{"id":"e-31df69d181e4ed73","operation":{"operation":"definition_equality"},"operation_detail":null,"conclusion_id":"n-2caa837a4ea68fa4","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":"dd44815a2f10144d58d5628de34208f20124e1a8f5cdcc8ac31c0ceebb2c7796","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"definition_equality","certificate_raw_size":28746,"certificate_compressed_size":5182,"conclusion_name":"shift_x_plus_one of shift_x_plus_one of Triangle read by rows, n>=1, 1<=k<=n, T(n,k) = k*binomial(n,k)^2/(n-k+1).","claims":[],"premises":[],"cited_by":[]}