Theorems · Theorem · order theory
Filter.limsSup_principal_eq_csSup
∀ {α : Type u_1} [inst : ConditionallyCompleteLattice α] {s : Set α},
BddAbove s → s.Nonempty → (Filter.principal s).limsSup = sSup s- Defined in
- Mathlib.Order.LiminfLimsup
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses propext, Quot.sound
- Assumes
- ConditionallyCompleteLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Set.ofPredproof · cited by 6,101
- Set.Nonemptystatement and proof · cited by 2,627
- SupSet.sSupstatement and proof · cited by 954
- InfSet.sInfproof · cited by 935
- Filter.principalstatement · cited by 740
- BddAbovestatement and proof · cited by 620
- ConditionallyCompleteLatticestatement and proof · cited by 364
- Filter.limsSupstatement · cited by 29
- csInf_upperBounds_eq_csSupproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Filter.limsup_top_eq_ciSupproof · cited by 1
- Filter.limsInf_principal_eq_csSupproof · cited by 1