{"id":"e-799c0a3741176149","operation":{"operation":"definition_equality"},"operation_detail":null,"conclusion_id":"n-477d9807e1cbb785","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":"ee1e20f83b2985fa87817b2a86a04d1fa3291efc5062b5da7e24d55ba5ffc5fc","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"definition_equality","certificate_raw_size":4776,"certificate_compressed_size":1474,"conclusion_name":"basis-map coefficients of Triangle read by rows: T(n,k) = binomial(k,n-k). shifted by x -> -x + 0","claims":[],"premises":[],"cited_by":[]}