{"id":"e-57274ad9278ea6a8","operation":{"operation":"definition_equality"},"operation_detail":null,"conclusion_id":"n-2a657d152d421a92","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":"05c930c4e8a15607bc9b3e146be27a9c16592ed8715b1044d2261a2566849504","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"definition_equality","certificate_raw_size":7543,"certificate_compressed_size":2203,"conclusion_name":"Triangle T(n,k) read by rows: (1/n) * C(2n+k,k-1) * C(n,k); n, k >= 1.","claims":[],"premises":[],"cited_by":[]}