theorem Th57:
  for G being Grating of d9 + 1 holds del Omega(G) = 0_(d9,G)
proof
  let G be Grating of d9 + 1;
  now
    let A be Cell of d9,G;
    star A /\ Omega(G) = star A by XBOOLE_1:28;
    then card(star A /\ Omega(G)) = 2* 1 by Th51;
    hence A in del Omega(G) iff A in 0_(d9,G) by Th48;
  end;
  hence thesis by SUBSET_1:3;
end;
