 The finite set of positions appearing in this finite subcover may be used as the neighborhood of position zero in a description of as a cellular automaton rule.The same proof applies more generally when the set of integer positions is replaced by any discrete group , the space of configurations is replaced by the set of functions from to a finite alphabet, and shift-equivariance is replaced by equivariance under the action of on itself.In particular, it applies to cellular automata defined on an integer grid of any dimension.