
theorem
  for c be Complex, seq1 be Real_Sequence, seq be Complex_Sequence st
  seq is convergent & seq1 is convergent for rseq be Real_Sequence st (for i be
  Nat holds rseq.i = |.seq.i-c.|*|.seq.i-c.|+seq1.i) holds rseq is
  convergent & lim rseq = |.lim seq-c.|*|.lim seq-c.|+lim seq1 by Lm23;
