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;
reserve d for Real;
reserve th,th1,th2 for Real;

theorem
  for th holds exp th=exp_R th
proof
  let th;
  thus exp th=Sum(th ExpSeq) by Def14
    .=Sum(th rExpSeq) by Lm9
    .=exp_R th by Def22;
end;
