A monic divisor of a polynomial with a type has a type.

import Definitions.Def_TypeDensity_Basic
import Definitions.Def_TypeDensity_Formula_LawAlgebra
import Definitions.Def_TypeDensity_Algebra_AlgebraType
import Theorems.Thm_TypeDensity_squarefree_monic_has_polynomial_type
import Mathlib.FieldTheory.RatFunc.Basic
import Mathlib.MeasureTheory.Measure.Haar.Unique
import Mathlib.NumberTheory.ArithmeticFunction.Moebius
import Mathlib.NumberTheory.Padics.PadicIntegers
import Mathlib.RingTheory.IntegralClosure.IntegralRestrict
import Mathlib.RingTheory.MvPowerSeries.Basic
import Mathlib.RingTheory.RamificationInertia.Basic
import Mathlib.Topology.Algebra.Nonarchimedean.AdicTopology
import Mathlib.FieldTheory.Finite.GaloisField
import Mathlib.RingTheory.AdicCompletion.Algebra
import Mathlib.RingTheory.RegularLocalRing.Defs
import Mathlib.RingTheory.Henselian
set_option autoImplicit false

open TypeDensity
open scoped TensorProduct
open Polynomial IsLocalRing
open UniqueFactorizationMonoid

theorem TypeDensity.polynomial_type_dvd (O : Type) [CommRing O] [IsDomain O]
    (F G : Polynomial (BaseField O)) (σ : FactorType)
    (hF : HasPolynomialTypeF O F σ) (hG : G.Monic) (hdvd : G ∣ F) :
    ∃ τ : FactorType, HasPolynomialTypeF O G τ := by sorry