
theorem
  for X be RealLinearSpace holds
    (IsoCPRLSP X)".(0.(product <*X*>)) = 0.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;
    J.(0.(product <*X*>)) = J.(I.(0.X)) by Th2;
    hence thesis by A1,FUNCT_1:34;
  end;
