reserve a, b for Real,
  r for Real,
  rr for Real,
  i, j, n for Nat,
  M for non empty MetrSpace,
  p, q, s for Point of TOP-REAL 2,
  e for Point of Euclid 2,
  w for Point of Euclid n,
  z for Point of M,
  A, B for Subset of TOP-REAL n,
  P for Subset of TOP-REAL 2,
  D for non empty Subset of TOP-REAL 2;
reserve a, b for Real;
reserve a, b for Real;
reserve r for Real;
reserve r1,r2,s1,s2 for Real;

theorem
  for p being Point of TOP-REAL n holds dist(p,p) = 0
proof
  let p be Point of TOP-REAL n;
  ex a, b being Point of Euclid n st a = p & b = p & dist(a,b) = dist(p,p)
  by Def1;
  hence thesis by METRIC_1:1;
end;
