{"id":"e-b2c5a8e7eea225e1","operation":{"operation":"obreschkoff_combination"},"operation_detail":null,"conclusion_id":"n-5a7a22b91157a0bd","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":"af4857868c8be0fa7cc3f1b2e65902cbde72f58d478a6eae1df8f2d18f59cc0d","verification_polytool":"replayed","verification_lean":"not_attempted","certificate_kind":"obreschkoff_combination","certificate_raw_size":8502,"certificate_compressed_size":2226,"conclusion_name":"obreschkoff_combination of Triangle of coefficients in expansion of (1+3*x)^n.","claims":[{"claim":"real_rooted","from_index":0,"region":{}}],"premises":[{"position":0,"node_id":"n-6a5af5e1168bb679","role":"sequence","name":"Triangle of coefficients in expansion of (1+3*x)^n.","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-6a5af5e1168bb679","role":"sequence","name":"Triangle of coefficients in expansion of (1+3*x)^n.","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-5a7a22b91157a0bd","claim":"real_rooted"}]}