Theorems · Theorem · general topology
LipschitzWith.mk_one
∀ {α : Type u} {β : Type v} [inst : PseudoMetricSpace α] [inst_1 : PseudoMetricSpace β] {f : α → β},
(∀ (x y : α), dist (f x) (f y) ≤ dist x y) → LipschitzWith 1 f- Defined in
- Mathlib.Topology.MetricSpace.Lipschitz
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 150 from the axioms · uses propext, Classical.choice, Quot.sound
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 · 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_dist_le_mulproof · cited by 13
Cited by6
Results whose statement or proof uses this declaration.
- PiNat.exists_lipschitz_retraction_of_isClosedproof · cited by 2
- BoundedContinuousFunction.lipschitz_compContinuousproof · cited by 2
- BoundedContinuousFunction.lipschitz_eval_constproof · cited by 1
- LipschitzWith.dist_leftproof · cited by 1
- GromovHausdorff.toGHSpace_lipschitzproof · cited by 1
- lp.lipschitzWith_one_evalproof · cited by 1