{"id":"e-4cad2095b142c753","operation":{"operation":"definition_equality"},"operation_detail":null,"conclusion_id":"n-c72653d9ab0ee8be","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":"8c10e8f643900fba2c82854959b607434164c59bc1c59cd4263cb31cead934f7","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"definition_equality","certificate_raw_size":9839,"certificate_compressed_size":2679,"conclusion_name":"Triangle read by rows, T(n,k) = T(n-1,k) + T(n-2,k) + T(n-1,k-1) + T(n-2,k-1) and T(0,0) = 1.","claims":[],"premises":[],"cited_by":[]}