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_1:14
  {x} (\/) {x,y} = {x,y}
proof
  now
    let i be object;
    assume
A1: i in I;
    hence ({x} (\/) {x,y}).i = {x}.i \/ {x,y}.i by PBOOLE:def 4
      .= {x.i} \/ {x,y}.i by A1,Def1
      .= {x.i} \/ {x.i,y.i} by A1,Def2
      .= {x.i,y.i} by ZFMISC_1:9
      .= {x,y}.i by A1,Def2;
  end;
  hence thesis;
end;
