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

theorem :: ZFMISC_1:90
  X c= A implies X (\) Y c= A
proof
  assume
A1: X c= A;
  let i be object;
  assume
A2: i in I;
  then X.i c= A.i by A1;
  then X.i \ Y.i c= A.i by XBOOLE_1:109;
  hence thesis by A2,PBOOLE:def 6;
end;
