
theorem
  for G1 being _finite connected _Graph, G2 being Subgraph of G1
  st G1.size() = G2.size() holds G1 == G2
proof
  let G1 be _finite connected _Graph, G2 be Subgraph of G1;
  assume A1: G1.size() = G2.size();
  card the_Edges_of G2 = G2.size() by GLIB_000:def 25
    .= card the_Edges_of G1 by A1, GLIB_000:def 25;
  then the_Edges_of G1 = the_Edges_of G2 by CARD_2:102;
  hence thesis by Th19;
end;
