Documentation Verification Report

Isometry

📁 Source: Mathlib/Analysis/Normed/Affine/Isometry.lean

Statistics

MetricCount
DefinitionsAffineIsometry, comp, id, instFunLike, instInhabited, instMonoid, linearIsometry, toAffineMap, toContinuousAffineMap, AffineIsometryEquiv, constVAdd, constVSub, instCoeContinuousAffineEquiv, instEquivLike, instGroup, instInhabited, linearIsometryEquiv, mk', ofEq, ofTop, pointReflection, refl, toAffineEquiv, toAffineIsometry, toContinuousAffineEquiv, toHomeomorph, toIsometryEquiv, trans, vaddConst, equivMapOfInjective, isometryEquivMap, subtypeₐᵢ, toAffineIsometry, toAffineIsometryEquiv, «term_→ᵃⁱ[_]_», «term_≃ᵃⁱ[_]_»
36
Theoremsantilipschitz, coeFn_injective, coe_comp, coe_id, coe_mul, coe_one, coe_toAffineMap, coe_toContinuousAffineMap, comp_assoc, comp_continuous_iff, comp_id, continuous, diam_image, diam_range, dist_map, ediam_image, ediam_range, edist_map, ext, ext_iff, id_apply, id_comp, id_toAffineMap, injective, isometry, linear_eq_linearIsometry, lipschitz, map_eq_iff, map_ne, map_vadd, map_vsub, nndist_map, norm_map, toAffineMap_injective, toContinuousAffineMap_id, toContinuousAffineMap_inj, toContinuousAffineMap_injective, antilipschitz, apply_symm_apply, bijective, coeFn_injective, coe_constVAdd, coe_constVSub, coe_inv, coe_mk, coe_mk', coe_mul, coe_ofEq_apply, coe_one, coe_refl, coe_symm_toAffineEquiv, coe_symm_toContinuousAffineEquiv, coe_symm_toHomeomorph, coe_symm_toIsometryEquiv, coe_symm_trans, coe_toAffineEquiv, coe_toAffineIsometry, coe_toContinuousAffineEquiv, coe_toHomeomorph, coe_toIsometryEquiv, coe_trans, coe_vaddConst, coe_vaddConst', coe_vaddConst_symm, comp_continuousOn_iff, comp_continuous_iff, constVAdd_zero, continuous, continuousAt, continuousOn, continuousWithinAt, diam_image, dist_map, dist_pointReflection_fixed, dist_pointReflection_self, dist_pointReflection_self', dist_pointReflection_self_real, ediam_image, edist_map, ext, ext_iff, injective, isometry, linearIsometryEquiv_mk', linear_eq_linear_isometry, lipschitz, map_eq_iff, map_ne, map_vadd, map_vsub, norm_map, ofEq_rfl, ofEq_symm, ofTop_apply, ofTop_symm_apply_coe, pointReflection_apply, pointReflection_fixed_iff, pointReflection_involutive, pointReflection_midpoint_left, pointReflection_midpoint_right, pointReflection_self, pointReflection_symm, pointReflection_toAffineEquiv, range_eq_univ, refl_trans, self_trans_symm, surjective, symm_apply_apply, symm_bijective, symm_constVSub, symm_symm, symm_trans_self, toAffineEquiv_injective, toAffineEquiv_refl, toAffineEquiv_symm, toContinuousAffineEquiv_inj, toContinuousAffineEquiv_injective, toContinuousAffineEquiv_refl, toContinuousAffineEquiv_symm, toHomeomorph_refl, toHomeomorph_symm, toIsometryEquiv_refl, toIsometryEquiv_symm, trans_assoc, trans_refl, vaddConst_toAffineEquiv, vadd_vsub, coe_subtypeₐᵢ, equivMapOfInjective_toFun, apply_symm_apply, coe_apply, toAffineMap_eq, linear_equivMapOfInjective, subtypeₐᵢ_linear, subtypeₐᵢ_linearIsometry, subtypeₐᵢ_toAffineMap, toContinuousAffineMap_subtypeₐᵢ, coe_toAffineIsometry, toAffineIsometry_linearIsometry, toAffineIsometry_toAffineMap, coe_toAffineIsometryEquiv, toAffineIsometryEquiv_linearIsometryEquiv, toAffineIsometryEquiv_toAffineEquiv, toAffineIsometryEquiv_toAffineIsometry
144
Total180

AffineIsometry

Definitions

NameCategoryTheorems
comp 📖CompOp
4 mathmath: comp_id, coe_comp, comp_assoc, id_comp
id 📖CompOp
6 mathmath: comp_id, id_apply, toContinuousAffineMap_id, coe_id, id_comp, id_toAffineMap
instFunLike 📖CompOp
50 mathmath: image_intrinsicClosure, Affine.Simplex.orthogonalProjectionSpan_map, Affine.Simplex.circumcenter_map, coeFn_injective, nndist_map, Affine.Simplex.incenter_map, Isometry.coe_affineIsometryOfStrictConvexSpace, EuclideanGeometry.reflection_map, coe_comp, Affine.Simplex.ExcenterExists.touchpoint_map, Affine.Simplex.ExcenterExists.excenter_map, id_apply, EuclideanGeometry.orthogonalProjection_map, coe_mul, AffineSubspace.coe_subtypeₐᵢ, lipschitz, comp_continuous_iff, Affine.Simplex.altitudeFoot_map, image_intrinsicInterior, diam_image, coe_toAffineMap, coe_id, map_vsub, coe_toAffineIsometryEquiv, map_eq_iff, AffineSubspace.isometryEquivMap.coe_apply, LinearIsometry.coe_toAffineIsometry, isometry, Isometry.affineIsometryOfStrictConvexSpace_apply, diam_range, toAffineIsometryEquiv_apply, map_vadd, ediam_range, Affine.Simplex.mongePoint_map, Affine.Simplex.eulerPoint_map, coe_one, ext_iff, edist_map, Affine.Simplex.ninePointCircle_map, AffineSubspace.isometryEquivMap.apply_symm_apply, antilipschitz, injective, EuclideanGeometry.Sphere.secondInter_map, angle_map, coe_toContinuousAffineMap, image_intrinsicFrontier, ediam_image, dist_map, continuous, AffineIsometryEquiv.coe_toAffineIsometry
instInhabited 📖CompOp
instMonoid 📖CompOp
2 mathmath: coe_mul, coe_one
linearIsometry 📖CompOp
6 mathmath: LinearIsometry.toAffineIsometry_linearIsometry, linear_eq_linearIsometry, map_vsub, map_vadd, AffineSubspace.subtypeₐᵢ_linearIsometry, EuclideanGeometry.Sphere.secondInter_map
toAffineMap 📖CompOp
31 mathmath: Affine.Simplex.orthogonalProjectionSpan_map, Affine.Simplex.circumcenter_map, Affine.Simplex.incenter_map, EuclideanGeometry.reflection_map, Affine.Simplex.ExcenterExists.touchpoint_map, Affine.Simplex.ExcenterExists.excenter_map, EuclideanGeometry.orthogonalProjection_map, LinearIsometry.toAffineIsometry_toAffineMap, Affine.Simplex.excenterWeightsUnnorm_map, Affine.Simplex.exradius_map, Affine.Simplex.altitudeFoot_map, linear_eq_linearIsometry, AffineSubspace.isometryEquivMap.toAffineMap_eq, Affine.Simplex.excenterExists_map, coe_toAffineMap, Affine.Simplex.height_map, norm_map, AffineSubspace.isometryEquivMap.coe_apply, AffineSubspace.subtypeₐᵢ_linear, Affine.Simplex.excenterWeights_map, Affine.Simplex.ExcenterExists.touchpointWeights_map, Affine.Simplex.mongePoint_map, Affine.Simplex.eulerPoint_map, Affine.Simplex.altitude_map, toAffineMap_injective, Affine.Simplex.ninePointCircle_map, AffineSubspace.isometryEquivMap.apply_symm_apply, Affine.Simplex.inradius_map, AffineSubspace.subtypeₐᵢ_toAffineMap, id_toAffineMap, Affine.Simplex.circumradius_map
toContinuousAffineMap 📖CompOp
5 mathmath: toContinuousAffineMap_inj, toContinuousAffineMap_id, AffineSubspace.toContinuousAffineMap_subtypeₐᵢ, toContinuousAffineMap_injective, coe_toContinuousAffineMap

Theorems

NameKindAssumesProvesValidatesDepends On
antilipschitz 📖mathematicalAntilipschitzWith
PseudoMetricSpace.toPseudoEMetricSpace
NNReal
instOneNNReal
DFunLike.coe
AffineIsometry
instFunLike
Isometry.antilipschitz
isometry
coeFn_injective 📖mathematicalAffineIsometry
DFunLike.coe
instFunLike
AffineMap.coeFn_injective
toAffineMap_injective
coe_comp 📖mathematicalDFunLike.coe
AffineIsometry
instFunLike
comp
coe_id 📖mathematicalDFunLike.coe
AffineIsometry
instFunLike
id
coe_mul 📖mathematicalDFunLike.coe
AffineIsometry
instFunLike
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
instMonoid
coe_one 📖mathematicalDFunLike.coe
AffineIsometry
instFunLike
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
instMonoid
coe_toAffineMap 📖mathematicalDFunLike.coe
AffineMap
NormedRing.toRing
NormedCommRing.toNormedRing
NormedField.toNormedCommRing
SeminormedAddCommGroup.toAddCommGroup
NormedSpace.toModule
NormedAddTorsor.toAddTorsor
AffineMap.instFunLike
toAffineMap
AffineIsometry
instFunLike
coe_toContinuousAffineMap 📖mathematicalDFunLike.coe
ContinuousAffineMap
NormedRing.toRing
NormedCommRing.toNormedRing
NormedField.toNormedCommRing
SeminormedAddCommGroup.toAddCommGroup
NormedSpace.toModule
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
NormedAddTorsor.toAddTorsor
ContinuousAffineMap.instFunLike
toContinuousAffineMap
AffineIsometry
instFunLike
comp_assoc 📖mathematicalcomp
comp_continuous_iff 📖mathematicalContinuous
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
DFunLike.coe
AffineIsometry
instFunLike
Isometry.comp_continuous_iff
isometry
comp_id 📖mathematicalcomp
id
ext
continuous 📖mathematicalContinuous
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
DFunLike.coe
AffineIsometry
instFunLike
Isometry.continuous
isometry
diam_image 📖mathematicalMetric.diam
Set.image
DFunLike.coe
AffineIsometry
instFunLike
Isometry.diam_image
isometry
diam_range 📖mathematicalMetric.diam
Set.range
DFunLike.coe
AffineIsometry
instFunLike
Set.univ
Isometry.diam_range
isometry
dist_map 📖mathematicalDist.dist
PseudoMetricSpace.toDist
DFunLike.coe
AffineIsometry
instFunLike
dist_eq_norm_vsub
map_vsub
LinearIsometry.norm_map
ediam_image 📖mathematicalMetric.ediam
PseudoMetricSpace.toPseudoEMetricSpace
Set.image
DFunLike.coe
AffineIsometry
instFunLike
Isometry.ediam_image
isometry
ediam_range 📖mathematicalMetric.ediam
PseudoMetricSpace.toPseudoEMetricSpace
Set.range
DFunLike.coe
AffineIsometry
instFunLike
Set.univ
Isometry.ediam_range
isometry
edist_map 📖mathematicalEDist.edist
PseudoEMetricSpace.toEDist
PseudoMetricSpace.toPseudoEMetricSpace
DFunLike.coe
AffineIsometry
instFunLike
edist_dist
dist_map
ext 📖DFunLike.coe
AffineIsometry
instFunLike
coeFn_injective
ext_iff 📖mathematicalDFunLike.coe
AffineIsometry
instFunLike
ext
id_apply 📖mathematicalDFunLike.coe
AffineIsometry
instFunLike
id
id_comp 📖mathematicalcomp
id
ext
id_toAffineMap 📖mathematicaltoAffineMap
id
AffineMap.id
NormedRing.toRing
NormedCommRing.toNormedRing
NormedField.toNormedCommRing
SeminormedAddCommGroup.toAddCommGroup
NormedSpace.toModule
NormedAddTorsor.toAddTorsor
injective 📖mathematicalDFunLike.coe
AffineIsometry
MetricSpace.toPseudoMetricSpace
instFunLike
Isometry.injective
isometry
isometry 📖mathematicalIsometry
PseudoMetricSpace.toPseudoEMetricSpace
DFunLike.coe
AffineIsometry
instFunLike
edist_map
linear_eq_linearIsometry 📖mathematicalAffineMap.linear
NormedRing.toRing
NormedCommRing.toNormedRing
NormedField.toNormedCommRing
SeminormedAddCommGroup.toAddCommGroup
NormedSpace.toModule
NormedAddTorsor.toAddTorsor
toAffineMap
LinearIsometry.toLinearMap
DivisionSemiring.toSemiring
Semifield.toDivisionSemiring
Field.toSemifield
NormedField.toField
RingHom.id
Semiring.toNonAssocSemiring
linearIsometry
LinearMap.ext
lipschitz 📖mathematicalLipschitzWith
PseudoMetricSpace.toPseudoEMetricSpace
NNReal
instOneNNReal
DFunLike.coe
AffineIsometry
instFunLike
Isometry.lipschitz
isometry
map_eq_iff 📖mathematicalDFunLike.coe
AffineIsometry
MetricSpace.toPseudoMetricSpace
instFunLike
injective
map_ne 📖injective
map_vadd 📖mathematicalDFunLike.coe
AffineIsometry
instFunLike
HVAdd.hVAdd
instHVAdd
AddSemigroupAction.toVAdd
AddMonoid.toAddSemigroup
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
SeminormedAddGroup.toAddGroup
SeminormedAddCommGroup.toSeminormedAddGroup
AddAction.toAddSemigroupAction
AddTorsor.toAddAction
NormedAddTorsor.toAddTorsor
LinearIsometry
DivisionSemiring.toSemiring
Semifield.toDivisionSemiring
Field.toSemifield
NormedField.toField
RingHom.id
Semiring.toNonAssocSemiring
NormedSpace.toModule
LinearIsometry.instFunLike
linearIsometry
AffineMap.map_vadd
map_vsub 📖mathematicalDFunLike.coe
LinearIsometry
DivisionSemiring.toSemiring
Semifield.toDivisionSemiring
Field.toSemifield
NormedField.toField
RingHom.id
Semiring.toNonAssocSemiring
NormedSpace.toModule
LinearIsometry.instFunLike
linearIsometry
VSub.vsub
AddTorsor.toVSub
SeminormedAddGroup.toAddGroup
SeminormedAddCommGroup.toSeminormedAddGroup
NormedAddTorsor.toAddTorsor
AffineIsometry
instFunLike
AffineMap.linearMap_vsub
nndist_map 📖mathematicalNNDist.nndist
PseudoMetricSpace.toNNDist
DFunLike.coe
AffineIsometry
instFunLike
nndist_dist
dist_map
norm_map 📖mathematicalNorm.norm
SeminormedAddCommGroup.toNorm
DFunLike.coe
LinearMap
Ring.toSemiring
NormedRing.toRing
NormedCommRing.toNormedRing
NormedField.toNormedCommRing
RingHom.id
Semiring.toNonAssocSemiring
AddCommGroup.toAddCommMonoid
SeminormedAddCommGroup.toAddCommGroup
NormedSpace.toModule
LinearMap.instFunLike
AffineMap.linear
NormedAddTorsor.toAddTorsor
toAffineMap
toAffineMap_injective 📖mathematicalAffineIsometry
AffineMap
NormedRing.toRing
NormedCommRing.toNormedRing
NormedField.toNormedCommRing
SeminormedAddCommGroup.toAddCommGroup
NormedSpace.toModule
NormedAddTorsor.toAddTorsor
toAffineMap
toContinuousAffineMap_id 📖mathematicaltoContinuousAffineMap
id
ContinuousAffineMap.id
NormedRing.toRing
NormedCommRing.toNormedRing
NormedField.toNormedCommRing
SeminormedAddCommGroup.toAddCommGroup
NormedSpace.toModule
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
NormedAddTorsor.toAddTorsor
toContinuousAffineMap_inj 📖mathematicaltoContinuousAffineMaptoContinuousAffineMap_injective
toContinuousAffineMap_injective 📖mathematicalAffineIsometry
ContinuousAffineMap
NormedRing.toRing
NormedCommRing.toNormedRing
NormedField.toNormedCommRing
SeminormedAddCommGroup.toAddCommGroup
NormedSpace.toModule
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
NormedAddTorsor.toAddTorsor
toContinuousAffineMap
coeFn_injective

AffineIsometryEquiv

Definitions

NameCategoryTheorems
constVAdd 📖CompOp
2 mathmath: coe_constVAdd, constVAdd_zero
constVSub 📖CompOp
2 mathmath: coe_constVSub, symm_constVSub
instCoeContinuousAffineEquiv 📖CompOp
instEquivLike 📖CompOp
85 mathmath: coe_constVSub, pointReflection_apply, coe_mk, pointReflection_involutive, EuclideanGeometry.reflection_orthogonal_vadd, coe_symm_toAffineEquiv, coe_refl, ofTop_apply, range_eq_univ, coe_symm_trans, edist_map, EuclideanGeometry.reflection_map, coe_constVAdd, LinearIsometryEquiv.coe_toAffineIsometryEquiv, EuclideanGeometry.reflection_vadd_smul_vsub_orthogonalProjection, comp_continuous_iff, coe_trans, pointReflection_midpoint_left, continuousAt, dist_pointReflection_fixed, continuousWithinAt, map_vsub, continuousOn, Affine.Triangle.dist_circumcenter_reflection_orthocenter, coe_ofEq_apply, EuclideanGeometry.reflection_reflection, ofTop_symm_apply_coe, coe_inv, continuous, EuclideanGeometry.reflection_eq_self_iff, pointReflection_fixed_iff, apply_symm_apply, dist_pointReflection_self, dist_pointReflection_self_real, Affine.Triangle.dist_orthocenter_reflection_circumcenter, coe_vaddConst, EuclideanGeometry.reflection_apply_of_mem, diam_image, AffineIsometry.coe_toAffineIsometryEquiv, AffineSubspace.isometryEquivMap.coe_apply, coe_mk', EuclideanGeometry.eq_or_eq_reflection_of_dist_eq, symm_apply_apply, map_eq_iff, dist_map, EuclideanGeometry.dist_reflection_eq_of_mem, EuclideanGeometry.dist_reflection, ext_iff, coe_vaddConst_symm, coe_toIsometryEquiv, pointReflection_self, surjective, Affine.Triangle.dist_circumcenter_reflection_orthocenter_finset, coe_one, AffineIsometry.toAffineIsometryEquiv_apply, EuclideanGeometry.reflection_eq_iff_orthogonalProjection_eq, IsometryEquiv.coeFn_toRealAffineIsometryEquiv, ediam_image, EuclideanGeometry.reflection_apply', bijective, lipschitz, map_vadd, injective, EuclideanGeometry.reflection_involutive, coe_symm_toContinuousAffineEquiv, EuclideanGeometry.reflection_subtype, comp_continuousOn_iff, AffineSubspace.isometryEquivMap.apply_symm_apply, coe_toHomeomorph, antilipschitz, coe_symm_toIsometryEquiv, EuclideanGeometry.eq_reflection_of_eq_subspace, Affine.Simplex.reflection_circumcenter_eq_affineCombination_of_pointsWithCircumcenter, Affine.Triangle.dist_orthocenter_reflection_circumcenter_finset, isometry, dist_pointReflection_self', coe_symm_toHomeomorph, EuclideanGeometry.reflection_mem_of_le_of_mem, EuclideanGeometry.reflection_apply, coeFn_injective, coe_mul, coe_toAffineIsometry, pointReflection_midpoint_right, coe_toAffineEquiv, coe_toContinuousAffineEquiv
instGroup 📖CompOp
3 mathmath: coe_inv, coe_one, coe_mul
instInhabited 📖CompOp
linearIsometryEquiv 📖CompOp
5 mathmath: linearIsometryEquiv_mk', linear_eq_linear_isometry, map_vsub, LinearIsometryEquiv.toAffineIsometryEquiv_linearIsometryEquiv, map_vadd
mk' 📖CompOp
2 mathmath: linearIsometryEquiv_mk', coe_mk'
ofEq 📖CompOp
3 mathmath: coe_ofEq_apply, ofEq_symm, ofEq_rfl
ofTop 📖CompOp
2 mathmath: ofTop_apply, ofTop_symm_apply_coe
pointReflection 📖CompOp
12 mathmath: pointReflection_apply, pointReflection_involutive, pointReflection_midpoint_left, pointReflection_toAffineEquiv, dist_pointReflection_fixed, pointReflection_fixed_iff, dist_pointReflection_self, dist_pointReflection_self_real, pointReflection_self, pointReflection_symm, dist_pointReflection_self', pointReflection_midpoint_right
refl 📖CompOp
11 mathmath: toHomeomorph_refl, coe_refl, symm_trans_self, toIsometryEquiv_refl, refl_trans, toContinuousAffineEquiv_refl, constVAdd_zero, self_trans_symm, ofEq_rfl, toAffineEquiv_refl, trans_refl
toAffineEquiv 📖CompOp
12 mathmath: coe_symm_toAffineEquiv, linear_eq_linear_isometry, pointReflection_toAffineEquiv, vaddConst_toAffineEquiv, AffineSubspace.isometryEquivMap.toAffineMap_eq, LinearIsometryEquiv.toAffineIsometryEquiv_toAffineEquiv, toAffineEquiv_injective, EuclideanGeometry.Sphere.orthRadius_map, toAffineEquiv_refl, norm_map, toAffineEquiv_symm, coe_toAffineEquiv
toAffineIsometry 📖CompOp
2 mathmath: LinearIsometryEquiv.toAffineIsometryEquiv_toAffineIsometry, coe_toAffineIsometry
toContinuousAffineEquiv 📖CompOp
6 mathmath: toContinuousAffineEquiv_symm, toContinuousAffineEquiv_refl, toContinuousAffineEquiv_inj, coe_symm_toContinuousAffineEquiv, toContinuousAffineEquiv_injective, coe_toContinuousAffineEquiv
toHomeomorph 📖CompOp
4 mathmath: toHomeomorph_refl, coe_toHomeomorph, toHomeomorph_symm, coe_symm_toHomeomorph
toIsometryEquiv 📖CompOp
5 mathmath: toIsometryEquiv_refl, IsometryEquiv.coe_toRealAffineIsometryEquiv, coe_toIsometryEquiv, coe_symm_toIsometryEquiv, toIsometryEquiv_symm
trans 📖CompOp
8 mathmath: symm_trans_self, coe_symm_trans, coe_trans, refl_trans, trans_assoc, symm_constVSub, self_trans_symm, trans_refl
vaddConst 📖CompOp
4 mathmath: vaddConst_toAffineEquiv, coe_vaddConst, symm_constVSub, coe_vaddConst_symm

Theorems

NameKindAssumesProvesValidatesDepends On
antilipschitz 📖mathematicalAntilipschitzWith
PseudoMetricSpace.toPseudoEMetricSpace
NNReal
instOneNNReal
DFunLike.coe
AffineIsometryEquiv
EquivLike.toFunLike
instEquivLike
Isometry.antilipschitz
isometry
apply_symm_apply 📖mathematicalDFunLike.coe
AffineIsometryEquiv
EquivLike.toFunLike
instEquivLike
symm
AffineEquiv.apply_symm_apply
bijective 📖mathematicalFunction.Bijective
DFunLike.coe
AffineIsometryEquiv
EquivLike.toFunLike
instEquivLike
AffineEquiv.bijective
coeFn_injective 📖mathematicalAffineIsometryEquiv
DFunLike.coe
EquivLike.toFunLike
instEquivLike
DFunLike.coe_injective
coe_constVAdd 📖mathematicalDFunLike.coe
AffineIsometryEquiv
EquivLike.toFunLike
instEquivLike
constVAdd
HVAdd.hVAdd
instHVAdd
AddSemigroupAction.toVAdd
AddMonoid.toAddSemigroup
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
SeminormedAddGroup.toAddGroup
SeminormedAddCommGroup.toSeminormedAddGroup
AddAction.toAddSemigroupAction
AddTorsor.toAddAction
NormedAddTorsor.toAddTorsor
coe_constVSub 📖mathematicalDFunLike.coe
AffineIsometryEquiv
SeminormedAddCommGroup.toPseudoMetricSpace
SeminormedAddCommGroup.toNormedAddTorsor
EquivLike.toFunLike
instEquivLike
constVSub
VSub.vsub
AddTorsor.toVSub
SeminormedAddGroup.toAddGroup
SeminormedAddCommGroup.toSeminormedAddGroup
NormedAddTorsor.toAddTorsor
coe_inv 📖mathematicalDFunLike.coe
AffineIsometryEquiv
EquivLike.toFunLike
instEquivLike
InvOneClass.toInv
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
Group.toDivisionMonoid
instGroup
symm
coe_mk 📖mathematicalNorm.norm
SeminormedAddCommGroup.toNorm
DFunLike.coe
LinearEquiv
Ring.toSemiring
NormedRing.toRing
NormedCommRing.toNormedRing
NormedField.toNormedCommRing
RingHom.id
Semiring.toNonAssocSemiring
RingHomInvPair.ids
AddCommGroup.toAddCommMonoid
SeminormedAddCommGroup.toAddCommGroup
NormedSpace.toModule
EquivLike.toFunLike
DFinsupp.instEquivLikeLinearEquiv
AffineEquiv.linear
NormedAddTorsor.toAddTorsor
AffineIsometryEquiv
instEquivLike
AffineEquiv
AffineEquiv.equivLike
RingHomInvPair.ids
coe_mk' 📖mathematicalHVAdd.hVAdd
instHVAdd
AddSemigroupAction.toVAdd
AddMonoid.toAddSemigroup
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
SeminormedAddGroup.toAddGroup
SeminormedAddCommGroup.toSeminormedAddGroup
AddAction.toAddSemigroupAction
AddTorsor.toAddAction
NormedAddTorsor.toAddTorsor
DFunLike.coe
LinearIsometryEquiv
DivisionSemiring.toSemiring
Semifield.toDivisionSemiring
Field.toSemifield
NormedField.toField
RingHom.id
Semiring.toNonAssocSemiring
RingHomInvPair.ids
NormedSpace.toModule
EquivLike.toFunLike
LinearIsometryEquiv.instEquivLike
VSub.vsub
AddTorsor.toVSub
AffineIsometryEquiv
instEquivLike
mk'
RingHomInvPair.ids
coe_mul 📖mathematicalDFunLike.coe
AffineIsometryEquiv
EquivLike.toFunLike
instEquivLike
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
instGroup
coe_ofEq_apply 📖mathematicalAffineSubspace
NormedRing.toRing
NormedCommRing.toNormedRing
NormedField.toNormedCommRing
SeminormedAddCommGroup.toAddCommGroup
NormedSpace.toModule
NormedAddTorsor.toAddTorsor
SetLike.instMembership
AffineSubspace.instSetLike
DFunLike.coe
AffineIsometryEquiv
Submodule
Ring.toSemiring
AddCommGroup.toAddCommMonoid
Submodule.setLike
AffineSubspace.direction
Submodule.seminormedAddCommGroup
Submodule.normedSpace
Algebra.toSMul
Semifield.toCommSemiring
Field.toSemifield
NormedField.toField
CommSemiring.toSemiring
Algebra.id
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DivisionSemiring.toSemiring
Semifield.toDivisionSemiring
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
Module.toDistribMulAction
Subtype.pseudoMetricSpace
AffineSubspace.toNormedAddTorsor
EquivLike.toFunLike
instEquivLike
ofEq
IsScalarTower.left
coe_one 📖mathematicalDFunLike.coe
AffineIsometryEquiv
EquivLike.toFunLike
instEquivLike
InvOneClass.toOne
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
Group.toDivisionMonoid
instGroup
coe_refl 📖mathematicalDFunLike.coe
AffineIsometryEquiv
EquivLike.toFunLike
instEquivLike
refl
coe_symm_toAffineEquiv 📖mathematicalDFunLike.coe
AffineEquiv
NormedRing.toRing
NormedCommRing.toNormedRing
NormedField.toNormedCommRing
SeminormedAddCommGroup.toAddCommGroup
NormedSpace.toModule
NormedAddTorsor.toAddTorsor
EquivLike.toFunLike
AffineEquiv.equivLike
AffineEquiv.symm
toAffineEquiv
AffineIsometryEquiv
instEquivLike
symm
coe_symm_toContinuousAffineEquiv 📖mathematicalDFunLike.coe
ContinuousAffineEquiv
NormedRing.toRing
NormedCommRing.toNormedRing
NormedField.toNormedCommRing
SeminormedAddCommGroup.toAddCommGroup
NormedSpace.toModule
NormedAddTorsor.toAddTorsor
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
ContinuousAffineEquiv.instFunLike
ContinuousAffineEquiv.symm
toContinuousAffineEquiv
AffineIsometryEquiv
EquivLike.toFunLike
instEquivLike
symm
coe_symm_toHomeomorph 📖mathematicalDFunLike.coe
Homeomorph
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
EquivLike.toFunLike
Homeomorph.instEquivLike
Homeomorph.symm
toHomeomorph
AffineIsometryEquiv
instEquivLike
symm
coe_symm_toIsometryEquiv 📖mathematicalDFunLike.coe
IsometryEquiv
PseudoMetricSpace.toPseudoEMetricSpace
EquivLike.toFunLike
IsometryEquiv.instEquivLike
IsometryEquiv.symm
toIsometryEquiv
AffineIsometryEquiv
instEquivLike
symm
coe_symm_trans 📖mathematicalDFunLike.coe
AffineIsometryEquiv
EquivLike.toFunLike
instEquivLike
symm
trans
coe_toAffineEquiv 📖mathematicalDFunLike.coe
AffineEquiv
NormedRing.toRing
NormedCommRing.toNormedRing
NormedField.toNormedCommRing
SeminormedAddCommGroup.toAddCommGroup
NormedSpace.toModule
NormedAddTorsor.toAddTorsor
EquivLike.toFunLike
AffineEquiv.equivLike
toAffineEquiv
AffineIsometryEquiv
instEquivLike
coe_toAffineIsometry 📖mathematicalDFunLike.coe
AffineIsometry
AffineIsometry.instFunLike
toAffineIsometry
AffineIsometryEquiv
EquivLike.toFunLike
instEquivLike
coe_toContinuousAffineEquiv 📖mathematicalDFunLike.coe
ContinuousAffineEquiv
NormedRing.toRing
NormedCommRing.toNormedRing
NormedField.toNormedCommRing
SeminormedAddCommGroup.toAddCommGroup
NormedSpace.toModule
NormedAddTorsor.toAddTorsor
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
ContinuousAffineEquiv.instFunLike
toContinuousAffineEquiv
AffineIsometryEquiv
EquivLike.toFunLike
instEquivLike
coe_toHomeomorph 📖mathematicalDFunLike.coe
Homeomorph
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
EquivLike.toFunLike
Homeomorph.instEquivLike
toHomeomorph
AffineIsometryEquiv
instEquivLike
coe_toIsometryEquiv 📖mathematicalDFunLike.coe
IsometryEquiv
PseudoMetricSpace.toPseudoEMetricSpace
EquivLike.toFunLike
IsometryEquiv.instEquivLike
toIsometryEquiv
AffineIsometryEquiv
instEquivLike
coe_trans 📖mathematicalDFunLike.coe
AffineIsometryEquiv
EquivLike.toFunLike
instEquivLike
trans
coe_vaddConst 📖mathematicalDFunLike.coe
AffineIsometryEquiv
SeminormedAddCommGroup.toPseudoMetricSpace
SeminormedAddCommGroup.toNormedAddTorsor
EquivLike.toFunLike
instEquivLike
vaddConst
HVAdd.hVAdd
instHVAdd
AddSemigroupAction.toVAdd
AddMonoid.toAddSemigroup
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
SeminormedAddGroup.toAddGroup
SeminormedAddCommGroup.toSeminormedAddGroup
AddAction.toAddSemigroupAction
AddTorsor.toAddAction
NormedAddTorsor.toAddTorsor
coe_vaddConst' 📖mathematicalDFunLike.coe
AffineEquiv
NormedRing.toRing
NormedCommRing.toNormedRing
NormedField.toNormedCommRing
SeminormedAddCommGroup.toAddCommGroup
NormedSpace.toModule
addGroupIsAddTorsor
AddCommGroup.toAddGroup
NormedAddTorsor.toAddTorsor
EquivLike.toFunLike
AffineEquiv.equivLike
AffineEquiv.vaddConst
HVAdd.hVAdd
instHVAdd
AddSemigroupAction.toVAdd
AddMonoid.toAddSemigroup
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
SeminormedAddGroup.toAddGroup
SeminormedAddCommGroup.toSeminormedAddGroup
AddAction.toAddSemigroupAction
AddTorsor.toAddAction
coe_vaddConst_symm 📖mathematicalDFunLike.coe
AffineIsometryEquiv
SeminormedAddCommGroup.toPseudoMetricSpace
SeminormedAddCommGroup.toNormedAddTorsor
EquivLike.toFunLike
instEquivLike
symm
vaddConst
VSub.vsub
AddTorsor.toVSub
SeminormedAddGroup.toAddGroup
SeminormedAddCommGroup.toSeminormedAddGroup
NormedAddTorsor.toAddTorsor
comp_continuousOn_iff 📖mathematicalContinuousOn
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
DFunLike.coe
AffineIsometryEquiv
EquivLike.toFunLike
instEquivLike
Isometry.comp_continuousOn_iff
isometry
comp_continuous_iff 📖mathematicalContinuous
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
DFunLike.coe
AffineIsometryEquiv
EquivLike.toFunLike
instEquivLike
Isometry.comp_continuous_iff
isometry
constVAdd_zero 📖mathematicalconstVAdd
NegZeroClass.toZero
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
SeminormedAddCommGroup.toAddCommGroup
refl
ext
zero_vadd
continuous 📖mathematicalContinuous
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
DFunLike.coe
AffineIsometryEquiv
EquivLike.toFunLike
instEquivLike
Isometry.continuous
isometry
continuousAt 📖mathematicalContinuousAt
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
DFunLike.coe
AffineIsometryEquiv
EquivLike.toFunLike
instEquivLike
Continuous.continuousAt
continuous
continuousOn 📖mathematicalContinuousOn
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
DFunLike.coe
AffineIsometryEquiv
EquivLike.toFunLike
instEquivLike
Continuous.continuousOn
continuous
continuousWithinAt 📖mathematicalContinuousWithinAt
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
DFunLike.coe
AffineIsometryEquiv
EquivLike.toFunLike
instEquivLike
Continuous.continuousWithinAt
continuous
diam_image 📖mathematicalMetric.diam
Set.image
DFunLike.coe
AffineIsometryEquiv
EquivLike.toFunLike
instEquivLike
Isometry.diam_image
isometry
dist_map 📖mathematicalDist.dist
PseudoMetricSpace.toDist
DFunLike.coe
AffineIsometryEquiv
EquivLike.toFunLike
instEquivLike
AffineIsometry.dist_map
dist_pointReflection_fixed 📖mathematicalDist.dist
PseudoMetricSpace.toDist
DFunLike.coe
AffineIsometryEquiv
EquivLike.toFunLike
instEquivLike
pointReflection
dist_map
pointReflection_self
dist_pointReflection_self 📖mathematicalDist.dist
PseudoMetricSpace.toDist
DFunLike.coe
AffineIsometryEquiv
EquivLike.toFunLike
instEquivLike
pointReflection
Real
Real.instMul
Norm.norm
NormedField.toNorm
instOfNatAtLeastTwo
AddMonoidWithOne.toNatCast
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
NormedRing.toRing
NormedCommRing.toNormedRing
NormedField.toNormedCommRing
Nat.instAtLeastTwoHAddOfNat
Nat.instAtLeastTwoHAddOfNat
dist_pointReflection_self'
two_nsmul
two_smul
norm_smul
NormedSpace.toNormSMulClass
dist_eq_norm_vsub
dist_pointReflection_self' 📖mathematicalDist.dist
PseudoMetricSpace.toDist
DFunLike.coe
AffineIsometryEquiv
EquivLike.toFunLike
instEquivLike
pointReflection
Norm.norm
SeminormedAddCommGroup.toNorm
AddMonoid.toNatSMul
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
SeminormedAddGroup.toAddGroup
SeminormedAddCommGroup.toSeminormedAddGroup
VSub.vsub
AddTorsor.toVSub
NormedAddTorsor.toAddTorsor
pointReflection_apply
dist_eq_norm_vsub
vadd_vsub_assoc
two_nsmul
dist_pointReflection_self_real 📖mathematicalDist.dist
PseudoMetricSpace.toDist
DFunLike.coe
AffineIsometryEquiv
Real
Real.normedField
EquivLike.toFunLike
instEquivLike
pointReflection
Real.instMul
instOfNatAtLeastTwo
Real.instNatCast
Nat.instAtLeastTwoHAddOfNat
Nat.instAtLeastTwoHAddOfNat
dist_pointReflection_self
Real.norm_two
ediam_image 📖mathematicalMetric.ediam
PseudoMetricSpace.toPseudoEMetricSpace
Set.image
DFunLike.coe
AffineIsometryEquiv
EquivLike.toFunLike
instEquivLike
Isometry.ediam_image
isometry
edist_map 📖mathematicalEDist.edist
PseudoEMetricSpace.toEDist
PseudoMetricSpace.toPseudoEMetricSpace
DFunLike.coe
AffineIsometryEquiv
EquivLike.toFunLike
instEquivLike
AffineIsometry.edist_map
ext 📖DFunLike.coe
AffineIsometryEquiv
EquivLike.toFunLike
instEquivLike
toAffineEquiv_injective
AffineEquiv.ext
ext_iff 📖mathematicalDFunLike.coe
AffineIsometryEquiv
EquivLike.toFunLike
instEquivLike
ext
injective 📖mathematicalDFunLike.coe
AffineIsometryEquiv
EquivLike.toFunLike
instEquivLike
AffineEquiv.injective
isometry 📖mathematicalIsometry
PseudoMetricSpace.toPseudoEMetricSpace
DFunLike.coe
AffineIsometryEquiv
EquivLike.toFunLike
instEquivLike
AffineIsometry.isometry
linearIsometryEquiv_mk' 📖mathematicalHVAdd.hVAdd
instHVAdd
AddSemigroupAction.toVAdd
AddMonoid.toAddSemigroup
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
SeminormedAddGroup.toAddGroup
SeminormedAddCommGroup.toSeminormedAddGroup
AddAction.toAddSemigroupAction
AddTorsor.toAddAction
NormedAddTorsor.toAddTorsor
DFunLike.coe
LinearIsometryEquiv
DivisionSemiring.toSemiring
Semifield.toDivisionSemiring
Field.toSemifield
NormedField.toField
RingHom.id
Semiring.toNonAssocSemiring
RingHomInvPair.ids
NormedSpace.toModule
EquivLike.toFunLike
LinearIsometryEquiv.instEquivLike
VSub.vsub
AddTorsor.toVSub
linearIsometryEquiv
mk'
RingHomInvPair.ids
LinearIsometryEquiv.ext
linear_eq_linear_isometry 📖mathematicalAffineEquiv.linear
NormedRing.toRing
NormedCommRing.toNormedRing
NormedField.toNormedCommRing
SeminormedAddCommGroup.toAddCommGroup
NormedSpace.toModule
NormedAddTorsor.toAddTorsor
toAffineEquiv
LinearIsometryEquiv.toLinearEquiv
DivisionSemiring.toSemiring
Semifield.toDivisionSemiring
Field.toSemifield
NormedField.toField
RingHom.id
Semiring.toNonAssocSemiring
RingHomInvPair.ids
linearIsometryEquiv
LinearEquiv.ext
RingHomInvPair.ids
lipschitz 📖mathematicalLipschitzWith
PseudoMetricSpace.toPseudoEMetricSpace
NNReal
instOneNNReal
DFunLike.coe
AffineIsometryEquiv
EquivLike.toFunLike
instEquivLike
Isometry.lipschitz
isometry
map_eq_iff 📖mathematicalDFunLike.coe
AffineIsometryEquiv
EquivLike.toFunLike
instEquivLike
injective
map_ne 📖injective
map_vadd 📖mathematicalDFunLike.coe
AffineIsometryEquiv
EquivLike.toFunLike
instEquivLike
HVAdd.hVAdd
instHVAdd
AddSemigroupAction.toVAdd
AddMonoid.toAddSemigroup
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
SeminormedAddGroup.toAddGroup
SeminormedAddCommGroup.toSeminormedAddGroup
AddAction.toAddSemigroupAction
AddTorsor.toAddAction
NormedAddTorsor.toAddTorsor
LinearIsometryEquiv
DivisionSemiring.toSemiring
Semifield.toDivisionSemiring
Field.toSemifield
NormedField.toField
RingHom.id
Semiring.toNonAssocSemiring
RingHomInvPair.ids
NormedSpace.toModule
LinearIsometryEquiv.instEquivLike
linearIsometryEquiv
AffineIsometry.map_vadd
map_vsub 📖mathematicalDFunLike.coe
LinearIsometryEquiv
DivisionSemiring.toSemiring
Semifield.toDivisionSemiring
Field.toSemifield
NormedField.toField
RingHom.id
Semiring.toNonAssocSemiring
RingHomInvPair.ids
NormedSpace.toModule
EquivLike.toFunLike
LinearIsometryEquiv.instEquivLike
linearIsometryEquiv
VSub.vsub
AddTorsor.toVSub
SeminormedAddGroup.toAddGroup
SeminormedAddCommGroup.toSeminormedAddGroup
NormedAddTorsor.toAddTorsor
AffineIsometryEquiv
instEquivLike
AffineIsometry.map_vsub
norm_map 📖mathematicalNorm.norm
SeminormedAddCommGroup.toNorm
DFunLike.coe
LinearEquiv
Ring.toSemiring
NormedRing.toRing
NormedCommRing.toNormedRing
NormedField.toNormedCommRing
RingHom.id
Semiring.toNonAssocSemiring
RingHomInvPair.ids
AddCommGroup.toAddCommMonoid
SeminormedAddCommGroup.toAddCommGroup
NormedSpace.toModule
EquivLike.toFunLike
DFinsupp.instEquivLikeLinearEquiv
AffineEquiv.linear
NormedAddTorsor.toAddTorsor
toAffineEquiv
ofEq_rfl 📖mathematicalofEq
AffineSubspace
NormedRing.toRing
NormedCommRing.toNormedRing
NormedField.toNormedCommRing
SeminormedAddCommGroup.toAddCommGroup
NormedSpace.toModule
NormedAddTorsor.toAddTorsor
refl
Submodule
Ring.toSemiring
AddCommGroup.toAddCommMonoid
SetLike.instMembership
Submodule.setLike
AffineSubspace.direction
AffineSubspace.instSetLike
Submodule.seminormedAddCommGroup
Submodule.normedSpace
Algebra.toSMul
Semifield.toCommSemiring
Field.toSemifield
NormedField.toField
CommSemiring.toSemiring
Algebra.id
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DivisionSemiring.toSemiring
Semifield.toDivisionSemiring
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
Module.toDistribMulAction
Subtype.pseudoMetricSpace
AffineSubspace.toNormedAddTorsor
IsScalarTower.left
ofEq_symm 📖mathematicalsymm
Submodule
Ring.toSemiring
NormedRing.toRing
NormedCommRing.toNormedRing
NormedField.toNormedCommRing
AddCommGroup.toAddCommMonoid
SeminormedAddCommGroup.toAddCommGroup
NormedSpace.toModule
SetLike.instMembership
Submodule.setLike
AffineSubspace.direction
NormedAddTorsor.toAddTorsor
AffineSubspace
AffineSubspace.instSetLike
Submodule.seminormedAddCommGroup
Submodule.normedSpace
Algebra.toSMul
Semifield.toCommSemiring
Field.toSemifield
NormedField.toField
CommSemiring.toSemiring
Algebra.id
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DivisionSemiring.toSemiring
Semifield.toDivisionSemiring
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
Module.toDistribMulAction
Subtype.pseudoMetricSpace
AffineSubspace.toNormedAddTorsor
ofEq
IsScalarTower.left
ofTop_apply 📖mathematicalTop.top
AffineSubspace
NormedRing.toRing
NormedCommRing.toNormedRing
NormedField.toNormedCommRing
SeminormedAddCommGroup.toAddCommGroup
NormedSpace.toModule
NormedAddTorsor.toAddTorsor
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
AffineSubspace.instCompleteLattice
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
DFunLike.coe
AffineIsometryEquiv
Submodule
Ring.toSemiring
AddCommGroup.toAddCommMonoid
SetLike.instMembership
Submodule.setLike
AffineSubspace.direction
AffineSubspace.instSetLike
Submodule.seminormedAddCommGroup
Submodule.normedSpace
Algebra.toSMul
Semifield.toCommSemiring
Field.toSemifield
NormedField.toField
CommSemiring.toSemiring
Algebra.id
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DivisionSemiring.toSemiring
Semifield.toDivisionSemiring
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
Module.toDistribMulAction
Subtype.pseudoMetricSpace
AffineSubspace.toNormedAddTorsor
EquivLike.toFunLike
instEquivLike
ofTop
IsScalarTower.left
ofTop_symm_apply_coe 📖mathematicalTop.top
AffineSubspace
NormedRing.toRing
NormedCommRing.toNormedRing
NormedField.toNormedCommRing
SeminormedAddCommGroup.toAddCommGroup
NormedSpace.toModule
NormedAddTorsor.toAddTorsor
OrderTop.toTop
Preorder.toLE
PartialOrder.toPreorder
SemilatticeSup.toPartialOrder
Lattice.toSemilatticeSup
CompleteLattice.toLattice
AffineSubspace.instCompleteLattice
BoundedOrder.toOrderTop
CompleteLattice.toBoundedOrder
SetLike.instMembership
AffineSubspace.instSetLike
DFunLike.coe
AffineIsometryEquiv
Submodule
Ring.toSemiring
AddCommGroup.toAddCommMonoid
Submodule.setLike
AffineSubspace.direction
Submodule.seminormedAddCommGroup
Submodule.normedSpace
Algebra.toSMul
Semifield.toCommSemiring
Field.toSemifield
NormedField.toField
CommSemiring.toSemiring
Algebra.id
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DivisionSemiring.toSemiring
Semifield.toDivisionSemiring
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
Module.toDistribMulAction
Subtype.pseudoMetricSpace
AffineSubspace.toNormedAddTorsor
EquivLike.toFunLike
instEquivLike
symm
ofTop
IsScalarTower.left
pointReflection_apply 📖mathematicalDFunLike.coe
AffineIsometryEquiv
EquivLike.toFunLike
instEquivLike
pointReflection
HVAdd.hVAdd
instHVAdd
AddSemigroupAction.toVAdd
AddMonoid.toAddSemigroup
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
SeminormedAddGroup.toAddGroup
SeminormedAddCommGroup.toSeminormedAddGroup
AddAction.toAddSemigroupAction
AddTorsor.toAddAction
NormedAddTorsor.toAddTorsor
VSub.vsub
AddTorsor.toVSub
pointReflection_fixed_iff 📖mathematicalDFunLike.coe
AffineIsometryEquiv
EquivLike.toFunLike
instEquivLike
pointReflection
Nat.instAtLeastTwoHAddOfNat
AffineEquiv.pointReflection_fixed_iff_of_module
pointReflection_involutive 📖mathematicalFunction.Involutive
DFunLike.coe
AffineIsometryEquiv
EquivLike.toFunLike
instEquivLike
pointReflection
Equiv.pointReflection_involutive
pointReflection_midpoint_left 📖mathematicalDFunLike.coe
AffineIsometryEquiv
Real
Real.normedField
EquivLike.toFunLike
instEquivLike
pointReflection
midpoint
Real.instRing
invertibleTwo
Semifield.toDivisionSemiring
Field.toSemifield
Real.instField
IsStrictOrderedRing.toCharZero
DivisionSemiring.toSemiring
Real.partialOrder
Real.instIsStrictOrderedRing
SeminormedAddCommGroup.toAddCommGroup
NormedSpace.toModule
NormedAddTorsor.toAddTorsor
AffineEquiv.pointReflection_midpoint_left
IsStrictOrderedRing.toCharZero
Real.instIsStrictOrderedRing
pointReflection_midpoint_right 📖mathematicalDFunLike.coe
AffineIsometryEquiv
Real
Real.normedField
EquivLike.toFunLike
instEquivLike
pointReflection
midpoint
Real.instRing
invertibleTwo
Semifield.toDivisionSemiring
Field.toSemifield
Real.instField
IsStrictOrderedRing.toCharZero
DivisionSemiring.toSemiring
Real.partialOrder
Real.instIsStrictOrderedRing
SeminormedAddCommGroup.toAddCommGroup
NormedSpace.toModule
NormedAddTorsor.toAddTorsor
AffineEquiv.pointReflection_midpoint_right
IsStrictOrderedRing.toCharZero
Real.instIsStrictOrderedRing
pointReflection_self 📖mathematicalDFunLike.coe
AffineIsometryEquiv
EquivLike.toFunLike
instEquivLike
pointReflection
AffineEquiv.pointReflection_self
pointReflection_symm 📖mathematicalsymm
pointReflection
toAffineEquiv_injective
AffineEquiv.pointReflection_symm
pointReflection_toAffineEquiv 📖mathematicaltoAffineEquiv
pointReflection
AffineEquiv.pointReflection
NormedRing.toRing
NormedCommRing.toNormedRing
NormedField.toNormedCommRing
SeminormedAddCommGroup.toAddCommGroup
NormedSpace.toModule
NormedAddTorsor.toAddTorsor
range_eq_univ 📖mathematicalSet.range
DFunLike.coe
AffineIsometryEquiv
EquivLike.toFunLike
instEquivLike
Set.univ
coe_toIsometryEquiv
IsometryEquiv.range_eq_univ
refl_trans 📖mathematicaltrans
refl
ext
self_trans_symm 📖mathematicaltrans
symm
refl
ext
symm_apply_apply
surjective 📖mathematicalDFunLike.coe
AffineIsometryEquiv
EquivLike.toFunLike
instEquivLike
AffineEquiv.surjective
symm_apply_apply 📖mathematicalDFunLike.coe
AffineIsometryEquiv
EquivLike.toFunLike
instEquivLike
symm
AffineEquiv.symm_apply_apply
symm_bijective 📖mathematicalFunction.Bijective
AffineIsometryEquiv
symm
Function.bijective_iff_has_inverse
symm_symm
symm_constVSub 📖mathematicalsymm
SeminormedAddCommGroup.toPseudoMetricSpace
SeminormedAddCommGroup.toNormedAddTorsor
constVSub
trans
LinearIsometryEquiv.toAffineIsometryEquiv
LinearIsometryEquiv.neg
DivisionSemiring.toSemiring
Semifield.toDivisionSemiring
Field.toSemifield
NormedField.toField
NormedSpace.toModule
vaddConst
ext
symm_symm 📖mathematicalsymm
symm_trans_self 📖mathematicaltrans
symm
refl
ext
apply_symm_apply
toAffineEquiv_injective 📖mathematicalAffineIsometryEquiv
AffineEquiv
NormedRing.toRing
NormedCommRing.toNormedRing
NormedField.toNormedCommRing
SeminormedAddCommGroup.toAddCommGroup
NormedSpace.toModule
NormedAddTorsor.toAddTorsor
toAffineEquiv
RingHomInvPair.ids
toAffineEquiv_refl 📖mathematicaltoAffineEquiv
refl
AffineEquiv.refl
NormedRing.toRing
NormedCommRing.toNormedRing
NormedField.toNormedCommRing
SeminormedAddCommGroup.toAddCommGroup
NormedSpace.toModule
NormedAddTorsor.toAddTorsor
toAffineEquiv_symm 📖mathematicaltoAffineEquiv
symm
AffineEquiv.symm
NormedRing.toRing
NormedCommRing.toNormedRing
NormedField.toNormedCommRing
SeminormedAddCommGroup.toAddCommGroup
NormedSpace.toModule
NormedAddTorsor.toAddTorsor
toContinuousAffineEquiv_inj 📖mathematicaltoContinuousAffineEquivtoContinuousAffineEquiv_injective
toContinuousAffineEquiv_injective 📖mathematicalAffineIsometryEquiv
ContinuousAffineEquiv
NormedRing.toRing
NormedCommRing.toNormedRing
NormedField.toNormedCommRing
SeminormedAddCommGroup.toAddCommGroup
NormedSpace.toModule
NormedAddTorsor.toAddTorsor
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
toContinuousAffineEquiv
coeFn_injective
toContinuousAffineEquiv_refl 📖mathematicaltoContinuousAffineEquiv
refl
ContinuousAffineEquiv.refl
NormedRing.toRing
NormedCommRing.toNormedRing
NormedField.toNormedCommRing
SeminormedAddCommGroup.toAddCommGroup
NormedSpace.toModule
NormedAddTorsor.toAddTorsor
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
toContinuousAffineEquiv_symm 📖mathematicaltoContinuousAffineEquiv
symm
ContinuousAffineEquiv.symm
NormedRing.toRing
NormedCommRing.toNormedRing
NormedField.toNormedCommRing
SeminormedAddCommGroup.toAddCommGroup
NormedSpace.toModule
NormedAddTorsor.toAddTorsor
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
toHomeomorph_refl 📖mathematicaltoHomeomorph
refl
Homeomorph.refl
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
toHomeomorph_symm 📖mathematicaltoHomeomorph
symm
Homeomorph.symm
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
toIsometryEquiv_refl 📖mathematicaltoIsometryEquiv
refl
IsometryEquiv.refl
PseudoMetricSpace.toPseudoEMetricSpace
toIsometryEquiv_symm 📖mathematicaltoIsometryEquiv
symm
IsometryEquiv.symm
PseudoMetricSpace.toPseudoEMetricSpace
trans_assoc 📖mathematicaltrans
trans_refl 📖mathematicaltrans
refl
ext
vaddConst_toAffineEquiv 📖mathematicaltoAffineEquiv
SeminormedAddCommGroup.toPseudoMetricSpace
SeminormedAddCommGroup.toNormedAddTorsor
vaddConst
AffineEquiv.vaddConst
NormedRing.toRing
NormedCommRing.toNormedRing
NormedField.toNormedCommRing
SeminormedAddCommGroup.toAddCommGroup
NormedSpace.toModule
NormedAddTorsor.toAddTorsor
vadd_vsub 📖mathematicalIsometry
PseudoMetricSpace.toPseudoEMetricSpace
VSub.vsub
AddTorsor.toVSub
SeminormedAddGroup.toAddGroup
SeminormedAddCommGroup.toSeminormedAddGroup
NormedAddTorsor.toAddTorsor
HVAdd.hVAdd
instHVAdd
AddSemigroupAction.toVAdd
AddMonoid.toAddSemigroup
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddAction.toAddSemigroupAction
AddTorsor.toAddAction
SeminormedAddCommGroup.toPseudoMetricSpaceIsometry.comp
isometry

AffineSubspace

Definitions

NameCategoryTheorems
equivMapOfInjective 📖CompOp
3 mathmath: isometryEquivMap.toAffineMap_eq, linear_equivMapOfInjective, equivMapOfInjective_toFun
isometryEquivMap 📖CompOp
3 mathmath: isometryEquivMap.toAffineMap_eq, isometryEquivMap.coe_apply, isometryEquivMap.apply_symm_apply
subtypeₐᵢ 📖CompOp
5 mathmath: coe_subtypeₐᵢ, toContinuousAffineMap_subtypeₐᵢ, subtypeₐᵢ_linear, subtypeₐᵢ_linearIsometry, subtypeₐᵢ_toAffineMap

Theorems

NameKindAssumesProvesValidatesDepends On
coe_subtypeₐᵢ 📖mathematicalDFunLike.coe
AffineIsometry
Submodule
Ring.toSemiring
NormedRing.toRing
NormedCommRing.toNormedRing
NormedField.toNormedCommRing
AddCommGroup.toAddCommMonoid
SeminormedAddCommGroup.toAddCommGroup
NormedSpace.toModule
SetLike.instMembership
Submodule.setLike
direction
NormedAddTorsor.toAddTorsor
AffineSubspace
instSetLike
Submodule.seminormedAddCommGroup
Submodule.normedSpace
Algebra.toSMul
Semifield.toCommSemiring
Field.toSemifield
NormedField.toField
CommSemiring.toSemiring
Algebra.id
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DivisionSemiring.toSemiring
Semifield.toDivisionSemiring
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
Module.toDistribMulAction
Subtype.pseudoMetricSpace
toNormedAddTorsor
AffineIsometry.instFunLike
subtypeₐᵢ
AffineMap
Submodule.addCommGroup
Submodule.module
toAddTorsor
AffineMap.instFunLike
subtype
IsScalarTower.left
equivMapOfInjective_toFun 📖mathematicalDFunLike.coe
AffineMap
NormedRing.toRing
NormedCommRing.toNormedRing
NormedField.toNormedCommRing
SeminormedAddCommGroup.toAddCommGroup
NormedSpace.toModule
NormedAddTorsor.toAddTorsor
AffineMap.instFunLike
AffineEquiv
AffineSubspace
SetLike.instMembership
instSetLike
map
Submodule
Ring.toSemiring
AddCommGroup.toAddCommMonoid
Submodule.setLike
direction
Submodule.addCommGroup
Submodule.module
toAddTorsor
nonempty_map
EquivLike.toFunLike
AffineEquiv.equivLike
equivMapOfInjective
Set
Set.instMembership
Set.image
SetLike.coe
nonempty_map
linear_equivMapOfInjective 📖mathematicalDFunLike.coe
AffineMap
NormedRing.toRing
NormedCommRing.toNormedRing
NormedField.toNormedCommRing
SeminormedAddCommGroup.toAddCommGroup
NormedSpace.toModule
NormedAddTorsor.toAddTorsor
AffineMap.instFunLike
AffineEquiv.linear
AffineSubspace
SetLike.instMembership
instSetLike
map
Submodule
Ring.toSemiring
AddCommGroup.toAddCommMonoid
Submodule.setLike
direction
Submodule.addCommGroup
Submodule.module
toAddTorsor
nonempty_map
equivMapOfInjective
LinearEquiv.trans
Submodule.map
RingHom.id
Semiring.toNonAssocSemiring
AffineMap.linear
Submodule.addCommMonoid
Submodule.equivMapOfInjective
LinearEquiv.ofEq
nonempty_map
subtypeₐᵢ_linear 📖mathematicalAffineMap.linear
Submodule
Ring.toSemiring
NormedRing.toRing
NormedCommRing.toNormedRing
NormedField.toNormedCommRing
AddCommGroup.toAddCommMonoid
SeminormedAddCommGroup.toAddCommGroup
NormedSpace.toModule
SetLike.instMembership
Submodule.setLike
direction
NormedAddTorsor.toAddTorsor
AffineSubspace
instSetLike
Submodule.seminormedAddCommGroup
Submodule.normedSpace
Algebra.toSMul
Semifield.toCommSemiring
Field.toSemifield
NormedField.toField
CommSemiring.toSemiring
Algebra.id
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DivisionSemiring.toSemiring
Semifield.toDivisionSemiring
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
Module.toDistribMulAction
Subtype.pseudoMetricSpace
toNormedAddTorsor
AffineIsometry.toAffineMap
subtypeₐᵢ
Submodule.subtype
IsScalarTower.left
subtypeₐᵢ_linearIsometry 📖mathematicalAffineIsometry.linearIsometry
Submodule
Ring.toSemiring
NormedRing.toRing
NormedCommRing.toNormedRing
NormedField.toNormedCommRing
AddCommGroup.toAddCommMonoid
SeminormedAddCommGroup.toAddCommGroup
NormedSpace.toModule
SetLike.instMembership
Submodule.setLike
direction
NormedAddTorsor.toAddTorsor
AffineSubspace
instSetLike
Submodule.seminormedAddCommGroup
Submodule.normedSpace
Algebra.toSMul
Semifield.toCommSemiring
Field.toSemifield
NormedField.toField
CommSemiring.toSemiring
Algebra.id
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DivisionSemiring.toSemiring
Semifield.toDivisionSemiring
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
Module.toDistribMulAction
Subtype.pseudoMetricSpace
toNormedAddTorsor
subtypeₐᵢ
Submodule.subtypeₗᵢ
IsScalarTower.left
subtypeₐᵢ_toAffineMap 📖mathematicalAffineIsometry.toAffineMap
Submodule
Ring.toSemiring
NormedRing.toRing
NormedCommRing.toNormedRing
NormedField.toNormedCommRing
AddCommGroup.toAddCommMonoid
SeminormedAddCommGroup.toAddCommGroup
NormedSpace.toModule
SetLike.instMembership
Submodule.setLike
direction
NormedAddTorsor.toAddTorsor
AffineSubspace
instSetLike
Submodule.seminormedAddCommGroup
Submodule.normedSpace
Algebra.toSMul
Semifield.toCommSemiring
Field.toSemifield
NormedField.toField
CommSemiring.toSemiring
Algebra.id
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DivisionSemiring.toSemiring
Semifield.toDivisionSemiring
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
Module.toDistribMulAction
Subtype.pseudoMetricSpace
toNormedAddTorsor
subtypeₐᵢ
subtype
IsScalarTower.left
toContinuousAffineMap_subtypeₐᵢ 📖mathematicalAffineIsometry.toContinuousAffineMap
Submodule
Ring.toSemiring
NormedRing.toRing
NormedCommRing.toNormedRing
NormedField.toNormedCommRing
AddCommGroup.toAddCommMonoid
SeminormedAddCommGroup.toAddCommGroup
NormedSpace.toModule
SetLike.instMembership
Submodule.setLike
direction
NormedAddTorsor.toAddTorsor
AffineSubspace
instSetLike
Submodule.seminormedAddCommGroup
Submodule.normedSpace
Algebra.toSMul
Semifield.toCommSemiring
Field.toSemifield
NormedField.toField
CommSemiring.toSemiring
Algebra.id
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DivisionSemiring.toSemiring
Semifield.toDivisionSemiring
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
Module.toDistribMulAction
Subtype.pseudoMetricSpace
toNormedAddTorsor
subtypeₐᵢ
subtypeA
UniformSpace.toTopologicalSpace
PseudoMetricSpace.toUniformSpace
IsScalarTower.left

AffineSubspace.isometryEquivMap

Theorems

NameKindAssumesProvesValidatesDepends On
apply_symm_apply 📖mathematicalDFunLike.coe
AffineIsometry
MetricSpace.toPseudoMetricSpace
AffineIsometry.instFunLike
AffineSubspace
NormedRing.toRing
NormedCommRing.toNormedRing
NormedField.toNormedCommRing
SeminormedAddCommGroup.toAddCommGroup
NormedSpace.toModule
NormedAddTorsor.toAddTorsor
SetLike.instMembership
AffineSubspace.instSetLike
AffineIsometryEquiv
Submodule
Ring.toSemiring
AddCommGroup.toAddCommMonoid
Submodule.setLike
AffineSubspace.direction
AffineSubspace.map
AffineIsometry.toAffineMap
Submodule.seminormedAddCommGroup
Submodule.normedSpace
Algebra.toSMul
Semifield.toCommSemiring
Field.toSemifield
NormedField.toField
CommSemiring.toSemiring
Algebra.id
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DivisionSemiring.toSemiring
Semifield.toDivisionSemiring
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
Module.toDistribMulAction
Subtype.pseudoMetricSpace
AffineSubspace.toNormedAddTorsor
AffineSubspace.nonempty_map
EquivLike.toFunLike
AffineIsometryEquiv.instEquivLike
AffineIsometryEquiv.symm
AffineSubspace.isometryEquivMap
IsScalarTower.left
AffineSubspace.nonempty_map
AffineIsometryEquiv.apply_symm_apply
coe_apply 📖mathematicalAffineSubspace
NormedRing.toRing
NormedCommRing.toNormedRing
NormedField.toNormedCommRing
SeminormedAddCommGroup.toAddCommGroup
NormedSpace.toModule
NormedAddTorsor.toAddTorsor
SetLike.instMembership
AffineSubspace.instSetLike
AffineSubspace.map
MetricSpace.toPseudoMetricSpace
AffineIsometry.toAffineMap
DFunLike.coe
AffineIsometryEquiv
Submodule
Ring.toSemiring
AddCommGroup.toAddCommMonoid
Submodule.setLike
AffineSubspace.direction
Submodule.seminormedAddCommGroup
Submodule.normedSpace
Algebra.toSMul
Semifield.toCommSemiring
Field.toSemifield
NormedField.toField
CommSemiring.toSemiring
Algebra.id
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DivisionSemiring.toSemiring
Semifield.toDivisionSemiring
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
Module.toDistribMulAction
Subtype.pseudoMetricSpace
AffineSubspace.toNormedAddTorsor
AffineSubspace.nonempty_map
EquivLike.toFunLike
AffineIsometryEquiv.instEquivLike
AffineSubspace.isometryEquivMap
AffineIsometry
AffineIsometry.instFunLike
IsScalarTower.left
AffineSubspace.nonempty_map
toAffineMap_eq 📖mathematicalAffineEquiv.toAffineMap
AffineSubspace
NormedRing.toRing
NormedCommRing.toNormedRing
NormedField.toNormedCommRing
SeminormedAddCommGroup.toAddCommGroup
NormedSpace.toModule
NormedAddTorsor.toAddTorsor
MetricSpace.toPseudoMetricSpace
SetLike.instMembership
AffineSubspace.instSetLike
AffineSubspace.map
AffineIsometry.toAffineMap
Submodule
Ring.toSemiring
AddCommGroup.toAddCommMonoid
Submodule.setLike
AffineSubspace.direction
Submodule.seminormedAddCommGroup
Submodule.normedSpace
Algebra.toSMul
Semifield.toCommSemiring
Field.toSemifield
NormedField.toField
CommSemiring.toSemiring
Algebra.id
IsScalarTower.left
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
DivisionSemiring.toSemiring
Semifield.toDivisionSemiring
DistribMulAction.toMulAction
AddCommMonoid.toAddMonoid
Module.toDistribMulAction
Subtype.pseudoMetricSpace
AffineSubspace.toNormedAddTorsor
AffineSubspace.nonempty_map
AffineIsometryEquiv.toAffineEquiv
AffineSubspace.isometryEquivMap
Submodule.addCommGroup
Submodule.module
AffineSubspace.toAddTorsor
AffineSubspace.equivMapOfInjective
AffineIsometry.injective
IsScalarTower.left
AffineSubspace.nonempty_map

LinearIsometry

Definitions

NameCategoryTheorems
toAffineIsometry 📖CompOp
4 mathmath: toAffineIsometry_linearIsometry, toAffineIsometry_toAffineMap, coe_toAffineIsometry, LinearIsometryEquiv.toAffineIsometryEquiv_toAffineIsometry

Theorems

NameKindAssumesProvesValidatesDepends On
coe_toAffineIsometry 📖mathematicalDFunLike.coe
AffineIsometry
SeminormedAddCommGroup.toPseudoMetricSpace
SeminormedAddCommGroup.toNormedAddTorsor
AffineIsometry.instFunLike
toAffineIsometry
LinearIsometry
DivisionSemiring.toSemiring
Semifield.toDivisionSemiring
Field.toSemifield
NormedField.toField
RingHom.id
Semiring.toNonAssocSemiring
NormedSpace.toModule
instFunLike
toAffineIsometry_linearIsometry 📖mathematicalAffineIsometry.linearIsometry
SeminormedAddCommGroup.toPseudoMetricSpace
SeminormedAddCommGroup.toNormedAddTorsor
toAffineIsometry
ext
toAffineIsometry_toAffineMap 📖mathematicalAffineIsometry.toAffineMap
SeminormedAddCommGroup.toPseudoMetricSpace
SeminormedAddCommGroup.toNormedAddTorsor
toAffineIsometry
LinearMap.toAffineMap
NormedRing.toRing
NormedCommRing.toNormedRing
NormedField.toNormedCommRing
SeminormedAddCommGroup.toAddCommGroup
NormedSpace.toModule
toLinearMap
DivisionSemiring.toSemiring
Semifield.toDivisionSemiring
Field.toSemifield
NormedField.toField
RingHom.id
Semiring.toNonAssocSemiring

LinearIsometryEquiv

Definitions

NameCategoryTheorems
toAffineIsometryEquiv 📖CompOp
5 mathmath: coe_toAffineIsometryEquiv, AffineIsometryEquiv.symm_constVSub, toAffineIsometryEquiv_toAffineEquiv, toAffineIsometryEquiv_linearIsometryEquiv, toAffineIsometryEquiv_toAffineIsometry

Theorems

NameKindAssumesProvesValidatesDepends On
coe_toAffineIsometryEquiv 📖mathematicalDFunLike.coe
AffineIsometryEquiv
SeminormedAddCommGroup.toPseudoMetricSpace
SeminormedAddCommGroup.toNormedAddTorsor
EquivLike.toFunLike
AffineIsometryEquiv.instEquivLike
toAffineIsometryEquiv
LinearIsometryEquiv
DivisionSemiring.toSemiring
Semifield.toDivisionSemiring
Field.toSemifield
NormedField.toField
RingHom.id
Semiring.toNonAssocSemiring
RingHomInvPair.ids
NormedSpace.toModule
instEquivLike
RingHomInvPair.ids
toAffineIsometryEquiv_linearIsometryEquiv 📖mathematicalAffineIsometryEquiv.linearIsometryEquiv
SeminormedAddCommGroup.toPseudoMetricSpace
SeminormedAddCommGroup.toNormedAddTorsor
toAffineIsometryEquiv
RingHomInvPair.ids
ext
toAffineIsometryEquiv_toAffineEquiv 📖mathematicalAffineIsometryEquiv.toAffineEquiv
SeminormedAddCommGroup.toPseudoMetricSpace
SeminormedAddCommGroup.toNormedAddTorsor
toAffineIsometryEquiv
LinearEquiv.toAffineEquiv
NormedRing.toRing
NormedCommRing.toNormedRing
NormedField.toNormedCommRing
SeminormedAddCommGroup.toAddCommGroup
NormedSpace.toModule
toLinearEquiv
DivisionSemiring.toSemiring
Semifield.toDivisionSemiring
Field.toSemifield
NormedField.toField
RingHom.id
Semiring.toNonAssocSemiring
RingHomInvPair.ids
RingHomInvPair.ids
toAffineIsometryEquiv_toAffineIsometry 📖mathematicalAffineIsometryEquiv.toAffineIsometry
SeminormedAddCommGroup.toPseudoMetricSpace
SeminormedAddCommGroup.toNormedAddTorsor
toAffineIsometryEquiv
LinearIsometry.toAffineIsometry
toLinearIsometry
DivisionSemiring.toSemiring
Semifield.toDivisionSemiring
Field.toSemifield
NormedField.toField
RingHom.id
Semiring.toNonAssocSemiring
RingHomInvPair.ids
NormedSpace.toModule
RingHomInvPair.ids

(root)

Definitions

NameCategoryTheorems
AffineIsometry 📖CompData
52 mathmath: AffineIsometry.image_intrinsicClosure, Affine.Simplex.orthogonalProjectionSpan_map, Affine.Simplex.circumcenter_map, AffineIsometry.coeFn_injective, AffineIsometry.nndist_map, Affine.Simplex.incenter_map, Isometry.coe_affineIsometryOfStrictConvexSpace, EuclideanGeometry.reflection_map, AffineIsometry.coe_comp, Affine.Simplex.ExcenterExists.touchpoint_map, Affine.Simplex.ExcenterExists.excenter_map, AffineIsometry.id_apply, EuclideanGeometry.orthogonalProjection_map, AffineIsometry.coe_mul, AffineSubspace.coe_subtypeₐᵢ, AffineIsometry.lipschitz, AffineIsometry.comp_continuous_iff, Affine.Simplex.altitudeFoot_map, AffineIsometry.image_intrinsicInterior, AffineIsometry.diam_image, AffineIsometry.coe_toAffineMap, AffineIsometry.coe_id, AffineIsometry.map_vsub, AffineIsometry.coe_toAffineIsometryEquiv, AffineIsometry.map_eq_iff, AffineSubspace.isometryEquivMap.coe_apply, LinearIsometry.coe_toAffineIsometry, AffineIsometry.isometry, Isometry.affineIsometryOfStrictConvexSpace_apply, AffineIsometry.diam_range, AffineIsometry.toAffineIsometryEquiv_apply, AffineIsometry.map_vadd, AffineIsometry.toContinuousAffineMap_injective, AffineIsometry.ediam_range, Affine.Simplex.mongePoint_map, Affine.Simplex.eulerPoint_map, AffineIsometry.coe_one, AffineIsometry.toAffineMap_injective, AffineIsometry.ext_iff, AffineIsometry.edist_map, Affine.Simplex.ninePointCircle_map, AffineSubspace.isometryEquivMap.apply_symm_apply, AffineIsometry.antilipschitz, AffineIsometry.injective, EuclideanGeometry.Sphere.secondInter_map, AffineIsometry.angle_map, AffineIsometry.coe_toContinuousAffineMap, AffineIsometry.image_intrinsicFrontier, AffineIsometry.ediam_image, AffineIsometry.dist_map, AffineIsometry.continuous, AffineIsometryEquiv.coe_toAffineIsometry
AffineIsometryEquiv 📖CompData
88 mathmath: AffineIsometryEquiv.coe_constVSub, AffineIsometryEquiv.pointReflection_apply, AffineIsometryEquiv.coe_mk, AffineIsometryEquiv.pointReflection_involutive, EuclideanGeometry.reflection_orthogonal_vadd, AffineIsometryEquiv.coe_symm_toAffineEquiv, AffineIsometryEquiv.coe_refl, AffineIsometryEquiv.ofTop_apply, AffineIsometryEquiv.range_eq_univ, AffineIsometryEquiv.coe_symm_trans, AffineIsometryEquiv.edist_map, EuclideanGeometry.reflection_map, AffineIsometryEquiv.coe_constVAdd, LinearIsometryEquiv.coe_toAffineIsometryEquiv, EuclideanGeometry.reflection_vadd_smul_vsub_orthogonalProjection, AffineIsometryEquiv.comp_continuous_iff, AffineIsometryEquiv.coe_trans, AffineIsometryEquiv.pointReflection_midpoint_left, AffineIsometryEquiv.continuousAt, AffineIsometryEquiv.dist_pointReflection_fixed, AffineIsometryEquiv.continuousWithinAt, AffineIsometryEquiv.map_vsub, AffineIsometryEquiv.continuousOn, Affine.Triangle.dist_circumcenter_reflection_orthocenter, AffineIsometryEquiv.coe_ofEq_apply, EuclideanGeometry.reflection_reflection, AffineIsometryEquiv.ofTop_symm_apply_coe, AffineIsometryEquiv.coe_inv, AffineIsometryEquiv.continuous, EuclideanGeometry.reflection_eq_self_iff, AffineIsometryEquiv.pointReflection_fixed_iff, AffineIsometryEquiv.apply_symm_apply, AffineIsometryEquiv.dist_pointReflection_self, AffineIsometryEquiv.dist_pointReflection_self_real, Affine.Triangle.dist_orthocenter_reflection_circumcenter, AffineIsometryEquiv.coe_vaddConst, EuclideanGeometry.reflection_apply_of_mem, AffineIsometryEquiv.diam_image, AffineIsometryEquiv.symm_bijective, AffineIsometry.coe_toAffineIsometryEquiv, AffineSubspace.isometryEquivMap.coe_apply, AffineIsometryEquiv.coe_mk', EuclideanGeometry.eq_or_eq_reflection_of_dist_eq, AffineIsometryEquiv.symm_apply_apply, AffineIsometryEquiv.map_eq_iff, AffineIsometryEquiv.dist_map, EuclideanGeometry.dist_reflection_eq_of_mem, EuclideanGeometry.dist_reflection, AffineIsometryEquiv.ext_iff, AffineIsometryEquiv.coe_vaddConst_symm, AffineIsometryEquiv.coe_toIsometryEquiv, AffineIsometryEquiv.pointReflection_self, AffineIsometryEquiv.surjective, Affine.Triangle.dist_circumcenter_reflection_orthocenter_finset, AffineIsometryEquiv.coe_one, AffineIsometry.toAffineIsometryEquiv_apply, AffineIsometryEquiv.toAffineEquiv_injective, EuclideanGeometry.reflection_eq_iff_orthogonalProjection_eq, IsometryEquiv.coeFn_toRealAffineIsometryEquiv, AffineIsometryEquiv.ediam_image, EuclideanGeometry.reflection_apply', AffineIsometryEquiv.bijective, AffineIsometryEquiv.lipschitz, AffineIsometryEquiv.map_vadd, AffineIsometryEquiv.injective, EuclideanGeometry.reflection_involutive, AffineIsometryEquiv.coe_symm_toContinuousAffineEquiv, EuclideanGeometry.reflection_subtype, AffineIsometryEquiv.comp_continuousOn_iff, AffineSubspace.isometryEquivMap.apply_symm_apply, AffineIsometryEquiv.coe_toHomeomorph, AffineIsometryEquiv.antilipschitz, AffineIsometryEquiv.coe_symm_toIsometryEquiv, EuclideanGeometry.eq_reflection_of_eq_subspace, AffineIsometryEquiv.toContinuousAffineEquiv_injective, Affine.Simplex.reflection_circumcenter_eq_affineCombination_of_pointsWithCircumcenter, Affine.Triangle.dist_orthocenter_reflection_circumcenter_finset, AffineIsometryEquiv.isometry, AffineIsometryEquiv.dist_pointReflection_self', AffineIsometryEquiv.coe_symm_toHomeomorph, EuclideanGeometry.reflection_mem_of_le_of_mem, EuclideanGeometry.reflection_apply, AffineIsometryEquiv.coeFn_injective, AffineIsometryEquiv.coe_mul, AffineIsometryEquiv.coe_toAffineIsometry, AffineIsometryEquiv.pointReflection_midpoint_right, AffineIsometryEquiv.coe_toAffineEquiv, AffineIsometryEquiv.coe_toContinuousAffineEquiv
«term_→ᵃⁱ[_]_» 📖CompOp
«term_≃ᵃⁱ[_]_» 📖CompOp

---

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