Fully Mechanized Proofs of Dilworths Theorem and Mirskys Theorem

Abstract: We present two fully mechanized proofs of Dilworths and Mirskys theorems in the Coq proof assistant. Dilworths Theorem states that in any finite partially ordered set (poset), the size of a smallest chain cover and a largest antichain are the same. Mirskys Theorem is a dual of Dilworths Theorem. We formalize the proofs by Perles 2 and by Mirsky 5. We also come up with a library of definitions and facts that can be used as a framework for formalizing other theorems on finite posets.