To provide high availability in distributed systems, object replicas allow concurrent updates. Although replicas eventually converge, they may diverge temporarily, for instance when the network fails. This makes it difficult for the developer to reason about the object's properties , and in particular, to prove invariants over its state. For the sub-class of state-based distributed systems, we propose a proof methodology for establishing that a given object maintains a given invariant, taking into account any concurrency control. Our approach allows reasoning about individual operations separately. We demonstrate that our rules are sound, and we illustrate their use with some representative examples. We automate the rule using Boogie, an SMT-based tool.