V is a stable morphism and V is a valuation object. V as any point of V is a specialization of K . X is a section of f making the diagram commutative. Let y ' be a specialization of y . X making that diagram commute.
V is a stable morphism.
X gives the desired morphism from V to X . Y is a morphism. D f is a closed special morphism. D f is quasi-compact and universally stable. Y is a quasi-compact morphism.