{"id":"e-e1afdf3c1fb62188","operation":{"operation":"definition_equality"},"operation_detail":null,"conclusion_id":"n-57b4b14604f4c0d7","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":"1df16380fe81b8afbb380afa2f978ba952261d4d3fc61989eff27d1e16a351c7","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"definition_equality","certificate_raw_size":15302,"certificate_compressed_size":3620,"conclusion_name":"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":[]}