Theorems · Theorem · order theory
isLUB_ciSup_set
∀ {α : Type u_1} {β : Type u_2} [inst : ConditionallyCompleteLattice α] {f : β → α} {s : Set β},
BddAbove (f '' s) → s.Nonempty → IsLUB (f '' s) (⨆ i, f ↑i)- Cited by
- 3 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses propext, Quot.sound
- Assumes
- ConditionallyCompleteLattice
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.
- 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
- ConditionallyCompleteLatticestatement and proof · cited by 364
- IsLUBstatement and proof · cited by 280
- Set.Nonempty.imageproof · cited by 87
- isLUB_csSupproof · cited by 34
- sSup_image'proof · cited by 10
Cited by3
Results whose statement or proof uses this declaration.
- Dense.ciSupproof · cited by 2
- isGLB_ciInf_setproof · cited by 1
- ciSup_set_le_iffproof · cited by 0