Theorems · Theorem · general topology
Filter.neBot_iff
∀ {α : Type u_1} {f : Filter α}, f.NeBot ↔ f ≠ ⊥- Defined in
- Mathlib.Order.Filter.Defs
- Cited by
- 27 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, 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
- Filter.NeBotstatement and proof · cited by 853
- Filter.NeBot.ne'proof · cited by 7
Cited by27
Results whose statement or proof uses this declaration.
- Filter.frequently_iff_neBotproof · cited by 7
- leftLim_eq_of_tendstoproof · cited by 5
- tendsto_leftLim_of_tendstoproof · cited by 5
- Filter.not_neBotproof · cited by 4
- Filter.HasBasis.eq_bot_iffproof · cited by 4
- Filter.mem_iff_inf_principal_complproof · cited by 4
- MeasureTheory.exists_decomposition_of_monotoneOn_hasDerivWithinAtproof · cited by 3
- MeasureTheory.Filtration.rightCont_eq_of_nhdsGT_eq_botproof · cited by 3
- MeasureTheory.ae_neBotproof · cited by 3
- mem_closure_iff_nhds_ne_botproof · cited by 2
- hasSum_botproof · cited by 2
- Filter.comap_eq_bot_iff_compl_rangeproof · cited by 2