{"id":"e-51b17c42943e3651","operation":{"operation":"definition_equality"},"operation_detail":null,"conclusion_id":"n-392f49b496f79fbf","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":"92807fdb5ab786ae8f13a8feb5431d15c541347f070075d5b77b17352a8f4e87","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"definition_equality","certificate_raw_size":9313,"certificate_compressed_size":2417,"conclusion_name":"Square array of binomial coefficients T(n,k) = binomial(n,k), n >= 0, k >= 0, read by downward antidiagonals.","claims":[],"premises":[],"cited_by":[]}