Theorems · Theorem · order theory
Filter.HasBasis.limsSup_eq_iInf_sSup
∀ {α : Type u_1} [inst : CompleteLattice α] {ι : Sort u_6} {p : ι → Prop} {s : ι → Set α} {f : Filter α},
f.HasBasis p s → f.limsSup = ⨅ i, ⨅ (_ : p i), sSup (s i)- Defined in
- Mathlib.Order.LiminfLimsup
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses no axioms
- Assumes
- CompleteLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
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.ofPredproof · cited by 6,101
- Filter.Eventuallyproof · cited by 3,134
- le_antisymmproof · cited by 2,068
- iInfstatement and proof · cited by 1,690
- CompleteLatticestatement and proof · cited by 1,048
- SupSet.sSupstatement and proof · cited by 954
- Filter.HasBasisstatement and proof · cited by 604
- sInf_leproof · cited by 110
- le_sSupproof · cited by 79
- le_iInf₂proof · cited by 67
Cited by5
Results whose statement or proof uses this declaration.
- Filter.limsup_eq_iInf_iSup_of_natproof · cited by 5
- Filter.limsup_eq_iInf_iSupproof · cited by 5
- Filter.HasBasis.limsup_eq_iInf_iSupproof · cited by 5
- Filter.limsSup_eq_iInf_sSupproof · cited by 1
- Filter.HasBasis.limsInf_eq_iSup_sInfproof · cited by 0