proposition: Lemma ith_eq_app : forall m l i (hi : i < length (l++m)) j (hj : j < length l), i = j -> ith hi = ith hj.
proof: Proof. induction l; simpl; intros. contradict hj; lia. subst j. destruct i. refl. apply IHl. refl. Qed.
imports: CoLoR(LogicUtil EqUtil RelUtil BoolUtil NatUtil) Coq(Setoid SetoidList FunInd)