{"id":"e-0a47be968c31d18b","operation":{"operation":"definition_equality"},"operation_detail":null,"conclusion_id":"n-118f91023ad73cd8","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":"6c5cdb246dd16c5ad1ff655ece80aa41ee9df2c55fea7e67e4d41d6cca4ce45d","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"definition_equality","certificate_raw_size":16893,"certificate_compressed_size":3488,"conclusion_name":"basis_map_A007318 of Triangle read by rows: T(n,k) is the number of lattice paths from (0,0) to (n,n) using steps E=(1,0), N=(0,1) and D=(1,1) (i.e., bilateral Schroeder paths), having k D=(1,1) steps.","claims":[],"premises":[],"cited_by":[]}