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 Th54:
  Ball(x,r) c= cl_Ball(x,r)
proof
  for y holds y in Ball(x,r) implies y in cl_Ball(x,r) by Th50;
  hence thesis by SUBSET_1:2;
end;
