{"id":"e-2ed63f4d16729a31","operation":{"operation":"definition_equality"},"operation_detail":null,"conclusion_id":"n-f61e14215f72611a","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":"67113f8df1cf19c7cce59cf17132881dd65b6a67c8e278a9baea635f730aa759","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"definition_equality","certificate_raw_size":12412,"certificate_compressed_size":3430,"conclusion_name":"shift_x_plus_one of Triangle T(n,k) = number of k-part order-consecutive partitions of n (1<=k<=n).","claims":[],"premises":[],"cited_by":[]}