{"id":"e-5012742dbb320f9a","operation":{"operation":"definition_equality"},"operation_detail":null,"conclusion_id":"n-aeb67fdaad2bc42e","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":"d38d04f81d081ea00648b2eae0f2bcabac10da568a765ec0d22e9cc405126d8c","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"definition_equality","certificate_raw_size":27030,"certificate_compressed_size":4684,"conclusion_name":"shift_x_plus_one of Triangle read by rows: T(n,k) = binomial(n+1-k,k) (n >= 0, 0 <= k <= n).","claims":[],"premises":[],"cited_by":[]}