Theorems · Theorem · general topology
Real.ediam_eq
∀ {s : Set ℝ}, Bornology.IsBounded s → Metric.ediam s = ENNReal.ofReal (sSup s - sInf s)For a bounded set s : Set ℝ, its ediam is equal to sSup s - sInf s reinterpreted as
ℝ≥0∞.
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 156 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites28
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
- Set.Nonemptyproof · cited by 2,627
- le_antisymmproof · cited by 2,068
- sub_selfproof · cited by 996
- SupSet.sSupstatement and proof · cited by 954
- InfSet.sInfstatement and proof · cited by 935
- ENNReal.ofRealstatement and proof · cited by 863
- Bornology.IsBoundedstatement and proof · cited by 293
- Set.eq_empty_or_nonemptyproof · cited by 248
- Metric.ediamstatement · cited by 159
Cited by4
Results whose statement or proof uses this declaration.
- Real.ediam_Iccproof · cited by 5
- Real.ediam_Iooproof · cited by 3
- Real.volume_le_diamproof · cited by 1
- Real.diam_eqproof · cited by 0