proposition: Lemma getTreeSupport_approx_0: forall (A : Set)(eqd : eq_dec A)(t : DistApproxTree A) a, ~In a (getTreeSupport eqd t) -> lowDistApproxFromTree eqd t a == 0.
proof: Proof. induction t; intuition; simpl in *. destruct o. simpl in *. intuition. destruct (eqd a a0); subst; intuition. intuition. rewrite IHt1. rewrite IHt2. rewrite ratMult_0_l. rewrite <- ratAdd_0_r. intuition. intuition. eapply H. unfold getTreeSupport in *. eapply in_getUnique. simpl. eapply in_or_app. right. eapply in_getUnique_if. eauto. intuition. eapply H. unfold getTreeSupport in *. eapply in_getUnique. simpl. eapply in_or_app. left. eapply in_getUnique_if. eauto. Qed.
imports: FCF.Comp FCF.DetSem FCF.DistSem FCF.Rat Arith FCF.StdNat FCF.Fold FCF.Limit Permutation ZifyNat