proposition: Lemma pos_lt_length : forall l, In x l -> pos l < length l.
proof: Proof. induction l; intro h; simpl. fo. destruct (eq_dec a x). lia. apply NatCompat.lt_n_S. fo. Qed.
imports: CoLoR(LogicUtil EqUtil RelUtil BoolUtil NatUtil) Coq(Setoid SetoidList FunInd)