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;

theorem
  exp(th*<i>)=cos(th)+(sin th)*<i>
proof
 exp(th*<i>)=Sum(th*<i> ExpSeq ) by Def14
    .=cos(th)+(sin th)*<i> by Lm3;
  hence thesis;
end;
