reserve x, y for set,
  T for TopStruct,
  GX for TopSpace,
  P, Q, M, N for Subset of T,
  F, G for Subset-Family of T,
  W, Z for Subset-Family of GX,
  A for SubSpace of T;

theorem Th7:
  for T being set, F being Subset-Family of T holds F <> {}
  implies union COMPLEMENT(F) = (meet F)`
proof
  let T be set, F be Subset-Family of T;
  assume F <> {};
  then union COMPLEMENT(F) = [#]T \ meet F by SETFAM_1:34
    .= T \ meet F;
  hence thesis;
end;
