Theorems · Theorem · general topology
EMetric.diam_pi_le_of_le
Deprecated since 2026-01-04Use Metric.ediam_pi_le_of_le instead.
∀ {ι : Type u_3} {X : ι → Type u_4} [inst : Fintype ι] [inst_1 : (i : ι) → PseudoEMetricSpace (X i)]
{s : (i : ι) → Set (X i)} {c : ENNReal}, (∀ (b : ι), Metric.ediam (s b) ≤ c) → Metric.ediam (Set.univ.pi s) ≤ cAlias of Metric.ediam_pi_le_of_le.
- Defined in
- Mathlib.Topology.EMetricSpace.Diam
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 151 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FintypePseudoEMetricSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- ENNRealstatement · cited by 9,879
- Fintypestatement · cited by 7,736
- Set.univstatement · cited by 3,945
- PseudoEMetricSpacestatement · cited by 1,536
- Set.pistatement · cited by 405
- Metric.ediamstatement · cited by 159
- Metric.ediam_pi_le_of_leproof · cited by 3
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