{"id":"e-0bcf293e4d350535","operation":{"operation":"definition_equality"},"operation_detail":null,"conclusion_id":"n-83e32d0bc1c10d45","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":"36d0f77002f9399bfcc8e09472d23d0a6b16ab9f976f3c50ca04d5803cf13b7b","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"definition_equality","certificate_raw_size":17483,"certificate_compressed_size":3861,"conclusion_name":"basis_map_A007318 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":[]}