We have implemented various symbolic model checking algorithms, such as BMC, k-Induction and IC3 for B, Event-B and other modeling languages. The high-level nature of software models accounts for complicated constraints arising in these symbolic analysis techniques. In this article we suggest using static information stemming from proof obligations to simplify occurring constraints. We show how to include proof information in the aforementioned algorithms. Using different benchmarks we compare explicit state to symbolic model checking as well as techniques with and without proof assistance. In particular for models with large branching factor, e.g., due to complicated data values being manipulated, the symbolic techniques fare much better than explicit state model checking. The inclusion of proof information results in further performance improvements.