 The way we have presented graphs, decorations, and AFA is a  very “minimalist” presentation.    If one would like some node of a graph G to be decorated by some set  a  the most obvious way would be to add all the elements of tc({x})  as fresh nodes in G, with y→ z  iff z ∈ y.    This means that one must take new copies if some of the sets in tc({x})  already happen to be nodes in G. This is often cumbersome: when working with graphs and decorations, one might well want to  pre-specify as much as possible the value of the decoration on a node.    There are several ways to do this with AFA, and we’ll indicate one here. 