{"id":"e-167ee17f7f3ebd58","operation":{"operation":"obreschkoff_combination"},"operation_detail":null,"conclusion_id":"n-e5a9584774d32c86","premise_count":2,"theorem":"Hermite--Kakeya--Obreschkoff: real-rooted f, g with interlacing zeros give a zero or real-rooted a f + b g for all real a, b (Obreschkoff 1963; Fisk, Polynomials, roots, and interlacing, Thm 1.43)","lean_route":null,"lean_declarations":[],"certificate_hash":"c3ba043a5d1c95d99e2295d86c861d88e5f0ca9d0a76747e1b4cb9f6dd71f046","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"obreschkoff_combination","certificate_raw_size":5909,"certificate_compressed_size":1601,"conclusion_name":"obreschkoff_combination of Expansion of e.g.f. (1 + y)^(1 + x).","claims":[{"claim":"real_rooted","from_index":0,"region":{}}],"premises":[{"position":0,"node_id":"n-ebe1ce47fcd8575c","role":"sequence","name":"Expansion of e.g.f. (1 + y)^(1 + x).","uses":{"claim":"real_rooted","from_index":0,"region":{}},"uses_text":"Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, +inf)"},{"position":1,"node_id":"n-ebe1ce47fcd8575c","role":"sequence","name":"Expansion of e.g.f. (1 + y)^(1 + x).","uses":{"claim":"interlacing","from_index":1,"kind":"weak","orientation":"unordered"},"uses_text":"Rows P_(m-1), P_m interlace (weak, unordered) for every m >= 1"}],"cited_by":[{"node_id":"n-e5a9584774d32c86","claim":"real_rooted"}]}