System verification in the broadest sense deals with those semantic properties that can be decided or deduced by analyzing a syntactical description of the system. Hence, one may consider the notions of redundancy and subsumption in this context as they are known from the area of rule-based systems. A rule is redundant if it can be removed without affecting the semantics of the system; it is subsumed by another rule if each application of the former one can be replaced by an application of the latter one with the same effect. In this paper, redundancy and subsumption are carried over from rule-based systems to high-level replacement systems, which in turn generalize graph and hypergraph grammars. The main results presented in this paper are a characterization of subsumption and a sufficient condition for redundancy, which involves composite productions.