Rewriting Induction for Existentially Quantified Equations in Logically Constrained Rewriting (Full Version)

Rewriting Induction (RI) is a principle to prove that an equation over terms is an inductive theorem of a rewrite system, i.e., that any ground instance of the equation is a theorem of the rewrite system. RI has been adapted to several kinds of rewrite systems, and RI for constrained rewrite systems has been extended to inequalities. In this paper, we extend RI for constrained equations to existentially quantified equations in logically constrained rewriting. To this end, we first extend constrained equations by introducing existential quantification to the equation part of constrained equations. Then, in applying a constrained rewrite rule to such extended constrained equations, we introduce existential quantification to extra variables of the applied rule. Finally, using the extended application of constrained rewrite rules, we extend RI for constrained equations to existentially quantified equations.