
theorem Th3:
  for G being _Graph, X being set holds G == G.set(OrderingSelector, X)
proof
  let G be _Graph, X be set;
  set G2 = G.set(OrderingSelector, X);
  the_Vertices_of G = the_Vertices_of G2 &
    the_Edges_of G = the_Edges_of G2 &
    the_Source_of G = the_Source_of G2 &
    the_Target_of G = the_Target_of G2 by Lm1, GLIB_000:10;
  hence thesis by GLIB_000:def 34;
end;
