{"id":"e-43ded58dbe73c25e","operation":{"operation":"definition_equality"},"operation_detail":null,"conclusion_id":"n-b4f19b398a718e0e","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":"ab619a55306b3f126be826866d96d861d4d29bd971ad5e8b658bddaf3c73a71f","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"definition_equality","certificate_raw_size":8783,"certificate_compressed_size":2527,"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 peaks (1 <= k <= n).","claims":[],"premises":[],"cited_by":[]}