theorem
  x in G.reachableDFrom(v1) & e DJoins x,y,G implies y in G .reachableDFrom(v1)
proof
  set RFV = G.reachableDFrom(v1);
  assume that
A1: x in RFV and
A2: e DJoins x,y,G;
  consider W being directed Walk of G such that
A3: W is_Walk_from v1,x by A1,Def6;
  W.addEdge(e) is directed & W.addEdge(e) is_Walk_from v1,y by A2,A3,
GLIB_001:123;
  hence thesis by Def6;
end;
