reserve X for set,
        n,m,k for Nat,
        K for Field,
        f for n-element real-valued FinSequence,
        M for Matrix of n,m,F_Real;

theorem Th8:
  for r be Real,
      q be Element of TOP-REAL n,
      g be Element of REAL-NS n
    st q = g
  holds r*q = r*g
  proof
    let r be Real,
        q be Element of TOP-REAL n,
        g be Element of REAL-NS n;
    assume
    A1: q = g;
    thus r*q
     = (the Mult of (the RLSStruct of TOP-REAL n)).(r,q)
    .= (the Mult of (the RLSStruct of REAL-NS n)).(r,q) by Th1
    .= r*g by A1;
  end;
