{"id":"e-21dd78e181b91ed1","operation":{"operation":"definition_equality"},"operation_detail":null,"conclusion_id":"n-6ad396ce174787e3","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":"fce3611117cc660cab010a0714a450737a786885a739548a775c9d1b820104dc","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"definition_equality","certificate_raw_size":16275,"certificate_compressed_size":3822,"conclusion_name":"basis_map_A007318 of Triangle read by rows: T(n,k) is the number of double rise-bicolored Dyck paths (double rises come in two colors; also called marked Dyck paths) of semilength n and having k peaks (1 <= k <= n).","claims":[],"premises":[],"cited_by":[]}