{"id":"e-c2621fb6b5bc9d56","operation":{"operation":"definition_equality"},"operation_detail":null,"conclusion_id":"n-fe5f0667f4ce56c9","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":"c72ab902dd9f2a8bc8f309d2a1f2682eb30b831f5848b6fda29cd9610d933ee1","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"definition_equality","certificate_raw_size":27038,"certificate_compressed_size":4700,"conclusion_name":"shift_x_plus_one of 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":[]}