{"id":"e-0d103fa5e9d4e10d","operation":{"operation":"definition_equality"},"operation_detail":null,"conclusion_id":"n-03d40c9aa990124e","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":"31b4cdd9944191e67f251c40a6dcbfff767812efa16c952ee68420a7b873b3bd","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"definition_equality","certificate_raw_size":9588,"certificate_compressed_size":2767,"conclusion_name":"shift_x_plus_one of Triangular array of generalized Narayana numbers T(n,k) = 2*binomial(n+1,k)* binomial(n-2,k-1)/(n+1) for n >= 1 and 0 <= k <= n-1, read by rows.","claims":[],"premises":[],"cited_by":[]}