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 Th50:
  y in Ball(x,r) implies y in cl_Ball(x,r)
proof
  assume y in Ball(x,r);
  then ||.x - y.|| <= r by Th40;
  hence thesis;
end;
