Theorems · Theorem · general topology

LipschitzOnWith.mono

∀ {α : Type u} {β : Type v} [inst : PseudoEMetricSpace α] [inst_1 : PseudoEMetricSpace β] {K : NNReal} {s t : Set α}
  {f : α → β}, LipschitzOnWith K f t → s ⊆ t → LipschitzOnWith K f s

Being Lipschitz on a set is monotone w.r.t. that set.

Defined in

Mathlib.Topology.EMetricSpace.Lipschitz

Cited by

9 results in Mathlib

Foundations

Depth 148 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PseudoEMetricSpacePseudoEMetricSpace