Before revision:  An edge e from the complement of G can be inserted {\em  into D(G) if there exists a simple drawing of G ' = (V, E\cup \{e \ D(G) as a subdrawing.
After revision:  An edge e from the complement of G can be inserted {\em into D(G) if there exists a simple drawing of G +e extending D(G) as a subdrawing.