Theorems · Theorem · general topology
Filter.Subsingleton.exists_le_pure
∀ {α : Type u_1} {l : Filter α} [Nonempty α], l.Subsingleton → ∃ a, l ≤ pure aA subsingleton filter on a nonempty type is less than or equal to pure a for some a.
- Defined in
- Mathlib.Order.Filter.Subsingleton
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Nonempty
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- Filterstatement and proof · cited by 8,121
- Filter.Subsingletonstatement · cited by 15
- Filter.subsingleton_iff_exists_le_pureproof · cited by 2
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