{"id":"e-fcbc5be6199b2413","operation":{"operation":"definition_equality"},"operation_detail":null,"conclusion_id":"n-4b0cf7bcb4c5bc01","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":"b3612c405b5dc9a6863baa1a4efd51922c9770fd4ab74c889dc9e67c1823ee4e","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"definition_equality","certificate_raw_size":10030,"certificate_compressed_size":2770,"conclusion_name":"shift_x_plus_one of Triangle T(n,k) with diagonals T(n,n-k) = binomial(n, 2*k).","claims":[],"premises":[],"cited_by":[]}