{"id":"e-a6999a1e90ac081b","operation":{"operation":"definition_equality"},"operation_detail":null,"conclusion_id":"n-d9956ec4f2e74f86","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":"82d0bee444f8672b643e41db6b5221937f44531fd293754cc6c0b8dedf52238d","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"definition_equality","certificate_raw_size":10341,"certificate_compressed_size":2852,"conclusion_name":"shift_x_plus_one of Triangle read by rows: T(n,0)=1, T(n,n)=2, T(n,m) = T(n-1,m-1) + Sum_{k=0..m} T(n-1-k,m-k).","claims":[],"premises":[],"cited_by":[]}