  The recently-proposed generic Dijkstra algorithm finds shortest paths in
networks with continuous and contiguous resources. The algorithm was proposed
in the context of optical networks, but is applicable to networks with finite
and discrete resources. The algorithm was published without a proof of
correctness, and with a minor shortcoming. We provide that missing proof and
offer a correction to the shortcoming. To prove the algorithm correct, we
generalize the Bellman's principle of optimality to algebraic structures with a
partial ordering. We also argue the stated problem is tractable by analyzing
the size of the search space in the worst-case.
