Theorems · Theorem · general topology
Metric.diam_le_of_subset_closedBall
∀ {α : Type u} {s : Set α} {x : α} [inst : PseudoMetricSpace α] {r : ℝ},
0 ≤ r → s ⊆ Metric.closedBall x r → Metric.diam s ≤ 2 * r- Defined in
- Mathlib.Topology.MetricSpace.Bounded
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 152 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoMetricSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- mul_commproof · cited by 2,262
- PseudoMetricSpacestatement and proof · cited by 1,550
- Metric.closedBallstatement and proof · cited by 704
- add_le_addproof · cited by 666
- mul_nonnegproof · cited by 397
- Metric.diamstatement · cited by 74
- zero_le_twoproof · cited by 44
- mul_twoproof · cited by 43
- dist_triangle_rightproof · cited by 16
- Metric.diam_le_of_forall_dist_leproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- Metric.diam_closedBallproof · cited by 4
- Metric.diam_ballproof · cited by 3