{"id":"e-de6bb4e1a71d4229","operation":{"operation":"definition_equality"},"operation_detail":null,"conclusion_id":"n-7d332fcb7bf9a0f7","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":"ca2b9708ca85c7856c47f7003eeb5f81e3d6fe9c9189c16ede8f1b092c6ee188","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"definition_equality","certificate_raw_size":7605,"certificate_compressed_size":2261,"conclusion_name":"Triangle read by rows: T(n,k) is the number of ways to tile a 2 X n rectangle with k pieces of 2 X 2 tiles and n-2k pieces of 1 X 2 tiles (0 <= k <= floor(n/2)).","claims":[],"premises":[],"cited_by":[]}