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
  s is convergent & (lim s)<>0c & s is non-zero implies lim (s")*' = ((
  lim s)*')"
proof
  assume
A1: s is convergent & (lim s)<>0c & s is non-zero;
  then s" is convergent by Th23;
  hence lim (s")*' = (lim s")*' by Th11
    .= ((lim s)")*' by A1,Th24
    .= ((lim s)*')" by COMPLEX1:36;
end;
