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

theorem :: ZFMISC_1:89
  X c= A or Y c= A implies X (/\) Y c= A
proof
  assume
A1: X c= A or Y c= A;
  per cases by A1;
  suppose
A2: X c= A;
    let i be object;
    assume
A3: i in I;
    then X.i c= A.i by A2;
    then X.i /\ Y.i c= A.i by XBOOLE_1:108;
    hence thesis by A3,PBOOLE:def 5;
  end;
  suppose
A4: Y c= A;
    let i be object;
    assume
A5: i in I;
    then Y.i c= A.i by A4;
    then X.i /\ Y.i c= A.i by XBOOLE_1:108;
    hence thesis by A5,PBOOLE:def 5;
  end;
end;
