reserve n,i,k,m for Nat;
reserve r,r1,r2,s,s1,s2 for Real;
reserve p,p1,p2,q1,q2 for Point of TOP-REAL n;
reserve P,Q for Subset of TOP-REAL 2,
  f,f1,f2 for FinSequence of the carrier of TOP-REAL 2,
  p,p1,p2,p3,q,q3 for Point of TOP-REAL 2;

theorem
  for p, q being Point of TOP-REAL n, p9, q9 being Point of Euclid n st
  p = p9 & q = q9 holds dist (p9, q9) = |. p - q .| by Th5;
