reserve S,T,W,Y for RealNormSpace;
reserve f,f1,f2 for PartFunc of S,T;
reserve Z for Subset of S;
reserve i,n for Nat;

theorem defISOA2:
  for X, Y be RealNormSpace holds
    (IsoCPNrSP(X,Y)").(0. product <*X,Y*>) = 0.[:X,Y:]
 proof
  let X, Y be RealNormSpace;
    set I = IsoCPNrSP(X,Y);
    set J = I";
    P0: dom I = the carrier of [:X,Y:] by FUNCT_2:def 1;
    J.(0. product <*X,Y*>) = J.(I.(0.[:X,Y:])) by ZeZe;
    hence thesis by P0,FUNCT_1:34;
end;
