reserve n,n1,n2,m for Nat;
reserve r,g1,g2,g,g9 for Complex;
reserve R,R2 for Real;
reserve s,s9,s1 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 Th11
    .= ((lim s) + (lim s9))*' by Th12
    .= (lim s)*' + (lim s9)*' by COMPLEX1:32;
end;
