{"id":"e-d6ef3d3814ca6f12","operation":{"operation":"definition_equality"},"operation_detail":null,"conclusion_id":"n-a5662819bbc56ccb","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":"05387f2c15df72ceae361273e31abdd6fc3fc41ffd38a03a39470626b3248703","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"definition_equality","certificate_raw_size":9413,"certificate_compressed_size":2513,"conclusion_name":"gamma_polynomial of Triangle T(n, k) is coefficient of z^n*w^k in 1/(1 - 2*z - 2*w - 2*z*w) read by rows in order 00, 10, 01, 20, 11, 02, ...","claims":[],"premises":[],"cited_by":[]}