Theorems · Theorem · functional analysis
Metric.diam_ball_eq
∀ {E : Type u_6} [inst : NormedAddCommGroup E] [NormedSpace ℝ E] [Nontrivial E] (x : E) {r : ℝ},
0 ≤ r → Metric.diam (Metric.ball x r) = 2 * r- Defined in
- Mathlib.Analysis.Normed.Module.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 158 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- Nontrivialstatement and proof · cited by 2,416
- le_antisymmproof · cited by 2,068
- le_of_ltproof · cited by 1,175
- Metric.ballstatement and proof · cited by 735
- mul_le_mul_of_nonneg_rightproof · cited by 301
- Metric.diamstatement and proof · cited by 74
- Metric.isBounded_ballproof · cited by 15
- Metric.diam_monoproof · cited by 7
- Metric.diam_nonnegproof · cited by 5
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