$E$-Reduct (SetAF)

For $E \subseteq A$, the $E$-reduct of a SetAF $S$ is the SetAF $S^E = (A', R')$ with $A' = A \setminus$ $E^\oplus_R$ and $R' = \{(T \setminus E, h) \mid (T, h) \in R,\ T \cap E^+_R = \emptyset,\ T \not\subseteq E,\ h \in A'\}$.