Theorems · Theorem · order theory
Filter.limsup_compl
∀ {α : Type u_1} {β : Type u_2} [inst : CompleteBooleanAlgebra α] (f : Filter β) (u : β → α),
(Filter.limsup u f)ᶜ = Filter.liminf (compl ∘ u) f- Defined in
- Mathlib.Order.LiminfLimsup
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 59 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CompleteBooleanAlgebra
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
- Compl.complstatement and proof · cited by 2,925
- iSupproof · cited by 2,415
- iInfproof · cited by 1,690
- iSup_congr_Propproof · cited by 247
- Filter.limsupstatement · cited by 226
- iInf_congr_Propproof · cited by 218
- Filter.liminfstatement · cited by 198
- CompleteBooleanAlgebrastatement and proof · cited by 32
- compl_iInfproof · cited by 6
- compl_iSupproof · cited by 6
Cited by2
Results whose statement or proof uses this declaration.
- Filter.sdiff_liminfproof · cited by 0
- Filter.mem_limsup_iff_frequently_memproof · cited by 0