{"id":"e-368ed38f1d3fa427","operation":{"operation":"definition_equality"},"operation_detail":null,"conclusion_id":"n-e7d0ffa461d9dbc4","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":"805a5f9da618b4598c6faecfade7a37c0eb05baa5379985220d81b1123c18327","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"definition_equality","certificate_raw_size":39147,"certificate_compressed_size":12946,"conclusion_name":"Triangle read by rows: T(n,k) = (k+1)^2*binomial(n,k) (0 <= k <= n).","claims":[],"premises":[],"cited_by":[]}