Definition 1.4.20.  Let S be a set, ⪯ be a relation on S, T ⊆ S, t ∈ T. We define:
t is a ⪯-greatest element of T  :⇔  t is a ⪯-upper bound of T  ⇔  t is a ⪯T-least element of T
Equivalence.  No proof.
References.