Theorems · Theorem · functional analysis
antilipschitzWith_lineMap
∀ {W : Type u_3} {Q : Type u_4} [inst : NormedAddCommGroup W] [inst_1 : MetricSpace Q] [inst_2 : NormedAddTorsor W Q]
{𝕜 : Type u_5} [inst_3 : NormedField 𝕜] [inst_4 : NormedSpace 𝕜 W] {p₁ p₂ : Q},
p₁ ≠ p₂ → AntilipschitzWith (nndist p₁ p₂)⁻¹ ⇑(AffineMap.lineMap p₁ p₂)- Defined in
- Mathlib.Analysis.Normed.Affine.AddTorsor
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 152 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Realproof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- NNRealstatement · cited by 4,310
- mul_oneproof · cited by 3,885
- le_reflproof · cited by 2,061
- MetricSpacestatement and proof · cited by 1,684
- Dist.distproof · cited by 1,539
- NormedAddTorsorstatement and proof · cited by 1,325
- NNReal.toRealproof · cited by 1,260
- NormedFieldstatement and proof · cited by 1,084
Cited by1
Results whose statement or proof uses this declaration.
- Complex.norm_le_of_forall_mem_frontier_norm_leproof · cited by 2