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 Th33:
  seq is convergent & lim seq = g implies ||.(seq + x) - (g + x)
  .|| is convergent & lim ||.(seq + x) - (g + x).|| = 0
proof
  assume seq is convergent & lim seq = g;
  then seq + x is convergent & lim (seq + x) = g + x by Th7,Th17;
  hence thesis by Th22;
end;
