
theorem Th34:
  for G1 being _finite _Graph, G2 being Subgraph of G1 st G1.size() = G2.size()
  holds G1 is addVertices of G2, the_Vertices_of G1 \ the_Vertices_of G2
proof
  let G1 be _finite _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 A2: the_Edges_of G1 = the_Edges_of G2 by CARD_2:102;
  G1 is Supergraph of G2 by GLIB_006:57;
  hence thesis by A2, Th33;
end;
