Theorems · Theorem · functional analysis
dist_homothety_self
∀ {V : Type u_1} {P : Type u_2} [inst : SeminormedAddCommGroup V] [inst_1 : PseudoMetricSpace P]
[inst_2 : NormedAddTorsor V P] {𝕜 : Type u_5} [inst_3 : NormedField 𝕜] [inst_4 : NormedSpace 𝕜 V] (p₁ p₂ : P) (c : 𝕜),
dist ((AffineMap.homothety p₁ c) p₂) p₂ = ‖1 - c‖ * dist p₁ p₂- Defined in
- Mathlib.Analysis.Normed.Affine.AddTorsor
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 122 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Realstatement and proof · cited by 25,697
- NormedSpacestatement and proof · cited by 12,499
- Norm.normstatement and proof · cited by 5,413
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.diststatement and proof · cited by 1,539
- NormedAddTorsorstatement and proof · cited by 1,325
- NormedFieldstatement and proof · cited by 1,084
- AffineMapstatement · cited by 674
- AffineMap.homothetystatement · cited by 51
- dist_lineMap_rightproof · cited by 7
Cited by2
Results whose statement or proof uses this declaration.
- dist_self_homothetyproof · cited by 1
- nndist_homothety_selfproof · cited by 0