{"id":"e-33efc42fb8feded5","operation":{"operation":"definition_equality"},"operation_detail":null,"conclusion_id":"n-21854f4257effb01","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":"d9258ddf50dba1cdda8dc5136eb0b5f1bd32935bdc926f1ac7caeb319b86fbc5","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"definition_equality","certificate_raw_size":9325,"certificate_compressed_size":2487,"conclusion_name":"Triangle read by rows: T(n,k) = binomial(k,n-k).","claims":[],"premises":[],"cited_by":[]}