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Theorems · Theorem · general topology

Metric.packingNumber_le_encard_self

∀ {X : Type u_1} [inst : PseudoEMetricSpace X] {ε : NNReal} (A : Set X), Metric.packingNumber ε A ≤ A.encard
Defined in
Mathlib.Topology.MetricSpace.CoveringNumbers
Cited by
2 results in Mathlib
Foundations
Depth 149 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.

Metric.packingNumber_singleton · cited by 0Metric.packingNumber_sing…Metric.packingNumber_zero · cited by 0Metric.packingNumber_zeroSet · cited by 53352SetENat · cited by 4985ENatNNReal · cited by 4310NNRealPseudoEMetricSpace · cited by 1536PseudoEMetricSpaceENNReal.ofNNReal · cited by 1279ENNReal.ofNNRealSet.encard · cited by 327Set.encardMetric.IsSeparated · cited by 28Metric.IsSeparatedMetric.packingNumber · cited by 14Metric.packingNumberSet.encard_le_encard · cited by 10Set.encard_le_encardMetric.packingNumber_le_encar…CITED BYCITES

Cites9

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.