reserve P,Q,X,Y,Z for set, p,x,x9,x1,x2,y,z for object;

theorem
  for f being Permutation of X holds (f")*f =id X & f*(f") = id X
proof
  let f be Permutation of X;
  dom f = X & rng f = X by Def3,Th51;
  hence thesis by FUNCT_1:39;
end;
