Theorems · Theorem · general topology
Filter.disjoint_principal_left
∀ {α : Type u_1} {f : Filter α} {s : Set α}, Disjoint (Filter.principal s) f ↔ sᶜ ∈ f- Defined in
- Mathlib.Order.Filter.Bases.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 72 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 and proof · cited by 2,925
- Disjointstatement · cited by 2,201
- Filter.principalstatement · cited by 740
- disjoint_commproof · cited by 49
- Filter.disjoint_principal_rightproof · cited by 10
Cited by4
Results whose statement or proof uses this declaration.
- disjoint_principal_nhdsSetproof · cited by 2
- Topology.IsInducing.sumElimproof · cited by 2
- existsUnique_eq_principal_sup_freeproof · cited by 1
- Filter.disjoint_principal_principalproof · cited by 1