{"id":"e-d32fa4f50d269032","operation":{"operation":"definition_equality"},"operation_detail":null,"conclusion_id":"n-a6f3b35778192ffb","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":"8e28b77a778dd63f732cfb8f5b3cfe75c42a3c328e3a0e846f27ec3b01851e51","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"definition_equality","certificate_raw_size":13840,"certificate_compressed_size":3040,"conclusion_name":"Triangle T(n,k) = number of k-part order-consecutive partitions of n (1<=k<=n).","claims":[],"premises":[],"cited_by":[]}