Restrictions, continued
Note that the result R of a general restriction is not necessarily a N-grid. In fact it is a N-grid iff the general restriction is decomposable into dimensional restrictions.
We can check the latter by considering dimensional projections of the set A onto the dimensions forming DI.
However even if a general restriction does not produce a N-grid, we can always consider R as a (N-k+1)-grid (where k is the length of the multiindex I) by deflating the set A into a virtual dimension. More precisely, it is possible to consider the R as a (N-k+hdim(A)+1)-grid because hdim(A)+1 is the maximal number of dimensions to which we could safely deflate A. One of these dimensions is virtual.