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

theorem Th4:
  for G2, E for G1 being reverseEdgeDirections of G2, E
  holds the_Vertices_of G1 = the_Vertices_of G2 &
    the_Edges_of G1 = the_Edges_of G2
proof
  let G2, E;
  let G1 be reverseEdgeDirections of G2, E;
  per cases;
  suppose E c= the_Edges_of G2;
    hence thesis by Def1;
  end;
  suppose not E c= the_Edges_of G2;
    then G1 == G2 by Def1;
    hence thesis by GLIB_000:def 34;
  end;
end;
