Theorems · Theorem · order theory
Directed.iSup_inf_eq
∀ {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 → (⨆ i, f i) ⊓ a = ⨆ i, f i ⊓ a- Defined in
- Mathlib.Order.CompactlyGenerated.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 30 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.
- iSupstatement and proof · cited by 2,415
- CompleteLatticestatement and proof · cited by 1,048
- Directedstatement and proof · cited by 213
- IsCompactlyGeneratedstatement and proof · cited by 37
- iSup_rangeproof · cited by 24
- Directed.directedOn_rangeproof · cited by 17
- DirectedOn.sSup_inf_eqproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Directed.disjoint_iSup_leftproof · cited by 1