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 Th17:
  Ball(x,r) misses Sphere(x,r)
proof
  assume not thesis;
  then consider q being object such that
A1: q in Ball(x,r) and
A2: q in Sphere(x,r) by XBOOLE_0:3;
  reconsider q as Point of TOP-REAL n by A1;
  |. q - x .| = r by A2,Th7;
  hence thesis by A1,Th5;
end;
