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_1:80
  { A } c= bool A
proof
  let i such that
A1: i in I;
  {A.i} c= bool (A.i) by ZFMISC_1:68;
  then {A}.i c= bool (A.i) by A1,Def1;
  hence thesis by A1,MBOOLEAN:def 1;
end;
