{"id":"e-8dbf1b338748464c","operation":{"operation":"definition_equality"},"operation_detail":null,"conclusion_id":"n-4689fb1386d440ad","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":"5cfc3ee8e937d98d9f52e6bbd4ba36d28066ea92d1bafed8e101f0abf88c7a5b","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"definition_equality","certificate_raw_size":20127,"certificate_compressed_size":3542,"conclusion_name":"T(n,k) = binomial(n,k)*binomial(n+k,k), 0 <= k <= n, triangle read by rows.","claims":[],"premises":[],"cited_by":[]}