{"id":"e-2729d81eb6e0aef8","operation":{"operation":"definition_equality"},"operation_detail":null,"conclusion_id":"n-6a5cb0b957c123da","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":"0f5e5773d5eada0303babc1276088814d0cc87e47492af84de4f9ee970d75c85","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"definition_equality","certificate_raw_size":9840,"certificate_compressed_size":2701,"conclusion_name":"shift_x_plus_one of basis_map_A013609 of Triangle read by rows: T(n, k) = binomial(2n, 2k).","claims":[],"premises":[],"cited_by":[]}