reserve G, G2 for _Graph, V, E for set,
  v for object;

theorem Th7:
  for G2, E for G1 being reverseEdgeDirections of G2, E, v1,e,v2 being object
  st E c= the_Edges_of G2 & e in E
  holds (e DJoins v1,v2,G2 iff e DJoins v2,v1,G1)
proof
  let G2, E;
  let G1 be reverseEdgeDirections of G2, E;
  let v1,e,v2 be object;
  assume A1: E c= the_Edges_of G2 & e in E;
  hence e DJoins v1,v2,G2 implies e DJoins v2,v1,G1 by Lm1;
  reconsider G3=G2 as reverseEdgeDirections of G1,E by Th3;
  E c= the_Edges_of G1 by Th4, A1;
  then e DJoins v2,v1,G1 implies e DJoins v1,v2,G3 by A1, Lm1;
  hence thesis;
end;
