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

theorem :: FRAENKEL:5
  (Funcs)(A,B) c= bool [|A, B|]
proof
  let i be object;
  assume
A1: i in I;
  then
A2: ((Funcs)(A,B)).i = Funcs (A.i, B.i) by PBOOLE:def 17;
  (bool [|A, B|]).i = bool ([|A, B|].i) by A1,Def1
    .= bool [:A.i, B.i:] by A1,PBOOLE:def 16;
  hence thesis by A2,FRAENKEL:2;
end;
