Theorems · Theorem · general topology
Metric.AreSeparated.finite_iUnion_left_iff
∀ {X : Type u_1} [inst : PseudoEMetricSpace X] {ι : Type u_3} {I : Set ι},
I.Finite → ∀ {s : ι → Set X} {t : Set X}, Metric.AreSeparated (⋃ i ∈ I, s i) t ↔ ∀ i ∈ I, Metric.AreSeparated (s i) t- Cited by
- 3 results in Mathlib
- Foundations
- Depth 152 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.
Cites12
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
- Set.iUnionstatement and proof · cited by 2,483
- Set.Finitestatement and proof · cited by 1,814
- PseudoEMetricSpacestatement and proof · cited by 1,536
- Set.iUnion_congr_Propproof · cited by 374
- Set.iUnion_emptyproof · cited by 68
- Set.iUnion_of_emptyproof · cited by 68
- Set.Finite.induction_onproof · cited by 39
- Metric.AreSeparatedstatement and proof · cited by 23
- Set.biUnion_insertproof · cited by 13
- Set.forall_mem_insertproof · cited by 4
- Metric.AreSeparated.union_left_iffproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- Metric.AreSeparated.finite_iUnion_right_iffproof · cited by 1
- Metric.AreSeparated.finset_iUnion_left_iffproof · cited by 1
- Metric.AreSeparated.finite_iUnion_leftproof · cited by 0