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 being convergent Complex_Sequence
  holds lim (r(#)s)*' = (r*')*(lim s)*'
proof
  let s being convergent Complex_Sequence;
  thus lim (r(#)s)*' = (lim (r(#)s))*' by Th11
    .= (r*(lim s))*' by Th14
    .= (r*')*(lim s)*' by COMPLEX1:35;
end;
