Theorems · Theorem · general topology
Metric.edist_le_ediam_of_mem
∀ {X : Type u_2} {s : Set X} {x y : X} [inst : PseudoEMetricSpace X], x ∈ s → y ∈ s → edist x y ≤ Metric.ediam sIf two points belong to some set, their edistance is bounded by the diameter of the set
- Defined in
- Mathlib.Topology.EMetricSpace.Diam
- Cited by
- 20 results in Mathlib
- Foundations
- Depth 150 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- ENNRealstatement · cited by 9,879
- le_rflproof · cited by 1,558
- PseudoEMetricSpacestatement and proof · cited by 1,536
- EDist.ediststatement · cited by 735
- Metric.ediamstatement · cited by 159
- Metric.edist_le_of_ediam_leproof · cited by 2
Cited by20
Results whose statement or proof uses this declaration.
- Metric.ediam_monoproof · cited by 14
- Metric.ediam_closureproof · cited by 5
- LipschitzWith.ediam_image_leproof · cited by 4
- Metric.ediam_union_le_add_edistproof · cited by 3
- Metric.edist_le_infEDist_add_ediamproof · cited by 3
- LipschitzOnWith.ediam_image2_leproof · cited by 3
- AntilipschitzWith.ediam_preimage_leproof · cited by 3
- convexHull_ediamproof · cited by 2
- CantorScheme.VanishingDiam.dist_ltproof · cited by 2
- Metric.dist_le_diam_of_mem'proof · cited by 2
- HolderOnWith.ediam_image_le_of_leproof · cited by 2
- BoxIntegral.integrable_of_bounded_and_ae_continuousWithinAtproof · cited by 2