Theorems · Theorem · order theory
Filter.limsSup_le_limsSup_of_le
∀ {α : Type u_1} [inst : ConditionallyCompleteLattice α] {f g : Filter α},
f ≤ g →
autoParam (Filter.IsCobounded (fun x1 x2 => x1 ≤ x2) f) Filter.limsSup_le_limsSup_of_le._auto_1 →
autoParam (Filter.IsBounded (fun x1 x2 => x1 ≤ x2) g) Filter.limsSup_le_limsSup_of_le._auto_3 →
f.limsSup ≤ g.limsSup- Defined in
- Mathlib.Order.LiminfLimsup
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext, Quot.sound
- Assumes
- ConditionallyCompleteLattice
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.
- Filterstatement and proof · cited by 8,121
- Set.ofPredproof · cited by 6,101
- Filter.Eventuallyproof · cited by 3,134
- ConditionallyCompleteLatticestatement and proof · cited by 364
- Filter.IsBoundedstatement and proof · cited by 45
- Filter.IsCoboundedstatement and proof · cited by 42
- Filter.limsSupstatement · cited by 29
- Filter.limsSup_le_limsSupproof · cited by 4
Cited by4
Results whose statement or proof uses this declaration.
- Filter.limsup_le_limsup_of_leproof · cited by 4
- ClusterPt.le_limsSupproof · cited by 3
- essSup_comp_le_essSup_map_measureproof · cited by 2
- limsInf_eq_of_le_nhdsproof · cited by 2