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

theorem
  for G2 for G1 being reverseEdgeDirections of G2
  for v1,e,v2 being object
  holds (e DJoins v1,v2,G2 iff e DJoins v2,v1,G1)
proof
  let G2;
  let G1 be reverseEdgeDirections of G2;
  let v1,e,v2 be object;
  hereby
    assume e DJoins v1,v2,G2;
    then e in the_Edges_of G2 & (the_Source_of G2).e = v1 &
      (the_Target_of G2).e = v2 by GLIB_000:def 14;
    then e in the_Edges_of G1 & (the_Target_of G1).e = v1 &
      (the_Source_of G1).e = v2 by Th26,Def1;
    hence e DJoins v2,v1,G1 by GLIB_000:def 14;
  end;
  assume e DJoins v2,v1,G1;
  then e in the_Edges_of G1 & (the_Source_of G1).e = v2 &
    (the_Target_of G1).e = v1 by GLIB_000:def 14;
  then e in the_Edges_of G2 & (the_Target_of G2).e = v2 &
    (the_Source_of G2).e = v1 by Th26,Def1;
  hence e DJoins v1,v2,G2 by GLIB_000:def 14;
end;
