{"id":"e-fbebeadd27b9d988","operation":{"operation":"definition_equality"},"operation_detail":null,"conclusion_id":"n-d9640fb05f96c50b","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":"dfb1ae0d514e2ca396bab9d26754ddad31028a56c959cb5d3f9b54b80d0b1231","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"definition_equality","certificate_raw_size":27216,"certificate_compressed_size":4659,"conclusion_name":"shift_x_plus_one of Triangle read by rows: T(n, k) (0<=k<=2n) is the number of Delannoy paths of length n, having k steps.","claims":[],"premises":[],"cited_by":[]}