Theorems · Theorem · general topology
Ultrafilter.finite_sUnion_mem_iff
∀ {α : Type u} {f : Ultrafilter α} {s : Set (Set α)}, s.Finite → (⋃₀ s ∈ f ↔ ∃ t ∈ s, t ∈ f)- Defined in
- Mathlib.Order.Filter.Ultrafilter.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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.Finitestatement and proof · cited by 1,814
- Set.sUnionstatement and proof · cited by 392
- Ultrafilterstatement and proof · cited by 193
- Set.Finite.induction_onproof · cited by 39
- Set.sUnion_emptyproof · cited by 17
- Set.sUnion_insertproof · cited by 11
Cited by5
Results whose statement or proof uses this declaration.
- Ultrafilter.finite_biUnion_mem_iffproof · cited by 3
- Hindman.FP_partition_regularproof · cited by 0
- Hindman.FS_partition_regularproof · cited by 0
- Hindman.exists_FP_of_finite_coverproof · cited by 0
- Hindman.exists_FS_of_finite_coverproof · cited by 0