Theorems · Theorem · general topology

LipschitzOnWith.mapsToRestrict

∀ {α : Type u} {β : Type v} [inst : PseudoEMetricSpace α] [inst_1 : PseudoEMetricSpace β] {K : NNReal} {s : Set α}
  {f : α → β} {t : Set β} (h : Set.MapsTo f s t), LipschitzOnWith K f s → LipschitzWith K (Set.MapsTo.restrict f s t h)

Alias of the forward direction of Set.MapsTo.lipschitzOnWith_iff_restrict.

Defined in

Mathlib.Topology.EMetricSpace.Lipschitz

Cited by

1 results in Mathlib

Foundations

Depth 150 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PseudoEMetricSpacePseudoEMetricSpace