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 Cauchy implies seq - x is Cauchy
proof
  assume seq is Cauchy;
  then seq + (-x) is Cauchy by Th63;
  hence thesis by CSSPACE:71;
end;
