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>)).| = 1 &
  for th being Real holds |.sin th.| <= 1 & |.cos th.| <= 1
proof
  thus |.exp((th*<i>)).| =|.Sum((th*<i>) ExpSeq ).| by Def14
    .=1 by Lm5;
  let th be Real;
  thus |.sin(th).| <= 1 by Lm5;
  thus thesis by Lm5;
end;
