Theorems · Theorem · order theory
compl_iInf
∀ {α : Type u} {ι : Sort w} [inst : CompleteBooleanAlgebra α] {f : ι → α}, (iInf f)ᶜ = ⨆ i, (f i)ᶜ- Defined in
- Mathlib.Order.CompleteBooleanAlgebra
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 57 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.
Cites11
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 · cited by 2,415
- le_antisymmproof · cited by 2,068
- iInfstatement · cited by 1,690
- le_iSupproof · cited by 207
- iSup_leproof · cited by 190
- iInf_leproof · cited by 104
- le_iInfproof · cited by 102
- CompleteBooleanAlgebrastatement and proof · cited by 32
- compl_le_complproof · cited by 14
- compl_le_of_compl_leproof · cited by 2
Cited by6
Results whose statement or proof uses this declaration.
- Set.compl_iInterproof · cited by 31
- compl_iSupproof · cited by 6
- Filter.limsup_complproof · cited by 2
- Filter.liminf_complproof · cited by 1
- Filter.cofinite.bliminf_set_eqproof · cited by 1
- compl_sInfproof · cited by 1