
theorem
  for X be RealLinearSpace,
      x be Point of X
  holds (IsoCPRLSP X)" . <*x*> = x
  proof
    let X be RealLinearSpace;
    set I = IsoCPRLSP(X);
    set J = I";
    A1: dom I = the carrier of X by FUNCT_2:def 1;
    for x be Point of X holds J.<*x*> = x
    proof
      let x be Point of X;
      A2: I.x = <*x*> by Def1;
      reconsider z = x as Point of X;
      thus thesis by A1,A2,FUNCT_1:34;
    end;
    hence thesis;
  end;
