reserve G,F for RealLinearSpace;

theorem Th5:
  for X,Y be non empty set
  ex I be Function of [:X,Y:],product <*X,Y*>
  st I is one-to-one & I is onto
  & for x,y be object st x in X & y in Y holds I.(x,y) = <*x,y*>
  proof
    let X,Y be non empty set;
    dom <*X,Y*> = {1,2} & <*X,Y*>.1 = X & <*X,Y*>.2 = Y
    by FINSEQ_1:2,89;
    hence thesis by Th3;
  end;
