
theorem
  for G1 being _finite edgeless _Graph, G2 being Subgraph of G1
  st G1.order() = G2.order() holds G1 == G2
proof
  let G1 be _finite edgeless _Graph, G2 be Subgraph of G1;
  assume A1: G1.order() = G2.order();
  A2: card the_Vertices_of G1 = G1.order() by GLIB_000:def 24
    .= card the_Vertices_of G2 by A1, GLIB_000:def 24;
  A3: the_Vertices_of G2 = the_Vertices_of G1 by A2, CARD_2:102;
  A4: the_Edges_of G1 = the_Edges_of G2;
  G1 is Subgraph of G1 by GLIB_000:40;
  hence thesis by A3, A4, GLIB_000:86;
end;
