Suppose that we intend to adjust our beliefs about a collection 
by observation of two further collections 
and 
of quantities. We adjust B
by the collection 
(i.e. the collection 
) but separate the effects of the subsets of data.
Therefore, we adjust B in stages, first by D, then adding F. We may show
that the additional adjustment of B by F, given that we have already adjusted by
D, is the same as the adjustment of B by 
, the belief structure 
adjusted by 
:
(This relation follows as adjusting F by D removes the `common variability' between F and D.) We call
the (partial) adjustment of B by F given D. Note the following properties of partial adjustment.
