Theorems · Theorem · general topology
Metric.diam_pos
∀ {α : Type u} {s : Set α} [inst : MetricSpace α], s.Nontrivial → Bornology.IsBounded s → 0 < Metric.diam s- Defined in
- Mathlib.Topology.MetricSpace.Bounded
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 155 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MetricSpace
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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
- Realstatement · cited by 25,697
- MetricSpacestatement and proof · cited by 1,684
- LT.lt.trans_leproof · cited by 678
- Bornology.IsBoundedstatement and proof · cited by 293
- Set.Nontrivialstatement and proof · cited by 145
- Metric.diamstatement · cited by 74
- Metric.dist_le_diam_of_memproof · cited by 14
- dist_posproof · cited by 12
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