Theorems · Theorem · order theory
Directed.isLUB_ciSup
∀ {α : Type u_1} {ι : Sort u_4} [inst : ConditionallyCompletePartialOrderSup α] [Nonempty ι] {f : ι → α},
Directed (fun x1 x2 => x1 ≤ x2) f → BddAbove (Set.range f) → IsLUB (Set.range f) (⨆ i, f i)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Set.rangestatement and proof · cited by 4,705
- iSupstatement · cited by 2,415
- BddAbovestatement and proof · cited by 620
- IsLUBstatement · cited by 280
- Directedstatement and proof · cited by 213
- Set.range_nonemptyproof · cited by 84
- ConditionallyCompletePartialOrderSupstatement and proof · cited by 52
- Directed.directedOn_rangeproof · cited by 17
- DirectedOn.isLUB_csSupproof · cited by 9
Cited by1
Results whose statement or proof uses this declaration.
- Directed.ciSup_le_iffproof · cited by 2