Theorems · Theorem · general topology
Filter.HasBasis.mem_of_mem
∀ {α : Type u_1} {ι : Sort u_4} {l : Filter α} {p : ι → Prop} {s : ι → Set α} {i : ι}, l.HasBasis p s → p i → s i ∈ l- Defined in
- Mathlib.Order.Filter.Bases.Basic
- Cited by
- 63 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses no axioms
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.HasBasisstatement and proof · cited by 604
- Set.Subset.rflproof · cited by 255
- Filter.HasBasis.mem_of_supersetproof · cited by 1
Cited by63
Results whose statement or proof uses this declaration.
- Filter.HasBasis.ge_iffproof · cited by 28
- Filter.HasBasis.prod_selfproof · cited by 19
- Filter.HasBasis.forall_iffproof · cited by 15
- IsCompact.compl_mem_cocompactproof · cited by 13
- Filter.HasBasis.exists_iffproof · cited by 12
- UniformFun.hasBasis_uniformity_of_basisproof · cited by 8
- Filter.HasBasis.exists_antitone_subbasisproof · cited by 8
- Filter.HasBasis.restrict_subsetproof · cited by 7
- Filter.HasAntitoneBasis.memproof · cited by 6
- TopologicalSpace.IsTopologicalBasis.of_hasBasis_nhdsproof · cited by 6
- Filter.HasBasis.iInf'proof · cited by 5
- balancedCore_mem_nhds_zeroproof · cited by 4