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

theorem :: ZFMISC_1:97
  union (A (/\) B) c= union A (/\) union B
proof
  let i be object;
  assume
A1: i in I;
  then
A2: (union (A (/\) B)).i = union (A.i /\ B.i) by Lm7;
  (union A (/\) union B).i = (union A).i /\ (union B).i by A1,PBOOLE:def 5
    .= union (A.i) /\ (union B).i by A1,Def2
    .= union (A.i) /\ union (B.i) by A1,Def2;
  hence thesis by A2,ZFMISC_1:79;
end;
