{"id":"e-0c799dd389d7cc9b","operation":{"operation":"definition_equality"},"operation_detail":null,"conclusion_id":"n-59c91677863bdf29","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":"438355c2c6c6b16c9ba70cff9114f7211a55bcacd59c18b0521fc625aac66441","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"definition_equality","certificate_raw_size":20005,"certificate_compressed_size":4043,"conclusion_name":"shift_x_plus_one of basis_map_A013610 of Triangle read by rows: T(n,k) = binomial(k,n-k).","claims":[],"premises":[],"cited_by":[]}