We present a Gentzen-style sequent calculus for program verification which accommodates both model checking-like verification based on global state space exploration, and compositional reasoning. To handle the complexities arising from the presence of fixed-point formulas, programs with dynamically evolving architecture, and cut rules we use transition assertions, and introduce fixed-point approximants explicitly into the assertion language. We address, in a game-based manner, the semantical basis of this approach, as it applies to the entailment subproblem. Soundness and completeness results are obtained, and examples are shown illustrating some of the concepts.