{"id":"e-e0757929e12c07e5","operation":{"operation":"definition_equality"},"operation_detail":null,"conclusion_id":"n-ce8106c936a63397","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":"5e8725812056952b3ab9f851cc4056495dc199ac928d7e95803da30fbee7f95a","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"definition_equality","certificate_raw_size":28184,"certificate_compressed_size":5068,"conclusion_name":"shift_x_plus_one of basis_map_A013610 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":[]}