Theorems · Theorem · order theory
DirectedOn.isLUB_ciSup_set
∀ {α : Type u_1} {β : Type u_2} [inst : ConditionallyCompletePartialOrderSup α] {f : β → α} {s : Set β},
DirectedOn (fun x1 x2 => x1 ≤ x2) (f '' s) → BddAbove (f '' s) → s.Nonempty → IsLUB (f '' s) (⨆ i, f ↑i)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Set.Elemstatement · cited by 7,166
- Set.imagestatement and proof · cited by 5,609
- Set.Nonemptystatement and proof · cited by 2,627
- iSupstatement · cited by 2,415
- BddAbovestatement and proof · cited by 620
- IsLUBstatement and proof · cited by 280
- DirectedOnstatement and proof · cited by 271
- Set.Nonempty.imageproof · cited by 87
- ConditionallyCompletePartialOrderSupstatement and proof · cited by 52
- sSup_image'proof · cited by 10
- DirectedOn.isLUB_csSupproof · cited by 9
Cited by1
Results whose statement or proof uses this declaration.
- DirectedOn.ciSup_set_le_iffproof · cited by 0