reserve G for _Graph;
reserve V for non empty set, E for Relation of V;
reserve E for symmetric Relation of V;
reserve G for GraphFromSymRel of V, E;

theorem
  for G1, G2 being GraphFromSymRel of V, E
  holds the_Vertices_of G1 = the_Vertices_of G2
proof
  let G1, G2 be GraphFromSymRel of V, E;
  set G0 = createGraph(V,E);
  the_Vertices_of G1 = the_Vertices_of G0 &
    the_Vertices_of G2 = the_Vertices_of G0 by GLIB_000:def 33;
  hence thesis;
end;
