
theorem
  for G1 being connected _Graph, G2 being Component of G1 holds G1 == G2
proof
  let G1 be connected _Graph;
  let G2 be Component of G1;
  reconsider G3 = G1 as Component of G1 by GLIB_002:30;
  set v = the Vertex of G2;
  reconsider w=v as Vertex of G1 by GLIB_000:42;
  the_Vertices_of G2 = G1.reachableFrom(w) by GLIB_002:33
    .= the_Vertices_of G3 by GLIB_002:16;
  hence thesis by GLIB_002:32;
end;
