Representation-finite triangular algebras form an open scheme

Let V be a valuation ring in an algebraically closed field K with the residue field R. Assume that A is a V-order such that the R-algebra Ā obtained from A by reduction modulo the radical of V is triangular and representation-finite. Then the K-algebra KA ≅ A ⊗ _V is again triangular and representation-finite. It follows by the van den Dries’s test that triangular representation-finite algebras form an open scheme.