Theorems · Theorem · general topology
Filter.Subsingleton.exists_eq_pure
∀ {α : Type u_1} {l : Filter α} [l.NeBot], l.Subsingleton → ∃ a, l = pure aA nontrivial subsingleton filter is equal to pure a for some a.
- Defined in
- Mathlib.Order.Filter.Subsingleton
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Filter.NeBot
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Filterstatement and proof · cited by 8,121
- Filter.NeBotstatement and proof · cited by 853
- Set.Subsingletonproof · cited by 276
- Filter.nonempty_of_memproof · cited by 36
- Filter.Subsingletonstatement and proof · cited by 15
- Filter.le_pure_iffproof · cited by 11
- Set.exists_eq_singleton_iff_nonempty_subsingletonproof · cited by 9
- Filter.NeBot.le_pure_iffproof · cited by 9
Cited by1
Results whose statement or proof uses this declaration.
- Filter.subsingleton_iff_bot_or_pureproof · cited by 1