Theorems · Theorem · general topology
Filter.nonempty_of_neBot
∀ {α : Type u} (f : Filter α) [f.NeBot], Nonempty α- Defined in
- Mathlib.Order.Filter.Basic
- Cited by
- 6 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.
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
- Filter.NeBotstatement and proof · cited by 853
- Filter.univ_memproof · cited by 96
- Filter.nonempty_of_memproof · cited by 36
Cited by6
Results whose statement or proof uses this declaration.
- Filter.atTop_neBot_iffproof · cited by 9
- Monotone.ciSup_comp_tendsto_atTopproof · cited by 4
- CauchySeq.nonemptyproof · cited by 1
- Cardinal.mk_of_countable_eventually_memproof · cited by 1
- iSup_eq_of_forall_le_of_tendstoproof · cited by 1
- Filter.atBot_neBot_iffproof · cited by 0