So I'm wondering about some finer points of relation algebra, a field in which I'm not an expert:
Given relations $A$, $B$ and $C$ over the same set $S$, is it always true that $A^*\subseteq (B\cup C)^*$ iff $(A\setminus B)^*\subseteq C^*$ ?
Here, $A^*$ denotes the reflexive, transitive closure of $A$, $\cup$ is set union, and $\setminus$ is set difference.