{"chains":[{"edge":{"id":"e-0968a5ea4bacadd5","operation":{"operation":"parent_provers","route":"root_domain"},"operation_detail":"root_domain","conclusion_id":"n-52497a04d5e26922","premise_count":0,"theorem":"polytool parent provers, route root_domain: every parent row P_n, n >= 1, is zero or real-rooted with coefficients of one sign","lean_route":null,"lean_declarations":[],"certificate_hash":"fc34caef2e4a19b245f7ad322ea9c4333de05151ee36b62b86478cb44fb16dd2","verification_polytool":"replayed","verification_lean":"not_attempted","claims":[{"claim":"real_rooted","from_index":1,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[]},"premises":[]},{"edge":{"id":"e-f953fa70efc27616","operation":{"operation":"theorem_check","theorem":"liu_wang"},"operation_detail":"liu_wang","conclusion_id":"n-52497a04d5e26922","premise_count":0,"theorem":"L. L. Liu and Y. Wang, A unified approach to polynomial sequences with only real zeros, Adv. in Appl. Math. 38 (2007) 542-560, Theorem 2.1 with g = f' (as in their Corollary 2.4), with nonnegativity of the coefficients replaced by an exact induction keeping every root in (-inf, 0)","lean_route":null,"lean_declarations":[],"certificate_hash":"c39cd0c84c1cf7e0415d84a34a2f79d65f913b0828b8776271f906d6302ccef9","verification_polytool":"replayed","verification_lean":"not_attempted","claims":[{"claim":"real_rooted","from_index":1,"region":{"upper":{"closed":false,"value":"0"}}},{"claim":"interlacing","from_index":2,"kind":"weak","orientation":"previous_interlaces_next"}],"premises":[]},"premises":[]}],"truncated":false,"expanded":2}
