Theorems · Theorem · order theory
Filter.iSup_liminf_le_liminf_iSup
∀ {α : Type u_1} {β : Type u_2} {ι : Type u_4} [inst : CompleteLattice α] {f : Filter β} {u : ι → β → α},
⨆ i, Filter.liminf (u i) f ≤ Filter.liminf (fun b => ⨆ i, u i b) f- Defined in
- Mathlib.Order.LiminfLimsup
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses no axioms
- Assumes
- CompleteLattice
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.
- Filterstatement and proof · cited by 8,121
- iSupstatement · cited by 2,415
- CompleteLatticestatement and proof · cited by 1,048
- Filter.Eventually.of_forallproof · cited by 526
- le_iSupproof · cited by 207
- Filter.liminfstatement · cited by 198
- iSup_leproof · cited by 190
- Filter.isBounded_ge_of_botproof · cited by 55
- Filter.isCobounded_ge_of_topproof · cited by 38
- Filter.liminf_le_liminfproof · cited by 10
Cited by1
Results whose statement or proof uses this declaration.
- Filter.limsup_iInf_le_iInf_limsupproof · cited by 0