Theorems · Theorem · general topology
Filter.empty_notMem
∀ {α : Type u} (f : Filter α) [f.NeBot], ∅ ∉ f- Defined in
- Mathlib.Order.Filter.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 53 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.
Cites5
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.NeBotstatement and proof · cited by 853
- Set.Nonempty.ne_emptyproof · cited by 65
- Filter.nonempty_of_memproof · cited by 36
Cited by5
Results whose statement or proof uses this declaration.
- ContinuousAt.eventuallyEq_nhds_iff_eventuallyEq_nhdsNEproof · cited by 6
- Filter.not_bddAbove_of_tendsto_atTopproof · cited by 1
- summable_const_iffproof · cited by 1
- Filter.not_bddBelow_of_tendsto_atBotproof · cited by 1
- Ultrafilter.empty_notMemproof · cited by 0