Theorems · Theorem · general topology
Filter.inter_mem
∀ {α : Type u_1} {f : Filter α} {s t : Set α}, s ∈ f → t ∈ f → s ∩ t ∈ f- Defined in
- Mathlib.Order.Filter.Defs
- Cited by
- 153 results in Mathlib
- Foundations
- Depth 7 from the axioms, rests on 15 definitions · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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.inter_setsproof · cited by 4
Cited by154
Results whose statement or proof uses this declaration.
- Filter.mp_memproof · cited by 1,537
- Filter.Eventually.andproof · cited by 157
- inter_mem_nhdsWithinproof · cited by 46
- Filter.Ioi_mem_atTopproof · cited by 36
- Filter.HasBasis.prod_selfproof · cited by 19
- ContDiffWithinAt.compproof · cited by 18
- ContMDiffWithinAt.compproof · cited by 18
- ContDiffWithinAt.prodMkproof · cited by 17
- ContDiffWithinAt.congr_of_eventuallyEqproof · cited by 9
- IsMaxFilter.bicomp_monoproof · cited by 8
- IsMinFilter.bicomp_monoproof · cited by 8
- Filter.HasBasis.exists_antitone_subbasisproof · cited by 8