{"id":"e-f042c28306dcf91e","operation":{"operation":"definition_equality"},"operation_detail":null,"conclusion_id":"n-c73008ca3f0e3c9c","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":"2f1a2cb9905952c0a0428ab878d2a3c377c8983c62b9245130bcf1221c840e31","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"definition_equality","certificate_raw_size":28811,"certificate_compressed_size":5207,"conclusion_name":"shift_x_plus_one of basis_map_A007318 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":[]}