{"id":"e-0947a754cac34b3a","operation":{"operation":"definition_equality"},"operation_detail":null,"conclusion_id":"n-e88e218539d1c5b8","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":"c21f629aff416e3737aeb6c74fb24b5193a759105c44d307fe7e8cab8cfd5e9f","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"definition_equality","certificate_raw_size":28236,"certificate_compressed_size":5086,"conclusion_name":"shift_x_plus_one of basis_map_A013611 of Triangle read by rows: T(n,k) = binomial(n+1-k,k) (n >= 0, 0 <= k <= n).","claims":[],"premises":[],"cited_by":[]}