Theorems · Theorem · general topology
Filter.HasBasis.neBot_iff
∀ {α : Type u_1} {ι : Sort u_4} {l : Filter α} {p : ι → Prop} {s : ι → Set α},
l.HasBasis p s → (l.NeBot ↔ ∀ {i : ι}, p i → (s i).Nonempty)- Defined in
- Mathlib.Order.Filter.Bases.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 54 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Filterstatement and proof · cited by 8,121
- Set.Nonemptystatement · cited by 2,627
- Filter.NeBotstatement · cited by 853
- Filter.HasBasisstatement and proof · cited by 604
- Set.Nonempty.monoproof · cited by 88
- Filter.HasBasis.forall_iffproof · cited by 15
- Filter.forall_mem_nonempty_iff_neBotproof · cited by 4
Cited by5
Results whose statement or proof uses this declaration.
- Filter.HasBasis.eq_bot_iffproof · cited by 4
- Filter.HasBasis.inf_basis_neBot_iffproof · cited by 3
- Filter.HasBasis.inf_principal_neBot_iffproof · cited by 2
- Filter.generate_neBot_iffproof · cited by 0
- BoxIntegral.IntegrationParams.toFilterDistortioniUnion_neBotproof · cited by 0