{"id":"e-d86ba9d5ebdfaca2","operation":{"operation":"definition_equality"},"operation_detail":null,"conclusion_id":"n-31db8029f5c1d671","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":"5e9427fcd97be87f98ca982d2c176c3dd23058afcbdf27db5ab33c5aae50cd4b","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"definition_equality","certificate_raw_size":11647,"certificate_compressed_size":3115,"conclusion_name":"shift_x_plus_one of reversal of Triangle read by rows: T(n,k) is the number of double rise-bicolored Dyck paths (double rises come in two colors; also called marked Dyck paths) of semilength n and having k peaks (1 <= k <= n).","claims":[],"premises":[],"cited_by":[]}