Theorems · Theorem · general topology
Real.diam_eq
∀ {s : Set ℝ}, Bornology.IsBounded s → Metric.diam s = sSup s - sInf sFor a bounded set s : Set ℝ, its Metric.diam is equal to sSup s - sInf s.
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- Foundations
- Depth 157 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites14
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
- ENNRealproof · cited by 9,879
- SupSet.sSupstatement and proof · cited by 954
- InfSet.sInfstatement and proof · cited by 935
- ENNReal.toRealproof · cited by 859
- Bornology.IsBoundedstatement and proof · cited by 293
- sub_nonnegproof · cited by 167
- ENNReal.toReal_ofRealproof · cited by 82
- Metric.diamstatement · cited by 74
- Bornology.IsBounded.bddBelowproof · cited by 9
- Bornology.IsBounded.bddAboveproof · cited by 7
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