We present an automated compositional program verification technique for safety properties based on conditional inductive invariants. For a given program part (e.g., a single loop) and a postcondition ϕ, we show how to, using a Max-SMT solver, an inductive invariant together with a precondition can be synthesized so that the precondition ensures the validity of the invariant and that the invariant implies ϕ. From this, we build a bottom-up program verification framework that propagates preconditions of small program parts as postconditions for preceding program parts. The method recovers from failures to prove the validity of a precondition, using the obtained intermediate results to restrict the search space for further proof attempts. As only small program parts need to be handled at a time, our method is scalable and distributable. The derived conditions can be viewed as implicit contracts between different parts of the program, and thus enable an incremental program analysis.