We introduce a new approach to analyze distributed hybrid systems by a
generalization of rely-guarantee reasoning. First, we give a system for
deductive verification of class invariants and method contracts in
object-oriented distributed hybrid systems. In a hybrid setting, the object
invariant must not only be the post-condition of a method, but also has to hold
in the post-region of a method. The post-region describes all reachable states
after method termination before another process is guaranteed to run. The
system naturally generalizes rely-guarantee reasoning of discrete
object-oriented languages to hybrid systems and carries over its modularity to
hybrid systems: Only one dL-proof obligation is generated per method. The
post-region can be approximated using lightweight analyses and we give a
general notion of soundness for such analyses. Post-region based verification
is implemented for the Hybrid Active Object language HABS