Theorems · Theorem · general topology
Metric.ediam_insert
∀ {X : Type u_2} {s : Set X} {x : X} [inst : PseudoEMetricSpace X],
Metric.ediam (insert x s) = max (⨆ y ∈ s, edist x y) (Metric.ediam s)- Defined in
- Mathlib.Topology.EMetricSpace.Diam
- Cited by
- 3 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.
Cites9
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 and proof · cited by 9,879
- iSupstatement · cited by 2,415
- PseudoEMetricSpacestatement and proof · cited by 1,536
- EDist.ediststatement and proof · cited by 735
- Metric.ediamstatement · cited by 159
- eq_of_forall_ge_iffproof · cited by 96
- PseudoEMetricSpace.edist_commproof · cited by 52
- PseudoEMetricSpace.edist_selfproof · cited by 50
Cited by3
Results whose statement or proof uses this declaration.
- Metric.ediam_tripleproof · cited by 2
- Metric.ediam_pairproof · cited by 2
- EMetric.diam_insertproof · cited by 0