AffineIsometryEquiv.injective
∀ {𝕜 : Type u_1} {V : Type u_2} {V₂ : Type u_5} {P : Type u_10} {P₂ : Type u_11} [inst : NormedField 𝕜]
[inst_1 : SeminormedAddCommGroup V] [inst_2 : NormedSpace 𝕜 V] [inst_3 : PseudoMetricSpace P]
[inst_4 : NormedAddTorsor V P] [inst_5 : SeminormedAddCommGroup V₂] [inst_6 : NormedSpace 𝕜 V₂]
[inst_7 : PseudoMetricSpace P₂] [inst_8 : NormedAddTorsor V₂ P₂] (e : P ≃ᵃⁱ[𝕜] P₂), Function.Injective ⇑e- Defined in
- Mathlib.Analysis.Normed.Affine.Isometry
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 51 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- NormedSpacestatement and proof · cited by 12,499
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- PseudoMetricSpacestatement and proof · cited by 1,550
- NormedAddTorsorstatement and proof · cited by 1,325
- NormedFieldstatement and proof · cited by 1,084
- AffineIsometryEquivstatement and proof · cited by 118
- AffineIsometryEquiv.toAffineEquivproof · cited by 20
- AffineEquiv.injectiveproof · cited by 11
Cited by3
Results whose statement or proof uses this declaration.
- AffineIsometryEquiv.map_eq_iffproof · cited by 0
- AffineIsometryEquiv.map_neproof · cited by 0
- EuclideanGeometry.reflection_symmproof · cited by 0