reserve X for ComplexUnitarySpace;
reserve x, y, w, g, g1, g2 for Point of X;
reserve z for Complex;
reserve p, q, r, M, M1, M2 for Real;
reserve seq, seq1, seq2, seq3 for sequence of X;
reserve k,n,m for Nat;
reserve Nseq for increasing sequence of 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;
