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_2:14;
end;
