{"chains":[{"edge":{"id":"e-fe357ce1dbcb978c","operation":{"operation":"theorem_check","theorem":"liu_wang_three_term"},"operation_detail":"liu_wang_three_term","conclusion_id":"n-854413c64ac5ddd8","premise_count":0,"theorem":"L. L. Liu and Y. Wang, Adv. Appl. Math. 38 (2007) 542-560, Theorem 2.1 and Corollary 2.4 (A unified approach to polynomial sequences with only real zeros; the lag row as the interlacer, b_n = 0), weak interlacing of consecutive rows, with nonnegativity of the coefficients replaced, where a root region is certified, by an exact root-location induction; Theorem 2.3 with the interlacers P'_(n-1) and P_(n-2) (Corollary 2.4 with b_n = V_n)","lean_route":null,"lean_declarations":[],"certificate_hash":"f26f887bfc3b11574402a394b86b31d8b257ba4fbdf2571f2d677bd08884dc71","verification_polytool":"replayed","verification_lean":"not_attempted","claims":[{"claim":"real_rooted","from_index":3,"region":{"upper":{"closed":true,"value":"0"}}},{"claim":"interlacing","from_index":4,"kind":"weak","orientation":"previous_interlaces_next"}],"premises":[]},"premises":[]}],"truncated":false,"expanded":1}