Theorems · Theorem · general topology
Pairwise.exists_mem_filter_of_disjoint
∀ {α : Type u} {ι : Type u_2} [Finite ι] {l : ι → Filter α},
Pairwise (Function.onFun Disjoint l) → ∃ s, (∀ (i : ι), s i ∈ l i) ∧ Pairwise (Function.onFun Disjoint s)- Defined in
- Mathlib.Order.Filter.Finite
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Finite
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- LE.le.transproof · cited by 3,151
- Finitestatement and proof · cited by 3,029
- Disjointstatement and proof · cited by 2,201
- Set.iInterproof · cited by 1,084
- Function.onFunstatement and proof · cited by 570
- Pairwisestatement and proof · cited by 516
- Set.inter_subset_leftproof · cited by 360
- Set.inter_subset_rightproof · cited by 329
- Filter.inter_memproof · cited by 153
- Function.sometimesproof · cited by 86
Cited by2
Results whose statement or proof uses this declaration.
- Set.PairwiseDisjoint.exists_mem_filterproof · cited by 1
- Pairwise.exists_mem_filter_basis_of_disjointproof · cited by 0