Theorems · Theorem · general topology

Dilation.diam_range

∀ {α : Type u_1} {β : Type u_2} {F : Type u_4} [inst : PseudoMetricSpace α] [inst_1 : PseudoMetricSpace β]
  [inst_2 : FunLike F α β] [inst_3 : DilationClass F α β] (f : F),
  Metric.diam (Set.range ⇑f) = ↑(Dilation.ratio f) * Metric.diam Set.univ

Defined in: Mathlib.Topology.MetricSpace.Dilation
Cited by: 0 results in Mathlib
Foundations: Depth 155 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: PseudoMetricSpace PseudoMetricSpace FunLike DilationClass

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

DFunLike.coestatement · cited by 62,936
Setproof · cited by 53,352
Realstatement and proof · cited by 25,697
Set.rangestatement · cited by 4,705
Set.univstatement and proof · cited by 3,945
FunLikestatement and proof · cited by 2,560
PseudoMetricSpacestatement and proof · cited by 1,550
NNReal.toRealstatement and proof · cited by 1,260
Set.image_univproof · cited by 322
Metric.diamstatement and proof · cited by 74
Dilation.ratiostatement and proof · cited by 43
DilationClassstatement and proof · cited by 41

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