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

theorem
  for f,g being Permutation of X st g*f = id X holds g = f"
proof
  let f,g be Permutation of X;
A1: dom f = X by Th51;
  rng f= X & dom g = X by Def3,Th51;
  hence thesis by A1,FUNCT_1:41;
end;
