Theorems · Theorem · general topology
Filter.exists_mem_subset_iff
∀ {α : Type u} {f : Filter α} {s : Set α}, (∃ t ∈ f, t ⊆ s) ↔ s ∈ f- Defined in
- Mathlib.Order.Filter.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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.mem_of_supersetproof · cited by 308
- Set.Subset.rflproof · cited by 255
Cited by7
Results whose statement or proof uses this declaration.
- Filter.basis_setsproof · cited by 105
- Filter.eventually_iff_exists_memproof · cited by 28
- Filter.mem_prod_principalproof · cited by 3
- codiscreteWithin_iff_locallyEmptyComplementWithinproof · cited by 3
- Filter.mem_bindproof · cited by 1
- Filter.mem_prod_iff_leftproof · cited by 1
- Filter.asBasis_filterproof · cited by 0