reserve n,n1,n2,m for Nat,
  r,r1,r2,p,g1,g2,g for Real,
  seq,seq9,seq1 for Real_Sequence,
  y for set;
reserve g for Complex;
reserve s,s1,s9 for Complex_Sequence;

theorem
    for s,s9 being convergent Complex_Sequence
  holds lim |.s - s9.| = |.(lim s) - (lim s9).|
proof
  let s,s9 be convergent Complex_Sequence;
  thus lim |.s - s9.| = |.lim (s - s9).| by Th27
    .= |.(lim s) - (lim s9).| by COMSEQ_2:26;
end;
