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Theorems · Theorem · general topology

Metric.ediam_eball_le

∀ {X : Type u_2} {x : X} [inst : PseudoEMetricSpace X] {r : ENNReal}, Metric.ediam (Metric.eball x r) ≤ 2 * r
Defined in
Mathlib.Topology.EMetricSpace.Diam
Cited by
2 results in Mathlib
Foundations
Depth 152 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
PseudoEMetricSpace
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

ContinuousWithinAt.oscillationWithin_eq_zero · cited by 2ContinuousWithinAt.oscill…EMetric.diam_ball · cited by 0EMetric.diam_ballENNReal · cited by 9879ENNRealPseudoEMetricSpace · cited by 1536PseudoEMetricSpacele_trans · cited by 985le_transMetric.eball · cited by 294Metric.eballMetric.ediam · cited by 159Metric.ediamMetric.ediam_mono · cited by 14Metric.ediam_monoMetric.eball_subset_closedEBall · cited by 5Metric.eball_subset_close…Metric.ediam_closedEBall_le · cited by 2Metric.ediam_closedEBall_…Metric.ediam_eball_leCITED BYCITES

Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.