{"id":"e-545f8764298a874b","operation":{"operation":"definition_equality"},"operation_detail":null,"conclusion_id":"n-7f1b09730105c8f0","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":"3346cc19bba5d7a28c658365f123d0bbfcc70bf1fb38bf8f9b924e8a1938fb60","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"definition_equality","certificate_raw_size":7206,"certificate_compressed_size":1947,"conclusion_name":"Triangle read by rows: T(n,k) = ((n+1)(n+2)/2) * binomial(n,k) (0 <= k <= n).","claims":[],"premises":[],"cited_by":[]}