Mathlib Map

Theorems · Theorem · general topology

dist_pair_smul

∀ {α : Type u_1} {β : Type u_2} [inst : PseudoMetricSpace α] [inst_1 : PseudoMetricSpace β] [inst_2 : Zero α]
  [inst_3 : Zero β] [inst_4 : SMul α β] [IsBoundedSMul α β] (x₁ x₂ : α) (y : β),
  dist (x₁ • y) (x₂ • y) ≤ dist x₁ x₂ * dist y 0
Defined in
Mathlib.Topology.MetricSpace.Algebra
Cited by
4 results in Mathlib
Foundations
Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
PseudoMetricSpacePseudoMetricSpaceZeroZeroSMulIsBoundedSMul
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

AbsolutelyContinuousOnInterval.smul · cited by 2AbsolutelyContinuousOnInt…PiLp.isBoundedSMulSeminormedAddCommGroupToPi · cited by 1PiLp.isBoundedSMulSeminor…Bornology.IsBounded.uniformContinuousOn_smul · cited by 1IsBounded.uniformContinuo…WithLp.isBoundedSMulSeminormedAddCommGroupToProd · cited by 0WithLp.isBoundedSMulSemin…Real · cited by 25697RealPseudoMetricSpace · cited by 1550PseudoMetricSpaceDist.dist · cited by 1539Dist.distIsBoundedSMul · cited by 329IsBoundedSMulIsBoundedSMul.dist_pair_smul' · cited by 1IsBoundedSMul.dist_pair_s…dist_pair_smulCITED BYCITES

Cites5

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.