Theorems · Theorem · general topology
Set.einfsep_insert
∀ {α : Type u_1} [inst : PseudoEMetricSpace α] {x : α} {s : Set α},
(insert x s).einfsep = min (⨅ y ∈ s, ⨅ (_ : x ≠ y), edist x y) s.einfsep- Defined in
- Mathlib.Topology.MetricSpace.Infsep
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 147 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_antisymmproof · cited by 2,068
- iInfstatement and proof · cited by 1,690
- PseudoEMetricSpacestatement and proof · cited by 1,536
- EDist.ediststatement and proof · cited by 735
- Set.subset_insertproof · cited by 96
- iInf_le_of_leproof · cited by 62
- PseudoEMetricSpace.edist_commproof · cited by 52
- Set.einfsepstatement and proof · cited by 47
- iInf₂_leproof · cited by 45
- le_minproof · cited by 21
Cited by1
Results whose statement or proof uses this declaration.
- Set.einfsep_tripleproof · cited by 1