  What does it mean for an algebraic rewrite rule to subsume another rule (that
may then be called a subrule)? We view subsumptions as rule morphisms such that
the simultaneous application of a rule and a subrule (i.e. the application of a
subsumption morphism) yields the same result as a single application of the
subsuming rule. Simultaneous applications of categories of rules are obtained
by Global Coherent Transformations and illustrated on graphs in the DPO
approach. Other approaches are possible since these transformations are
formulated in an abstract Rewriting Environment, and such environments exist
for various approaches to Algebraic Rewriting, including DPO, SqPO and PBPO.
