theorem Th1:
  for M being non empty Reflexive MetrStruct, u being Point of M, r
  being Real holds r > 0 implies u in Ball(u,r)
proof
  let M be non empty Reflexive MetrStruct, u be Point of M, r be Real;
A1: Ball(u,r) = {q where q is Point of M:dist(u,q)<r} & dist(u,u) = 0 by
METRIC_1:1,17;
  assume r > 0;
  hence thesis by A1;
end;
