{"id":"e-d5b983027f36fb5d","operation":{"operation":"definition_equality"},"operation_detail":null,"conclusion_id":"n-7fbdda6d907a2282","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":"1aeb170c3c89469ec5a6c7c64c7433b37656327357bd5e56f1316a1cc4b02b93","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"definition_equality","certificate_raw_size":11678,"certificate_compressed_size":3116,"conclusion_name":"shift_x_plus_one of 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":[]}