Theorems · Theorem · general topology
Filter.HasBasis.disjoint_iff_right
∀ {α : Type u_1} {ι : Sort u_4} {l l' : Filter α} {p : ι → Prop} {s : ι → Set α},
l.HasBasis p s → (Disjoint l' l ↔ ∃ i, p i ∧ (s i)ᶜ ∈ l')- Defined in
- Mathlib.Order.Filter.Bases.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 75 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
- Filterstatement and proof · cited by 8,121
- Compl.complstatement · cited by 2,925
- Disjointstatement · cited by 2,201
- Filter.HasBasisstatement and proof · cited by 604
- disjoint_commproof · cited by 49
- Filter.HasBasis.disjoint_iff_leftproof · cited by 11
Cited by3
Results whose statement or proof uses this declaration.
- regularSpace_TFAEproof · cited by 6
- Filter.disjoint_cocompact_rightproof · cited by 3
- Filter.disjoint_cofinite_leftproof · cited by 1