proposition: Lemma all_mem_pos_all_mem_bounded : forall l1 l2, length l1 = length l2 -> all_mem_pos l1 -> all_mem_bounded (combine l1 l2) -> all_mem_pos l2.
proof: Proof. intros l1 l2;functional induction (combine l1 l2). destruct l';intros Hlength;try discriminate;tauto. intros abs;discriminate. intros Hlength;injection Hlength;clear Hlength;intro Hlength;simpl in *; inversion 1; inversion 1;auto with zarith. Qed.
imports: Coq(ZArith ZArithRing Ring_polynom Bool List FunInd Lia) CoLoR(closure)