One approach to verify the correctness of a system is to prove that it implements an executable (specification) model whose correctness is more obvious. Here, we define a kind of automata whose state is the product of values of multiple variables that we name State Transition System (STS). We define the semantics of TLA+ (specification language of the Temporal Logic of Actions) constructs using STSs, in particular the notions of TLA+ models, data hiding, and implication between models. We implement these concepts and prove their usefulness by applying them to the verification of C programs against abstract (TLA+ or STS) models and properties.