Theorems · Theorem · general topology
Metric.lipschitz_infDist_set
∀ {α : Type u_1} [inst : MetricSpace α] (x : α), LipschitzWith 1 fun s => Metric.infDist x ↑s- Defined in
- Mathlib.Topology.MetricSpace.Closeds
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 163 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MetricSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- SetLike.coestatement and proof · cited by 8,199
- NNRealstatement · cited by 4,310
- MetricSpacestatement and proof · cited by 1,684
- LipschitzWithstatement · cited by 316
- dist_commproof · cited by 188
- TopologicalSpace.NonemptyCompactsstatement and proof · cited by 137
- Metric.infDiststatement and proof · cited by 68
- edist_ne_topproof · cited by 17
- LipschitzWith.of_le_addproof · cited by 7
- Metric.infDist_le_infDist_add_hausdorffDistproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Metric.lipschitz_infDistproof · cited by 1