{"id":"e-c12d924c8e8c7d11","operation":{"operation":"definition_equality"},"operation_detail":null,"conclusion_id":"n-6e441e5fd2d6315b","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":"77b66a08f9409dfc19cdc022ab50c09c0236e3bbf6bc9588bd42c3f1753f3eea","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"definition_equality","certificate_raw_size":13209,"certificate_compressed_size":3528,"conclusion_name":"shift_x_plus_one of basis_map_A013611 of Triangle read by rows. T(n, k) = binomial(n, k)*binomial(n - 1, n - k - 1).","claims":[],"premises":[],"cited_by":[]}