{"id":"e-cfa07bd223f21b32","operation":{"operation":"definition_equality"},"operation_detail":null,"conclusion_id":"n-622af52a4165c278","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":"7d7535c4deabe282cbd8b45caf6ab6ec3f5204a334d80a0b7a151458ca25da27","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"definition_equality","certificate_raw_size":10690,"certificate_compressed_size":2880,"conclusion_name":"shift_x_plus_one of Square array of binomial coefficients T(n,k) = binomial(n,k), n >= 0, k >= 0, read by upward antidiagonals.","claims":[],"premises":[],"cited_by":[]}