Theorems · Theorem · general topology
Metric.hausdorffEDist_union_le
∀ {α : Type u} [inst : PseudoEMetricSpace α] {s₁ s₂ t₁ t₂ : Set α},
Metric.hausdorffEDist (s₁ ∪ s₂) (t₁ ∪ t₂) ≤ max (Metric.hausdorffEDist s₁ t₁) (Metric.hausdorffEDist s₂ t₂)- Cited by
- 4 results in Mathlib
- Foundations
- Depth 154 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.
Cites10
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 and proof · cited by 9,879
- Set.iUnionproof · cited by 2,483
- iSupproof · cited by 2,415
- PseudoEMetricSpacestatement and proof · cited by 1,536
- SupSetproof · cited by 154
- Metric.hausdorffEDiststatement and proof · cited by 76
- Set.union_eq_iUnionproof · cited by 28
- sup_eq_iSupproof · cited by 7
- Metric.hausdorffEDist_iUnion_leproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- TopologicalSpace.NonemptyCompacts.lipschitz_supproof · cited by 1
- TopologicalSpace.Closeds.lipschitz_supproof · cited by 1
- TopologicalSpace.Compacts.lipschitz_supproof · cited by 0
- EMetric.hausdorffEdist_union_leproof · cited by 0