A Omitted Proofs

We present the proof for Theorem 2 in the TACAS submission. We first need to define several definitions. Given a parameterized system instance sys(¯ k t) and state s ∈ S where S is the set of states in sys(¯ k t), we use q ip (s) and e ip (s) to denote the state of process i p in the system state s, and the set of outstanding events of process i p in the system state s, respectively, where p ∈ [1, t] and i ∈ [1, k p ].