Theorems · Theorem · general topology
Filter.le_principal_iff
∀ {α : Type u} {s : Set α} {f : Filter α}, f ≤ Filter.principal s ↔ s ∈ f- Defined in
- Mathlib.Order.Filter.Basic
- Cited by
- 87 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- Filter.principalstatement and proof · cited by 740
- Filter.mem_of_supersetproof · cited by 308
- Set.Subset.rflproof · cited by 255
Cited by87
Results whose statement or proof uses this declaration.
- isOpen_iff_mem_nhdsproof · cited by 48
- IsCompact.inter_rightproof · cited by 30
- IsCompact.image_of_continuousOnproof · cited by 24
- isCompact_emptyproof · cited by 17
- Filter.mem_lift'proof · cited by 15
- TopologicalSpace.IsTopologicalBasis.mem_nhds_iffproof · cited by 13
- Set.EqOn.eventuallyEq_of_memproof · cited by 12
- Filter.le_pure_iffproof · cited by 11
- Set.Finite.isCompact_biUnionproof · cited by 11
- Filter.map_comapproof · cited by 10
- Filter.map_comap_of_memproof · cited by 9
- pure_le_nhdsWithinproof · cited by 9