Theorems · Theorem · general topology
Metric.ediam_union_le_add_edist
∀ {X : Type u_2} {s t : Set X} {x y : X} [inst : PseudoEMetricSpace X],
x ∈ s → y ∈ t → Metric.ediam (s ∪ t) ≤ Metric.ediam s + edist x y + Metric.ediam tThe extended diameter of a union is controlled by the diameter of the sets, and the edistance between two points in the sets.
- Defined in
- Mathlib.Topology.EMetricSpace.Diam
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 151 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.
Cites15
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
- le_reflproof · cited by 2,061
- PseudoEMetricSpacestatement and proof · cited by 1,536
- add_assocproof · cited by 746
- EDist.ediststatement and proof · cited by 735
- add_le_addproof · cited by 666
- Metric.ediamstatement and proof · cited by 159
- le_self_addproof · cited by 68
- PseudoEMetricSpace.edist_commproof · cited by 52
- le_add_selfproof · cited by 51
- Set.mem_unionproof · cited by 47
Cited by3
Results whose statement or proof uses this declaration.
- Metric.diam_unionproof · cited by 2
- Metric.ediam_union_leproof · cited by 1
- EMetric.diam_unionproof · cited by 0