{"id":"e-907ff3ac724c18dd","operation":{"operation":"definition_equality"},"operation_detail":null,"conclusion_id":"n-3ce0bead7a116750","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":"f67130aa94047df16c0fff2c11f26681d9cd1d57b19bdcadc347707bd85c62bb","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"definition_equality","certificate_raw_size":19843,"certificate_compressed_size":3734,"conclusion_name":"shift_x_plus_one of Triangle read by rows: T(n,k) = C(n+k,n)*C(n,k)/(k+1), for n >= 0, k = 0..n.","claims":[],"premises":[],"cited_by":[]}