{"id":"e-bc62b354048e24a0","operation":{"operation":"definition_equality"},"operation_detail":null,"conclusion_id":"n-3177bea1e7729b42","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":"a4274b31f5d731c24d72b0cf8c7613b5911eda8681786c18aa3061cfc9ab1ec8","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"definition_equality","certificate_raw_size":28137,"certificate_compressed_size":5024,"conclusion_name":"shift_x_plus_one of basis_map_A013609 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":[]}