reserve i for object, I for set,
  f for Function,
  x, x1, x2, y, A, B, X, Y, Z for ManySortedSet of I;

theorem     :: ZFMISC_1:119
  x1 c= A & x2 c= B implies [|x1,x2|] c= [|A,B|]
proof
  assume that
A1: x1 c= A and
A2: x2 c= B;
  let i;
  assume
A3: i in I;
  then
A4: x1.i c= A.i by A1;
  x2.i c= B.i by A2,A3;
  then [:x1.i,x2.i:] c= [:A.i,B.i:] by A4,ZFMISC_1:96;
  then [|x1,x2|].i c= [:A.i,B.i:] by A3,PBOOLE:def 16;
  hence thesis by A3,PBOOLE:def 16;
end;
