{"id":"e-0431973470657681","operation":{"operation":"definition_equality"},"operation_detail":null,"conclusion_id":"n-78ba05b4a3dd925d","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":"4f5777a256d8c2b0c85e0d15cf0a4eacdf350db9365aa4c4fa0a5ce4ff5345b4","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"definition_equality","certificate_raw_size":15197,"certificate_compressed_size":3451,"conclusion_name":"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":[]}