{"id":"e-f5047d7bd9492925","operation":{"operation":"definition_equality"},"operation_detail":null,"conclusion_id":"n-b262f410552e359a","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":"9e1e906c51326cdd23572e918b466925d578b72077cd9f28be88e46750fcea1d","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"definition_equality","certificate_raw_size":26924,"certificate_compressed_size":4636,"conclusion_name":"shift_x_plus_one of Triangle of scaled 1-tiered binomial coefficients, T(n,k) = 2^(n+1)*(n-k,k)_1 (n >= 0, 0 <= k <= n), where (N,M)_1 is the 1-tiered binomial coefficient.","claims":[],"premises":[],"cited_by":[]}