Theorems · Theorem · general topology
Metric.hausdorffEDist_iUnion_le
∀ {α : Type u} [inst : PseudoEMetricSpace α] {ι : Sort u_2} {s t : ι → Set α},
Metric.hausdorffEDist (⋃ i, s i) (⋃ i, t i) ≤ ⨆ i, Metric.hausdorffEDist (s i) (t i)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 153 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.
Cites17
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
- ENNRealstatement · cited by 9,879
- LE.le.transproof · cited by 3,151
- Set.iUnionstatement and proof · cited by 2,483
- iSupstatement and proof · cited by 2,415
- le_rflproof · cited by 1,558
- PseudoEMetricSpacestatement and proof · cited by 1,536
- Metric.infEDistproof · cited by 147
- iInf_leproof · cited by 104
- le_iSup_of_leproof · cited by 79
- Metric.hausdorffEDiststatement · cited by 76
- le_iSup₂_of_leproof · cited by 52
Cited by2
Results whose statement or proof uses this declaration.
- Metric.hausdorffEDist_union_leproof · cited by 4
- EMetric.hausdorffEdist_iUnion_leproof · cited by 0