Theorems · Theorem · general topology
EMetric.edist_le_of_diam_le
Deprecated since 2026-01-04Use Metric.edist_le_of_ediam_le instead.
∀ {X : Type u_2} {s : Set X} {x y : X} [inst : PseudoEMetricSpace X] {d : ENNReal},
x ∈ s → y ∈ s → Metric.ediam s ≤ d → edist x y ≤ dAlias of Metric.edist_le_of_ediam_le.
- Defined in
- Mathlib.Topology.EMetricSpace.Diam
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 150 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoEMetricSpace
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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.ediamstatement · cited by 159
- Metric.edist_le_of_ediam_leproof · cited by 2
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