Theorems · Theorem · order theory
Filter.liminf_top_eq_ciInf
∀ {α : Type u_1} {β : Type u_2} [inst : ConditionallyCompleteLattice α] {u : β → α} [Nonempty β],
BddBelow (Set.range u) → Filter.liminf u ⊤ = ⨅ i, u i- Defined in
- Mathlib.Order.LiminfLimsup
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 53 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement and proof · cited by 9,680
- Filterstatement and proof · cited by 8,121
- Set.rangestatement and proof · cited by 4,705
- iInfstatement and proof · cited by 1,690
- BddBelowstatement and proof · cited by 401
- ConditionallyCompleteLatticestatement and proof · cited by 364
- Filter.liminfstatement · cited by 198
- Set.range_nonemptyproof · cited by 84
- Filter.limsInfproof · cited by 31
- sInf_rangeproof · cited by 17
- Filter.map_topproof · cited by 6
- Filter.limsInf_principal_eq_csSupproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- essInf_eq_ciInfproof · cited by 2