Theorems · Theorem · general topology
Filter.iInf_sets_eq_finite
∀ {α : Type u} {ι : Type u_2} (f : ι → Filter α), (⨅ i, f i).sets = ⋃ t, (⨅ i ∈ t, f i).sets- Defined in
- Mathlib.Order.Filter.Finite
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 59 from the axioms · uses propext, Classical.choice, Quot.sound
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
- Finsetstatement and proof · cited by 13,712
- Filterstatement and proof · cited by 8,121
- Set.iUnionstatement and proof · cited by 2,483
- iInfstatement and proof · cited by 1,690
- Filter.setsstatement and proof · cited by 56
- directed_of_isDirected_leproof · cited by 8
- biInf_monoproof · cited by 8
- iInf_eq_iInf_finsetproof · cited by 3
- Filter.iInf_sets_eqproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Filter.mem_iInf_finiteproof · cited by 2
- Filter.iInf_sets_eq_finite'proof · cited by 1