Theorems · Definition · order theory
Filter.limsInf
{α : Type u_1} → [ConditionallyCompleteLattice α] → Filter α → αThe limsInf of a filter f is the supremum of the a such that the inequality
x ≥ a eventually holds for f.
- Defined in
- Mathlib.Order.LiminfLimsup
- Cited by
- 31 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses no axioms
- Assumes
- ConditionallyCompleteLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- Set.ofPredproof · cited by 6,101
- Filter.Eventuallyproof · cited by 3,134
- SupSet.sSupproof · cited by 954
- ConditionallyCompleteLatticestatement and proof · cited by 364
Cited by32
Results whose statement or proof uses this declaration.
- Filter.liminfproof · cited by 198
- Monotone.map_limsInf_of_continuousAtstatement and proof · cited by 5
- Filter.liminf_botproof · cited by 4
- Antitone.map_limsInf_of_continuousAtstatement and proof · cited by 3
- limsInf_eq_of_le_nhdsstatement · cited by 2
- ClusterPt.limsInfstatement · cited by 2
- Filter.limsInf_le_limsInf_of_lestatement · cited by 2
- Filter.limsInf_le_limsSupstatement · cited by 2
- Filter.gt_mem_sets_of_limsInf_gtstatement · cited by 2
- Filter.le_limsInf_of_lestatement · cited by 2
- limsInf_nhdsstatement · cited by 1
- Filter.liminf_nat_addproof · cited by 1