proposition: Lemma alternate1_p l1 x l2: all_eq0 l1 -> x <0 -> alternate_1 l2 -> alternate (l1++x :: l2).
proof: Proof. elim:l1; first by move => _ xn h //=; rewrite xn. by move => a l Hrec /= /andP [az lz] xz; rewrite az (eqP az) ltxx; apply: Hrec. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice fintype order) mathcomp(binomial bigop ssralg poly ssrnum ssrint rat) mathcomp(polyrcf) pol