theorem Th7:
  for p,q be Element of TOP-REAL n,
      f,g be Element of REAL-NS n
    st p=f & q=g
  holds p+q = f+g
  proof
    let p,q be Element of TOP-REAL n,
        f,g be Element of REAL-NS n;
    assume
    A1: p=f & q=g;
    thus p+q
     = (the addF of (the RLSStruct of TOP-REAL n)).(p,q)
    .= (the addF of (the RLSStruct of REAL-NS n)).(p,q) by Th1
    .= f+g by A1;
  end;
