theorem
  for G1 being _finite _Graph, G2 being spanning Subgraph of G1
  st G1.size() = G2.size() holds G1 == G2
proof
  let G1 be _finite _Graph, G2 be spanning Subgraph of G1;
  assume A1: G1.size() = G2.size();
  card the_Edges_of G1 = card the_Edges_of G2 by A1;
  then the_Edges_of G1 = the_Edges_of G2 by CARD_2:102;
  hence thesis by Th118;
end;
