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 Th27:
  s9 is convergent & s is convergent & (lim s)<>0c & s is non-zero
  implies lim(s9/"s)=(lim s9)/(lim s)
proof
  assume that
A1: s9 is convergent and
A2: s is convergent & (lim s)<>0c & s is non-zero;
  s" is convergent by A2,Th23;
  then lim (s9(#)(s"))=(lim s9)*(lim s") by A1,Th20
    .=(lim s9)*(lim s)" by A2,Th24
    .=(lim s9)/(lim s) by XCMPLX_0:def 9;
  hence thesis;
