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 Th20
    .= (lim s)*' * (lim s9)*' by COMPLEX1:35;
end;
