{"id":"e-11a7be78b851c6a1","operation":{"operation":"definition_equality"},"operation_detail":null,"conclusion_id":"n-6148d4afd1c19fd9","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":"f8ac8d15dce8ed43fff261805f793aa724b8de3d3c56ce7632dbd71b147d2e42","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"definition_equality","certificate_raw_size":28027,"certificate_compressed_size":4973,"conclusion_name":"shift_x_plus_one of 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":[]}