A Language for Encoding and Reconstruction of Rewriting Proofs

We present a language for encoding semiautomatic proofs of theorems in the inductive theory generated by a system of equations oriented as rewriting rules. These proofs can be made using a rewriting induction principle with a special notion of cover set. The proofs can include simple or conditional rewriting steps using auxiliary lemmas and case analysis subprooofs. The language allows the encoding of partially finished proofs for their later reconstruction and continuance. The language has been added to the p3f system and the successful experiments performed indicate its viability and usefulness for encoding and reconstruction of rewriting proofs.