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;

theorem Th5:
  for u1,u2 being Point of Euclid n, v1,v2 being Element of REAL n
  st v1=u1 & v2=u2 holds dist(u1,u2) = |.v1-v2.|
proof
  let u1,u2 be Point of Euclid n, v1,v2 be Element of REAL n;
  assume v1=u1 & v2=u2;
  hence dist(u1,u2) = (Pitag_dist n).(v1,v2) by METRIC_1:def 1
    .= |.v1-v2.| by EUCLID:def 6;
end;
