{"id":"e-f4e0dab53593f1d4","operation":{"operation":"definition_equality"},"operation_detail":null,"conclusion_id":"n-864f996c2a017221","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":"9273f51040ff1059fb79e474168c52c270da91616fd2fce97109b8ea7117c8ed","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"definition_equality","certificate_raw_size":20012,"certificate_compressed_size":3790,"conclusion_name":"shift_x_plus_one of Triangle read by rows: T(n, k) = binomial(n - 1, k - 1)*binomial(n + k, k).","claims":[],"premises":[],"cited_by":[]}