{"id":"e-5f2e71a1e47d5fe3","operation":{"operation":"definition_equality"},"operation_detail":null,"conclusion_id":"n-c2eaf5212a4dec13","premise_count":0,"theorem":"all-index identity Q_n = P_n certified by exact Ore-algebra division and identifying rows (polytool preserver-image certificate of the identity map)","lean_route":null,"lean_declarations":[],"certificate_hash":"8cf6162eb8c6172d737f778d31a5dfac753ed799769f4cd075771a6c9af91f1c","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"definition_equality","certificate_raw_size":16152,"certificate_compressed_size":3689,"conclusion_name":"Triangle of Narayana numbers T(n,k) = C(n-1,k-1)*C(n,k-1)/k with 1 <= k <= n, read by rows. Also called the Catalan triangle.","claims":[],"premises":[],"cited_by":[]}