reserve n for Nat,
  i,j for Nat,
  r,s,r1,s1,r2,s2,r9,s9 for Real,
  p,q for Point of TOP-REAL 2,
  G for Go-board,
  x,y for set,
  v for Point of Euclid 2;

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;
