Theorems · Theorem · functional analysis
dist_lineMap_lineMap
∀ {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)
(c₁ c₂ : 𝕜), dist ((AffineMap.lineMap p₁ p₂) c₁) ((AffineMap.lineMap p₁ p₂) c₂) = dist c₁ c₂ * dist p₁ p₂- Defined in
- Mathlib.Analysis.Normed.Affine.AddTorsor
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 120 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Realstatement and proof · cited by 25,697
- NormedSpacestatement and proof · cited by 12,499
- Norm.normproof · cited by 5,413
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- HVAdd.hVAddproof · cited by 1,820
- 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
- VSub.vsubproof · cited by 817
- AffineMapstatement · cited by 674
Cited by5
Results whose statement or proof uses this declaration.
- dist_lineMap_leftproof · cited by 7
- dist_lineMap_rightproof · cited by 7
- antilipschitzWith_lineMapproof · cited by 1
- lipschitzWith_lineMapproof · cited by 1
- nndist_lineMap_lineMapproof · cited by 0