{"id":"e-0104f9a2eba42f9b","operation":{"operation":"definition_equality"},"operation_detail":null,"conclusion_id":"n-07d0d70f782a78c7","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":"bc1566b3cc39b37a6280a7d7059f477f3937a5e479955dee9ec1651c15e772dd","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"definition_equality","certificate_raw_size":18432,"certificate_compressed_size":3662,"conclusion_name":"shift_x_plus_one of Triangle read by rows, T(n,k) = (k+1)*(n+1)!*(n+k)!/((k+1)!^2*(n-k)!) with n >= 0 and 0 <= k <= n.","claims":[],"premises":[],"cited_by":[]}