{"paper":{"title":"Fully Mechanized Proofs of Dilworths Theorem and Mirskys Theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"cs.LO","authors_text":"Abhishek Kr Singh","submitted_at":"2017-03-17T17:55:35Z","abstract_excerpt":"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] (for Dilworths Theorem) and by Mirsky [5] (for the dual theorem). 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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.06133","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}