reserve a, I for set,
  S for non empty non void ManySortedSign;

theorem Th5:
  ex A being ManySortedSet of I st {A} = I --> {a}
proof
  reconsider A = I --> a as ManySortedSet of I;
  take A;
  now
    let i be object;
    assume
A1: i in I;
    hence {A}.i = {A.i} by PZFMISC1:def 1
      .= {a} by A1,FUNCOP_1:7
      .= (I --> {a}).i by A1,FUNCOP_1:7;
  end;
  hence thesis;
end;
