Theorems · Theorem · general topology
Set.le_einfsep_of_forall_dist_le
∀ {α : Type u_1} [inst : PseudoMetricSpace α] {s : Set α} {d : ℝ},
(∀ x ∈ s, ∀ y ∈ s, x ≠ y → d ≤ dist x y) → ENNReal.ofReal d ≤ s.einfsep- Defined in
- Mathlib.Topology.MetricSpace.Infsep
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 147 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoMetricSpace
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Cites10
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
- Realstatement and proof · cited by 25,697
- ENNRealstatement · cited by 9,879
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.diststatement and proof · cited by 1,539
- ENNReal.ofRealstatement · cited by 863
- ENNReal.ofReal_le_ofRealproof · cited by 61
- Set.einfsepstatement · cited by 47
- edist_distproof · cited by 39
- Set.le_einfsepproof · cited by 3
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