reserve x, y, z, E, E1, E2, E3 for set,
  sE for Subset-Family of E,
  f for Function of E, E,
  k, l, m, n for Nat;

theorem Th4:
  sE is covering iff union sE = E
proof
  union union bool bool E = union bool E by ZFMISC_1:81
    .= E by ZFMISC_1:81;
  hence thesis;
end;
