Theorems · Theorem · general topology
LipschitzWith.iff_le_add_mul
∀ {α : Type u} [inst : PseudoMetricSpace α] {f : α → ℝ} {K : NNReal},
LipschitzWith K f ↔ ∀ (x y : α), f x ≤ f y + ↑K * dist x y- Defined in
- Mathlib.Topology.MetricSpace.Lipschitz
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 155 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoMetricSpace
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Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- NNRealstatement and proof · cited by 4,310
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.diststatement · cited by 1,539
- NNReal.toRealstatement · cited by 1,260
- LipschitzWithstatement · cited by 316
- LipschitzWith.of_le_add_mulproof · cited by 4
- LipschitzWith.le_add_mulproof · cited by 1
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