reserve UA for Universal_Algebra,
  f, g for Function of UA, UA;

theorem Th5:
  for f be Element of UAAut UA holds f" in UAAut UA
proof
  let f be Element of UAAut UA;
A1: f is_isomorphism by Def1;
  then f" is Function of UA, UA by Lm1;
  then consider ff be Function of UA, UA such that
A2: ff = f";
  ff is_isomorphism by A1,A2,ALG_1:10;
  hence thesis by A2,Def1;
end;
