
theorem Th7:
  for X being 1-sorted, F being Subset-Family of X holds union
  COMPLEMENT F = (Intersect F)`
proof
  let X be 1-sorted, F be Subset-Family of X;
  thus union COMPLEMENT F = (union COMPLEMENT F)``
    .= (Intersect COMPLEMENT COMPLEMENT F)` by Th6
    .= (Intersect F)`;
end;
