Theorems · Theorem · general topology
EMetric.infEdist_le_edist_of_mem
Deprecated since 2026-01-08Use Metric.infEDist_le_edist_of_mem instead.
∀ {α : Type u} [inst : PseudoEMetricSpace α] {x y : α} {s : Set α}, y ∈ s → Metric.infEDist x s ≤ edist x yAlias of Metric.infEDist_le_edist_of_mem.
The edist to a set is bounded above by the edist to any of its points
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 149 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoEMetricSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- ENNRealstatement · cited by 9,879
- PseudoEMetricSpacestatement · cited by 1,536
- EDist.ediststatement · cited by 735
- Metric.infEDiststatement · cited by 147
- Metric.infEDist_le_edist_of_memproof · cited by 13
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.