A <least upper bound> of $S$ is an element $u\in A$ such that $s\preceq u$ for every $s\in S$, and such that $u\preceq v$ for every other <upper bound> $v\in A$ of $S$. It need not belong to $S$. The <antisymmetric relation> axiom makes it unique whenever it exists.

Solution

Past exam of the year 1 of the computer science course of the University of Oxford / 2023 / Discrete mathematics, probability and continuous mathematics / 1 / c / i / 2 / Solution

 Solution (source code)