
theorem
  for G1, G2 being _Graph st G1 == G2
  holds id G1 = id G2 & id G1 is PGraphMapping of G1, G2
proof
  let G1, G2 be _Graph;
  assume A1: G1 == G2;
  thus id G1
     = [id the_Vertices_of G2, id the_Edges_of G1] by A1, GLIB_000:def 34
    .= id G2 by A1, GLIB_000:def 34;
  thus thesis by A1, Th9;
end;
