{"id":"e-a99385591de0c3db","operation":{"operation":"definition_equality"},"operation_detail":null,"conclusion_id":"n-569a801b809b6abd","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":"4fbc0239729ed4067ae242a20063da65ffaf7e5cadcd8ca0644a34f25e9070bf","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"definition_equality","certificate_raw_size":8713,"certificate_compressed_size":2385,"conclusion_name":"Triangle read by rows: T(n,k) = binomial(n+1-k,k) (n >= 0, 0 <= k <= n).","claims":[],"premises":[],"cited_by":[]}