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
  the TopStruct of TOP-REAL n = TopSpaceNorm REAL-NS n
  proof
    thus the TopStruct of TOP-REAL n
     = TopSpaceMetr(Euclid n) by EUCLID:def 8
    .= TopSpaceNorm(REAL-NS n) by Th2;
  end;
