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_1:12
  {x} c= {x,y} & {y} c= {x,y}
proof
  thus {x} c= {x,y}
  proof
    let i such that
A1: i in I;
    {x.i} c= {x.i,y.i} by ZFMISC_1:7;
    then {x}.i c= {x.i,y.i} by A1,Def1;
    hence thesis by A1,Def2;
  end;
  let i such that
A2: i in I;
  {y.i} c= {x.i,y.i} by ZFMISC_1:7;
  then {y}.i c= {x.i,y.i} by A2,Def1;
  hence thesis by A2,Def2;
end;
