
theorem
  for G being vertex-finite non-Dmulti _Graph
  holds G.size() <= G.order()^2
proof
  let G be vertex-finite non-Dmulti _Graph;
  G.order() *` G.order() = card [: G.order(), G.order() :] by CARD_2:def 2
    .= card G.order() * G.order() by CARD_2:46
    .= Segm(G.order() * G.order());
  then Segm(G.size()) c= Segm(G.order() * G.order()) by Th2;
  then G.size() <= G.order() * G.order() by NAT_1:39;
  hence thesis by SQUARE_1:def 1;
end;
