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

theorem
  for f, g st f is Element of UAAut UA & g = f" holds g is_isomorphism
proof
  let f, g;
  assume that
A1: f is Element of UAAut UA and
A2: g = f";
  f is_isomorphism by A1,Def1;
  hence thesis by A2,ALG_1:10;
end;
