  In the present paper we introduce the generalized inverse operators which
have an interesting role in operator theory. We establish Douglas'
factorization theorem type for Hilbert pro-$C^{\ast}$-module. We introduce the
notion of atomic system and of $K$-frame in Hilbert pro-$C^{\ast}$-module and
we study the relationship between them. We also demonstrat some properties of
$K$-frame by using Douglas' factorization theorem.Finally we demonstrate that
the sum of two $K$-frames in a Hilbert pro-$C^{\ast}$-module with certain
conditions is once again a $K$-frame.
