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Theorems · Theorem · general topology

Prod.edist_eq

∀ {α : Type u} {β : Type v} [inst : PseudoEMetricSpace α] [inst_1 : PseudoEMetricSpace β] (x y : α × β),
  edist x y = max (edist x.1 y.1) (edist x.2 y.2)
Defined in
Mathlib.Topology.EMetricSpace.Defs
Cited by
4 results in Mathlib
Foundations
Depth 131 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
PseudoEMetricSpacePseudoEMetricSpace
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Around this declaration

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

LipschitzWith.prodMk · cited by 4LipschitzWith.prodMkLipschitzOnWith.prodMk · cited by 1LipschitzOnWith.prodMkIsometry.inl · cited by 1Isometry.inlIsometry.inr · cited by 1Isometry.inrENNReal · cited by 9879ENNRealPseudoEMetricSpace · cited by 1536PseudoEMetricSpaceEDist.edist · cited by 735EDist.edistProd.edist_eqCITED BYCITES

Cites3

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

Cited by4

Results whose statement or proof uses this declaration.