
theorem Th4:
  for G1, G2 being _Graph st G1 == G2 & G1 is Dcomplete holds G2 is Dcomplete
proof
  let G1, G2 be _Graph;
  assume A1: G1 == G2 & G1 is Dcomplete;
  let v,w be Vertex of G2;
  A2: v is Vertex of G1 & w is Vertex of G1 by A1, GLIB_000:def 34;
  assume v <> w;
  then consider e being object such that
    A3: e DJoins v,w,G1 by A1, A2;
  take e;
  thus e DJoins v,w,G2 by A1, A3, GLIB_000:88;
end;
