Theorems · Theorem · general topology
Filter.eq_or_neBot
∀ {α : Type u} (f : Filter α), f = ⊥ ∨ f.NeBotEither f = ⊥ or Filter.NeBot f. This is a version of eq_or_ne that uses Filter.NeBot
as the second alternative, to be used as an instance.
- Defined in
- Mathlib.Order.Filter.Basic
- Cited by
- 62 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- Bot.botstatement and proof · cited by 4,720
- eq_or_neproof · cited by 1,117
- Filter.NeBotstatement · cited by 853
Cited by62
Results whose statement or proof uses this declaration.
- Monotone.leftLim_leproof · cited by 13
- Monotone.le_leftLimproof · cited by 9
- Filter.Tendsto.of_neBot_impproof · cited by 8
- tendsto_of_le_liminf_of_limsup_leproof · cited by 7
- tendsto_leftLim_of_tendstoproof · cited by 5
- Monotone.continuousWithinAt_Iio_iff_leftLim_eqproof · cited by 4
- MeasureTheory.measurableSet_exists_tendstoproof · cited by 4
- Monotone.tendstoLocallyUniformly_of_forall_tendstoproof · cited by 4
- ContinuousWithinAt.leftLim_eqproof · cited by 4
- Convex.sdiff_singleton_eventually_mem_nhdsproof · cited by 3
- MeasureTheory.StronglyMeasurable.measurableSet_exists_tendstoproof · cited by 3
- mapClusterPt_leftLimproof · cited by 3