Theorems · Theorem · order theory
Filter.liminf_nat_add
∀ {α : Type u_1} [inst : ConditionallyCompleteLattice α] (f : ℕ → α) (k : ℕ),
Filter.liminf (fun i => f (i + k)) Filter.atTop = Filter.liminf f Filter.atTop- Defined in
- Mathlib.Order.LiminfLimsup
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, 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.
- Filterproof · cited by 8,121
- Filter.atTopstatement and proof · cited by 2,405
- Filter.mapproof · cited by 819
- ConditionallyCompleteLatticestatement and proof · cited by 364
- Filter.liminfstatement and proof · cited by 198
- Filter.map_mapproof · cited by 80
- Filter.limsInfproof · cited by 31
- Filter.map_add_atTop_eq_natproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- Filter.limsup_nat_addproof · cited by 1