reserve n for Nat,
  a, b, r, w for Real,
  x, y, z for Point of TOP-REAL n,
  e for Point of Euclid n;

theorem
  y in Ball(0.TOP-REAL n,r) implies |.y.| < r
proof
  assume y in Ball(0.TOP-REAL n,r);
  then |. y-0.TOP-REAL n .| < r by Th5;
  hence thesis by RLVECT_1:13;
end;
