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

theorem :: ZFMISC_1:32
  union (I --> { {x},{y} }) = I --> {x,y}
proof
  now
    let i be object;
    assume
A1: i in I;
    hence (union (I --> {{x},{y}})).i = union ((I --> {{x},{y}}).i) by Def2
      .= union {{x},{y}} by A1,FUNCOP_1:7
      .= {x,y} by ZFMISC_1:26
      .= (I --> {x,y}).i by A1,FUNCOP_1:7;
  end;
  hence thesis;
end;
