{"id":"e-828cb1728507cda8","operation":{"operation":"definition_equality"},"operation_detail":null,"conclusion_id":"n-e1a2b20716b1e97c","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":"6bc22fee32e58758c25075dd4458ad4d755ca5f6eef810a96742ee5fd6cc1096","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"definition_equality","certificate_raw_size":28133,"certificate_compressed_size":5032,"conclusion_name":"shift_x_plus_one of basis_map_A013610 of Triangle read by rows: T(n,k) is the number of Schroeder paths of semilength n containing exactly k peaks but no peaks at level one (n >= 1; 0 <= k <= n-1).","claims":[],"premises":[],"cited_by":[]}