Theorems · Theorem · general topology
Filter.IsBasis.filter_eq_generate
∀ {α : Type u_1} {ι : Sort u_4} {p : ι → Prop} {s : ι → Set α} (h : Filter.IsBasis p s),
h.filter = Filter.generate {U | ∃ i, p i ∧ s i = U}- Defined in
- Mathlib.Order.Filter.Bases.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 64 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
- Filterstatement and proof · cited by 8,121
- Set.ofPredstatement and proof · cited by 6,101
- FilterBasis.setsproof · cited by 42
- Filter.generatestatement and proof · cited by 30
- FilterBasisproof · cited by 23
- Filter.IsBasisstatement and proof · cited by 14
- Filter.IsBasis.filterstatement · cited by 6
- FilterBasis.generateproof · cited by 4
- Filter.IsBasis.filterBasisproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- Filter.HasBasis.eq_generateproof · cited by 1