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 implies lim (seq - x) = (lim seq) - x
proof
  assume seq is convergent;
  then lim (seq + (-x)) = (lim seq) + (-x) by Th17;
  then lim (seq - x) = (lim seq) + (-x) by CSSPACE:71;
  hence thesis by RLVECT_1:def 11;
end;
