theorem Th8:
  ((z+w) |^ n) / (n!) = Partial_Sums(Expan_e(n,z,w)).n
proof
  thus ((z+w) |^ n)/(n! )
  = (Partial_Sums(Expan(n,z,w)).n) * (1r/(n! )) by Th6
    .= ((1r/(n! )) (#) (Partial_Sums(Expan(n,z,w)))).n by VALUED_1:6
    .= Partial_Sums( (1r/(n! )) (#) Expan(n,z,w)).n by COMSEQ_3:29
    .= Partial_Sums(Expan_e(n,z,w)).n by Th7;
end;
