  The a-theorem is demonstrated for the RG flows of entanglement entropy in two
and four dimensions. In four dimensions we relate it to the term quadratic in
intrinsic derivative of the dilaton along the entangling surface in the dilaton
entropy. The a-theorem, similarly to the c-theorem in two dimensions, then
follows from the positivity of the 2-point function of stress-energy tensor. We
suggest that the a-theorem, provided it is properly reformulated in terms of
the entanglement entropy, may follow from the c-theorem.
