Theorems · Theorem · general topology
Filter.subsingleton_iff_exists_singleton_mem
∀ {α : Type u_1} {l : Filter α} [Nonempty α], l.Subsingleton ↔ ∃ a, {a} ∈ l- Defined in
- Mathlib.Order.Filter.Subsingleton
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Nonempty
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 · cited by 53,352
- Filterstatement and proof · cited by 8,121
- Filter.Subsingletonstatement · cited by 15
Cited by1
Results whose statement or proof uses this declaration.
- Filter.eventuallyConst_iff_exists_eventuallyEqproof · cited by 3