Theorems · Theorem · order theory
Directed.disjoint_iSup_left
∀ {ι : Sort u_1} {α : Type u_2} [inst : CompleteLattice α] {f : ι → α} [IsCompactlyGenerated α] {a : α},
Directed (fun x1 x2 => x1 ≤ x2) f → (Disjoint (⨆ i, f i) a ↔ ∀ (i : ι), Disjoint (f i) a)- Defined in
- Mathlib.Order.CompactlyGenerated.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Bot.botproof · cited by 4,720
- iSupstatement · cited by 2,415
- Disjointstatement · cited by 2,201
- CompleteLatticestatement and proof · cited by 1,048
- Directedstatement and proof · cited by 213
- IsCompactlyGeneratedstatement and proof · cited by 37
- Directed.iSup_inf_eqproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Module.End.disjoint_genEigenspaceproof · cited by 7