
theorem LM04:
  for I be set, X, Y, Z be ManySortedSet of I st (X c= (Y (\) Z) &
  (for i, j be object st i in I & j in I &
  i <> j holds Y.i /\ Z.j = {}))
  holds Union(X) c= (Union Y) \ (Union Z)
proof
  let I be set, X, Y, Z be ManySortedSet of I;
  assume X c= Y (\) Z; then
B1: Union X c= Union (Y (\) Z) by MSAFREE4:1;
  assume for i, j be object st i in I & j in I & i <> j
  holds Y.i /\ Z.j = {};
  hence thesis by LM03, B1;
end;
