Theorems · Theorem · general topology

LipschitzOnWith.le_add_mul

∀ {α : Type u} [inst : PseudoMetricSpace α] {s : Set α} {f : α → ℝ} {K : NNReal},
  LipschitzOnWith K f s → ∀ {x : α}, x ∈ s → ∀ {y : α}, y ∈ s → f x ≤ f y + ↑K * dist x y

Defined in

Mathlib.Topology.MetricSpace.Lipschitz

Cited by

2 results in Mathlib

Foundations

Depth 153 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PseudoMetricSpace