{"id":"e-e785025134c5ea24","operation":{"operation":"definition_equality"},"operation_detail":null,"conclusion_id":"n-4e8690098ee9d7b4","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":"e925621f35bd0505414c51eb5abefdc20596a4f2f37cd832ef091e9f9a763dae","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"definition_equality","certificate_raw_size":26710,"certificate_compressed_size":4656,"conclusion_name":"shift_x_plus_one of Triangle T(n,k) read by rows: number of size-k antisymmetric subsets of {1,2,...,n}.","claims":[],"premises":[],"cited_by":[]}