
theorem
  for S,T being non empty RelStr, f being Function of S,T st f is isomorphic
  for g being Function of T,S st g = f" holds g is isomorphic
proof
  let S,T be non empty RelStr, f be Function of S,T;
  assume
A1: f is isomorphic;
  then
A2: ex h being Function of T,S st ( h = f")&( h is monotone) by Def38;
  let g be Function of T,S;
  assume
A3: g = f";
  per cases;
  case T is non empty & S is non empty;
    thus g is one-to-one monotone by A1,A2,A3,FUNCT_1:40;
    f" " = f by A1,FUNCT_1:43;
    hence thesis by A1,A3;
  end;
  case T is empty or S is empty;
    hence thesis;
  end;
end;
