Answer by Ittay Weiss for How is a complete lattice defined solely by a least-upper bound?

If $P$ is a poset such that every $S\subseteq P$ has a supremum (i.e., lub), then the the infimum (i.e., glb) of a fixed set $S$ is the the supremum of all the lower bounds of $S$. The proof is obtained just by deciphering the definitions.