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 Th6:
  y in cl_Ball(x,r) iff |. y-x .| <= r
proof
  hereby
    assume y in cl_Ball(x,r);
    then ex p being Point of TOP-REAL n st y = p & |. p-x .| <= r;
    hence |. y-x .| <= r;
  end;
  thus thesis;
end;
