Theorems · Theorem · general topology
Filter.mem_pure
∀ {α : Type u_1} {a : α} {s : Set α}, s ∈ pure a ↔ a ∈ s- Defined in
- Mathlib.Order.Filter.Defs
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Cited by14
Results whose statement or proof uses this declaration.
- pure_le_nhdsproof · cited by 39
- TopologicalSpace.isClosed_range_singletonproof · cited by 2
- Filter.mem_zeroproof · cited by 2
- Filter.mem_traverseproof · cited by 2
- Filter.mem_oneproof · cited by 2
- Filter.zero_mem_zeroproof · cited by 2
- Filter.disjoint_pure_atBotproof · cited by 1
- Filter.disjoint_pure_atTopproof · cited by 1
- Filter.one_mem_oneproof · cited by 1
- Hindman.exists_idempotent_ultrafilter_le_FPproof · cited by 1
- Hindman.exists_idempotent_ultrafilter_le_FSproof · cited by 1
- exists_Icc_mem_subset_of_mem_nhdsLEproof · cited by 1