  Let $B$ be a generalized Koszul algebra over a finite dimensional algebra
$S$. We construct a bimodule Koszul resolution of $B$ when the projective
dimension of $S_B$ equals 2. Using this we prove a Poincar\'e-Birkhoff-Witt
(PBW) type theorem for a deformation of a generalized Koszul algebra. When the
projective dimension of $S_B$ is greater than 2, we construct bimodule Koszul
resolutions for generalized smash product algebras obtained from braidings
between finite dimensional algebras and Koszul algebras, and then prove the PBW
type theorem. The results obtained can be applied to standard Koszul
Artin-Schelter Gorenstein algebras in the sense of Minamoto and Mori.
