Theorems · Theorem · general topology
LipschitzOnWith.to_restrict
∀ {α : Type u} {β : Type v} [inst : PseudoEMetricSpace α] [inst_1 : PseudoEMetricSpace β] {K : NNReal} {s : Set α}
{f : α → β}, LipschitzOnWith K f s → LipschitzWith K (s.domRestrict f)Alias of the forward direction of lipschitzOnWith_iff_restrict.
- Defined in
- Mathlib.Topology.EMetricSpace.Lipschitz
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 149 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Set.Elemstatement · cited by 7,166
- NNRealstatement and proof · cited by 4,310
- PseudoEMetricSpacestatement and proof · cited by 1,536
- Set.domRestrictstatement · cited by 383
- LipschitzWithstatement · cited by 316
- LipschitzOnWithstatement · cited by 164
- lipschitzOnWith_iff_restrictproof · cited by 4
Cited by5
Results whose statement or proof uses this declaration.
- LipschitzWith.comp_lipschitzOnWithproof · cited by 4
- LipschitzOnWith.compproof · cited by 3
- ApproximatesLinearOn.lipschitz_subproof · cited by 2
- LipschitzOnWith.uniformContinuousOnproof · cited by 2
- LipschitzOnWith.edist_lt_of_edist_lt_divproof · cited by 0