 reserve n for Nat;
 reserve s1 for sequence of Euclid n,
         s2 for sequence of REAL-NS n;

theorem Th15:
  MetricSpaceNorm REAL-NS n = Euclid n
  proof
    set MS = MetricSpaceNorm REAL-NS n;
A1: MS = MetrStruct(# the carrier of REAL-NS n, distance_by_norm_of
      REAL-NS n #) by NORMSP_2:def 2; then
A2: the carrier of MS = REAL n by REAL_NS1:def 4;
    Euclid n = MetrStruct(# REAL n,Pitag_dist n #) by EUCLID:def 7;
    hence thesis by A1,A2,Th14;
  end;
