{"id":"e-a8e50b0e95b009dc","operation":{"operation":"definition_equality"},"operation_detail":null,"conclusion_id":"n-a12ea22caf034cea","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":"02a73ecc7f0cded3dc0b6fcecffbb1ce6c503143bf81c81e39df36aa457af7d6","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"definition_equality","certificate_raw_size":7427,"certificate_compressed_size":2011,"conclusion_name":"Triangular array read by rows: T(n,k) = binomial(n,2)*binomial(n,k), n>=0, 0<=k<=n.","claims":[],"premises":[],"cited_by":[]}