{"chains":[{"edge":{"id":"e-8d7bc643ffd1dd86","operation":{"operation":"theorem_check","theorem":"liu_wang_three_term"},"operation_detail":"liu_wang_three_term","conclusion_id":"n-714479c216bddb04","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; Proposition 3.3 (the case B_n(x) = -(c_n x + d_n)^2)","lean_route":"sign","lean_declarations":["RealRooted.threeTerm_interlaces_of_eval_nonpos","RealRooted.threeTerm_interlaces","RealRooted.eval_nonpos_of_natDegree_le_two"],"certificate_hash":"df0aa5730c9fc4b48c728f137583c04b4b1332a6f3185d037564e4170d4f2771","verification_polytool":"replayed","verification_lean":"not_attempted","claims":[{"claim":"real_rooted","from_index":0,"region":{}},{"claim":"interlacing","from_index":1,"kind":"weak","orientation":"previous_interlaces_next"}],"premises":[]},"premises":[]}],"truncated":false,"expanded":1}