Theorems · Theorem · general topology
Set.PairwiseDisjoint.exists_mem_filter
∀ {α : Type u} {ι : Type u_2} {l : ι → Filter α} {t : Set ι},
t.PairwiseDisjoint l → t.Finite → ∃ s, (∀ (i : ι), s i ∈ l i) ∧ t.PairwiseDisjoint s- Defined in
- Mathlib.Order.Filter.Finite
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- Filterstatement and proof · cited by 8,121
- Set.Elemproof · cited by 7,166
- Finiteproof · cited by 3,029
- Disjointproof · cited by 2,201
- Set.Finitestatement and proof · cited by 1,814
- Function.onFunproof · cited by 570
- Pairwiseproof · cited by 516
- Set.PairwiseDisjointstatement and proof · cited by 275
- Set.Finite.to_subtypeproof · cited by 44
- Pairwise.set_of_subtypeproof · cited by 4
- Set.Pairwise.subtypeproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Set.PairwiseDisjoint.exists_mem_filter_basisproof · cited by 1