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

theorem :: ZFMISC_1:105
  [|X, Y|] c= bool bool (X (\/) Y)
proof
  let i be object;
  assume
A1: i in I;
  then
A2: [|X, Y|].i = [:X.i, Y.i:] by PBOOLE:def 16;
  (bool bool (X (\/) Y)).i = bool ((bool (X (\/) Y)).i) by A1,Def1
    .= bool bool (X.i \/ Y.i) by A1,Lm2;
  hence thesis by A2,ZFMISC_1:86;
end;
