{"id":"e-c53ed9793f68356e","operation":{"operation":"definition_equality"},"operation_detail":null,"conclusion_id":"n-c8b3f39d03de798f","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":"94d1b0e8154badba0176b3bf7eb54d991a8bcfa6b1df300c00b871eaa3b5d90c","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"definition_equality","certificate_raw_size":8705,"certificate_compressed_size":2361,"conclusion_name":"Square array of binomial coefficients T(n,k) = binomial(n,k), n >= 0, k >= 0, read by upward antidiagonals.","claims":[],"premises":[],"cited_by":[]}