{"id":"e-9efbd63f6346959f","operation":{"operation":"definition_equality"},"operation_detail":null,"conclusion_id":"n-51a2369b25b8e3ba","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":"f96227cf78329d7658568b52d838aa62e44ea9251077740ca69fa4bc417d5f82","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"definition_equality","certificate_raw_size":19546,"certificate_compressed_size":3871,"conclusion_name":"shift_x_plus_one of Triangle read by rows: T(n,k) = binomial(k,n-k).","claims":[],"premises":[],"cited_by":[]}