We formalize a multivariate quantifier elimination (QE) algorithm in the theorem prover Isabelle/HOL. Our algorithm is complete, in that it is able to reduce any quantified formula in the first-order logic of real arithmetic to a logically equivalent quantifier-free formula. The algorithm we formalize is a hybrid mixture of Tarski's original QE algorithm and the Ben-Or, Kozen, and Reif algorithm, and it is the first complete multivariate QE algorithm formalized in Isabelle/HOL.
- Kosaian, K., Tan, Y. K., & Platzer, A. (2023). A First Complete Algorithm for Real Quantifier Elimination in Isabelle/HOL. Proceedings of the 12th ACM SIGPLAN International Conference on Certified Programs and Proofs. https://doi.org/10.1145/3573105.3575672