On Terminating Lemma Speculations

AbstractThe improvement of theorem provers by reusing previously computed proofs is investigated. A method for reusing proofs is formulated as an instance of the problem reduction paradigm such that lemmata are speculated as proof obligations, being subject for subsequent reuse attempts. We motivate and develop a termination requirement, prove its soundness, and show that the reusability of proofs is not spoiled by the termination requirement imposed on the reuse procedure. Additional evidence for the general usefulness of the proposed termination order is given for lemma speculation in induction theorem proving