Observability concepts contribute to a better understanding of software correctness. In order to prove observational properties, the concept of Context Induction has been developed by Hennicker (Hennicker, Formal Aspects of Computing 3(4) (1991) 326–345). We propose in this paper to embed Context Induction in the implicit induction framework of (Bouhoula and Rusinowitch, Journal of Automated Reasoning 14(2) (1995) 189–235). The proof system we obtain applies to conditional specifications. It allows for many rewriting techniques and for the refutation of false observational conjectures. Under reasonable assumptions our method is refutationally complete, i.e. it can refute any conjecture which is not observationally valid. Moreover this proof system is operational: it has been implemented within the Spike prover and interesting computer experiments are reported.