proposition: Lemma bterm_poly_pos : forall (k : nat) (t : bterm k), P t.
proof: Proof. intros k t. apply (bterm_ind (@P k) (@Q k)). intros v Hv. unfold P. simpl. intuition. unfold Q. intros f ts H. unfold P. simpl. apply coef_pos_pcomp. apply (PI_WM f). unfold P in H. apply Vforall_map_intro. auto. unfold Q. simpl. trivial. intros t' n' s' H1. unfold Q. intro H2. simpl. split; hyp. Qed.
imports: CoLoR(ATerm ABterm ListUtil VecUtil PositivePolynom AInterpretation ZUtil NaryFunction ARelation RelUtil LogicUtil SN Polynom MonotonePolynom NatUtil ATrs BoundNat AWFMInterpretation ZUtil ACompat AMannaNess)