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
  for n be non empty Nat,
     af be Element of F_Real,
     at be Real,
     xv be Element of n -VectSp_over F_Real,
     xt be Element of TOP-REAL n
    st af = at & xv = xt
  holds af * xv = at * xt by Th54;
