Theorems · Theorem · order theory
compl_iSup
∀ {α : Type u} {ι : Sort w} [inst : CompleteBooleanAlgebra α] {f : ι → α}, (iSup f)ᶜ = ⨅ i, (f i)ᶜ- Defined in
- Mathlib.Order.CompleteBooleanAlgebra
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 58 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Compl.complstatement and proof · cited by 2,925
- iSupstatement and proof · cited by 2,415
- iInfstatement and proof · cited by 1,690
- compl_complproof · cited by 229
- CompleteBooleanAlgebrastatement and proof · cited by 32
- compl_injectiveproof · cited by 22
- compl_iInfproof · cited by 6
Cited by6
Results whose statement or proof uses this declaration.
- Set.compl_iUnionproof · cited by 32
- Filter.limsup_complproof · cited by 2
- compl_sSupproof · cited by 1
- Filter.liminf_complproof · cited by 1
- disjointed_eq_inf_complproof · cited by 1
- Filter.cofinite.bliminf_set_eqproof · cited by 1