Let
![$I$](img14.png)
be a squarefree monomial ideal of a polynomial algebra over a field minimally generated by
![$f_1,\ldots,f_r$](img15.png)
of degree
![$ d\geq 1$](img16.png)
, and a set
![$E$](img17.png)
of monomials of degree
![$\geq d+1$](img18.png)
. Let
![$J\subsetneq I$](img19.png)
be a squarefree monomial ideal generated in degree
![$\geq d+1$](img18.png)
. Suppose that all squarefree monomials of
![$I\setminus (J\cup E)$](img20.png)
of degree
![$d+1$](img21.png)
are some least common multiples of
![$f_i$](img22.png)
. If
![$J$](img23.png)
contains all least common multiples of two of
![$(f_i)$](img24.png)
of degree
![$d+2$](img25.png)
then depth
![$\depth_SI/J\leq d+1$](img26.png)
and Stanley's Conjecture holds for
![$I/J$](img27.png)
.