Theorems · Theorem · general topology
LipschitzWith.of_le_add
∀ {α : Type u} [inst : PseudoMetricSpace α] {f : α → ℝ}, (∀ (x y : α), f x ≤ f y + dist x y) → LipschitzWith 1 f- Defined in
- Mathlib.Topology.MetricSpace.Lipschitz
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 155 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoMetricSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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 · cited by 4,310
- one_mulproof · cited by 2,841
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.diststatement and proof · cited by 1,539
- LipschitzWithstatement · cited by 316
- LipschitzWith.of_le_add_mulproof · cited by 4
Cited by7
Results whose statement or proof uses this declaration.
- lipschitzWith_maxproof · cited by 3
- LipschitzWith.dist_rightproof · cited by 3
- Metric.lipschitz_infDist_ptproof · cited by 2
- lipschitzWith_minproof · cited by 2
- Metric.lipschitz_infDist_setproof · cited by 1
- Metric.lipschitz_infNndist_ptproof · cited by 1
- MeasureTheory.MeasuredSets.lipschitzWith_measureRealproof · cited by 0