reserve X for Banach_Algebra,
  w,z,z1,z2 for Element of X,
  k,l,m,n,n1,n2 for Nat,
  seq,seq1,seq2,s,s9 for sequence of X,
  rseq for Real_Sequence;

theorem Th37:
  exp(0.X) = 1.X
proof
  exp(0.X) =Sum( 0.X rExpSeq) by Def10
    .=1.X by Th20;
  hence thesis;
end;
