Theorems · Theorem · general topology
Filter.NeBot.le_pure_iff
∀ {α : Type u} {f : Filter α} {a : α}, f.NeBot → (f ≤ pure a ↔ f = pure a)- Defined in
- Mathlib.Order.Filter.Ultrafilter.Defs
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Filterstatement and proof · cited by 8,121
- Filter.NeBotstatement and proof · cited by 853
- le_of_eqproof · cited by 366
- Ultrafilter.toFilterproof · cited by 172
- Ultrafilter.uniqueproof · cited by 5
Cited by9
Results whose statement or proof uses this declaration.
- Filter.subsingleton_iff_exists_le_pureproof · cited by 2
- Filter.add_eq_zero_iffproof · cited by 1
- DiscreteUniformity.eq_pure_of_cauchyproof · cited by 1
- Ultrafilter.eq_of_le_pureproof · cited by 1
- Filter.Subsingleton.exists_eq_pureproof · cited by 1
- Filter.mul_eq_one_iffproof · cited by 1
- Filter.NeBot.nonpos_iffproof · cited by 0
- Filter.NeBot.eq_pure_iffproof · cited by 0
- Filter.NeBot.le_one_iffproof · cited by 0