reserve q,th,r for Real,
  a,b,p for Real,
  w,z for Complex,
  k,l,m,n,n1,n2 for Nat,
  seq,seq1,seq2,cq1 for Complex_Sequence,
  rseq,rseq1,rseq2 for Real_Sequence,
  rr for set,
  hy1 for 0-convergent non-zero Real_Sequence;

theorem
  for z1, z2 being Complex holds exp(z1+z2)=exp(z1) *exp(z2)
proof
  let z1,z2 be Complex;
 exp(z1+z2)=Sum((z1+z2) ExpSeq) by Def14
    .=Sum(z1 ExpSeq)*Sum(z2 ExpSeq) by Lm2
    .=exp(z1)*Sum(z2 ExpSeq) by Def14
    .=exp(z1) *exp(z2) by Def14;
  hence thesis;
end;
