right, ProbabilityTheory.condIndepSet_iff, MeasureTheory.lintegral_comp_eq_lintegral_meas_le_mul_of_measurable, ProbabilityTheory.differentiableOn_mgf, contDiffOn_abs, ProbabilityTheory.analyticAt_complexMGF, HurwitzZeta.hurwitzEvenFEPair_zero_symm, AlgebraOfCoalgebra.mul_def, MeasureTheory.Integrable.integral_norm_condExpKernel, circleIntegral.integral_sub_zpow_of_undef, ContinuousLinearMap.apply_norm_eq_sqrt_inner_adjoint_right, EuclideanGeometry.image_inversion_perpBisector, innerₗ_apply, SmoothBumpFunction.contMDiffAt, Orientation.rightAngleRotation_symm, Affine.Simplex.mongePlane_def, Affine.Triangle.acuteAngled_iff_angle_lt, PeriodPair.weierstrassPExcept_eq_tsum, ContinuousLinearMap.IsPositive.isSymmetric, Real.one_div_sub_hasFPowerSeriesOnBall_zero, OrthonormalBasis.equiv_apply, ContDiff.euclidean_dist, inner_eq_sum_norm_sq_div_four, MeasureTheory.condExp_mul_of_aestronglyMeasurable_left, LinearIsometryEquiv.conjStarAlgEquiv_trans, MeasurableEmbedding.withDensity_ofReal_comap_apply_eq_integral_abs_det_fderiv_mul, Bundle.ContMDiffRiemannianMetric.pos, ProbabilityTheory.tilted_mul_apply_eq_ofReal_integral_cgf', signedDist_triangle_left, TemperedDistribution.fourier_toTemperedDistributionCLM_eq, LinearMap.IsSymmetric.continuous, IsContMDiffRiemannianBundle.exists_contMDiff, sum_Ico_le_integral_of_le, Affine.Simplex.excenterExists_map, integral_sin_pow_mul_cos_pow_odd, LinearIsometry.extend_apply, rank_rankOne, LinearMap.isSymmetric_sum, integral_rpow_mul_exp_neg_mul_rpow, SmoothBumpCovering.sum_toSmoothPartitionOfUnity_eq, Submodule.isOrtho_top_left, ProbabilityTheory.integral_gaussianPDFReal_eq_one, toDual_apply_apply, Affine.Simplex.vectorSpan_isOrtho_altitude_direction, integral_exp_mul_I_eq_sinc, ContinuousLinearMap.adjointAux_apply, contMDiff_subtype_coe_Icc, ContinuousLinearMap.nonneg_iff_isPositive, Orientation.inner_rotation_pi_div_two_right, Affine.Simplex.exsphere_reindex, ContinuousLinearMap.inner_map_map_iff_adjoint_comp_self, Submodule.linearEquiv_det_reflection, LinearMap.isSymmetric_linearIsometryEquiv_conj_iff, ProperCone.innerDual_singleton, Submodule.IsOrtho.map, EuclideanGeometry.reflection_eq_self_iff, NumberField.mixedEmbedding.fundamentalCone.completeBasis_apply_of_eq, InformationTheory.integral_klFun_rnDeriv, differentiable_inner, intervalIntegral.abs_integral_mono_interval, PeriodPair.meromorphic_derivWeierstrassP, OrthonormalBasis.volume_parallelepiped, hasFDerivAt_integral_of_dominated_loc_of_lip', Submodule.toLinearMap_starProjection_eq_isComplProjection, integral_id, Affine.Simplex.altitudeFoot_mem_affineSpan, rankOne_def, TensorProduct.nnnorm_map, Orientation.oangle_rotation, ExistsContDiffBumpBase.u_int_pos, SchwartzMap.integral_mul_laplacian_right_eq_left, stereoToFun_apply, ContinuousLinearMap.adjointAux_inner_left, SchwartzMap.convolution_apply, Submodule.sub_starProjection_mem_orthogonal, Real.differentiableAt_Gamma, orthogonalBilin_innerₗ, NumberField.mixedEmbedding.mem_span_latticeBasis, ProbabilityTheory.evariance_eq_lintegral_ofReal, TemperedDistribution.fourierTransformInv_toTemperedDistributionCLM_eq, ProbabilityTheory.integral_condVar_add_variance_condExp, ContDiffWithinAt.norm_sq, Function.hasTemperateGrowth_norm_sq, ProbabilityTheory.analyticOn_cgf, LinearIsometryEquiv.conjStarAlgEquiv_ext_iff, OrthonormalBasis.repr_apply_apply, ProbabilityTheory.covarianceBilin_comm, intervalIntegral.integral_congr_codiscreteWithin, ProbabilityTheory.Kernel.tendsto_integral_density_of_monotone, Orientation.inner_rotation_pi_div_two_left, ContinuousLinearMap.IsStarNormal.ker_adjoint_eq_ker, SchwartzMap.integral_bilin_fourier_eq, InformationTheory.klDiv_of_ac_of_integrable, gradient_eq_deriv', Orientation.oangle_rotation_self_left, ClosedSubmodule.orthogonal_eq_inter, Orientation.kahler_neg_orientation, MeasureTheory.L2.integral_inner_eq_sq_eLpNorm, MonotoneOn.intervalIntegrable_slope, Affine.Triangle.circumsphere_eq_of_dist_of_oangle, NumberField.mixedEmbedding.euclidean.volumePreserving_toMixed, SchwartzMap.fourierInv_apply_eq, SchwartzMap.smulRightCLM_apply_apply, Real.differentiableOn_Gamma_Ioi, LinearIsometryEquiv.conjStarAlgEquiv_refl, ProbabilityTheory.analyticAt_cgf, InformationTheory.klDiv_def, MeasureTheory.L2.inner_indicatorConstLp_one, LinearMap.IsSymmetric.toSelfAdjoint_apply, EuclideanGeometry.image_inversion_sphere_dist_center, volume_ball, EuclideanGeometry.orthogonalProjection_subtype, NumberField.mixedEmbedding.negAt_apply_isReal_and_notMem, Submodule.coe_orthogonalDecomposition, fderiv_norm_smul_neg, SchwartzMap.toTemperedDistributionCLM_apply_apply, integrableOn_Ioi_deriv_ofReal_cpow, ExistsContDiffBumpBase.u_exists, EuclideanGeometry.Sphere.sbtw_secondInter, Submodule.finrank_orthogonal_span_singleton, integral_exp_mul_I_eq_sin, Orientation.oangle_eq_iff_eq_pos_smul_rotation_of_ne_zero, NumberField.Units.dirichletUnitTheorem.unitLattice_span_eq_top, LinearMap.isPositive_natCast, inner_smul_real_right, Affine.Triangle.sOppSide_affineSpan_pair_excenter_singleton_point, intervalIntegral.integral_eq_zero_iff_of_le_of_nonneg_ae, TensorProduct.toLinearEquiv_congrIsometry, dense_differentiableAt_norm, AntitoneOn.sum_le_integral_Ico, Complex.one_add_cpow_hasFPowerSeriesAt_zero, Submodule.isOrtho_iSup_left, NumberField.mixedEmbedding.fundamentalCone.expMap_basis_of_eq, intervalIntegral.integral_hasStrictFDerivAt_of_tendsto_ae, ContDiff.norm_sq, MonotoneOn.intervalIntegral_deriv_mem_uIcc, Submodule.mem_orthogonal', NumberField.mixedEmbedding.volume_preserving_negAt, Affine.Simplex.ExcenterExists.sign_signedInfDist_lineMap_excenter_touchpoint, LinearMap.toMatrixOrthonormal_symm_apply, ContinuousLinearMap.IsStarNormal.orthogonal_range, Matrix.posDef_gram_iff_linearIndependent, MeasureTheory.Lp.instFourierSMul, UpperHalfPlane.contMDiff_num, SmoothPartitionOfUnity.sum_eq_one', UpperHalfPlane.mdifferentiable_denom, LinearMap.toMatrix_innerₛₗ_apply, integral_sin_mul_cos₁, ContinuousLinearMap.IsStarNormal.adjoint_apply_eq_zero_iff, MeasureTheory.Measure.withDensityᵥ_absolutelyContinuous, Orientation.rightAngleRotation_map', TensorProduct.toLinearEquiv_commIsometry, EuclideanGeometry.oangle_midpoint_left, ProbabilityTheory.iCondIndepSets_singleton_iff, NumberField.mixedEmbedding.negAt_apply_isComplex, Real.integral_rpowIntegrand₀₁_one_pos, ProbabilityTheory.hasFiniteIntegral_compProd_iff', ProbabilityTheory.isGaussian_iff_charFun_eq, Orientation.inner_rotation_pi_div_two_left_smul, Submodule.norm_sq_eq_add_norm_sq_projection, ProbabilityTheory.integral_truncation_eq_intervalIntegral_of_nonneg, Affine.Simplex.circumsphere_unique_dist_eq, Submodule.orthogonal_gc, integral_sin_pow_aux, integral_comp_abs, ProbabilityTheory.setIntegral_stieltjesOfMeasurableRat, Matrix.PosSemidef.toLinearMap₂'_zero_iff, Submodule.starProjection_isSymmetric, Submodule.starProjection_apply, integral_div_sq_add_sq, Polynomial.rootSet_derivative_subset_convexHull_rootSet, Submodule.HasOrthogonalProjection.map_linearIsometryEquiv', SmoothPartitionOfUnity.mem_finsupport, VonNeumannAlgebra.mem_carrier, Real.Wallis.W_eq_integral_sin_pow_div_integral_sin_pow, EuclideanGeometry.preimage_inversion_sphere_dist_center, has_antideriv_at_fourier_neg, IsOpen.exists_contMDiff_support_eq, Orientation.rotation_neg_orientation_eq_neg, ProbabilityTheory.IndepFun.integral_fun_mul_eq_mul_integral, ContinuousLinearMap.rayleighQuotient_add, Matrix.instNonnegSpectrumClass, Orientation.eq_rotation_self_iff, VonNeumannAlgebra.centralizer_centralizer, NumberField.mixedEmbedding.normAtComplexPlaces_normAtAllPlaces, DifferentiableAt.norm_sq, LinearMap.isSelfAdjoint_iff', ProbabilityTheory.sum_variance_truncation_le, Orientation.areaForm'_apply, contDiffAt_euclidean, innerSLFlip_apply_apply, MeasureTheory.condExp_stronglyMeasurable_mul_of_bound, eqOn_iteratedDerivWithin_cotTerm_upperHalfPlaneSet, Affine.Triangle.dist_orthocenter_reflection_circumcenter, OrthogonalFamily.hasSum_linearIsometry, signedDist_smul_of_pos, finrank_euclideanSpace, LinearMap.IsPositive.isSelfAdjoint, IsContinuousRiemannianBundle.exists_continuous, Submodule.top_orthogonal_eq_bot, Submodule.fst_orthogonalDecomposition_apply, HilbertBasis.dense_span, Real.contDiff_fourierIntegral, Complex.one_div_sub_sq_hasFPowerSeriesOnBall_zero, Submodule.orthogonal_orthogonal_eq_closure, Affine.Simplex.exradius_reindex, MonotoneOn.sum_le_integral_Ico, Submodule.smul_starProjection_singleton, Affine.Simplex.ninePointCircle_reindex, ProbabilityTheory.condExp_set_generateFrom_singleton, Orientation.inner_comp_rightAngleRotation, intervalIntegral.integral_hasStrictFDerivAt, TensorProduct.ext_iff_inner_right, NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_apply, signedDist_lineMap_lineMap, LinearEquiv.isPositive_symm_iff, enorm_rankOne, Orthonormal.inner_finsupp_eq_sum_right, continuousLinearMapOfBilin_zero, mfderiv_coe_sphere_injective, ProbabilityTheory.variance_eq_sub, ContinuousLinearMap.toLinearMap_innerSL_apply, Affine.Triangle.dist_div_sin_oangle_eq_two_mul_circumradius, Submodule.orthogonalFamily_self, NumberField.mixedEmbedding.mem_negAt_plusPart_of_mem, NumberField.Units.regOfFamily_of_isMaxRank, intervalIntegral.inv_mul_integral_comp_add_div, inner_map_complex, analyticAt_sigmoid, LinearMap.IsSymmetric.adjoint_eq, contDiffAt_norm, LinearMap.isPositive_sum, tendsto_integral_mul_one_add_inv_smul_sq_pow, Submodule.starProjection_norm_le, contDiffOn_euclidean, HasGradientAt.hasFDerivAt, integral_sin_pow_even_mul_cos_pow_even, Submodule.inner_orthogonalProjection_eq_of_mem_right, Submodule.reflection_reflection, ProbabilityTheory.Kernel.setIntegral_density_of_measurableSet, signedDist_vadd_left_swap, Submodule.isOrtho_iff_le, OpenPartialHomeomorph.contDiffOn_univUnitBall_symm, MeasureTheory.integrable_prod_iff, Polynomial.eq_centerMass_of_eval_derivative_eq_zero, sum_mul_Ico_le_integral_of_monotone_antitone, eqOn_iteratedDeriv_cotTerm, ProbabilityTheory.meas_ge_le_variance_div_sq, differentiableAt_abs_neg, ClosedSubmodule.iInf_orthogonal, Orientation.oangle_eq_iff_eq_pos_smul_rotation_or_eq_zero, Complex.one_div_one_sub_pow_hasFPowerSeriesOnBall_zero, hasDerivAt_fourier_neg, Orientation.rotation_zero, ProbabilityTheory.isGaussian_gaussianReal, integral_inner, deriv_abs_zero, VectorFourier.fderiv_fourierIntegral, LinearMap.IsSymmetric.isSymmetric_smul_iff, LinearMap.isPositive_linearIsometryEquiv_conj_iff, hasStrictDerivAt_abs, OrthonormalBasis.equiv_self_rfl, EuclideanGeometry.OrthocentricSystem.affineIndependent, SchwartzMap.fourierInv_lineDerivOp_eq, Affine.Simplex.touchpointWeights_reindex, EuclideanGeometry.Sphere.secondInter_smul, coe_gramSchmidtBasis, Bundle.RiemannianMetric.symm, MeasureTheory.integral_charFun_Icc, strongConcaveOn_iff_convex, Affine.Simplex.height_map, Submodule.reflection_inv, ProbabilityTheory.Kernel.tendsto_integral_density_of_antitone, ContDiffWithinAt.dist, ProbabilityTheory.moment_truncation_eq_intervalIntegral_of_nonneg, Affine.Simplex.orthogonalProjection_circumcenter, Matrix.ofLp_toEuclideanCLM, MeasureTheory.mul_le_integral_rnDeriv_of_ac, intervalIntegral.inv_mul_integral_comp_sub_div, EulerSine.integral_sin_mul_sin_mul_cos_pow_eq, Submodule.norm_starProjection, ClosedSubmodule.sup_orthogonal, Function.Periodic.tendsto_atBot_intervalIntegral_of_pos', LinearMap.IsSymmetric.orthogonalFamily_eigenspaces', Unitary.linearIsometryEquiv_coe_symm_apply, NumberField.mixedEmbedding.det_basisOfFractionalIdeal_eq_norm, DifferentiableOn.norm_sq, NumberField.mixedEmbedding.fundamentalCone.normAtAllPlaces_mem_fundamentalCone_iff, fourierCoeff_toLp, Orientation.oangle_rotation_oangle_left, ContinuousLinearMap.rayleighQuotient_le_norm, OrthonormalBasis.det_to_matrix_orthonormalBasis, ProbabilityTheory.hasDerivAt_complexMGF, intervalIntegral.integral_mono_ae, LinearMap.isPositive_toContinuousLinearMap_iff, OrthogonalFamily.summable_of_lp, ProbabilityTheory.IsGaussian.charFunDual_eq, ProbabilityTheory.variance_continuousLinearMap_gaussianReal, ProbabilityTheory.covarianceBilin_eq_covarianceBilinDual, norm_inner_eq_norm_tfae, ModularFormClass.qExpansion_coeff, Submodule.isCompl_orthogonal_of_hasOrthogonalProjection, ProbabilityTheory.covariance_eq_sub, MeasureTheory.integrable_conv_iff, Submodule.reflection_mul_reflection, signedDist_vadd_right, instIsContPerfPairRealInnerₗOfCompleteSpace, RCLike.inner_tmul_eq, hasSum_sq_fourierCoeffOn, Real.circleAverage_mono_on_of_le_circle, gramSchmidt_triangular, ProbabilityTheory.strong_law_aux6, Submodule.starProjection_map_apply, MeasureTheory.tendsto_sum_indicator_atTop_iff', LinearMap.star_eq_adjoint, torusIntegral_const_mul, differentiableWithinAt_euclidean, LinearMap.IsSymmetric.orthogonalComplement_iSup_eigenspaces_eq_bot', MeasureTheory.integral_prod_mul, contDiff_norm_sq, tendsto_integral_mulExpNegMulSq_comp, SmoothBumpCovering.embeddingPiTangent_injective_mfderiv, intervalAverage_congr_codiscreteWithin, Polynomial.logMahlerMeasure_def, LinearPMap.adjointDomainMkCLM_apply, Orientation.oangle_sign_smul_left, deriv_abs_pos, Matrix.isPositive_toEuclideanLin_iff, TensorProduct.enorm_tmul, ProbabilityTheory.hasFPowerSeriesAt_mgf, Complex.integral_exp_neg_mul_rpow, Submodule.starProjection_bot, NumberField.mixedEmbedding.fundamentalCone.hasFDerivAt_expMap, MeasureTheory.Measure.integrable_compProd_iff, ContDiff.inner, Affine.Simplex.touchpoint_mem_affineSpan, EuclideanGeometry.Sphere.inv_tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_center, HasGradientAt.differentiableAt, intervalIntegral.measure_integral_sub_linear_isLittleO_of_tendsto_ae, EuclideanGeometry.oangle_eq_zero_or_eq_pi_iff_collinear, ProbabilityTheory.covarianceBilin_self_nonneg, Orientation.rightAngleRotation_rightAngleRotation, Submodule.orthogonal_closure, ProbabilityTheory.integral_linearMap_gaussianReal, LinearMap.IsSymmetric.orthogonalFamily_eigenspace_inf_eigenspace, MeasureTheory.Measure.exists_integral_isMulLeftInvariant_eq_smul_of_hasCompactSupport, TensorProduct.inner_assoc_assoc, exists_msmooth_support_eq_eq_one_iff, Polynomial.Chebyshev.integral_eval_T_real_measureT_zero, hasSum_mellin_pi_mul, MeasureTheory.integral_le_liminf_integral_of_forall_isOpen_measure_le_liminf_measure, ProbabilityTheory.condIndepSets_iff, ContinuousLinearMap.reApplyInnerSelf_apply, Orientation.oangle_sign_smul_add_smul_smul_add_smul, le_radius_cauchyPowerSeries, Affine.Simplex.direction_mongePlane, integral_inv_of_neg, ProbabilityTheory.covarianceBilinDual_self_eq_variance, ProperCone.innerDual_union, ProbabilityTheory.iCondIndepSet_iff, LinearMap.le_def, Affine.Simplex.dist_point_centroid, MeasureTheory.integral_condExpL2_eq_of_fin_meas_real, hasStrictFDerivAt_norm_sq, Submodule.starProjection_unit_singleton, Affine.Simplex.altitudeFoot_reindex, SmoothPartitionOfUnity.coe_finsupport, SchwartzMap.fourier_evalCLM_eq, LinearMap.adjoint_toSpanSingleton, OrthonormalBasis.coe_toBasis, ConcaveOn.le_map_integral, Affine.Simplex.affineCombination_eq_touchpoint_iff, Emetric.exists_contMDiffMap_forall_closedBall_subset, hasMellin_one_Ioc, Orientation.oangle_sign_smul_sub_left, Submodule.reflection_sub, TemperedDistribution.instLineDerivSMulReal, MeasureTheory.MemLp.condExp, ProbabilityTheory.differentiableAt_iteratedDeriv_mgf, Affine.Simplex.altitudeFoot_mem_altitude, LinearMap.IsSymmetric.natCast, Orientation.rotation_eq_self_iff_angle_eq_zero, InnerProductGeometry.angle_smul_right_of_neg, Affine.Triangle.inv_tan_div_two_smul_rotation_pi_div_two_vadd_midpoint_eq_circumcenter, ClosedSubmodule.mem_orthogonal, ProbabilityTheory.condVar_ae_le_condExp_sq, MDifferentiableOn.inner_bundle, MeasureTheory.Measure.toTemperedDistribution_apply, Complex.analyticOn_iff_differentiableOn, tendsto_integral_exp_smul_cocompact_of_inner_product, ProbabilityTheory.Kernel.setIntegral_densityProcess, SchwartzMap.instContinuousFourierInv, LinearMap.re_inner_adjoint_mul_self_nonneg, EuclideanGeometry.oangle_ne_zero_and_ne_pi_iff_affineIndependent, Orientation.oangle_rotation_right, nullSubmodule_le_ker_toDualMap_left, Affine.Triangle.affineSpan_orthocenter_point_le_altitude, LinearMap.isPositive_self_comp_adjoint, differentiableAt_norm_smul, AntitoneOn.integral_le_sum_Ico, MeasureTheory.setIntegral_abs_condExp_le, Metric.exists_contMDiffMap_forall_closedBall_subset, ProbabilityTheory.IndepFun.integral_fun_comp_mul_comp, ContinuousLinearMap.instStarModuleId, EuclideanGeometry.Cospherical.affineIndependent, EuclideanGeometry.orthogonalProjection_affineSpan_singleton, LinearIsometryEquiv.toLinearEquiv_lTensor, Differentiable.norm_sq, Matrix.linearIndependent_of_posDef_gram, exists_msmooth_zero_iff_one_iff_of_isClosed, ConcaveOn.set_average_mem_hypograph, MeasureTheory.SignedMeasure.haveLebesgueDecomposition_smul_real, ProbabilityTheory.covarianceBilinDual_self_nonneg, IccLeftChart_extend_bot, NumberField.mixedEmbedding.stdBasis_apply_isComplex_fst, ContDiffBump.measure_closedBall_le_integral, TemperedDistribution.fourier_lineDerivOp_eq, Matrix.l2_opNNNorm_def, ProbabilityTheory.Kernel.integral_densityProcess, MeasureTheory.Integrable.integral_eq_integral_meas_le, EuclideanGeometry.Sphere.IsTangentAt_of_angle_eq_pi_div_two, SmoothPartitionOfUnity.finsum_smul_mem_convex, TemperedDistribution.fourier_delta_zero, ContinuousLinearMap.adjointAux_adjointAux, intervalIntegral.mul_integral_comp_add_mul, PeriodPair.order_weierstrassP, Submodule.coe_inner, Orientation.rotation_trans, Submodule.orthogonalProjection_apply_eq_linearProjOfIsCompl, signedDist_lineMap_left, MeromorphicNFOn.Gamma, MeasureTheory.condExpL2_indicator_of_measurable, LinearMap.IsSymmetric.orthogonalComplement_iSup_eigenspaces_eq_bot, ProbabilityTheory.covarianceBilin_real_self, LinearMap.eq_adjoint_iff, MeasureTheory.BoundedContinuousFunction.integral_eq_integral_meas_le, iteratedDerivWithin_cot_pi_mul_eq_mul_tsum_zpow, PositiveLinearMap.gnsStarAlgHom_apply, Orthonormal.inner_right_finsupp, integral_univ_inv_one_add_sq, MeasureTheory.Integrable.integral_norm_compProd, NumberField.mixedEmbedding.fundamentalDomain_stdBasis, SmoothPartitionOfUnity.sum_le_one', OrthonormalBasis.tensorProduct_apply', EuclideanSpace.basisFun_repr, NumberField.mixedEmbedding.span_latticeBasis, SchwartzMap.integral_pow_mul_iteratedFDeriv_le, integral_exp_neg_rpow, real_inner_smul_right, Orientation.nonneg_inner_and_areaForm_eq_zero_iff_sameRay, InformationTheory.klDiv_eq_integral_klFun, Orientation.oangle_sub_right_smul_rotation_pi_div_two, LinearMap.isPositive_iff_complex, VectorFourier.fourierSMulRight_apply, ContinuousLinearMap.isSelfAdjoint_iff', Submodule.sndL_comp_coe_orthogonalDecomposition, UnitAddTorus.instContinuousSMulComplexSubtypeAEEqFunVolumeMemAddSubgroupLp, OrthonormalBasis.equiv_apply_euclideanSpace, MeasureTheory.Integrable.integral_eq_integral_meas_lt, stereographic_neg_apply, integral_cexp_quadratic, TemperedDistribution.lineDerivOp_toTemperedDistributionCLM_eq, MeasureTheory.tendsto_ae_condExp, isSelfAdjoint_starProjection, Affine.Simplex.sOppSide_excenter_singleton_point, gramSchmidt_def', ProbabilityTheory.evariance_def', MeasureTheory.condExpL2_indicator_eq_toSpanSingleton_comp, instIsRiemannianManifoldModelWithCornersSelfReal, eventually_norm_symmL_trivializationAt_self_comp_lt, OrthonormalBasis.det_adjustToOrientation, integral_inv, SmoothBumpCovering.embeddingPiTangent_ker_mfderiv, ContMDiffOn.inner_bundle, Complex.orthonormalBasisOneI_repr_symm_apply, SmoothPartitionOfUnity.sum_nonneg, intervalIntegral.abs_integral_le_integral_abs, Manifold.riemannianEDist_def, hasDerivAt_circleMap, Real.one_div_one_sub_rpow_hasFPowerSeriesOnBall_zero, EuclideanGeometry.oangle_homothety, Affine.Simplex.ExcenterExists.sOppSide_point_excenter_iff, intervalIntegral.measure_integral_sub_linear_isLittleO_of_tendsto_ae', signedDist_anticomm, Submodule.sInf_orthogonal, UnitAddTorus.hasSum_mFourier_series_L2, TemperedDistribution.laplacian_eq_sum, Affine.Simplex.dist_circumcenter_eq_circumradius, NumberField.mixedEmbedding.stdBasis_repr_eq_matrixToStdBasis_mul, Orientation.areaForm_comp_rightAngleRotation, Submodule.isOrtho_span, modelWithCornersEuclideanHalfSpace_zero, Matrix.PosSemidef.isUnit_sqrt_iff, MeasureTheory.lintegral_nnnorm_condExpL2_indicator_le_real, ProbabilityTheory.exponentialCDFReal_eq_integral, differentiableWithinAt_abs_neg, ContDiffAt.norm_sq, MeasureTheory.integral_comp, TemperedDistribution.instContinuousLineDeriv, ProbabilityTheory.iteratedDeriv_mgf_zero, ProbabilityTheory.moment_truncation_eq_intervalIntegral, ContinuousLinearMap.le_def, VectorFourier.pow_mul_norm_iteratedFDeriv_fourierIntegral_le, hasDerivAt_fourier, ProbabilityTheory.cdf_expMeasure_eq_integral, ProbabilityTheory.condExp_zero_or_one_of_measurableSet_limsup, MeasureTheory.rnDeriv_ae_eq_condExp, OpenPartialHomeomorph.contDiff_univBall, LinearMap.isPositive_zero, EuclideanGeometry.Sphere.direction_orthRadius_le_iff, NumberField.mixedEmbedding.fundamentalCone.norm_normAtAllPlaces, ContinuousLinearMap.IsPositive.re_inner_nonneg_left, Complex.one_div_sub_pow_hasFPowerSeriesOnBall_zero, MeasureTheory.Measure.haarScalarFactor_eq_integral_div, LinearIsometry.orthonormal_comp_iff, EuclideanGeometry.Sphere.IsTangentAt.mem_and_mem_iff_eq, Matrix.coe_toEuclideanCLM_eq_toEuclideanLin, ProbabilityTheory.isGaussian_iff_gaussian_charFunDual, EuclideanGeometry.collinear_iff_eq_or_eq_or_sin_eq_zero, ProbabilityTheory.hasFiniteIntegral_comp_iff', ProbabilityTheory.covarianceOperator_inner, rankOne_def', Complex.HadamardThreeLines.diffContOnCl_interpStrip, Submodule.isClosed_orthogonal, hasStrictDerivAt_abs_neg, MDifferentiableWithinAt.inner_bundle, Orientation.inner_rightAngleRotation_left, AffineSubspace.mem_perpBisector_iff_inner_eq_inner, InnerProductGeometry.angle_eq_angle_add_angle_iff, ProbabilityTheory.norm_uncenteredCovarianceBilinDual_le, integral_cos_pow_three, EuclideanGeometry.Sphere.IsTangent.infDist_eq_radius, SchwartzMap.integral_sesq_fourierIntegral_eq, LSeries_eq_mul_integral, ContinuousLinearMap.IsPositive.inner_nonneg_left, ContinuousLinearMap.apply_norm_eq_sqrt_inner_adjoint_left, HasFDerivAt.inner, LinearMap.adjoint_lTensor, ProbabilityTheory.paretoCDFReal_eq_integral, norm_inner_div_norm_mul_norm_eq_one_of_ne_zero_of_ne_zero_mul, OrthonormalBasis.map_apply, LinearMap.toMatrixOrthonormal_apply, hasFPowerSeriesOn_cauchy_integral, Submodule.isSymmetricProjection_starProjection, UpperHalfPlane.contMDiff_denom_zpow, Complex.circleIntegral_div_sub_of_differentiable_on_off_countable, SmoothBumpCovering.exists_finset_toSmoothPartitionOfUnity_eventuallyEq, integral_one_div_of_pos, OrthogonalFamily.inner_sum, EuclideanGeometry.inversion_def, deriv_circleMap, LinearMap.IsPositive.smul_of_nonneg, Affine.Simplex.inner_vsub_altitudeFoot_vsub_altitudeFoot_eq_zero, ProbabilityTheory.covarianceBilin_apply_pi, ProbabilityTheory.deriv_mgf, SchwartzMap.integral_bilinear_laplacian_right_eq_left, ClosedSubmodule.mem_orthogonal_toSubmodule_iff, ExistsContDiffBumpBase.u_smooth, intervalIntegral.intervalIntegral_pos_of_pos_on, DifferentiableOn.hasFPowerSeriesOnBall, VectorFourier.hasFTaylorSeriesUpTo_fourierIntegral', Real.contDiff_fourier, ProbabilityTheory.condExpKernel_ae_eq_condExp, OrthonormalBasis.sum_repr_symm, Orientation.kahler_apply_self, Affine.Simplex.dist_circumcenter_eq_circumradius', EuclideanGeometry.Sphere.IsTangent.notMem_of_dist_lt, signedDist_triangle_right, Affine.Simplex.orthogonalProjectionSpan_faceOpposite_eq_point_rev, Orthonormal.inner_left_sum, Orientation.inner_smul_rotation_pi_div_two_right, ProbabilityTheory.hasFiniteIntegral_comp_iff, EuclideanGeometry.Sphere.IsIntTangentAt.wbtw, Complex.analyticOn_univ_iff_differentiable, Pi.orthonormalBasis.toBasis, LinearIsometry.map_starProjection, contMDiffWithinAt_comp_projIcc_iff, Orientation.inner_mul_areaForm_sub', hasFDerivAt_polarCoord_symm, fourierIntegral_gaussian_innerProductSpace, MeasureTheory.dist_convolution_le', EuclideanGeometry.Sphere.IsTangentAt.le_orthRadius, EuclideanGeometry.Sphere.isDiameter_of_angle_eq_pi_div_two, ContinuousLinearMap.isSelfAdjoint_toLinearMap_iff, EuclideanGeometry.dist_orthogonalProjection_eq_infNndist, Submodule.inf_orthogonal, Differentiable.contDiff, ProbabilityTheory.hasDerivAt_neg_exp_mul_exp, abs_signedDist_eq_dist_iff_vsub_mem_span, innerSL_norm, HurwitzZeta.hurwitzOddFEPair_f₀, Submodule.IsOrtho.le, Submodule.reflection_map, Affine.Simplex.ExcenterExists.isTangentAt_exsphere_iff_eq_touchpoint, span_gramSchmidt_Iic, LinearMap.IsSymmetric.direct_sum_isInternal, Submodule.det_reflection, Orientation.kahler_rotation_left', ProbabilityTheory.Kernel.integral_density, TensorProduct.inner_comm_comm, Affine.Simplex.ExcenterExists.excenter_notMem_affineSpan_pair, Submodule.inner_orthogonalProjection_eq_of_mem_left, Affine.Simplex.pointsWithCircumcenter_point, Orientation.oangle_eq_zero_or_eq_pi_iff_not_linearIndependent, eventually_norm_symmL_trivializationAt_comp_self_lt, ContinuousLinearMap.IsPositive.add, Real.eulerMascheroniConstant_eq_neg_deriv, ProbabilityTheory.IsGaussian.integral_dual, Affine.Simplex.mongePoint_reindex, Affine.Triangle.affineSpan_pair_eq_orthRadius_insphere, Orientation.abs_areaForm_le, EuclideanGeometry.cospherical_or_collinear_of_two_zsmul_oangle_eq, cot_pi_mul_contDiffWithinAt, IsOpen.exists_msmooth_support_eq_aux, Affine.Simplex.mongePoint_eq_smul_vsub_vadd_circumcenter, EuclideanGeometry.angle_homothety, InnerProductGeometry.angle_smul_smul, integral_log_sin_zero_pi, Polynomial.Chebyshev.integral_eval_T_real_mul_eval_T_real_measureT, NumberField.mixedEmbedding.fundamentalCone.hasFDerivAt_expMapBasis, intervalIntegral.integral_pos_iff_support_of_nonneg_ae, OpenPartialHomeomorph.contDiff_unitBallBall, Affine.Simplex.altitude_reindex, linearIndependent_of_ne_zero_of_inner_eq_zero, MeasureTheory.L2.inner_indicatorConstLp_eq_setIntegral_inner, MeasureTheory.Integrable.integral_norm_condDistrib, LinearPMap.isSelfAdjoint_def, NumberField.mixedEmbedding.euclidean.instIsZLatticeRealMixedSpaceIntegerLattice, signedDist_neg, PeriodPair.coeff_weierstrassPSeries, ProbabilityTheory.covarianceBilin_apply_basisFun, exists_contMDiff_zero_iff_one_iff_of_isClosed, Orientation.oangle_sign_smul_right, Orientation.normSq_kahler, hasGradientAt_iff_hasFDerivAt, Submodule.toLinearMap_orthogonalProjection_eq_linearProjOfIsCompl, ProbabilityTheory.condExpKernel_ae_eq_trim_condExp, integral_inv_sq_add_sq, NumberField.mixedEmbedding.fundamentalCone.hasDerivAt_expMap_single, maximal_orthonormal_iff_orthogonalComplement_eq_bot, locallyFinsuppWithin.logCounting_divisor, ProbabilityTheory.setIntegral_preCDF_fst, Submodule.reflection_orthogonal, NumberField.mixedEmbedding.negAt_symm, VectorFourier.contDiff_fourierIntegral, ConcaveOn.le_map_average, Submodule.isOrtho_top_right, LinearMap.IsSymmetric.smul, HilbertBasis.repr_symm_single, HilbertBasis.repr_apply_apply, ProbabilityTheory.integrable_compProd_iff, intervalIntegral.measure_integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae_left, TensorProduct.assocIsometry_apply, Matrix.toLin_conjTranspose, Orthonormal.inner_finsupp_eq_sum_left, Polynomial.sum_sq_norm_coeff_eq_circleAverage, ContDiffBump.contDiff_normed, integral_rpow, Orientation.oangle_sign_add_smul_left, HurwitzZeta.hurwitzOddFEPair_ε, ProbabilityTheory.iCondIndepSets_iff, Diffeology.isPlot_iff_contDiff, Matrix.PosSemidef.sq_sqrt, signedDist_vsub_self_rev, InformationTheory.toReal_klDiv_of_measure_eq, LinearIsometryEquiv.rTensor_apply, intervalIntegral.measure_integral_sub_integral_sub_linear_isLittleO_of_tendsto_ae, LinearIsometryEquiv.inner_map_map, EuclideanGeometry.Sphere.dist_orthogonalProjection_eq_radius_iff_isTangent, Orientation.neg_rotation_pi_div_two, isStarProjection_rankOne_self, ProperCone.relative_hyperplane_separation, contDiffAt_inner, NumberField.mixedEmbedding.volume_fundamentalDomain_fractionalIdealLatticeBasis, OrthonormalBasis.measurePreserving_repr_symm, NumberField.mixedEmbedding.instIsZLatticeRealMixedSpaceIntegerLattice, MeasureTheory.measureReal_abs_gt_le_integral_charFun, DifferentiableOn.inner, ClosedSubmodule.orthogonal_eq_top_iff, eventually_enorm_mfderiv_extChartAt_lt, enorm_tangentSpace_vectorSpace, integral_exp_neg_Ioi, EuclideanSpace.piLpCongrLeft_single, Differentiable.inner, EuclideanGeometry.dist_reflection, signedDist_linear_apply, NumberField.mixedEmbedding.negAt_apply_isReal_and_mem, Orientation.rotation_eq_matrix_toLin, oneTangentSpaceIcc_def, Orientation.inner_rightAngleRotation_swap, Real.abs_circleAverage_le_circleAverage_abs, IccRightChart_extend_top_mem_frontier, NumberField.mixedEmbedding.volume_negAt_plusPart, hasFDerivWithinAt_euclidean, ClosedSubmodule.mem_orthogonal_iff, Orientation.oangle_sub_left_smul_rotation_pi_div_two, EuclideanGeometry.orthogonalProjection_eq_orthogonalProjection_iff_vsub_mem, ProperCone.innerDual_insert, ProbabilityTheory.integral_truncation_le_integral_of_nonneg, ZLattice.covolume.tendsto_card_div_pow', SmoothPartitionOfUnity.sum_eq_one, LinearMap.IsSymmetricProjection.hasOrthogonalProjection_range, SchwartzMap.hasDerivAt, MeasureTheory.tendsto_eLpNorm_condExp, Submodule.starProjection_orthogonal, Orientation.oangle_eq_iff_eq_norm_div_norm_smul_rotation_or_eq_zero, ContinuousLinearMap.instNonnegSpectrumClassRealId, MeasureTheory.eLpNorm_one_condExp_le_eLpNorm, Affine.Simplex.incenter_eq_affineCombination, integral_log, signedDist_self, integral_sqrt_one_sub_sq, tendsto_setIntegral_pow_smul_of_unique_maximum_of_isCompact_of_measure_nhdsWithin_pos, Matrix.IsHermitian.eigenvectorUnitary_coe, circleAverage_log_norm_add_const_eq_posLog, Real.Gamma_eq_integral, signedDist_vsub_self, EuclideanGeometry.inversion_mul, stereographic_target, MeasureTheory.SignedMeasure.rnDeriv_smul, Unitary.norm_map, LinearMap.instStarModuleId, RCLike.linearIndependent_of_ne_zero_of_wInner_cWeight_eq_zero, Submodule.starProjection_apply_mem, signedDist_smul, LinearIsometryEquiv.symm_conjStarAlgEquiv_apply_apply, rankOne_comp_rankOne, TemperedDistribution.fourierTransform_apply, Orientation.oangle_add_right_smul_rotation_pi_div_two, Orientation.inner_smul_rotation_pi_div_two_left, ZLattice.volume_image_eq_volume_div_covolume, MeasureTheory.SignedMeasure.haveLebesgueDecomposition_smul, LinearIsometry.toLinearMap_rTensor, ContDiffOn.norm_sq, Real.map_linearMap_volume_pi_eq_smul_volume_pi, intervalIntegral.inv_mul_integral_comp_div_sub, Matrix.toEuclideanLin_eq_toLin, Affine.Simplex.sOppSide_point_excenter_singleton, Euclidean.closedBall_eq_preimage, Matrix.isHermitian_iff_isSymmetric, NumberField.mixedEmbedding.iUnion_negAt_plusPart_union, AffineSubspace.mem_perpBisector_iff_dist_eq', Matrix.PosSemidef.inv_sqrt, Submodule.le_orthogonal_iff_le_orthogonal, intervalIntegral.differentiable_integral_of_continuous, integral_log_from_zero_of_pos, LipschitzWith.locallyIntegrable_lineDeriv, laplacian_eq_iteratedFDeriv_stdOrthonormalBasis, Affine.Simplex.ninePointCircle_center_mem_affineSpan, Submodule.IsOrtho.comap_iff, rankOne_comp, SmoothBumpCovering.embeddingPiTangent_injOn, hasSum_mellin_pi_mul₀, Submodule.mem_orthogonal, EulerSine.integral_cos_pow_eq, MeasureTheory.measureReal_abs_dual_gt_le_integral_charFunDual, Orientation.kahler_rightAngleRotation_left, intervalIntegral.hasFDerivAt_integral_of_dominated_of_fderiv_le, ConvexOn.average_mem_epigraph, MeasureTheory.integrable_condExpL2_of_isFiniteMeasure, MeasureTheory.Measure.map_linearMap_addHaar_pi_eq_smul_addHaar, inner_smul_right, toMatrix_rankOne, MeasureTheory.integral_condExp_indicator, eventually_norm_symmL_trivializationAt_lt, differentiableAt_euclidean, PeriodPair.hasFPowerSeriesOnBall_weierstrassP, AffineSubspace.perpBisector_eq_top, EuclideanGeometry.dist_orthogonalProjection_eq_infDist, OrthonormalBasis.reindex_toBasis, EuclideanGeometry.orthogonalProjection_mem, isSymmetric_rankOne_self, Orientation.oangle_smul_right_of_neg, Orientation.abs_areaForm_of_orthogonal, ProbabilityTheory.Kernel.tendsto_setIntegral_densityProcess, LipschitzOnWith.ae_differentiableWithinAt_real, MeasureTheory.AEStronglyMeasurable.ae_integrable_condDistrib_map_iff, integral_sin, PeriodPair.weierstrassPSeries_hasSum, LinearIsometryEquiv.symm_rTensor, LinearMap.isSymmetricProjection_iff, innerₗ_apply_apply, Matrix.toEuclideanLin_conjTranspose_eq_adjoint, LinearMap.eq_adjoint_iff_basis, TensorProduct.commIsometry_symm, isStarProjection_starProjection, Function.hasTemperateGrowth_inner_left, unitary.norm_map, exists_eq_const_mul_intervalIntegral_of_ae_nonneg, AffineSubspace.midpoint_mem_perpBisector, inner_sum_smul_sum_smul_of_sum_eq_zero, ProbabilityTheory.hasDerivAt_iteratedDeriv_mgf, Affine.Simplex.touchpoint_reindex, LinearEquiv.isSymmetric_symm_iff, gramSchmidt_def'', Real.hasDerivAt_fourierChar, Real.le_integral_rpowIntegrand₀₁_one, bilinFormOfRealInner_orthogonal, ContinuousLinearMap.intervalIntegral_apply, OrthonormalBasis.equiv_symm, span_fourierLp_closure_eq_top, analyticWithinAt_sigmoid, circleIntegral.integral_sub_zpow_of_ne, EuclideanGeometry.inner_weightedVSub, Orientation.kahler_rotation_left, LindemannWeierstrass.integral_exp_mul_eval, ProbabilityTheory.variance_le_expectation_sq, MeasureTheory.Integrable.withDensityᵥ_trim_eq_integral, analyticOn_sigmoid, EuclideanGeometry.Sphere.center_mem_orthRadius_iff, LSeries.iteratedDeriv_alternating, MeasureTheory.integral_fin_nat_prod_eq_prod, EuclideanGeometry.collinear_of_sin_eq_zero, OrthonormalBasis.orthonormal_adjustToOrientation, MeasureTheory.Measure.integral_isMulLeftInvariant_eq_smul_of_hasCompactSupport, Affine.Simplex.ExcenterExists.excenter_mem_affineSpan_range, ContDiffBump.integral_le_measure_closedBall, SchwartzMap.inner_fourierTransformCLM_toL2_eq, mdifferentiableWithinAt_comp_projIcc_iff, inner_map_self_eq_zero, OrthogonalFamily.eq_ite, Orientation.inner_sq_add_areaForm_sq, intervalIntegral.integral_nonneg_of_ae_restrict, signedDist_smul_of_neg, Real.iteratedFDeriv_fourier, differentiableOn_euclidean, Real.hasFPowerSeriesOnBall_linear_zero, differentiableAt_abs_pos, SchwartzMap.convolution_continuous_left, ContinuousLinearMap.adjoint_toSpanSingleton, circleIntegral.integral_smul_const, mem_span_gramSchmidt, inner_smul_real_left, Affine.Triangle.orthocenter_mem_altitude, MeasureTheory.integrable_condExpL2_indicator, Polynomial.Chebyshev.integral_eval_T_real_measureT_of_ne_zero, Real.hasDerivAt_Gamma_one_half, ProbabilityTheory.isPosSemidef_covarianceBilinDual, EuclideanGeometry.angle_left_midpoint_eq_pi_div_two_of_dist_eq, fderiv_norm_smul, Diffeology.IsContDiffCompatible.isPlot_iff, MeasureTheory.Measure.integrable_integral_norm_of_integrable_comp, laplacian_eq_iteratedFDeriv_complexPlane, NumberField.mixedEmbedding.injective_mixedSpaceOfRealSpace, EuclideanGeometry.dist_orthogonalProjection_eq_zero_iff, SchwartzMap.integral_fourier_mul_eq, range_mfderiv_coe_sphere, ProbabilityTheory.strong_law_aux7, EuclideanGeometry.Sphere.isDiameter_iff_mem_and_mem_and_dist, PeriodPair.hasFPowerSeriesOnBall_derivWeierstrassPExcept, ClosedSubmodule.inf_orthogonal_eq_bot, Affine.Triangle.eulerPoint_eq_midpoint, Submodule.reflection_eq_self_iff, MeasureTheory.integrable_prod_iff', stereographic_source, Affine.Simplex.sign_signedInfDist_touchpoint_empty, MeasureTheory.SignedMeasure.singularPart_add_withDensity_rnDeriv_eq, Matrix.ofLp_toEuclideanLin_apply, Real.one_add_rpow_hasFPowerSeriesAt_zero, integral_sin_pow_odd_mul_cos_pow, signedDist_vadd_right_swap, ProbabilityTheory.integral_condCDF, ValueDistribution.proximity_zero_of_complexValued, Real.hasFDerivAt_fourierIntegral, SchwartzMap.integralCLM_apply, EulerSine.tendsto_integral_cos_pow_mul_div, rankOne_one_right_eq_toSpanSingleton, Affine.Simplex.midpoint_faceOppositeCentroid_eulerPoint, MeasureTheory.withDensityᵥ_toReal, ProbabilityTheory.Kernel.condExp_densityProcess, Polynomial.fourierCoeff_toAddCircle_natCast, innerSLFlip_apply, iccLeftChart_extend_zero, SmoothBumpCovering.comp_embeddingPiTangent_mfderiv, EuclideanGeometry.Sphere.IsTangentAt.eq_orthogonalProjection, Submodule.ker_starProjection, toContinuousLinearMap_toDualMap, MeasureTheory.SignedMeasure.singularPart_smul_nnreal, ProbabilityTheory.covarianceBilin_real, MeasureTheory.MemLp.condExpL2_ae_eq_condExp', bernoulliFun_eq_integral, ProbabilityTheory.moment_def, SchwartzMap.fourier_coe, Affine.Triangle.dist_circumcenter_reflection_orthocenter_finset, ProbabilityTheory.iIndepFun.integral_prod_eq_prod_integral, Euclidean.ball_eq_preimage, SchwartzMap.lineDerivOp_fourierInv_eq, LinearIsometryEquiv.symm_conjStarAlgEquiv, Submodule.topologicalClosure_eq_top_iff, InformationTheory.rightDeriv_klFun_one, hasDerivAt_abs, NumberField.mixedEmbedding.stdBasis_apply_isReal, Function.RCLike.hasTemperateGrowth_ofReal, EuclideanGeometry.Sphere.secondInter_vsub_mem_affineSpan, LinearMap.IsSymmetric.zero, TensorProduct.enorm_assoc, ContDiffAt.norm, OrthonormalBasis.repr_symm_single, intervalIntegral.integral_hasFDerivWithinAt_of_tendsto_ae, Orientation.inner_eq_zero_iff_eq_zero_or_eq_smul_rotation_pi_div_two, ProbabilityTheory.covarianceBilin_of_not_memLp, InformationTheory.rightDeriv_klFun, interior_range_modelWithCornersEuclideanHalfSpace, ExistsContDiffBumpBase.y_smooth, contDiff_inner, ProbabilityTheory.condVar_bot', Submodule.reflection_bot, Affine.Simplex.point_eq_affineCombination_of_pointsWithCircumcenter, innerSL_apply_norm, Real.hasDerivAt_Gamma_one, toDual_apply_eq_toDualMap_apply, AffineSubspace.perpBisector_self, IntervalIntegrable.intervalIntegrable_slope, SchwartzMap.fourierInv_coe, ContinuousLinearMap.isPositive_def', LinearMap.adjoint_inner_left, PeriodPair.analyticOnNhd_derivWeierstrassP, ProperCone.innerDual_empty, ConvexOn.map_integral_le, Matrix.star_dotProduct_gram_mulVec, Differentiable.dist, GaussianFourier.integral_cexp_neg_mul_sq_add_real_mul_I, Orientation.oangle_map, EulerSine.antideriv_cos_comp_const_mul, ProbabilityTheory.condVar_of_sigmaFinite, OrthogonalFamily.range_linearIsometry, EuclideanGeometry.reflection_eq_iff_orthogonalProjection_eq, hasFPowerSeriesOnBall_cuspFunction, EuclideanGeometry.Sphere.isDiameter_iff_mem_and_mem_and_wbtw, ContDiffAt.dist, Submodule.ker_orthogonalProjection, EuclideanGeometry.oangle_midpoint_rev_right, Orientation.kahler_mul, LinearMap.IsSymmetric.hasEigenvalue_iInf_of_finiteDimensional, innerSL_real_flip, GaussianFourier.integral_cexp_neg_mul_sum_add, tsum_sq_fourierCoeffOn, Submodule.reflection_map_apply, ProbabilityTheory.covarianceBilinDual_comm, TensorProduct.dist_tmul_le, ModularFormClass.qExpansion_coeff_eq_circleIntegral, ProbabilityTheory.isGaussian_iff_charFunDual_eq, ProbabilityTheory.iteratedDeriv_two_cgf, SchwartzMap.integral_smul_lineDerivOp_right_eq_neg_left, integral_exp_mul_Ioi, Submodule.sup_orthogonal_of_hasOrthogonalProjection, integral_sin_mul_cos_sq, TensorProduct.norm_lid, SmoothPartitionOfUnity.exists_pos_of_mem, ProbabilityTheory.deriv_mgf_zero, MeasureTheory.charFun_eq_charFunDual_toDualMap, Complex.one_div_one_sub_cpow_hasFPowerSeriesOnBall_zero, Affine.Simplex.incenter_mem_affineSpan_range, Submodule.starProjection_orthogonalComplement_singleton_eq_zero, Submodule.isOrtho_iSup_right, TensorProduct.toLinearEquiv_assocIsometry, Orientation.oangle_smul_smul_self_of_nonneg, fourierIntegral_gaussian, Real.deriv_sigmoid, Submodule.IsOrtho.disjoint, ZLattice.volume_image_eq_volume_div_covolume', PeriodPair.meromorphic_weierstrassP, flip_innerₗ, EuclideanGeometry.orthogonalProjection_orthogonalProjection, toMatrix_innerSL_apply, OrthonormalBasis.equiv_apply_basis, ClosedSubmodule.sInf_orthogonal, Affine.Simplex.eulerPoint_reindex, one_add_rpow_hasFPowerSeriesAt_zero, ProbabilityTheory.iCondIndepFun_iff, circleAverage_log_norm_sub_const_eq_posLog, Orientation.rightAngleRotation_trans_neg_orientation, Orientation.volumeForm_robust', exists_smooth_zero_one_of_isClosed, Submodule.HasOrthogonalProjection.exists_orthogonal, NumberField.mixedEmbedding.instIsZLatticeRealMixedSpaceIdealLattice, Submodule.starProjection_top, ContMDiff.inner_bundle, Affine.Simplex.excenterWeights_map, EulerSine.antideriv_sin_comp_const_mul, PeriodPair.analyticAt_derivWeierstrassPExcept, Submodule.iInf_orthogonal, Affine.Simplex.sum_inv_height_sq_smul_vsub_eq_zero, analyticAt_log, MeasureTheory.ae_mem_limsup_atTop_iff, signedDist_vadd_left, Diffeology.IsPlot.contDiff, ContDiffBump.convolution_eq_right, TemperedDistribution.instFourierInvSMul, ExistsContDiffBumpBase.w_def, ProbabilityTheory.deriv_cgf, isBoundedBilinearMap_inner, TensorProduct.nnnorm_assoc, integral_gaussian_sq_complex, contDiff_stereoInvFunAux, Affine.Simplex.incenter_notMem_affineSpan_pair, intervalIntegral.integral_hasFDerivWithinAt, circleAverage_log_norm_factorizedRational, SmoothBumpCovering.embeddingPiTangent_injective, ContinuousLinearMap.orthogonal_range, Submodule.lipschitzWith_starProjection, ContinuousLinearMap.isPositive_iff_complex, LinearIsometryEquiv.toMeasurableEquiv_symm, HurwitzZeta.hurwitzOddFEPair_g₀, instIsContMDiffRiemannianBundleTrivial, SchwartzMap.toLp_fourierTransform_eq, ContDiff.dist, ProbabilityTheory.covarianceBilin_apply, exists_contMDiff_support_eq_eq_one_iff, AffineSubspace.mem_perpBisector_iff_inner_pointReflection_vsub_eq_zero, span_gramSchmidt, Affine.Simplex.touchpoint_eq_point_rev, EuclideanGeometry.hasFDerivAt_inversion, Orientation.kahler_map, TemperedDistribution.instFourierInvAdd, dist_div_norm_sq_smul, MeasureTheory.Lp.fourierInv_toTemperedDistribution_eq, volume_regionBetween_eq_integral', MeasureTheory.ae_bdd_condExp_of_ae_bdd, hasDerivAt_norm_rpow, Affine.Simplex.signedInfDist_reindex, UnitAddTorus.hasSum_prod_mFourierCoeff, OrthonormalBasis.span_apply, ContMDiffAt.inner_bundle, NumberField.mixedEmbedding.latticeBasis_apply, ClosedSubmodule.orthogonal_toSubmodule_eq, ContinuousLinearMap.isStarProjection_iff_isIdempotentElem_and_isStarNormal, ContinuousLinearMap.isPositive_iff, TensorProduct.mapIsometry_apply, SmoothPartitionOfUnity.sum_finsupport_smul_eq_finsum, ProbabilityTheory.uncenteredCovarianceBilin_of_not_memLp, circleIntegral.circleIntegral_congr_codiscreteWithin, signedDist_apply_linear_apply, SchwartzMap.integral_mul_deriv_eq_neg_deriv_mul, TemperedDistribution.fourierInv_apply, EuclideanGeometry.inversion_mem_perpBisector_inversion_iff, ProbabilityTheory.HasGaussianLaw.charFunDual_map_eq_fun, Affine.Simplex.neg_one_lt_inner_vsub_altitudeFoot_div, Affine.Simplex.ExcenterExists.touchpointWeights_map, MonotoneOn.exists_tendsto_deriv_liminf_lintegral_enorm_le, LinearMap.IsSymmetric.sub, EuclideanGeometry.collinear_of_angle_eq_pi, ProbabilityTheory.covarianceBilin_map, IsHilbertSum.linearIsometryEquiv_symm_apply_dfinsupp_sum_single, Affine.Simplex.mongePoint_map, HurwitzZeta.hurwitzOddFEPair_f, Affine.Simplex.eulerPoint_map, fourierCoeff.const_mul, SchwartzMap.instFourierSMul, MeasureTheory.measureReal_abs_inner_gt_le_integral_charFun, Orientation.two_zsmul_oangle_smul_right_self, Affine.Triangle.sOppSide_affineSpan_pair_point_excenter_singleton, SchwartzMap.fourierTransformCLM_apply, AffineSubspace.signedInfDist_singleton, EuclideanGeometry.angle_midpoint_eq_pi, Orientation.coe_basisRightAngleRotation, TemperedDistribution.fourierTransform_toTemperedDistributionCLM_eq, intervalIntegral.mul_integral_comp_mul_add, one_add_cpow_hasFPowerSeriesOnBall_zero, SchwartzMap.fderivCLM_fourier_eq, Bundle.ContinuousRiemannianMetric.pos, ProbabilityTheory.strong_law_aux4, TemperedDistribution.instLineDerivAdd, SchwartzMap.derivCLM_apply, TensorProduct.toLinearMap_mapIsometry, ProbabilityTheory.condExp_zero_or_one_of_measurableSet_limsup_atTop, Affine.Simplex.affineCombination_touchpointWeights, intervalIntegral.integral_nonneg_of_ae, Orientation.volumeForm_zero_neg, SmoothPartitionOfUnity.contMDiff_finsum_smul, Unitary.inner_map_map, ContDiffBump.dist_normed_convolution_le, Orientation.oangle_eq_iff_eq_norm_div_norm_smul_rotation_of_ne_zero, SmoothPartitionOfUnity.sum_finsupport, TensorProduct.enorm_map, Orientation.areaForm_map, Affine.Triangle.orthocenter_mem_affineSpan, EuclideanGeometry.oangle_ne_zero_and_ne_pi_iff_not_collinear, Complex.GammaSeq_eq_approx_Gamma_integral, LinearMap.IsSymmetric.id, OrthonormalBasis.toMatrix_orthonormalBasis_mem_unitary, ContinuousLinearMap.adjoint_comp, deriv_bernoulliFun, det_fderivPiPolarCoordSymm, isConformalMap_iff, ProbabilityTheory.condVar_bot_ae_eq, Affine.Simplex.faceOppositeCentroid_mem_ninePointCircle, Affine.Simplex.mongePoint_mem_affineSpan, SchwartzMap.integral_clm_comp_deriv_right_eq_neg_left, NumberField.mixedEmbedding.commMap_apply_of_isReal, Fourier.norm_fourierIntegral_le_integral_norm, EuclideanGeometry.Sphere.IsTangent.isTangentAt, ZSpan.fundamentalDomain_pi_basisFun, LipschitzWith.ae_differentiableAt_of_real, ProperCone.mem_innerDual, toLinearMap_rankOne, EuclideanGeometry.Sphere.orthRadius_le_orthRadius_iff, ContinuousLinearMap.adjointAux_inner_right, MeasureTheory.Measure.integrable_comp_iff, Bundle.RiemannianMetric.pos, IsOpen.exists_contDiff_support_eq, integral_zpow, TemperedDistribution.instLineDerivSMulComplex, LSeries_analyticOn, exists_eq_interval_average_of_measure, HilbertBasis.repr_self, TensorProduct.commIsometry_apply, NumberField.mixedEmbedding.hasFDerivAt_polarCoordReal_symm, Function.Complex.hasTemperateGrowth_ofReal, ConvexOn.map_average_le, ProbabilityTheory.analyticOnNhd_mgf, TensorProduct.congrIsometry_symm, integral_one_div_one_add_sq, EuclideanGeometry.collinear_iff_eq_or_eq_or_angle_eq_zero_or_angle_eq_pi, Complex.log_eq_integral, MeasureTheory.BoundedContinuousFunction.integral_le_of_levyProkhorovEDist_lt, Affine.Simplex.incenter_reindex, integral_one, circleAverage_log_norm_sub_const₂, LinearMap.isStarProjection_toContinuousLinearMap_iff, ContinuousLinearMap.IsPositive.orthogonalProjection_comp, Manifold.pathELength_eq_lintegral_mfderiv_Icc, AffineSubspace.mem_perpBisector_iff_dist_eq, LinearMap.IsSymmetric.orthogonal_range, MeasureTheory.hasFiniteIntegral_prod_iff, dimH_orthogonalProjection_le, Complex.one_div_one_sub_sq_hasFPowerSeriesOnBall_zero, Orientation.inner_rightAngleRotationAux₁_right, hasFDerivAt_pi_polarCoord_symm, Submodule.re_inner_starProjection_nonneg, ContDiffWithinAt.inner, NumberField.mixedEmbedding.latticeBasis_repr_apply, Submodule.adjoint_orthogonalProjection, norm_tangentSpace_vectorSpace, Affine.Simplex.mongePoint_vsub_face_centroid_eq_weightedVSub_of_pointsWithCircumcenter, InformationTheory.not_differentiableWithinAt_klFun_Ioi_zero, DifferentiableWithinAt.norm_sq, EuclideanGeometry.reflection_apply', SchwartzMap.integral_fourierInv_mul_eq, hasFDerivWithinAt_iff_hasGradientWithinAt, Real.fourierIntegral_continuousLinearMap_apply', TemperedDistribution.laplacian_toTemperedDistributionCLM_eq, Submodule.id_eq_sum_starProjection_self_orthogonalComplement, integral_sin_pow_succ_le, Submodule.isOrtho_bot_right, LinearMap.adjoint_comp, ProbabilityTheory.iteratedDeriv_two_cgf_eq_integral, signedDist_right_lineMap, ProbabilityTheory.uncenteredCovarianceBilin_zero, LinearMap.IsPositive.inner_nonneg_right, VonNeumannAlgebra.coe_toStarSubalgebra, Matrix.toEuclideanLin_apply_piLp_toLp, Real.differentiable_fourierChar, span_gramSchmidt_Iio, hasFDerivAt_integral_of_dominated_of_fderiv_le, LinearIsometryEquiv.lTensor_def, EuclideanGeometry.Sphere.mem_tangentSet_iff, VectorFourier.fourierPowSMulRight_apply, mdifferentiable_jacobiTheta, inner_eq_norm_mul_iff_real, Affine.Simplex.altitude_map, Submodule.mem_orthogonal_singleton_iff_inner_left, ProbabilityTheory.tilted_mul_apply_eq_ofReal_integral_cgf, SmoothBumpCovering.support_toSmoothPartitionOfUnity_subset, Submodule.mem_adjoint_iff, DifferentiableOn.dist, LinearMap.isSymmetric_iff_isSelfAdjoint, NumberField.mixedEmbedding.normAtPlace_negAt, Submodule.reflection_involutive, Chebyshev.integral_theta_div_log_sq_isBigO, SchwartzMap.convolution_flip, Orthonormal.orthogonalFamily, AlternatingMap.measure_def, LinearMap.isSymmetric_iff_sesqForm, ContinuousLinearMap.IsPositive.adjoint_conj, PeriodPair.hasFPowerSeriesOnBall_weierstrassPExcept, LinearIsometryEquiv.reflections_generate_dim, Complex.isometryOfOrthonormal_apply, LinearMap.isSymmetricProjection_iff_eq_coe_starProjection, SchwartzMap.laplacian_eq_sum, Real.tendsto_Icc_vitaliFamily_left, Complex.sameRay_iff, integral_le_sum_Ico_of_le, EuclideanGeometry.Sphere.isTangentAt_center_iff, integral_gaussian, LinearMap.isSymmetricProjection_iff_eq_coe_starProjection_range, intervalIntegral.integral_smul_const, MeasureTheory.hausdorffMeasure_orthogonalProjection_le, ContinuousLinearMap.isPositive_iff', ProbabilityTheory.hasDerivAt_iteratedDeriv_complexMGF, intervalIntegral.mul_integral_comp_sub_mul, Submodule.finrank_add_finrank_orthogonal, contMDiffOn_comp_projIcc_iff, intervalIntegral.abs_integral_eq_abs_integral_uIoc, NumberField.mixedEmbedding.finrank, Orientation.two_zsmul_oangle_smul_right_of_ne_zero, ContinuousLinearMap.star_eq_adjoint, integral_one_div, ProbabilityTheory.integral_id_gaussianReal, SchwartzMap.integral_fourier_smul_eq, ProbabilityTheory.meas_ge_le_evariance_div_sq, SmoothBumpFunction.contMDiff, Submodule.orthogonal_eq_top_iff, HurwitzZeta.hurwitzOddFEPair_k, Submodule.lipschitzWith_orthogonalProjection, Orientation.inner_rightAngleRotation_right, UpperHalfPlane.contMDiffAt_ofComplex, GaussianFourier.integral_cexp_neg_sum_mul_add, LinearMap.IsSymmetric.orthogonalComplement_iSup_eigenspaces, NumberField.mixedEmbedding.fractionalIdealLatticeBasis_apply, eventually_norm_mfderivWithin_symm_extChartAt_comp_lt, MeasureTheory.Measure.exists_integral_isAddLeftInvariant_eq_smul_of_hasCompactSupport, ConcaveOn.average_mem_hypograph, integral_sin_sq_mul_cos, orthogonalFamily_iff_pairwise, ProbabilityTheory.IsRatCondKernelCDFAux.setIntegral_iInf_rat_gt, intervalIntegral.norm_integral_le_integral_norm, Complex.sameRay_iff_arg_div_eq_zero, Affine.Simplex.ExcenterExists.signedInfDist_excenter, ModularForm.holo', Orientation.volumeForm_apply_le, LinearMap.IsSymmetric.im_inner_apply_self, Submodule.inf_orthogonal_eq_bot, SmoothPartitionOfUnity.finite_tsupport, VectorFourier.hasFTaylorSeriesUpTo_fourierIntegral, ProbabilityTheory.analyticOn_complexMGF, Complex.integral_rpow_mul_exp_neg_mul_rpow, Submodule.isOrtho_sSup_left, NumberField.mixedEmbedding.negAt_apply_norm_isReal, innerₛₗ_apply, Chebyshev.integral_theta_div_log_sq_isLittleO, laplacian_eq_iteratedFDeriv_orthonormalBasis, Affine.Simplex.orthogonalProjectionSpan_reindex, SchwartzMap.instFourierInvAdd, innerSL_apply, OrthonormalBasis.coe_toBasis_repr, abs_real_inner_div_norm_mul_norm_eq_one_of_ne_zero_of_ne_zero_mul, EulerSine.integral_cos_pow_pos, MonotoneOn.integral_le_sum, MeasureTheory.pdf.IsUniform.integral_eq, ContDiff.norm, isIdempotentElem_rankOne_self_iff, OpenPartialHomeomorph.contDiffOn_univBall_symm, AntitoneOn.sum_le_integral, iteratedDerivWithin_cot_sub_inv_eq_add_mul_tsum, stereographic_apply, Affine.Triangle.sbtw_touchpoint_empty, MeasureTheory.inner_condExpL2_eq_inner_fun, StrongDual.toLp_apply, OrthogonalFamily.norm_sum, Orientation.rotation_apply, integral_pow_mul_le_of_le_of_pow_mul_le, inner_map_polarization, Submodule.inner_starProjection_left_eq_right, ContinuousLinearMap.IsPositive.spectrumRestricts, Real.deriv_fourierChar, OrthonormalBasis.sum_repr, TemperedDistribution.derivCLM_toTemperedDistributionCLM_eq, DifferentiableOn.analyticOnNhd, Real.iteratedFDeriv_fourierIntegral, MeasureTheory.integrableOn_condExpL2_of_measure_ne_top, hasDerivWithinAt_abs_neg, StieltjesFunction.ae_hasDerivAt, contDiffWithinAt_abs, hasSum_sq_fourierCoeff, ProbabilityTheory.strong_law_aux1, ProbabilityTheory.condExp_zero_or_one_of_measurableSet_limsup_atBot, Affine.Simplex.touchpoint_empty_notMem_affineSpan_of_ne, EuclideanGeometry.Sphere.IsTangentAt_iff_angle_eq_pi_div_two, Submodule.fstL_comp_coe_orthogonalDecomposition, UpperHalfPlane.contMDiffAt_iff, Orientation.kahler_apply_apply, isStarProjection_iff_eq_starProjection_range, ContinuousLinearMap.reApplyInnerSelf_smul, Orientation.inner_rightAngleRotationAux₁_left, UpperHalfPlane.instIsManifoldComplexModelWithCornersSelfTopWithTopENat, IsHilbertSum.linearIsometryEquiv_symm_apply_single, Complex.taylorSeries_eq_on_eball', VonNeumannAlgebra.mem_commutant_iff, exists_embedding_euclidean_of_compact, UnitAddTorus.mFourierBasis_repr, HasDerivAt.inner, LinearIsometryEquiv.toLinearIsometry_rTensor, LineDeriv.tensorLineDerivTwo_canonicalCovariantTensor_eq_sum, Orientation.areaForm_apply_self, Function.Periodic.contDiff_qParam, Submodule.starProjection_minimal, EuclideanGeometry.orthogonalProjection_linear, Orientation.oangle_smul_add_right_eq_zero_or_eq_pi_iff, Complex.analyticOnNhd_iff_differentiableOn, ProbabilityTheory.hasFiniteIntegral_compProd_iff, Real.differentiable_fourierChar_neg_bilinear_right, OrthonormalBasis.sum_rankOne_eq_id, MeasureTheory.Lp.ker_toTemperedDistributionCLM_eq_bot, Affine.Simplex.sSameSide_point_excenter_singleton, ProbabilityTheory.variance_linearMap_gaussianReal, MeasureTheory.Lp.toTemperedDistribution_toLp_eq, fourierBasis_repr, MeasureTheory.condExp_stronglyMeasurable_mul_of_bound₀, AffineSubspace.signedInfDist_def, NumberField.mixedEmbedding.fundamentalCone.expMapBasis_apply, Complex.analyticAt_of_differentiable_on_punctured_nhds_of_continuousAt, Submodule.starProjection_mem_subspace_eq_self, Affine.Simplex.acuteAngled_reindex_iff, MeasureTheory.BoundedContinuousFunction.inner_toLp, ContinuousLinearMap.adjoint_inner_right, Submodule.angle_coe, Real.tendsto_integral_gaussian_smul, MeasureTheory.integral_fintype_prod_volume_eq_prod, TensorProduct.norm_tmul, LinearMap.isPositive_iff, Affine.Simplex.mem_altitude, Affine.Simplex.isDiameter_ninePointCircle, ProbabilityTheory.IsGaussian.integral_dual_conv_map_neg_eq_zero, signedDist_lineMap_right, TemperedDistribution.laplacian_apply_apply, MeasureTheory.Integrable.uniformIntegrable_condExp_filtration, Affine.Triangle.sSameSide_affineSpan_pair_point_excenter_singleton, Affine.Triangle.dist_div_sin_angle_div_two_eq_circumradius, Real.integral_rpow_mul_exp_neg_mul_Ioi, SchwartzMap.tsupport_derivCLM_subset, Affine.Simplex.orthogonalProjectionSpan_eulerPoint_mem_ninePointCircle, OrthonormalBasis.coe_toBasis_repr_apply, Affine.Simplex.mongePlane_reindex, UpperHalfPlane.mdifferentiable_coe, LinearIsometryEquiv.star_eq_symm, Manifold.lintegral_norm_mfderiv_Icc_eq_pathELength_projIcc, SchwartzMap.integral_smul_laplacian_right_eq_left, SchwartzMap.le_seminorm', EuclideanGeometry.reflection_involutive, OrthonormalBasis.coe_equiv_euclideanSpace, differentiable_norm_rpow, VectorFourier.fourierIntegral_probChar, SchwartzMap.instFourierInvPair, Affine.Simplex.sign_signedInfDist_incenter, Affine.Simplex.ExcenterExists.sign_signedInfDist_excenter, Orientation.rightAngleRotation_map, ProbabilityTheory.evariance_eq_zero_iff, integral_inv_one_add_sq, VectorFourier.norm_fourierSMulRight_le, AlternatingMap.measure_parallelepiped, EuclideanGeometry.Sphere.isTangentAt_iff_dist_sq_eq_power, PeriodPair.weierstrassPExceptSeries_hasSum, Orientation.two_zsmul_oangle_smul_left_self, Orientation.kahler_rotation_right, integral_Ioi_cpow_of_lt, Submodule.orthogonalProjectionFn_eq, ProbabilityTheory.Kernel.setIntegral_density, ModularFormClass.analyticAt_cuspFunction_zero, TensorProduct.nnnorm_comm, Submodule.IsOrtho.ge, Affine.Simplex.signedInfDist_affineCombination, NumberField.mixedEmbedding.volume_fundamentalDomain_latticeBasis, TemperedDistribution.lineDerivOp_apply_apply, Complex.HadamardThreeLines.diffContOnCl_invInterpStrip, ProbabilityTheory.strong_law_aux2, Submodule.bot_orthogonal_eq_top, intervalIntegral.mul_integral_comp_mul_right, Real.one_div_sub_pow_hasFPowerSeriesOnBall_zero, signedDist_apply, Polynomial.Gal.card_complex_roots_eq_card_real_add_card_not_gal_inv, ContinuousLinearMap.IsPositive.conj_starProjection, ProbabilityTheory.iIndepFun.integral_fun_prod_eq_prod_integral, intervalIntegral.norm_integral_le_abs_integral_norm, Orthonormal.comp_linearIsometryEquiv, UnitAddTorus.hasSum_sq_mFourierCoeff, TemperedDistribution.lineDerivOp_fourierInv_eq, Submodule.map_orthogonal, Polynomial.Chebyshev.integral_eval_T_real_mul_eval_T_real_measureT_of_ne, HurwitzZeta.hurwitzOddFEPair_g, VonNeumannAlgebra.coe_commutant, integral_sin_pow_odd, EuclideanGeometry.dist_affineCombination, Complex.circleTransformDeriv_bound, ProbabilityTheory.hasDerivAt_integral_pow_mul_exp_real, Orientation.oangle_sign_smul_add_smul_right, Complex.hasFPowerSeriesOnBall_of_differentiable_off_countable, signedDist_eq_dist_iff_vsub_mem_span, EuclideanGeometry.Sphere.mem_commonIntTangents_iff, AffineSubspace.direction_perpBisector, volume_regionBetween_eq_integral, AffineSubspace.angle_coe, LinearMap.IsSymmetric.conj_inner_sym, analyticAt_clog, OrthonormalBasis.same_orientation_iff_det_eq_det, ProbabilityTheory.IsGaussian.charFun_eq, ClosedSubmodule.orthogonal_disjoint, Affine.Simplex.ninePointCircle_map, ContinuousLinearMap.isAdjointPair_inner, VectorFourier.norm_fourierPowSMulRight_le, TensorProduct.norm_map, EuclideanGeometry.dist_smul_vadd_eq_dist, ContinuousLinearMap.coe_le_coe_iff, integral_gaussian_complex, AddChar.linearIndependent, SmoothPartitionOfUnity.mem_fintsupport_iff, Emetric.exists_smooth_forall_closedBall_subset, ProbabilityTheory.norm_uncenteredCovarianceBilin_le, Real.hasFDerivAt_fourierChar_neg_bilinear_right, EuclideanGeometry.orthogonalProjection_eq_self_iff, intervalIntegral.inv_mul_integral_comp_div, AffineSubspace.mem_perpBisector_iff_inner_eq, EuclideanGeometry.reflection_subtype, ProbabilityTheory.strong_law_aux3, Submodule.orthogonal_le_orthogonal_iff, MeasureTheory.BoundedContinuousFunction.integral_eq_integral_meas_le_of_hasFiniteIntegral, SchwartzMap.integral_inner_fourier_fourier, Submodule.orthogonal_le_iff_orthogonal_le, ModularFormClass.holo, VectorFourier.norm_fourierSMulRight, volume_closedBall, Function.Periodic.integral_le_sSup_add_zsmul_of_pos, differentiableOn_abs, ProbabilityTheory.hasDerivAt_mgf, OrthonormalBasis.toMatrix_orthonormalBasis_self_mul_conjTranspose, ContinuousLinearMap.isPositive_zero, integral_exp_mul_complex_Iic, circleIntegral.integral_sub_center_inv, MeasureTheory.Lp.toTemperedDistribution_apply, Submodule.snd_orthogonalDecomposition_apply, TemperedDistribution.smulLeftCLM_const, strongConvexOn_iff_convex, EuclideanGeometry.angle_right_midpoint_eq_pi_div_two_of_dist_eq, Orientation.oangle_eq_pi_iff_sameRay_neg, SchwartzMap.fourier_fderivCLM_eq, Unitary.conjStarAlgAut_symm_unitaryLinearIsometryEquiv, SchwartzMap.fourier_convolution_apply, intervalIntegral.integral_eq_zero_iff_of_nonneg_ae, ProbabilityTheory.strong_law_ae_real, SchwartzMap.instContinuousFourier, Submodule.starProjection_le_starProjection_iff, ContDiffAt.inner, real_inner_smul_left, ExistsContDiffBumpBase.w_integral, NumberField.mixedEmbedding.fundamentalCone.abs_det_fderiv_expMapBasis, ProbabilityTheory.deriv_cgf_zero, Orientation.oangle_rotation_self_right, LipschitzWith.integral_inv_smul_sub_mul_tendsto_integral_lineDeriv_mul, NumberField.mixedEmbedding.euclidean.finrank, LinearMap.eq_adjoint_iff_basis_right, DifferentiableAt.norm, Real.differentiable_fourierChar_neg_bilinear_left, Submodule.instOrthogonalCompleteSpace, ProbabilityTheory.IsGaussian.ext_iff, fderiv_norm_smul_pos, EuclideanGeometry.concyclic_or_collinear_of_two_zsmul_oangle_eq, integral_Ioi_inv_one_add_sq, Real.circleAverage_mono, NumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_expMap_symm, fourierCoeff_liftIoc_eq, Affine.Simplex.ExcenterExists.signedInfDist_excenter_eq_mul_sum_inv, MeasureTheory.Measure.integral_isAddLeftInvariant_isAddRightInvariant_combo, instOrderIsoClassContinuousLinearMapIdOfNonUnitalAlgEquivClassOfStarHomClassOfContinuousMapClass, TemperedDistribution.instContinuousFourierInv, Polynomial.Chebyshev.integral_eval_T_real_mul_self_measureT_zero, NumberField.mixedEmbedding.measurableSet_negAt_plusPart, LinearMap.isStarProjection_iff_isSymmetricProjection, LinearIsometryEquiv.toLinearEquiv_rTensor, innerₛₗ_apply_coe, Complex.one_add_cpow_hasFPowerSeriesOnBall_zero, Submodule.orthogonalDecomposition_apply, Submodule.isOrtho_self, range_modelWithCornersEuclideanHalfSpace, LinearIsometryEquiv.toLinearIsometry_lTensor, VectorFourier.fourierPowSMulRight_iteratedFDeriv_fourierIntegral, VonNeumannAlgebra.instStarMemClass, NumberField.mixedEmbedding.euclidean.volumePreserving_toMixed_symm, ProbabilityTheory.iIndepFun.integral_fun_prod_comp, OrthonormalBasis.toMatrix_orthonormalBasis_conjTranspose_mul_self, integral_exp_neg_Ioi_zero, ClosedSubmodule.orthogonal_closure, nnnorm_tangentSpace_vectorSpace, OrthonormalBasis.toMatrix_orthonormalBasis_mem_orthogonal, TemperedDistribution.fourier_apply, Matrix.PosSemidef.sqrt_mul_self, Orientation.areaForm_rightAngleRotation_right, OrthonormalBasis.orientation_adjustToOrientation, MDifferentiableAt.inner_bundle, contDiff_norm_rpow, exists_contDiff_tsupport_subset, ProbabilityTheory.indepFun_iff_integral_comp_mul, EuclideanGeometry.orthogonalProjection_vsub_mem_direction_orthogonal, hasMellin_cpow_Ioc, EisensteinSeries.eisensteinSeries_SIF_MDifferentiable, tsum_sq_fourierCoeff, Submodule.orthogonal_eq_inter, VectorFourier.integral_fourierIntegral_smul_eq_flip, MeasureTheory.eLpNorm_condExpL2_le, intervalIntegral.integral_pos, Affine.Simplex.touchpoint_mem_affineSpan_simplex, Orientation.inner_smul_rotation_pi_div_two_smul_left, integral_sin_pow, ProbabilityTheory.iIndepFun.integral_prod_comp, SchwartzMap.coe_apply, real_inner_div_norm_mul_norm_eq_one_of_ne_zero_of_pos_mul, integral_mul_cpow_one_add_sq, EuclideanGeometry.angle_eq_zero_iff_ne_and_wbtw, AntitoneOn.integral_le_sum, integral_gaussian_Ioi, DifferentiableOn.analyticAt, Orientation.oangle_smul_right_of_pos, LinearMap.IsPositive.adjoint_eq, abs_real_inner_div_norm_mul_norm_eq_one_iff, fderiv_norm_rpow, ContinuousLinearMap.norm_map_iff_adjoint_comp_self, Matrix.toEuclideanLin_eq_toLin_orthonormal, Submodule.starProjection_orthogonal_val, Affine.Simplex.circumsphere_reindex, isStarProjection_iff_eq_starProjection, ContinuousLinearMap.norm_adjoint_comp_self, LinearPMap.mem_adjoint_domain_iff, Orientation.inner_smul_rotation_pi_div_two_smul_right, LinearMap.IsSymmetricProjection.le_iff_range_le_range, CircleIntegrable.out, RCLike.intervalIntegral_ofReal, VonNeumannAlgebra.instSubringClass, EuclideanGeometry.eq_orthogonalProjection_of_eq_subspace, Real.Icc_mem_vitaliFamily_at_right, EuclideanGeometry.orthogonalProjection_apply, ConcaveOn.le_map_set_average, Complex.one_div_one_sub_hasFPowerSeriesOnBall_zero, EuclideanGeometry.Sphere.direction_orthRadius, UpperHalfPlane.mdifferentiableAt_iff, Complex.rightAngleRotation, 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, PeriodPair.analyticOnNhd_weierstrassPExcept, LinearIsometry.rTensor_apply, Submodule.norm_orthogonalProjection, Submodule.instHasOrthogonalProjectionTop, AffineSubspace.signedInfDist_apply_self, EuclideanGeometry.orthogonalProjection_vsub_orthogonalProjection, LinearIsometry.toLinearMap_lTensor, EuclideanGeometry.orthogonalProjection_mem_orthogonal, coe_innerₛₗ_apply, integral_sin_sq_mul_cos_sq, ProbabilityTheory.covarianceBilinDual_of_not_memLp, integral_mul_rpow_one_add_sq, HasGradientAt.hasDerivAt, TensorProduct.nndist_tmul_le, InnerProductGeometry.angle_eq_pi_iff, deriv_circleMap_eq_zero_iff, ArithmeticFunction.iteratedDeriv_LSeries_alternating, continuousLinearMapOfBilin_apply, NumberField.mixedEmbedding.normAtAllPlaces_mixedSpaceOfRealSpace, ProbabilityTheory.condVar_ae_eq_condExp_sq_sub_sq_condExp, NumberField.mixedEmbedding.det_fderivPolarCoordRealSymm, Matrix.cstar_norm_def, abs_integral_sub_setIntegral_mulExpNegMulSq_comp_lt, PeriodPair.indep, ProperCone.innerDual_iUnion, SchwartzMap.tsum_eq_tsum_fourierIntegral, ProbabilityTheory.uncenteredCovarianceBilinDual_apply, Orientation.kahler_rightAngleRotation_right, Submodule.HasOrthogonalProjection.map_linearIsometryEquiv, MeasureTheory.condExpIndSMul_ae_eq_smul, Quaternion.linearIsometryEquivTuple_apply, EuclideanGeometry.Sphere.orthRadius_parallel_orthRadius_iff, integral_Iic_inv_one_add_sq, SmoothPartitionOfUnity.toPartitionOfUnity_toFun, ProbabilityTheory.IsRatCondKernelCDFAux.tendsto_integral_of_monotone, SmoothPartitionOfUnity.contMDiff_smul, ProbabilityTheory.condIndepFun_iff, Affine.Triangle.sSameSide_affineSpan_pair_excenter_singleton_point, MeasureTheory.charFun_eq_integral_innerProbChar, HasGradientAt.fderiv_apply, SchwartzMap.instFourierInvSMul, TemperedDistribution.derivCLM_apply_apply, OrthonormalBasis.tensorProduct_apply, integral_cos_sq, abs_signedDist_le_dist, Orientation.norm_kahler, NumberField.mixedEmbedding.disjoint_span_commMap_ker, mfderiv_subtype_coe_Icc_one, Complex.taylorSeries_eq_of_entire', Complex.isometryOfOrthonormal_symm_apply, Real.integral_rpowIntegrand₀₁_eq_rpow_mul_const, intervalIntegral.integral_hasFDerivAt, ProperCone.innerDual_toSubmodule, Meromorphic.Gamma, Orientation.inner_rightAngleRotation_self, ValueDistribution.proximity_coe, Affine.Triangle.dist_div_sin_oangle_div_two_eq_circumradius, MeasureTheory.tendsto_iff_forall_lipschitz_integral_tendsto, intervalIntegral.fderiv_integral, ProbabilityTheory.gaussianReal_apply_eq_integral, EuclideanGeometry.affineIndependent_iff_of_two_zsmul_oangle_eq, eventually_norm_trivializationAt_lt, TensorProduct.congrIsometry_apply, ProbabilityTheory.IsGaussian.charFunDual_eq', OrthonormalBasis.addHaar_eq_volume, OrthonormalBasis.det_to_matrix_orthonormalBasis_real, MeasureTheory.integral_prod_smul, ProbabilityTheory.condExp_eq_zero_or_one_of_condIndepSet_self, ContinuousLinearMap.apply_norm_sq_eq_inner_adjoint_right, innerSL_apply_coe, ProbabilityTheory.analyticOnNhd_complexMGF, ProbabilityTheory.IsRatCondKernelCDFAux.setIntegral, ContinuousLinearMap.isPositive_one, ContinuousLinearMap.isPositive_sum, Real.hasDerivAt_Gamma_nat, Orientation.oangle_smul_right_self_of_nonneg, HasStrictFDerivAt.inner, MeasureTheory.ContinuousMap.inner_toLp, gradient_eq_deriv, differentiableAt_abs, ProbabilityTheory.setIntegral_stieltjesOfMeasurableRat_rat, Submodule.orthogonalProjection_comp_subtypeL_eq_zero_iff, LipschitzWith.integral_inv_smul_sub_mul_tendsto_integral_lineDeriv_mul', intervalIntegral.norm_integral_le_abs_of_norm_le, ProbabilityTheory.analyticAt_iteratedDeriv_mgf, LinearMap.toMatrix_adjoint, ProbabilityTheory.isPositive_covarianceOperator, Affine.Simplex.reflection_circumcenter_eq_affineCombination_of_pointsWithCircumcenter, Affine.Simplex.height_reindex, exists_eq_interval_average, exists_smooth_zero_one_nhds_of_isClosed, DifferentiableOn.norm, Affine.Simplex.inradius_map, Complex.map_isometryOfOrthonormal, integral_exp_Iic_zero, TemperedDistribution.fourierTransformInv_apply, Orientation.oangle_neg_orientation_eq_neg, Orientation.oangle_sign_smul_add_smul_left, LinearMap.isSymmetric_iff_inner_map_self_real, EuclideanGeometry.coe_orthogonalProjection_eq_iff_mem, ContDiffOn.norm, ModularFormClass.qExpansionFormalMultilinearSeries_coeff, EuclideanGeometry.Sphere.secondInter_eq_lineMap, ContinuousLinearMap.isPositive_adjoint_comp_self, SchwartzMap.integral_clm_comp_laplacian_right_eq_left, UpperHalfPlane.contMDiff_smul, TensorProduct.nnnorm_lid, LinearMap.im_inner_adjoint_mul_self_eq_zero, eqOn_iteratedDerivWithin_cotTerm_integerComplement, ClosedSubmodule.orthogonal_closure', Matrix.l2_opNorm_def, signedDist_apply_linear, EuclideanGeometry.Sphere.secondInter_map, OrthogonalFamily.linearIsometry_apply, Matrix.toEuclideanLin_toLp, Bundle.RiemannianMetric.continuousAt, continuous_stereoInvFun, parallelepiped_orthonormalBasis_one_dim, Submodule.orthogonalProjection_eq_zero_iff, integral_log_from_zero, MeasureTheory.integrable_mconv_iff, UpperHalfPlane.contMDiff_denom, VectorFourier.norm_fourierIntegral_le_integral_norm, EuclideanGeometry.Sphere.angle_eq_pi_div_two_iff_mem_sphere_ofDiameter, real_inner_smul_self_right, Manifold.exists_lt_of_riemannianEDist_lt, MeasureTheory.integral_abs_condExp_le, StrictConvexOn.ae_eq_const_or_map_average_lt, norm_innerSL_le, VectorFourier.hasFDerivAt_fourierChar_smul, Orientation.rotation_pi, Complex.one_div_sub_sq_sub_one_div_sq_hasFPowerSeriesOnBall_zero, InformationTheory.not_differentiableAt_klFun_zero, PeriodPair.lattice_eq_span_range_basis, ContinuousLinearMap.IsPositive.isSelfAdjoint, MeasureTheory.measure_unitBall_eq_integral_div_gamma, integral_cos_sq_sub_sin_sq, ProbabilityTheory.variance_tilted_mul, OrthonormalBasis.sum_repr', Submodule.coe_orthogonalProjection_apply, Submodule.starProjection_coe_eq_isCompl_projection, MeasureTheory.le_integral_rnDeriv_of_ac, AffineSubspace.mem_perpBisector_pointReflection_iff_inner_eq_zero, SmoothBumpCovering.embeddingPiTangent_coe, EisensteinSeries.eisensteinSeriesSIF_mdifferentiable, SchwartzMap.integral_smul_deriv_right_eq_neg_left, SmoothPartitionOfUnity.nonneg', ProbabilityTheory.covarianceBilinDual_of_not_memLp', LinearMap.posSemidef_toMatrix_iff, Affine.Triangle.orthocenter_vsub_circumcenter_eq_sum_vsub, Function.hasTemperateGrowth_one_add_norm_sq_rpow, Orientation.two_zsmul_oangle_smul_smul_self, Submodule.starProjection_apply_eq_zero_iff, SchwartzMap.fourier_convolution, tendsto_setIntegral_pow_smul_of_unique_maximum_of_isCompact_of_continuousOn, ContDiffWithinAt.norm, Complex.log_inv_eq_integral, SmoothPartitionOfUnity.IsSubordinate.contMDiff_finsum_smul, UnitAddTorus.span_mFourierLp_closure_eq_top, Orientation.rotation_symm_apply, AbsolutelyContinuousOnInterval.integral_mul_deriv_eq_deriv_mul, ProbabilityTheory.analyticOn_iteratedDeriv_mgf, MeasureTheory.Integrable.integral_norm_condKernel, Affine.Simplex.altitudeFoot_mem_affineSpan_faceOpposite, Orthonormal.inner_right_fintype, PeriodPair.analyticOnNhd_weierstrassP, intervalIntegral.inv_mul_integral_comp_div_add, UpperHalfPlane.mdifferentiable_denom_zpow, OrthonormalBasis.abs_det_adjustToOrientation, HasGradientWithinAt.hasFDerivWithinAt, Pi.orthonormalBasis_repr, EuclideanGeometry.inversion_eq_lineMap, MeromorphicOn.Gamma, Complex.integral_cpow_mul_exp_neg_mul_Ioi, IsHilbertSum.linearIsometryEquiv_apply_dfinsupp_sum_single, Orthonormal.tmul, norm_fderiv_norm_id_rpow, NumberField.Units.basisOfIsMaxRank_fundSystem, LinearMap.isAdjointPair_inner, LinearMap.IsPositive.adjoint_conj, LinearMap.isPositive_one, NumberField.mixedEmbedding.fundamentalCone.linearIndependent_completeFamily, intervalIntegral.norm_integral_le_integral_norm_uIoc, Affine.Triangle.dist_orthocenter_reflection_circumcenter_finset, Affine.Simplex.affineSpan_pair_eq_altitude_iff, AffineIsometry.angle_map, NumberField.mixedEmbedding.commMap_canonical_eq_mixed, Orientation.rotation_oangle_eq_iff_norm_eq, Affine.Simplex.signedInfDist_apply_of_ne, integral_cos_mul_complex, exists_contMDiffMap_one_nhds_of_subset_interior, dist_sq_lineMap_of_inner_eq_zero, Polynomial.fourierCoeff_toAddCircle, signedDist_left_lineMap, Complex.hasFPowerSeriesOnBall_ofScalars_mul_add_zero, Affine.Simplex.direction_altitude, LinearIsometryEquiv.symm_lTensor, DifferentiableWithinAt.inner, NumberField.mixedEmbedding.norm_negAt, Orientation.oangle_sign_smul_sub_right, SmoothPartitionOfUnity.sum_le_one, Submodule.isOrtho_bot_left, VectorFourier.fourierIntegral_fderiv, ProbabilityTheory.HasCondSubgaussianMGF.ae_trim_condExp_le, IccRightChart_extend_top, ModularFormClass.qExpansion_coeff_eq_intervalIntegral, integral_one_div_of_neg, Affine.Simplex.circumcenter_eq_centroid, ContDiffBump.convolution_tendsto_right_of_continuous, Affine.Simplex.excenter_reindex, Complex.approx_Gamma_integral_tendsto_Gamma_integral, MeasureTheory.Lp.fourier_toTemperedDistribution_eq, fderivInnerCLM_apply, intervalIntegral.integral_lt_integral_of_ae_le_of_measure_setOf_lt_ne_zero, eventually_norm_mfderiv_extChartAt_lt, ContMDiffWithinAt.inner_bundle, EuclideanGeometry.orthogonalProjection_eq_iff_mem, ProbabilityTheory.HasGaussianLaw.charFunDual_map_eq, MeasureTheory.Integrable.integral_eq_integral_Ioc_meas_le, Affine.Simplex.ninePointCircle_center, EuclideanGeometry.dist_orthogonalProjection_line_eq_of_two_zsmul_oangle_eq, boundary_Icc, Submodule.orthogonalProjection_coe_eq_linearProjOfIsCompl, SchwartzMap.toLp_fourier_eq, MeasureTheory.tendsto_integral_meas_thickening_le, LinearMap.IsSymmetric.coe_re_inner_apply_self, VectorFourier.norm_fourierPowSMulRight_iteratedFDeriv_fourierIntegral_le, Real.fderiv_fourierChar_neg_bilinear_left_apply, OrthogonalFamily.summable_iff_norm_sq_summable, hasContDiffBump_of_innerProductSpace, Real.exists_measure_rpow_eq_integral, Real.fourierIntegral_continuousMultilinearMap_apply', HasGradientAtFilter.hasDerivAtFilter, ValueDistribution.proximity_top, Affine.Triangle.sSameSide_affineSpan_pair_incenter_point, Real.differentiable_fourier, ProbabilityTheory.integrable_comp_iff, LinearIsometryEquiv.conjStarAlgEquiv_apply_apply, UpperHalfPlane.mdifferentiable_iff, MeasureTheory.lintegral_comp_eq_lintegral_meas_lt_mul, Submodule.orthogonalProjection_norm_le, integral_sin_pow_antitone, Matrix.PosDef.posDef_sqrt, integral_pow_abs_sub_uIoc, Real.circleAverage_nonneg_of_nonneg, Complex.analyticAt_iff_eventually_differentiableAt, Orientation.rightAngleRotation_neg_orientation, PositiveLinearMap.gnsNonUnitalStarAlgHom_apply, Orientation.rotationAux_apply, finrank_euclideanSpace_fin, Submodule.orthogonalProjection_orthogonal, intervalIntegral.integral_nonneg_of_forall, Affine.Simplex.centroid_eq_affineCombination_of_pointsWithCircumcenter, InformationTheory.deriv_klFun, one_add_rpow_hasFPowerSeriesOnBall_zero, boundary_product, LinearIsometryEquiv.rTensor_def, Manifold.exists_lt_locally_constant_of_riemannianEDist_lt, MeasureTheory.norm_condExpL2_le_one, differentiable_sigmoid, NumberField.mixedEmbedding.normAtPlace_mixedSpaceOfRealSpace, Affine.Simplex.incenter_notMem_affineSpan_faceOpposite, Affine.Simplex.touchpoint_empty_mem_interior_faceOpposite, OrthonormalBasis.repr_reindex, MeasureTheory.condExpL2_comp_continuousLinearMap, LindemannWeierstrass.hasDerivAt_cexp_mul_sumIDeriv, SchwartzMap.laplacian_apply, symm_toEuclideanLin_rankOne, MeasureTheory.charFun_map_smul, ProbabilityTheory.IsGaussian.eq_gaussianReal, Real.one_div_sub_sq_hasFPowerSeriesOnBall_zero, Submodule.orthogonalProjection_orthogonalComplement_singleton_eq_zero, Submodule.isOrtho_sup_left, ProbabilityTheory.uncenteredCovarianceBilinDual_zero, ContinuousLinearMap.adjoint_innerSL_apply, Submodule.IsOrtho.comap, UpperHalfPlane.mdifferentiableAt_ofComplex, OrthogonalFamily.inner_right_fintype, ProbabilityTheory.integral_tilted_mul_self, LSeries_eq_mul_integral', integrableOn_Ioi_deriv_norm_ofReal_cpow, AffineSubspace.right_mem_perpBisector, EuclideanGeometry.Sphere.dist_orthogonalProjection_eq_radius_iff_isTangentAt, Submodule.orthogonalProjection_eq_linearProjOfIsCompl, Orthonormal.inner_sum, EuclideanGeometry.reflection_apply, intervalIntegral.integral_mul_const, AbsolutelyContinuousOnInterval.intervalIntegrable_deriv, ProbabilityTheory.cdf_gammaMeasure_eq_integral, MeasureTheory.integral_comap_eq_mulEquivHaarChar_smul, fourier_gaussian_pi, Real.fourier_smul_convolution_eq, Function.Periodic.tendsto_atTop_intervalIntegral_of_pos', ContinuousLinearMap.IsPositive.re_inner_nonneg_right, EuclideanGeometry.Sphere.mem_orthRadius_iff_inner_left, not_differentiableAt_abs_zero, MonotoneOn.ae_differentiableWithinAt, MeasureTheory.condExpL2_const_inner, LinearMap.IsSymmetric.intCast, TemperedDistribution.laplacianCLM_apply, SchwartzMap.instFourierAdd, continuousAt_gaussian_integral, ProperCone.innerDual_innerDual, TensorProduct.ext_iff_inner_right_threefold, NumberField.mixedEmbedding.fundamentalCone.expMap_basis_of_ne, Orientation.areaForm_rightAngleRotation_left, Differentiable.norm, contDiff_sigmoid, Complex.taylorSeries_eq_on_emetric_ball', LinearIsometry.angle_map, fourierCoeff_liftIco_eq, NumberField.mixedEmbedding.disjoint_negAt_plusPart, DifferentiableAt.dist, contDiff_euclidean, IccLeftChart_extend_bot_mem_frontier, fderiv_norm_sq_apply, Submodule.starProjection_eq_self_iff, LipschitzWith.ae_differentiableAt_real, OrthonormalBasis.tensorProduct_repr_tmul_apply, EuclideanGeometry.Sphere.finrank_orthRadius, NumberField.mixedEmbedding.volume_fundamentalDomain_stdBasis, EulerSine.integral_cos_mul_cos_pow_even, circleIntegral.integral_const_mul, Icc_isBoundaryPoint_top, integral_sin_pow_even, Affine.Simplex.points_vsub_eulerPoint, TensorProduct.assocIsometry_symm_apply, MeasureTheory.condExp_mul_of_stronglyMeasurable_left, InnerProductGeometry.angle_smul_left_of_pos, gramSchmidt_mem_span, LinearMap.IsSymmetric.add, TensorProduct.inner_map_map, Orientation.measure_orthonormalBasis, Affine.Simplex.ExcenterExists.sSameSide_excenter_point_iff, Differentiable.analyticAt, fderiv_norm_sq, LinearMap.IsSymmetric.orthogonalFamily_iInf_eigenspaces, MeasureTheory.addEquivAddHaarChar_smul_integral_map, TensorProduct.toLinearMap_mapInclIsometry, MeasureTheory.charFun_eq_integral_probChar, OrthogonalFamily.inner_right_dfinsupp, Complex.one_div_sub_hasFPowerSeriesOnBall_zero, Orientation.inner_mul_inner_add_areaForm_mul_areaForm', ContDiffOn.dist, EuclideanGeometry.angle_eq_pi_iff_sbtw, MDifferentiable.inner_bundle, orthonormal_span, ContinuousLinearMap.innerSL_apply_comp, conformalAt_iff', TensorProduct.lidIsometry_symm_apply, ContinuousLinearMap.instStarOrderedRingRCLike, surjective_stereographic, fourierIntegral_gaussian_pi', ContinuousLinearMap.toSesqForm_apply_norm_le, hasDerivAt_abs_pos, Orientation.oangle_smul_left_of_pos, HilbertBasis.hasSum_repr_symm, hasFDerivAt_stereoInvFunAux_comp_coe, LinearMap.adjoint_id, inner_smul_left, LipschitzWith.integral_lineDeriv_mul_eq, nullSubmodule_le_ker_toDualMap_right, Affine.Triangle.dist_point_centroid, integral_gaussian_complex_Ioi, MeasureTheory.condExpL2_indicator_nonneg, ContinuousLinearMap.adjoint_adjoint, Affine.Triangle.orthocenter_reindex, HasCompactSupport.hasFDerivAt_convolution_left, Affine.Simplex.circumradius_map, instIsManifoldIcc, Bundle.ContinuousRiemannianMetric.isVonNBounded, Matrix.PosSemidef.sqrt_eq_iff_eq_sq, TemperedDistribution.smulLeftCLM_apply_apply, NumberField.mixedEmbedding.mem_rat_span_latticeBasis, ProbabilityTheory.hasSubgaussianMGF_of_mem_Icc, hasSum_mellin_pi_mul_sq, Orientation.inner_mul_areaForm_sub, ProbabilityTheory.integral_preCDF_fst, fderiv_inner_apply, SmoothBumpCovering.toSmoothPartitionOfUnity_zero_of_zero, contDiffAt_abs, ProbabilityTheory.covarianceOperator_of_not_memLp, MeasureTheory.Integrable.uniformIntegrable_condExp, SmoothPartitionOfUnity.contMDiff_sum, EuclideanGeometry.Sphere.infDist_eq_radius_iff_isTangent, Affine.Simplex.altitude_def, contMDiffOn_projIcc, NumberField.mixedEmbedding.fundamentalCone.logMap_normAtAllPlaces, ContDiffBump.integral_pos, ContinuousLinearMap.orthogonal_ker, NumberField.mixedEmbedding.fundamentalCone.normAtAllPlaces_normLeOne, Complex.rotation, Metric.exists_contMDiffMap_forall_closedEBall_subset, BoxIntegral.unitPartition.tag_mem_smul_span, signedDist_vadd_vadd, parallelepiped_single, contMDiff_circleExp, norm_rankOne, SchwartzMap.tsum_eq_tsum_fourier, NumberField.mixedEmbedding.normAtAllPlaces_normAtAllPlaces, ProbabilityTheory.IndepFun.integral_mul_eq_mul_integral, hasFDerivAt_integral_of_dominated_loc_of_lip, Submodule.isHilbertSumOrthogonal, EuclideanGeometry.Sphere.self_mem_orthRadius, intervalIntegral.norm_integral_le_of_norm_le, norm_jacobiTheta₂_term_fderiv_le, Affine.Simplex.insphere_reindex, real_inner_I_smul_self, LinearIsometry.lTensor_def, PeriodPair.instIsZLatticeRealComplexLattice, Orthonormal.inner_right_sum, GaussianFourier.integral_rexp_neg_mul_sq_norm, TensorProduct.edist_tmul_le, Real.tendsto_Icc_vitaliFamily_right, unitary.inner_map_map, LinearMap.IsPositive.conj_adjoint, intervalIntegral.differentiableOn_integral_of_continuous, differentiable_circleMap, UpperHalfPlane.mdifferentiable_smul, LinearMap.IsSymmetric.pow, EuclideanGeometry.orthogonalProjection_mem_subspace_eq_self, Affine.Simplex.sSameSide_point_incenter, Submodule.orthogonalProjectionFn_mem, LinearMap.IsPositive.re_inner_nonneg_left, Polynomial.fourierCoeff_toAddCircle_eq_zero_of_lt_zero, ContinuousLinearMapWOT.ext_inner_iff, intervalIntegral.integral_nonneg, NumberField.mixedEmbedding.mixedSpaceOfRealSpace_apply, norm_inner_div_norm_mul_norm_eq_one_iff, LinearIsometryEquiv.coe_symm_toMeasurableEquiv, ProbabilityTheory.analyticOnNhd_iteratedDeriv_mgf, Submodule.mem_iff_norm_starProjection, Orientation.abs_volumeForm_apply_le, Affine.Simplex.ExcenterExists.sSameSide_point_excenter_iff, intervalIntegral.mul_integral_comp_mul_left, DifferentiableOn.analyticOn, Orthonormal.comp_linearIsometry, hasStrictFDerivAt_euclidean, fourierCoeff_fourier, unitary.linearIsometryEquiv_coe_apply, Affine.Simplex.signedInfDist_incenter, HilbertBasis.finite_spans_dense, Affine.Simplex.inner_vsub_vsub_altitudeFoot_eq_height_sq
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