{"id":"e-4bbc13aea32d7e48","operation":{"operation":"definition_equality"},"operation_detail":null,"conclusion_id":"n-d938c1937a93c4df","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":"a14ebeed2ef27ee5c0236f76b1d5d6b3d8ea7d1f5fb2dd180bf4b8223c174dd1","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"definition_equality","certificate_raw_size":17086,"certificate_compressed_size":3308,"conclusion_name":"Triangle of numbers T(n,k) = k!*Stirling2(n,k) read by rows (n >= 1, 1 <= k <= n).","claims":[],"premises":[],"cited_by":[]}