{"id":"e-3b4345e33c507301","operation":{"operation":"definition_equality"},"operation_detail":null,"conclusion_id":"n-14d5814e0f152cf3","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":"778055aaa75ab326fc3013a66a66715664f831ac9157b255517fd0fb7085348e","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"definition_equality","certificate_raw_size":33917,"certificate_compressed_size":9518,"conclusion_name":"Triangle read by rows: T(n, k) = (n-k+1)*(k+1)*binomial(n, k).","claims":[],"premises":[],"cited_by":[]}