Effective coordination of inference (à la theorem proving) and search (à la model checking) is one of the most important and interesting research topics in formal methods. We have developed several techniques for coordinating inference and search for verification with proof scores in CafeOBJ. The generate & check methods proposed in this paper are recent developments for invariant verification of this kind. The methods are based on (1) state representations as sets of observers, and (2) systematic generation of finite state patterns which subsume all possible infinite states. This paper describes the generate & check methods and their theoretical foundation. The methods and theory are explained with a small but instructive example of mutual exclusion protocol. The explanation is intended to be self-contained, and includes necessary basics of the CafeOBJ language/system also.リサーチレポート（北陸先端科学技術大学院大学情報科学研究科
