{"id":"e-b21254b1ce82559a","operation":{"operation":"definition_equality"},"operation_detail":null,"conclusion_id":"n-08ac2c6d9914754c","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":"238233186c7674a0d28604f7c28dffd834ec7ee6cef91d0f62e48ea2c1a8b60e","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"definition_equality","certificate_raw_size":13741,"certificate_compressed_size":3264,"conclusion_name":"Triangle T(n, k) = coefficients of p(x, n) where p(x,n) = (x+1)*p(x, n-1) + n*(n-1)*x*p(x, n-2), read by rows.","claims":[],"premises":[],"cited_by":[]}