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 Th5:
  the carrier of (n -VectSp_over F_Real) = the carrier of REAL-NS n
  proof
    thus the carrier of (n -VectSp_over F_Real)
     = the carrier of TOP-REAL n by Lm2
    .= the carrier of REAL-NS n by Th4;
  end;
