∀ {K : Type u_1} [inst : Field K] {θ : NumberField.RingOfIntegers K} {p : ℕ} [inst_1 : Fact (Nat.Prime p)],
  Ideal.map (↑(Polynomial.mapEquiv (Int.quotientSpanNatEquivZMod p)))
      (Ideal.span {Polynomial.map (Ideal.Quotient.mk (Ideal.span {↑p})) (minpoly ℤ θ)}) =
    Ideal.map (↑(Polynomial.mapEquiv (Int.quotientSpanNatEquivZMod p)))
      (Ideal.span {Polynomial.map (Ideal.Quotient.mk (Ideal.span {↑p})) (minpoly ℤ θ)})