{"id":"e-b3a592a78406eb38","operation":{"operation":"definition_equality"},"operation_detail":null,"conclusion_id":"n-4b3c71e576f04d69","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":"83583ed7ec9f689334e4dc51b0ef41f6504256c7d023a7f8d0f84c0f916a1e27","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"definition_equality","certificate_raw_size":13173,"certificate_compressed_size":3524,"conclusion_name":"shift_x_plus_one of basis_map_A013610 of Triangle read by rows. T(n, k) = binomial(n, k)*binomial(n - 1, n - k - 1).","claims":[],"premises":[],"cited_by":[]}