reserve n,n1,n2,m for Nat,
  r,r1,r2,p,g1,g2,g for Real,
  seq,seq9,seq1 for Real_Sequence,
  y for set;

theorem
  seq9 is convergent & seq is convergent & lim seq <> 0
  & seq is non-zero implies lim(seq9/"seq)=(lim seq9)/(lim seq)
proof
  assume that
A1: seq9 is convergent and
A2: seq is convergent and
A3: (lim seq)<>0 and
A4: seq is non-zero;
  seq" is convergent by A2,A3,A4,Th21;
  then lim (seq9(#)(seq"))=(lim seq9)*(lim seq") by A1,Th15
    .=(lim seq9)*(lim seq)" by A2,A3,A4,Th22
    .=(lim seq9)/(lim seq) by XCMPLX_0:def 9;
  hence thesis;
end;
