Weierstrass Curve tate A₆ eq eval Int

theorem WeierstrassCurve.tateA₆_eq_evalInt (q : k) (hq : valuation k q < 1) :    tateA₆ q = TateCurve.evalInt q TateCurve.a₆Formal := by  have h12 : ∀ d : ℤ, (12 : ℤ) ∣ 5 * d ^ 3 + 7 * d ^ 5 := by    intro d    have hz : ((5 * d ^ 3 + 7 * d ^ 5 : ℤ) : ZMod 12) = 0 := by      push_cast      generalize (d : ZMod 12) = r      revert r      decide    exact_mod_cast (ZMod.intCast_zmod_eq_zero_iff_dvd _ 12).mp hz  set c : ℕ → ℤ := fun d ↦ -((5 * (d : ℤ) ^ 3 + 7 * (d : ℤ) ^ 5) / 12) with hc  -- the coefficients of `a₆Formal` are the divisor sums of `c`: the divisor sum commutes  -- with the exact division by `12`  have hF : ∀ N, PowerSeries.coeff N TateCurve.a₆Formal = ∑ d ∈ N.divisors, c d := by    intro N    rw [TateCurve.coeff_a₆Formal]    symm    simp only [hc]    have hσ : ∑ d ∈ N.divisors, (5 * (d : ℤ) ^ 3 + 7 * (d : ℤ) ^ 5)        = 5 * (σ 3 N : ℤ) + 7 * (σ 5 N : ℤ) := by      rw [Finset.sum_add_distrib, ← Finset.mul_sum, ← Finset.mul_sum,        ArithmeticFunction.sigma_apply, ArithmeticFunction.sigma_apply]      push_cast      ring    have hsum : (12 : ℤ) ∣ 5 * (σ 3 N : ℤ) + 7 * (σ 5 N : ℤ) := by      rw [← hσ]      exact Finset.dvd_sum fun d _ ↦ h12 d    have hterm : ∀ d ∈ N.divisors, -((5 * (d : ℤ) ^ 3 + 7 * (d : ℤ) ^ 5) / 12) * 12        = -(5 * (d : ℤ) ^ 3 + 7 * (d : ℤ) ^ 5) := fun d _ ↦ by      rw [neg_mul, Int.ediv_mul_cancel (h12 d)]    apply mul_right_cancel₀ (b := (12 : ℤ)) (by norm_num)    rw [Finset.sum_mul, Finset.sum_congr rfl hterm, neg_mul, Int.ediv_mul_cancel hsum,      ← hσ, Finset.sum_neg_distrib]  rw [← TateCurve.tsum_lambert_eq_evalInt q hq c hF]  simp only [tateA₆]  refine tsum_congr fun m ↦ ?_  simp only [hc]  push_cast  ring