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Theorems · Theorem · general topology

Metric.AreSeparated.finset_iUnion_right_iff

∀ {X : Type u_1} [inst : PseudoEMetricSpace X] {ι : Type u_3} {I : Finset ι} {s : Set X} {t : ι → Set X},
  Metric.AreSeparated s (⋃ i ∈ I, t i) ↔ ∀ i ∈ I, Metric.AreSeparated s (t i)
Defined in
Mathlib.Topology.MetricSpace.MetricSeparated
Cited by
1 results in Mathlib
Foundations
Depth 154 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
PseudoEMetricSpace
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Around this declaration

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Metric.AreSeparated.finset_iUnion_right · cited by 1AreSeparated.finset_iUnio…Set · cited by 53352SetFinset · cited by 13712FinsetSet.iUnion · cited by 2483Set.iUnionPseudoEMetricSpace · cited by 1536PseudoEMetricSpaceFinset.finite_toSet · cited by 210Finset.finite_toSetMetric.AreSeparated · cited by 23Metric.AreSeparatedMetric.AreSeparated.finite_iUnion_right_iff · cited by 1AreSeparated.finite_iUnio…AreSeparated.finset_iUnion_ri…CITED BYCITES

Cites7

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Cited by1

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