AffineSubspace.isometryEquivMap.toAffineMap_eq
∀ {𝕜 : Type u_1} {V₁' : Type u_4} {V₂ : Type u_5} {P₁' : Type u_9} {P₂ : Type u_11} [inst : NormedField 𝕜]
[inst_1 : SeminormedAddCommGroup V₁'] [inst_2 : NormedSpace 𝕜 V₁'] [inst_3 : MetricSpace P₁']
[inst_4 : NormedAddTorsor V₁' P₁'] [inst_5 : SeminormedAddCommGroup V₂] [inst_6 : NormedSpace 𝕜 V₂]
[inst_7 : PseudoMetricSpace P₂] [inst_8 : NormedAddTorsor V₂ P₂] (φ : P₁' →ᵃⁱ[𝕜] P₂) (E : AffineSubspace 𝕜 P₁')
[inst_9 : Nonempty ↥E],
↑(AffineSubspace.isometryEquivMap φ E).toAffineEquiv = ↑(E.equivMapOfInjective φ.toAffineMap ⋯)- Defined in
- Mathlib.Analysis.Normed.Affine.Isometry
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 161 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NormedSpacestatement and proof · cited by 12,499
- Submodulestatement · cited by 7,192
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- MetricSpacestatement and proof · cited by 1,684
- PseudoMetricSpacestatement and proof · cited by 1,550
- NormedAddTorsorstatement and proof · cited by 1,325
- NormedFieldstatement and proof · cited by 1,084
- AffineSubspacestatement and proof · cited by 871
- AffineMapstatement · cited by 674
- AffineSubspace.directionstatement · cited by 339
- AffineIsometrystatement and proof · cited by 79
- AffineSubspace.mapstatement · cited by 78
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