{"id":"e-ff79e0a5be8a3b3e","operation":{"operation":"definition_equality"},"operation_detail":null,"conclusion_id":"n-ca15886a6e790e73","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":"258cf595b91ac555c6a54d6fca606f2e5a2b52d05d5aa1029d3c54fb40b6690a","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"definition_equality","certificate_raw_size":9907,"certificate_compressed_size":2856,"conclusion_name":"shift_x_plus_one of shift_x_plus_one of Triangle read by rows: T(n, k) = (n-k+1)*(k+1)*binomial(n, k).","claims":[],"premises":[],"cited_by":[]}