reserve x,y for set;
reserve G for Graph;
reserve vs,vs9 for FinSequence of the carrier of G;
reserve IT for oriented Chain of G;
reserve N for Nat;
reserve n,m,k,i,j for Nat;
reserve r,r1,r2 for Real;
reserve X for non empty set;
reserve p,p1,p2 for Point of TOP-REAL N;

theorem Th28:
  for x1,x2 being Point of Euclid N st x1=p1 & x2=p2 holds |.p1 -
  p2.| = dist(x1,x2)
proof
  let x1,x2 be Point of Euclid N;
  assume
A1: x1=p1 & x2=p2;
  reconsider x19=x1,x29=x2 as Element of REAL N;
  (Pitag_dist N).(x19,x29) = |.x19-x29.| by EUCLID:def 6
    .=|.p1-p2.| by A1;
  hence thesis by METRIC_1:def 1;
end;
