{"id":"e-8d798a959a00be52","operation":{"operation":"definition_equality"},"operation_detail":null,"conclusion_id":"n-c7b2a4255e084d17","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":"ce6cd051aec6962e1e470c21e0f65b25b71bba93c20a8ecf7ce00bca6d9cb0d6","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"definition_equality","certificate_raw_size":12957,"certificate_compressed_size":3419,"conclusion_name":"shift_x_plus_one of basis_map_A007318 of Triangle read by rows. T(n, k) = binomial(n, k)*binomial(n - 1, n - k - 1).","claims":[],"premises":[],"cited_by":[]}