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

theorem
  for f,g being Function of X,X st f*g = f & f is one-to-one holds g = id X
proof
  let f,g be Function of X,X;
A1: rng g c= X;
  dom f = X & dom g = X by Th51;
  hence thesis by A1,FUNCT_1:28;
end;
