Theorems · Theorem · order theory
Filter.sup_liminf
∀ {α : Type u_1} {β : Type u_2} [inst : CompleteDistribLattice α] {f : Filter β} {u : β → α} (a : α),
a ⊔ Filter.liminf u f = Filter.liminf (fun x => a ⊔ u x) f- Defined in
- Mathlib.Order.LiminfLimsup
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Quot.sound
- Assumes
- CompleteDistribLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Filterstatement and proof · cited by 8,121
- Set.univproof · cited by 3,945
- iSupproof · cited by 2,415
- iInfproof · cited by 1,690
- iSup_congr_Propproof · cited by 247
- iInf_congr_Propproof · cited by 218
- Filter.liminfstatement · cited by 198
- sup_commproof · cited by 165
- Filter.univ_memproof · cited by 96
- CompleteDistribLatticestatement and proof · cited by 17
- Filter.liminf_eq_iSup_iInfproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- Filter.sdiff_liminfproof · cited by 0
- Filter.inf_limsupproof · cited by 0