{"id":"e-bff1938bf7a843de","operation":{"operation":"definition_equality"},"operation_detail":null,"conclusion_id":"n-6758fe7729845be8","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":"980e4671d9f4d3de029dc8fa938a8b8d0a22aee5c864ea3e2628b0b2b3d56553","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"definition_equality","certificate_raw_size":11898,"certificate_compressed_size":2956,"conclusion_name":"Triangular array binomial(2*n-k, k), k=0..n, n >= 0.","claims":[],"premises":[],"cited_by":[]}