reserve x, y for object, I for set,
  A, B, X, Y for ManySortedSet of I;

theorem :: ZFMISC_1:91
  X c= A & Y c= A implies X (\+\) Y c= A
proof
  assume
A1: X c= A & Y c= A;
  let i be object;
  assume
A2: i in I;
  then X.i c= A.i & Y.i c= A.i by A1;
  then X.i \+\ Y.i c= A.i by XBOOLE_1:110;
  then X.i \+\ Y.i in bool (A.i);
  then (X (\+\) Y).i in bool (A.i) by A2,PBOOLE:4;
  hence thesis;
end;
