Theorems · Theorem · general topology
FilterBasis.mem_filter_of_mem
∀ {α : Type u_1} (B : FilterBasis α) {U : Set α}, U ∈ B → U ∈ B.filter- Defined in
- Mathlib.Order.Filter.Bases.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, 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 · cited by 8,121
- Set.Subset.reflproof · cited by 66
- FilterBasisstatement and proof · cited by 23
- FilterBasis.filterstatement · cited by 19
Cited by4
Results whose statement or proof uses this declaration.
- FilterBasis.generateproof · cited by 4
- GroupFilterBasis.nhds_eqproof · cited by 3
- AddGroupFilterBasis.nhds_eqproof · cited by 3
- withSeminorms_iff_mem_nhds_isVonNBoundedproof · cited by 1