Theorem 2 of this ICML paper only holds for structural constraints. Unfortunately the hypothesis for parameter constraints is not strong enough to obtain the same result, as they can imply in changes to the score of the node. We have not worked with parameter constraints anymore, mostly not because of this incorrect result but because they showed less appealing in our applications. It still remains to show any similar result with parameter constraints. Please refer to our JMLR paper "Efficient Structure Learning of Bayesian Networks using Constraints" 12:663-689, 2011, for a more detailed discussion.