reserve G for _Graph;
reserve G2 for _Graph, G1 for Supergraph of G2;

theorem
  for G2, G1 holds G2.order() c= G1.order() & G2.size() c= G1.size()
proof
  let G2, G1;
  the_Vertices_of G2 c= the_Vertices_of G1 &
    the_Edges_of G2 c= the_Edges_of G1 by Def9;
  then card the_Vertices_of G2 c= card the_Vertices_of G1 &
    card the_Edges_of G2 c= card the_Edges_of G1 by CARD_1:11;
  then G2.order() c= card the_Vertices_of G1 &
    G2.size() c= card the_Edges_of G1 by GLIB_000:def 24, GLIB_000:def 25;
  hence thesis by GLIB_000:def 24, GLIB_000:def 25;
end;
