On Mechanizing Proofs within a Complete Proof System for Unity

The solution proposed by Sanders in 14] consists of eliminating the need of the substitution axiom from Unity in order to eliminate the unsoundness problem caused by this axiom in Unity without loss of completeness. Sander's solution is based on the strongest invariant concept and provides theoretical advantages by formally capturing the eeects of the initial conditions on the properties of a program. This solution is less convincing from a practical point of view because it assumes proofs of strongest invariant in the meta-level. In this paper we reconsider this solution showing that the general concept of invariant is suucient to eliminate the substitution axiom and to provide a sound and relatively complete proof system for Unity logic. The advantage of the new solution is that proofs of invariants are mechanized inside the Unity logic itself.