$D$_{i} describes all shortest paths with not more than $i$ edges.
Consequence: $D$_{n-1} = D
Proof
Assume shortest path $p$ with more than $n-1$ edges. Then there is some node
$v$ twice in this path i.e. $p=<i,\; ...,$v, ..., v,
..., j >. But then path $p\text{'}=<i,\; ...,\; v,\; ...,\; j\; >$
is shorter!