{"id":"e-d6bf80c66f6fc720","operation":{"operation":"definition_equality"},"operation_detail":null,"conclusion_id":"n-79beb834849e7646","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":"3406d5c6dbb6f5d541c50326ddbef05026b4ccb24f7349717cd7836596690908","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"definition_equality","certificate_raw_size":18438,"certificate_compressed_size":3668,"conclusion_name":"shift_x_plus_one of Triangle read by rows. T(n, k) = binomial(n - 1, k - 1)*(n + k)! / k!.","claims":[],"premises":[],"cited_by":[]}