-- Lean 4 proof step from Mathlib.RingTheory.DedekindDomain.Factorization (goal)
Goal:
R : Type u_1
inst : CommRing R
K : Type u_2
inst_1 : Field K
inst_2 : Algebra R K
inst_3 : IsFractionRing R K
inst_4 : IsDedekindDomain R
I : FractionalIdeal.{u_1, u_2} (R := R) R⁰ K
hI : ¬I = 0
⊢ ∀ᶠ (v : HeightOneSpectrum R) in Filter.cofinite, count K v I = 0
have h : ∀ (x : HeightOneSpectrum R),
  count K x I =
    HSub.hSub (α := ℤ)
      (↑(Associates.count (Associates.mk x.asIdeal)
            (Associates.factors
              (Associates.mk
                (choose (p := fun (x : Ideal R) ↦
                  choose (p := fun (x : R) ↦
                        ∃ (aI : Ideal R),
                          x ≠ 0 ∧
                            I =
                              HMul.hMul (α := FractionalIdeal.{u_1, u_2} (R := R) R⁰ K) (β :=
                                FractionalIdeal.{u_1, u_2} (R := R) R⁰ K)
                                (spanSingleton R⁰ ((algebraMap R K : (a : R) → K) x)⁻¹ :
                                  FractionalIdeal.{u_1, u_2} (R := R) R⁰ K)
                                ((↑aI : FractionalIdeal.{u_1, u_2} (R := R) R⁰ K) :
                                  FractionalIdeal.{u_1, u_2} (R := R) R⁰ K))
                        sorry ≠
                      0 ∧
                    I =
                      HMul.hMul (α := FractionalIdeal.{u_1, u_2} (R := R) R⁰ K) (β :=
                        FractionalIdeal.{u_1, u_2} (R := R) R⁰ K)
                        (spanSingleton R⁰
                            ((algebraMap R K : (a : R) → K)
                                (choose (p := fun (x : R) ↦
                                  ∃ (aI : Ideal R),
                                    x ≠ 0 ∧
                                      I =
                                        HMul.hMul (α := FractionalIdeal.{u_1, u_2} (R := R) R⁰ K) (β :=
                                          FractionalIdeal.{u_1, u_2} (R := R) R⁰ K)
                                          (spanSingleton R⁰ ((algebraMap R K : (a : R) → K) x)⁻¹ :
                                            FractionalIdeal.{u_1, u_2} (R := R) R⁰ K)
                                          ((↑aI : FractionalIdeal.{u_1, u_2} (R := R) R⁰ K) :
                                            FractionalIdeal.{u_1, u_2} (R := R) R⁰ K))
                                  sorry))⁻¹ :
                          FractionalIdeal.{u_1, u_2} (R := R) R⁰ K)
                        ((↑x : FractionalIdeal.{u_1, u_2} (R := R) R⁰ K) : FractionalIdeal.{u_1, u_2} (R := R) R⁰ K))
                  sorry)))) :
        ℤ)
      (↑(Associates.count (Associates.mk x.asIdeal)
            (Associates.factors
              (Associates.mk
                (Ideal.span
                  {choose (p := fun (x : R) ↦
                      ∃ (aI : Ideal R),
                        x ≠ 0 ∧
                          I =
                            HMul.hMul (α := FractionalIdeal.{u_1, u_2} (R := R) R⁰ K) (β :=
                              FractionalIdeal.{u_1, u_2} (R := R) R⁰ K)
                              (spanSingleton R⁰ ((algebraMap R K : (a : R) → K) x)⁻¹ :
                                FractionalIdeal.{u_1, u_2} (R := R) R⁰ K)
                              ((↑aI : FractionalIdeal.{u_1, u_2} (R := R) R⁰ K) :
                                FractionalIdeal.{u_1, u_2} (R := R) R⁰ K))
                      sorry})))) :
        ℤ)
Tactic: convert! finite_factors' hI (choose_spec (choose_spec (exists_eq_spanSingleton_mul I))).2