{"id":"e-cdca5f77258a98bd","operation":{"operation":"definition_equality"},"operation_detail":null,"conclusion_id":"n-14506fb9ff389955","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":"b22000201e2bc95f3bff8a240859c33309c55e0ed13151a9597cde302047ebf7","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"definition_equality","certificate_raw_size":28020,"certificate_compressed_size":4958,"conclusion_name":"shift_x_plus_one of basis_map_A013609 of Triangle of Narayana numbers T(n,k) = C(n-1,k-1)*C(n,k-1)/k with 1 <= k <= n, read by rows. Also called the Catalan triangle.","claims":[],"premises":[],"cited_by":[]}