addGroupIsAddTorsor 📖 | CompOp | 513 mathmath: AffineSubspace.wOppSide_lineMap_right, AffineMap.lineMap_apply_module, AffineMap.hasStrictDerivAt_lineMap, AffineMap.lineMap_vsub_left, Convex.intrinsicClosure, Submodule.mem_toAffineSubspace, ContinuousAffineMap.lineMap_apply', smooth_barycentric_coord, AffineMap.coe_smul, affineSpan_le_toAffineSubspace_span, ContinuousAffineMap.neg_contLinear, AffineEquiv.linear_vaddConst, AffineMap.lineMap_linear, fderivWithin_comp_add_left, AddCircle.isAddQuotientCoveringMap_zsmul_of_ne_zero, rank_le_card_isVisible, Filter.Tendsto.lineMap, ConvexOn.monotoneOn_slope_lt, AffineMap.hasDerivAtFilter, Finset.affineCombination_apply_eq_lineMap_sum, curveIntegrable_segment, HasDerivWithinAt.liminf_right_slope_le, right_lt_lineMap_iff_one_lt, AffineMap.pi_lineMap_apply, AffineSubspace.smul_mem_smul_iff₀, dist_sq_lineMap_lineMap_of_inner_eq_zero, Convex.lineMap_mem, midpoint_add_self, wbtw_sub_const_iff, ContinuousAffineMap.neg_apply, sbtw_iff_mem_image_Ioo_and_ne, Wbtw.right_mem_image_Ici_of_left_ne, MonotoneOn.slope_nonneg, ContinuousAffineMap.coe_sub, AffineBasis.coe_smul, AffineMap.lineMap_rev_mem_affineSpan_pair, derivWithin_comp_const_sub, AffineMap.hasDerivWithinAt, Convex.affine_image, ContinuousAffineMap.smul_apply, lintegral_fderiv_lineMap_eq_edist, signedDist_right_congr, lineMap_le_map_iff_slope_le_slope_right, AffineBasis.linear_eq_sumCoords, Affine.Simplex.sign_signedInfDist_lineMap_incenter_touchpoint, iteratedFDerivWithin_comp_add_right', AffineSubspace.sOppSide_lineMap_left, AddCircle.isAddQuotientCoveringMap_nsmul_of_ne_zero, lineMap_inv_two, Circle.isAddQuotientCoveringMap_exp, AddCircle.isAddQuotientCoveringMap_nsmul, ContinuousAffineMap.coe_lineMap_eq, AffineBasis.coord_apply_ne, slope_pos_iff_of_le, Convex.mapsTo_lineMap, AmpleSet.preimage_iff, signedDist_left_congr, curveIntegralFun_segment, signedDist_triangle, LinearMap.toAffineMap_linear, dslope_eventuallyEq_slope_nhdsNE, ContinuousAffineMap.lineMap_toAffineMap, wbtw_lineMap_iff, nndist_right_lineMap, signedDist_linear_apply_apply, sbtw_iff_left_ne_and_right_mem_image_Ioi, ContinuousAffineMap.decomp, AffineEquiv.apply_lineMap, wbtw_const_vsub_iff, ContinuousAffineMap.zero_apply, AffineBasis.convexHull_eq_nonneg_coord, AddCircle.isAddQuotientCoveringMap_coe, nndist_left_lineMap, AffineBasis.coord_apply, ContinuousLinearMap.toContinuousAffineMap_map_zero, ContinuousAffineMap.smul_contLinear, Convex.closure_subset_interior_image_homothety_of_one_lt, signedDist_le_dist, AffineSpace.asymptoticNhds_bind_asymptoticNhds, StarConvex.affine_image, List.SortedLE.wbtw, affineSpan_eq_affineSpan_lineMap_units, lineMap_mono_endpoints, signedDist_apply_apply, AffineMap.lineMap_injective, ConcaveOn.antitoneOn_slope_gt, map_lt_lineMap_iff_slope_lt_slope_right, Submodule.toAffineSubspace_direction, sbtw_vadd_const_iff, iteratedFDerivWithin_comp_add_left, ContinuousLinearEquiv.coe_toContinuousAffineEquiv, hasDerivAtFilter_iff_tendsto_slope, AffineMap.differentiableWithinAt, Polygon.edgeSet_eq_image_edgePath, affinity_unitClosedBall, AffineSubspace.coe_smul, Finset.affineCombination_eq_linear_combination, AffineBasis.basisOf_smul, ContinuousAffineMap.vadd_toAffineMap, image_openSegment, AffineMap.apply_lineMap, AffineMap.hasDerivAt_lineMap, AffineBasis.reindex_smul, affineSpan_convexHull, sbtw_const_vsub_iff, midpoint_eq_smul_add, AffineMap.left_vsub_lineMap, midpoint_sub_right, AffineMap.hasDerivWithinAt_lineMap, AffineMap.smul_linear, curveIntegral_segment, hasDerivAt_iff_tendsto_slope_left_right, AffineBasis.toMatrix_apply, AffineMap.decomp', AffineMap.lineMap_vsub_right, ContinuousLinearEquiv.toContinuousAffineEquiv_toContinuousAffineMap, AffineMap.lineMap_continuous, ContinuousAffineMap.coe_add, dist_lineMap_left, midpoint_le_right, signedDist_eq_zero_of_orthogonal, lineMap_lt_right_iff_lt_one, AffineSpace.asymptoticNhds_vadd_pure, lineMap_le_lineMap_iff_of_lt', lineMap_strict_mono_endpoints, ContinuousOn.lineMap, midpoint_le_midpoint, Sbtw.vsub_const, bddAbove_slope_gt_of_mem_interior, Sbtw.right_mem_image_Ioi, asymptoticCone_asymptoticCone, right_lt_lineMap_iff_lt, AffineSubspace.signedInfDist_eq_signedDist_of_mem, lineMap_mem_openSegment, convexHull_vadd, right_le_lineMap_iff_le, List.exists_map_eq_of_sorted_nonempty_iff_sbtw, signedDist_zero, AffineSubspace.signedInfDist_eq_signedDist_orthogonalProjection, AffineMap.lineMap_lineMap_right, ConcaveOn.slope_anti, AffineEquiv.coe_constVSub, mem_vadd_const_affineSegment, AffineSubspace.smul_bot, AffineMap.lineMap_mem, Filter.Tendsto.atTop_smul_nhds_tendsto_asymptoticNhds, Finset.weightedVSub_smul, slope_neg_fun, AffineMap.lineMap_mono, AffineMap.vadd_linear, AffineMap.right_vsub_lineMap, Wbtw.left_mem_image_Ici_of_right_ne, signedDist_triangle_left, ConcaveOn.comp_affineMap, IsClosed.exists_wbtw_isVisible, AffineSubspace.wOppSide_lineMap_left, slope_eq_zero_iff, sbtw_iff_right_ne_and_left_mem_image_Ioi, lineMap_le_left_iff_nonpos, AmpleSet.preimage, AffineMap.vadd_lineMap, mem_affineSpan_pair_iff_exists_lineMap_rev_eq, affinity_unitBall, AffineMap.neg_linear, AmpleSet.vadd, sbtw_const_sub_iff, StrictConvex.affinity, ConcaveOn.antitoneOn_slope_lt, eq_pos_convex_span_of_mem_convexHull, iteratedFDerivWithin_comp_sub, Affine.Simplex.ExcenterExists.sign_signedInfDist_lineMap_excenter_touchpoint, differentiableWithinAt_comp_sub, ContinuousAffineMap.sub_contLinear, AffineMap.hasDerivAt, List.exists_map_eq_of_sorted_nonempty_iff_wbtw, AffineSubspace.smul_top, AffineMap.vsub_lineMap, AffineMap.vsub_apply, lineMap_le_right_iff_le, dist_lineMap_right, AffineMap.differentiableAt, AffineSubspace.smul_mem_smul_iff_of_isUnit, AffineBasis.instIsScalarTower, map_lt_lineMap_iff_slope_lt_slope_left, MeasureTheory.hausdorffMeasure_lineMap_image, AffineMap.isCentralScalar, affineIndependent_iff, signedDist_smul_of_pos, wbtw_zero_one_iff, AffineMap.lineMap_apply_module', ContinuousAffineMap.apply_lineMap', AffineSubspace.convex, eqOn_dslope_slope, AffineSubspace.wSameSide_lineMap_left, midpoint_add_sub, ContinuousWithinAt.lineMap, slope_pos_iff, Geometry.SimplicialComplex.indep, signedDist_lineMap_lineMap, AffineBasis.sum_coord_apply_eq_one, midpoint_neg_self, Sbtw.const_vsub, affineSpan_subset_span, signedDist_vadd_left_swap, LinearEquiv.coe_toAffineEquiv, AffineBasis.coord_apply_combination_of_notMem, midpoint_le_left, AffineMap.lineMap_vsub, wbtw_add_const_iff, Seminorm.vadd_closedBall, affineIndependent_smul, AffineMap.lineMap_eq_lineMap_iff, signedDist_vadd_right, lineMap_lt_left_iff_lt, midpoint_sub_add, List.exists_map_eq_of_sorted_iff_sbtw, LinearMap.coe_toAffineMap, affineSegment_const_vsub_image, Sbtw.of_lt_of_lt, map_le_lineMap_iff_slope_le_slope_right, AffineMap.image_uIcc, AffineMap.lineMap_vadd_apply, sbtw_vsub_const_iff, iteratedFDerivWithin_comp_add_right, nndist_lineMap_right, wbtw_const_sub_iff, Finset.centroid_eq_centerMass, AntitoneOn.slope_nonpos, midpoint_vadd_midpoint, signedDist_lineMap_left, AffineMap.lineMap_apply_zero, Finset.affineCombination_affineCombinationLineMapWeights, Wbtw.of_le_of_le, ContinuousAffineMap.coe_zero, AffineMap.fst_lineMap, ConvexOn.slope_mono, AmpleSet.vadd_iff, vectorSpan_segment, signedDist_anticomm, dslope_of_ne, Convex.midpoint_mem, slope_def_field, ContinuousAffineMap.add_apply, eq_lineMap_of_dist_eq_mul_of_dist_eq_mul, ContinuousAffineMap.to_affine_map_contLinear, Finset.weightedVSubOfPoint_smul, AffineMap.derivWithin, AffineMap.add_linear, AffineMap.lineMap_apply, AffineBasis.coord_apply_eq, AffineBasis.coord_apply_centroid, left_le_lineMap_iff_le, sbtw_mul_sub_add_iff, differentiableWithinAt_comp_add_right, Wbtw.const_vsub, LinearMap.slope_comp, mem_affineSpan_pair_iff_exists_lineMap_eq, openSegment_eq_image_lineMap, List.Sorted.sbtw, wbtw_iff_right_eq_or_left_mem_image_Ici, signedDist_triangle_right, ContinuousAffineMap.add_contLinear, AffineBasis.instSMulCommClass, abs_signedDist_eq_dist_iff_vsub_mem_span, wbtw_iff_left_eq_or_right_mem_image_Ici, AmpleSet.image_iff, lineMap_lt_map_iff_slope_lt_slope, AffineMap.toConstProdLinearMap_apply, left_lt_lineMap_iff_lt, slope_neg, image_segment, wbtw_const_add_iff, AffineMap.lineMap_anti, signedDist_neg, dslope_eventuallyEq_slope_of_ne, AffineSubspace.sSameSide_lineMap_right, continuous_barycentric_coord, signedDist_vsub_self_rev, AffineMap.lineMap_same_apply, affineSegment_eq_segment, ContinuousAffineMap.coe_smul, AffineMap.sub_linear, Finset.centroid_mem_convexHull, AffineMap.toConstProdLinearMap_symm_apply, bddBelow_slope_lt_of_mem_interior, midpoint_vsub_midpoint, signedDist_linear_apply, wbtw_one_zero_iff, AffineMap.lineMap_apply_ring, AffineSubspace.sOppSide_lineMap_right, Affine.Simplex.span_eq_top, AffineMap.vsub_linear, signedDist_self, Sbtw.left_mem_image_Ioi, signedDist_vsub_self, signedDist_smul, HasDerivAt.tendsto_slope, AffineMap.coe_lineMap, lineMap_le_map_iff_slope_le_slope, AffineEquiv.coe_constVSub_symm, AffineMap.lineMap_eq_right_iff, AffineSubspace.smul_eq_map, Filter.Tendsto.atTop_smul_const_tendsto_asymptoticNhds, Bornology.IsVonNBounded.vadd, ContinuousAffineMap.apply_lineMap, slope_pos_iff_gt, sbtw_sub_const_iff, AffineBasis.coords_apply, Finset.centroid_vsub_const, AffineMap.lineMap_apply_one, AffineMap.lineMap_apply', AffineMap.vadd_apply, HasDerivWithinAt.limsup_slope_le', Caratheodory.affineIndependent_minCardFinsetOfMemConvexHull, signedDist_smul_of_neg, right_le_lineMap_iff_one_le, lineMap_le_lineMap_iff_of_lt, List.exists_map_eq_of_sorted_iff_wbtw, AffineSubspace.smul_mem_smul_iff, AffineMap.zero_linear, signedDist_vadd_right_swap, AffineMap.decomp, isVisible_iff_lineMap, lineMap_lt_map_iff_slope_lt_slope_left, lineMap_le_right_iff_le_one, ContinuousAffineMap.sub_apply, List.Sorted.wbtw, hasFDerivWithinAt_comp_add_right, ContinuousAffineMap.vadd_contLinear, slope_vadd_const, StrictAntiOn.slope_neg, affineSegment_vadd_const_image, AffineBasis.surjective_coord, ContinuousMap.Homotopy.affine_apply, AffineMap.lineMap_eq_left_iff, AffineMap.coe_neg, AffineMap.coe_add, Finset.weightedVSub_eq_linear_combination, vectorSpan_add_self, ContinuousLinearMap.toContinuousAffineMap_contLinear, dist_left_lineMap, mem_const_vsub_affineSegment, affineCombination_mem_convexHull, signedDist_vadd_left, lineMap_lt_right_iff_lt, map_le_lineMap_iff_slope_le_slope, AffineMap.coe_homothetyAffine, affineSegment_vsub_const_image, AffineMap.snd_lineMap, iteratedFDerivWithin_comp_add_left', lineMap_one_half, mem_segment_iff_wbtw, sbtw_add_const_iff, List.SortedLT.sbtw, signedDist_apply_linear_apply, AffineSubspace.signedInfDist_singleton, slope_nonpos_iff_of_le, AffineSubspace.sSameSide_lineMap_left, lineMap_le_left_iff_le, AffineMap.lineMap_lineMap_left, AffineMap.hasStrictDerivAt, wbtw_vsub_const_iff, IsClosed.convexHull_subset_affineSpan_isVisible, slope_sub_smul, left_le_midpoint, AffineMap.lineMap_same, surjOn_extremePoints_image, Continuous.lineMap, signedDist_right_lineMap, mem_vsub_const_affineSegment, AffineMap.pi_eq_zero, segment_eq_image_lineMap, AffineMap.lineMap_continuous_uncurry, ContinuousAffineMap.vsub_toAffineMap, instIsTopologicalAddTorsor, midpoint_mem_segment, nndist_lineMap_lineMap, AffineMap.differentiableOn, AffineSpace.asymptoticNhds_eq_smul, AffineSubspace.direction_smul, derivWithin_comp_add_const, AffineMap.comp_lineMap, Bornology.isVonNBounded_vadd, Convex.subset_interior_image_homothety_of_one_lt, AddCircle.isAddQuotientCoveringMap_zsmul, AffineBasis.coord_vadd, ContinuousAt.lineMap, norm_sub_le_mul_volume_of_norm_fderiv_le, AffineMap.homothety_def, sbtw_lineMap_iff, midpoint_sub_left, AffineMap.coe_zero, AffineEquiv.vaddConst_symm_apply, AffineEquiv.vaddConst_apply, AffineSubspace.wSameSide_lineMap_right, Equiv.pointReflection_eq_subLeft, AffineSubspace.signedInfDist_def, ConvexOn.comp_affineMap, signedDist_lineMap_right, ConvexOn.monotoneOn_slope_gt, AffineMap.lineMap_symm, affineCombination_eq_centerMass, ContinuousAffineMap.vsub_apply, slope_neg_iff_of_le, Seminorm.vadd_ball, isOpenMap_barycentric_coord, signedDist_apply, convexHull_eq_union, signedDist_eq_dist_iff_vsub_mem_span, hasFDerivWithinAt_comp_sub, derivWithin_comp_sub_const, slope_fun_def_field, AffineMap.lineMap_apply_ring', AffineIsometryEquiv.coe_vaddConst', asymptoticCone_submodule, right_le_midpoint, map_le_lineMap_iff_slope_le_slope_left, AffineMap.differentiable, AffineMap.image_convexHull, WithIdealFilter.mem_nhds_iff, dist_right_lineMap, AffineBasis.affineCombination_coord_eq_self, AffineBasis.coe_coord_of_subsingleton_eq_one, map_lt_lineMap_iff_slope_lt_slope, AffineMap.homothety_add, wbtw_vadd_const_iff, right_sub_midpoint, differentiableWithinAt_comp_add_left, AffineMap.pi_zero, AffineBasis.coord_smul, AffineBasis.coord_apply_combination_of_mem, ContinuousAffineMap.vsub_contLinear, Convex.closure_subset_image_homothety_interior_of_one_lt, derivWithin_comp_const_add, wbtw_neg_iff, convex_vadd, sbtw_zero_one_iff, AffineIndependent.affineCombination_eq_lineMap_iff_weight_lineMap, lineMap_lt_lineMap_iff_of_lt', Path.segment_apply, lipschitzWith_lineMap, AffineMap.lineMap_apply_one_sub, slope_nonneg_iff_of_le, AffineBasis.linear_combination_coord_eq_self, Affine.Simplex.interior_eq_image_Ioo, abs_signedDist_le_dist, hasDerivAt_iff_tendsto_slope, lineMap_mono_left, iteratedFDerivWithin_comp_sub', lineMap_le_map_iff_slope_le_slope_left, asymptoticCone_eq_closure_of_forall_smul_mem, AffineIndependent.units_lineMap, lineMap_slope_lineMap_slope_lineMap, sbtw_one_zero_iff, EuclideanGeometry.Sphere.secondInter_eq_lineMap, Convex.affine_preimage, vsub_eq_sub, lineMap_strict_mono_left, AffineMap.coe_sub, fderivWithin_comp_add_right, mem_finsuppAffineCoords_iff_linearCombination, ContinuousLinearMap.coe_toContinuousAffineMap, signedDist_apply_linear, hasDerivWithinAt_iff_tendsto_slope', antilipschitzWith_lineMap, sbtw_const_add_iff, AffineMap.deriv, lineMap_slope_slope_sub_div_sub, AmpleSet.image, ContinuousAffineMap.zero_contLinear, EuclideanGeometry.inversion_eq_lineMap, AffineMap.lineMap_mem_affineSpan_pair, StrictMonoOn.slope_pos, dist_sq_lineMap_of_inner_eq_zero, hasDerivWithinAt_iff_tendsto_slope, StrictConvex.vadd, signedDist_left_lineMap, wbtw_iff_of_le, Sbtw.mem_image_Ioo, ContinuousAffineMap.coe_neg, AffineMap.lineMap_vadd, lineMap_lt_map_iff_slope_lt_slope_right, midpoint_zero_add, slope_def_module, affineSpan_insert_zero, left_lt_lineMap_iff_pos, convexHull_subset_affineSpan, fderivWithin_comp_sub, lineMap_strict_mono_right, wbtw_mul_sub_add_iff, midpoint_self_neg, AffineMap.homothety_eq_lineMap, sbtw_neg_iff, ContinuousAffineMap.instIsCentralScalar, AffineMap.lineMap_vadd_lineMap, convexHull_range_eq_exists_affineCombination, lineMap_lt_lineMap_iff_of_lt, left_sub_midpoint, lineMap_mono_right, dist_lineMap_lineMap, hasFDerivWithinAt_comp_add_left, AffineMap.lineMap_vsub_lineMap, Path.eqOn_extend_segment, Wbtw.vsub_const, nndist_lineMap_left, Convex.combo_affine_apply, signedDist_vadd_vadd, HasDerivWithinAt.limsup_slope_le, left_le_lineMap_iff_nonneg, lineMap_lt_left_iff_neg, ContinuousAffineMap.vadd_apply, Convex.asymptoticCone, AffineSubspace.smul_span
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