We investigate the combination of the weak second-order monadic logic of one successor (WS1S) with higher-order logic (HOL). We show how these two logics can be combined, how theorem provers based on them can be safely integrated, and how the result can be used. In particular, we present an embedding of the semantics of WS1S in HOL that provides a basis for coupling the MONA system, a decision procedure for WS1S, with an implementation of HOL in the Isabelle system. Afterwards, we describe methods that reduce problems formalized in HOL to problems in the language of WS1S. We present applications to arithmetic reasoning and proving properties of parameterized sequential systems.

An existential theorem, for the specification or implementation of hardware, states that for any inputs there must exist at least one output which is consistent with it. It is proved to prevent an inconsistent model being produced and it is required to formally import the verification result from one verification system to another system. In this paper