{"id":"e-fa78f1f74242ae8d","operation":{"operation":"definition_equality"},"operation_detail":null,"conclusion_id":"n-b6cda967a092feb1","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":"2b63a36589f8b430381f76a72e81f679b50331c71fad87323fd961e6ec1063c9","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"definition_equality","certificate_raw_size":17205,"certificate_compressed_size":3809,"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 double rises (0 <= k <= n-1).","claims":[],"premises":[],"cited_by":[]}