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_1:32
  union { {x},{y} } = {x,y}
proof
  now
    let i be object;
    assume
A1: i in I;
    hence (union { {x},{y} }).i = union ({{x},{y}}.i) by MBOOLEAN:def 2
      .= union {{x}.i,{y}.i} by A1,Def2
      .= union {{x.i},{y}.i} by A1,Def1
      .= union {{x.i},{y.i}} by A1,Def1
      .= {x.i,y.i} by ZFMISC_1:26
      .= {x,y}.i by A1,Def2;
  end;
  hence thesis;
end;
