{"id":"e-efa87cd8b4b765e4","operation":{"operation":"definition_equality"},"operation_detail":null,"conclusion_id":"n-97fcfd2b195b6955","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":"e65bf0966599d8ca9ec3e67a24bb94a43d5b25f36aa8e2b4fc6263d683717360","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"definition_equality","certificate_raw_size":28067,"certificate_compressed_size":4985,"conclusion_name":"shift_x_plus_one of basis_map_A013610 of Triangle of Narayana numbers T(n,k) = C(n-1,k-1)*C(n,k-1)/k with 1 <= k <= n, read by rows. Also called the Catalan triangle.","claims":[],"premises":[],"cited_by":[]}