Theorems · Theorem · general topology
Metric.AreSeparated.finset_iUnion_right
∀ {X : Type u_1} [inst : PseudoEMetricSpace X] {ι : Type u_3} {I : Finset ι} {s : Set X} {t : ι → Set X},
(∀ i ∈ I, Metric.AreSeparated s (t i)) → Metric.AreSeparated s (⋃ i ∈ I, t i)Alias of the reverse direction of Metric.AreSeparated.finset_iUnion_right_iff.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 155 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoEMetricSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Finsetstatement and proof · cited by 13,712
- Set.iUnionstatement · cited by 2,483
- PseudoEMetricSpacestatement and proof · cited by 1,536
- Metric.AreSeparatedstatement · cited by 23
- Metric.AreSeparated.finset_iUnion_right_iffproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.OuterMeasure.IsMetric.finset_iUnion_of_pairwise_separatedproof · cited by 1