theorem
  for X being set, F,G being Subset-Family of X holds COMPLEMENT(F \/ G)
  = COMPLEMENT F \/ COMPLEMENT G
proof
  let X be set, F,G be Subset-Family of X;
  for P being Subset of X holds P in COMPLEMENT F \/ COMPLEMENT G iff P`
  in F \/ G
  proof
    let P be Subset of X;
    P in COMPLEMENT F or P in COMPLEMENT G iff P` in F or P` in G by Def7;
    hence thesis by XBOOLE_0:def 3;
  end;
  hence thesis by Def7;
end;
