reserve G,G1,G2 for _Graph;
reserve e,x,y for set;
reserve v,v1,v2 for Vertex of G;
reserve W for Walk of G;

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;
