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
  seq is convergent & lim seq = g implies ||.z * seq.|| is convergent &
  lim ||.z * seq.|| = ||.z * g.||
proof
  assume seq is convergent & lim seq = g;
  then z * seq is convergent & lim (z * seq) = z * g by Th5,Th15;
  hence thesis by Th21;
end;
