{"id":"e-86c00447f74e63c7","operation":{"operation":"definition_equality"},"operation_detail":null,"conclusion_id":"n-c1e8f5a3e0c5db28","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":"2dd4eb337db2e4e1804bd107a345f29f94786918d6e81813f859edaa0007c115","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"definition_equality","certificate_raw_size":29084,"certificate_compressed_size":5349,"conclusion_name":"shift_x_plus_one of gamma_polynomial of Triangle T(n, k) of numbers of square lattice walks that start and end at origin after 2*n steps and contain exactly k steps to the east, possibly touching origin at intermediate stages.","claims":[],"premises":[],"cited_by":[]}