{"id":"e-17841f9b7ad2ac5d","operation":{"operation":"definition_equality"},"operation_detail":null,"conclusion_id":"n-984320118b653f6b","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":"51f556abf2f48d6e039b9636a4ccfcdc4cee4fe51b38542153d4831b8e18ec86","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"definition_equality","certificate_raw_size":11766,"certificate_compressed_size":3001,"conclusion_name":"Triangle read by rows, n>=1, 1<=k<=n, T(n,k) = k*binomial(n,k)^2/(n-k+1).","claims":[],"premises":[],"cited_by":[]}