reserve X for set,
  Y for non empty set;
reserve n for Nat;
reserve r for Real,
  M for non empty MetrSpace;
reserve n for Nat,
  p,q,q1,q2 for Point of TOP-REAL 2,
  r,s1,s2,t1,t2 for Real,
  x,y for Point of Euclid 2;

theorem Th22:
  p <> q implies dist(p,q) > 0
proof
  ex p9, q9 being Point of Euclid 2 st p9 = p & q9 = q & dist(p,q) = dist(
  p9,q9) by TOPREAL6:def 1;
  hence thesis by METRIC_1:7;
end;
