reserve X for RealUnitarySpace;
reserve x, y, z, g, g1, g2 for Point of X;
reserve a, q, r for Real;
reserve seq, seq1, seq2, seq9 for sequence of X;
reserve k, n, m, m1, m2 for Nat;

theorem Th55:
  Sphere(x,r) c= cl_Ball(x,r)
proof
  now
    let y;
    assume y in Sphere(x,r);
    then ||.x - y.|| = r by Th51;
    hence y in cl_Ball(x,r);
  end;
  hence thesis by SUBSET_1:2;
end;
