∀ {R : Type u_1} [inst : CommRing R] [inst_1 : IsDomain R] [inst_2 : IsDiscreteValuationRing R] {a b : R},
  (IsDiscreteValuationRing.addVal R) (a * b) =
    (IsDiscreteValuationRing.addVal R) a + (IsDiscreteValuationRing.addVal R) b