Weierstrass equation

theorem weierstrass_equation : Y ^ 2 + X * Y = X ^ 3 + a₄ * X + a₆ := by  rw [← sub_eq_zero]  refine eq_zero_of_forall_hasSum_zero _    {u : ℂ | Transcendental ℚ u ∧ 0 < ‖u‖ ∧ ‖u‖ < 1}    transcendental_punctured_unit_disk_infinite fun u hu ↦ ⟨‖u‖, hu.2.1, fun q hq0 hqu ↦ ?_⟩  obtain ⟨htr, -, hu1⟩ := hu  have hq1 : ‖q‖ < 1 := hqu.trans hu1  have hX := hasSum_X_eval htr hq0 hqu hu1  have hY := hasSum_Y_eval htr hq0 hqu hu1  have hY2 : HasSum (fun n : ℕ ↦ evalAt u ((PowerSeries.coeff n) (Y ^ 2)) * q ^ n)      (YAn u q ^ 2) := by simpa [pow_two] using hasSum_evalAt_mul htr hY hY  have hX3 : HasSum (fun n : ℕ ↦ evalAt u ((PowerSeries.coeff n) (X ^ 3)) * q ^ n)      (XAn u q ^ 3) := by    have hX2 : HasSum (fun n : ℕ ↦ evalAt u ((PowerSeries.coeff n) (X ^ 2)) * q ^ n)        (XAn u q ^ 2) := by simpa [pow_two] using hasSum_evalAt_mul htr hX hX    simpa [pow_succ, pow_two, mul_assoc] using hasSum_evalAt_mul htr hX2 hX  have hsum := hasSum_evalAt_sub htr    (hasSum_evalAt_add htr hY2 (hasSum_evalAt_mul htr hX hY))    (hasSum_evalAt_add htr (hasSum_evalAt_add htr hX3      (hasSum_evalAt_mul htr (hasSum_a₄_eval u hq1) hX)) (hasSum_a₆_eval u hq1))  convert hsum using 1  rw [analytic_weierstrass hq0 hqu hu1]  ring