Theorems · Definition · order theory
IsLUB
{α : Type u_1} → [LE α] → Set α → α → Propa is a least upper bound of a set s; for a partial order, it is unique if exists.
- Defined in
- Mathlib.Order.Bounds.Defs
- Cited by
- 280 results in Mathlib
- Foundations
- Depth 6 from the axioms, rests on 14 definitions · uses no axioms
- Assumes
- LE
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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
- upperBoundsproof · cited by 263
- IsLeastproof · cited by 122
Cited by331
Results whose statement or proof uses this declaration.
- GaloisConnection.l_supproof · cited by 81
- GaloisConnection.l_iSupproof · cited by 78
- IsCompactElementproof · cited by 34
- isLUB_csSupstatement · cited by 34
- DirSupClosedproof · cited by 31
- DirSupClosedOnproof · cited by 26
- DirSupInaccOnproof · cited by 26
- IsGreatest.isLUBstatement · cited by 25
- isLUB_le_iffstatement and proof · cited by 24
- ScottContinuousproof · cited by 24
- LeftOrdContinuousproof · cited by 24
- DirSupInaccproof · cited by 23
Showing the 200 most cited of 331.