proposition: Lemma root_unique : forall x y, root x -> root y -> x = y.
proof: Proof. intros x y. unfold root. intros H_x H_y. case (fin_compare n x y); intro cmp; case cmp; intro H_cmp. - inversion H_cmp; auto. - inversion H_cmp. unfold fin_lt in H. rewrite H_x in H. rewrite H_y in H. contradict H. auto with arith. - inversion H_cmp. unfold fin_lt in H. rewrite H_x in H. rewrite H_y in H. contradict H. auto with arith. Qed.
imports: Verdi(Verdi) StructTact(Fin) Coq(OrderedType) Coq(MSetInterface)