awhecmu/canonical-drafter-extract-mathlib huggingface dataset:
-- Module: Mathlib.NumberTheory.ModularForms.LevelOne.DimensionFormula
Goal:
k : ℕ
hk : 3 ≤ k
hk2 : Even k
f : ModularForm (MonoidHom.range (G := SL(2, ℤ)) (Matrix.SpecialLinearGroup.mapGL ℝ)) (↑k : ℤ)
h : LT.lt (α := ℝ) 0 1
h₁ : 1 ∈ Subgroup.strictPeriods (MonoidHom.range (G := SL(2, ℤ)) (Matrix.SpecialLinearGroup.mapGL ℝ))
h₂ : LT.lt (α := ℝ) 0 1
h₃ : 1 ∈ Subgroup.strictPeriods (MonoidHom.range (G := SL(2, ℤ)) (Matrix.SpecialLinearGroup.mapGL ℝ))
⊢ HSMul.hSMul (α := ℂ) (β :=
      HasQuotient.Quotient (ModularForm (MonoidHom.range (G := SL(2, ℤ)) (Matrix.SpecialLinearGroup.mapGL ℝ)) (↑k : ℤ))
        (B := Submodule ℂ (ModularForm (MonoidHom.range (G := SL(2, ℤ)) (Matrix.SpecialLinearGroup.mapGL ℝ)) (↑k : ℤ)))
        (cuspFormSubmodule (MonoidHom.range (G := SL(2, ℤ)) (Matrix.SpecialLinearGroup.mapGL ℝ)) (↑k : ℤ)))
      ((PowerSeries.coeff 0 : (a : PowerSeries ℂ) → ℂ) (qExpansion 1 (⇑f : (a : ℍ) → ℂ)) : ℂ)
      (Submodule.Quotient.mk (E hk)) =
    Submodule.Quotient.mk f

Tactic:
rw [← Submodule.Quotient.mk_smul, Submodule.Quotient.eq, mem_cuspFormSubmodule_iff,
      isCuspForm_iff_coeffZero_eq_zero, ModularForm.coe_sub, ModularForm.qExpansion_sub,
      IsGLPos.coe_smul, ModularForm.qExpansion_smul, map_sub,
      PowerSeries.coeff_smul, E_qExpansion_coeff_zero hk hk2, smul_eq_mul, mul_one, sub_self]

Premises used: Submodule.Quotient.eq, map_sub, sub_self, ModularForm.isCuspForm_iff_coeffZero_eq_zero, ModularForm.mem_cuspFormSubmodule_iff, Submodule.Quotient.mk_smul, PowerSeries.coeff_smul, ModularForm.IsGLPos.coe_smul, ModularForm.qExpansion_sub, ModularForm.qExpansion_smul, smul_eq_mul, mul_one, EisensteinSeries.E_qExpansion_coeff_zero, ModularForm.coe_sub
-- Module: Mathlib.NumberTheory.ModularForms.LevelOne.DimensionFormula
Goal:
k : ℕ
hk : 3 ≤ k
hk2 : Even k
f : ModularForm (MonoidHom.range (G := SL(2, ℤ)) (Matrix.SpecialLinearGroup.mapGL ℝ)) (↑k : ℤ)
⊢ LT.lt (α := ℝ) 0 1

Tactic:
simp
-- Module: Mathlib.NumberTheory.ModularForms.LevelOne.DimensionFormula
Goal:
k : ℕ
hk : 3 ≤ k
hk2 : Even k
f : ModularForm (MonoidHom.range (G := SL(2, ℤ)) (Matrix.SpecialLinearGroup.mapGL ℝ)) (↑k : ℤ)
⊢ 1 ∈ Subgroup.strictPeriods (MonoidHom.range (G := SL(2, ℤ)) (Matrix.SpecialLinearGroup.mapGL ℝ))

Tactic:
simp
-- Module: Mathlib.NumberTheory.ModularForms.LevelOne.DimensionFormula
Goal:
⊢ 3 ≤ HAdd.hAdd (α := ℕ) 2 2

Tactic:
norm_num
-- Module: Mathlib.NumberTheory.ModularForms.LevelOne.DimensionFormula
Goal:
⊢ LT.lt (α := ℤ) (↑(HAdd.hAdd (α := ℕ) 2 2) : ℤ) 12

Tactic:
norm_num
-- Module: Mathlib.NumberTheory.ModularForms.LevelOne.DimensionFormula
Goal:
norm_cast norm_cast₁ norm_cast₂ norm_cast₃ : HAdd.hAdd (α := ℕ) 1 0 = 1
⊢ HAdd.hAdd (α := Cardinal.{0}) 1 0 = 1

Tactic:
norm_cast
-- Module: Mathlib.NumberTheory.ModularForms.LevelOne.DimensionFormula
Goal:
⊢ 3 ≤ HAdd.hAdd (α := ℕ) 3 3

Tactic:
norm_num
-- Module: Mathlib.NumberTheory.ModularForms.LevelOne.DimensionFormula
Goal:
⊢ LT.lt (α := ℤ) (↑(HAdd.hAdd (α := ℕ) 3 3) : ℤ) 12

Tactic:
norm_num
-- Module: Mathlib.NumberTheory.ModularForms.LevelOne.DimensionFormula
Goal:
⊢ bernoulli 4 = -1 / 30

Tactic:
decide +kernel
-- Module: Mathlib.NumberTheory.ModularForms.LevelOne.DimensionFormula
Goal:
⊢ Eq (α := ℂ) ((PowerSeries.coeff 1 : (a : PowerSeries ℂ) → ℂ) (qExpansion 1 (⇑E₄ : (a : ℍ) → ℂ)) : ℂ) (240 : ℂ)

Tactic:
norm_num [E_qExpansion_coeff _ ⟨2, rfl⟩, show bernoulli 4 = -1 / 30 by decide +kernel]

Premises used: EisensteinSeries.E_qExpansion_coeff, Exists.intro, OfNat.ofNat, rfl
-- Module: Mathlib.NumberTheory.ModularForms.LevelOne.DimensionFormula
Goal:
⊢ bernoulli 6 = 1 / 42

Tactic:
decide +kernel
-- Module: Mathlib.NumberTheory.ModularForms.LevelOne.DimensionFormula
Goal:
⊢ Eq (α := ℂ) ((PowerSeries.coeff 1 : (a : PowerSeries ℂ) → ℂ) (qExpansion 1 (⇑E₆ : (a : ℍ) → ℂ)) : ℂ) (-504 : ℂ)

Tactic:
norm_num [E_qExpansion_coeff _ ⟨3, rfl⟩, show bernoulli 6 = 1 / 42 by decide +kernel]

Premises used: EisensteinSeries.E_qExpansion_coeff, Exists.intro, OfNat.ofNat, rfl
-- Module: Mathlib.NumberTheory.ModularForms.LevelOne.DimensionFormula
Goal:
p p4 p6 : PowerSeries ℂ
c4 c6 : ℂ
hp4_0 : Eq (α := ℂ) ((PowerSeries.coeff 0 : (a : PowerSeries ℂ) → ℂ) p4 : ℂ) (1 : ℂ)
hp6_0 : Eq (α := ℂ) ((PowerSeries.coeff 0 : (a : PowerSeries ℂ) → ℂ) p6 : ℂ) (1 : ℂ)
hp4_1 : Eq (α := ℂ) ((PowerSeries.coeff 1 : (a : PowerSeries ℂ) → ℂ) p4 : ℂ) (240 : ℂ)
hp6_1 : Eq (α := ℂ) ((PowerSeries.coeff 1 : (a : PowerSeries ℂ) → ℂ) p6 : ℂ) (-504 : ℂ)
hqc4 : c4 • p4 = HPow.hPow (β := ℕ) p 2
hqc6 : c6 • p6 = HPow.hPow (β := ℕ) p 3
⊢ Eq (α := ℂ) ((PowerSeries.constantCoeff : (a : PowerSeries ℂ) → ℂ) p4 : ℂ) (1 : ℂ)

Tactic:
simp_all only [PowerSeries.coeff_zero_eq_constantCoeff]

Premises used: PowerSeries.coeff_zero_eq_constantCoeff
-- Module: Mathlib.NumberTheory.ModularForms.LevelOne.DimensionFormula
Goal:
p p4 p6 : PowerSeries ℂ
c4 c6 : ℂ
hp4_0 : Eq (α := ℂ) ((PowerSeries.coeff 0 : (a : PowerSeries ℂ) → ℂ) p4 : ℂ) (1 : ℂ)
hp6_0 : Eq (α := ℂ) ((PowerSeries.coeff 0 : (a : PowerSeries ℂ) → ℂ) p6 : ℂ) (1 : ℂ)
hp4_1 : Eq (α := ℂ) ((PowerSeries.coeff 1 : (a : PowerSeries ℂ) → ℂ) p4 : ℂ) (240 : ℂ)
hp6_1 : Eq (α := ℂ) ((PowerSeries.coeff 1 : (a : PowerSeries ℂ) → ℂ) p6 : ℂ) (-504 : ℂ)
hqc4 : c4 • p4 = HPow.hPow (β := ℕ) p 2
hqc6 : c6 • p6 = HPow.hPow (β := ℕ) p 3
hp4_0₁ : Eq (α := ℂ) ((PowerSeries.constantCoeff : (a : PowerSeries ℂ) → ℂ) p4 : ℂ) (1 : ℂ)
⊢ Eq (α := ℂ) ((PowerSeries.constantCoeff : (a : PowerSeries ℂ) → ℂ) p6 : ℂ) (1 : ℂ)

Tactic:
simp_all only [PowerSeries.coeff_zero_eq_constantCoeff]

Premises used: PowerSeries.coeff_zero_eq_constantCoeff
-- Module: Mathlib.NumberTheory.ModularForms.LevelOne.DimensionFormula
Goal:
p p4 p6 : PowerSeries ℂ
c4 c6 : ℂ
hp4_0 : Eq (α := ℂ) ((PowerSeries.coeff 0 : (a : PowerSeries ℂ) → ℂ) p4 : ℂ) (1 : ℂ)
hp6_0 : Eq (α := ℂ) ((PowerSeries.coeff 0 : (a : PowerSeries ℂ) → ℂ) p6 : ℂ) (1 : ℂ)
hp4_1 : Eq (α := ℂ) ((PowerSeries.coeff 1 : (a : PowerSeries ℂ) → ℂ) p4 : ℂ) (240 : ℂ)
hp6_1 : Eq (α := ℂ) ((PowerSeries.coeff 1 : (a : PowerSeries ℂ) → ℂ) p6 : ℂ) (-504 : ℂ)
hqc4 : c4 • p4 = HPow.hPow (β := ℕ) p 2
hqc6 : c6 • p6 = HPow.hPow (β := ℕ) p 3
hp4_0₁ : Eq (α := ℂ) ((PowerSeries.constantCoeff : (a : PowerSeries ℂ) → ℂ) p4 : ℂ) (1 : ℂ)
hp6_0₁ : Eq (α := ℂ) ((PowerSeries.constantCoeff : (a : PowerSeries ℂ) → ℂ) p6 : ℂ) (1 : ℂ)
⊢ Eq (α := ℂ) ((PowerSeries.coeff 1 : (a : PowerSeries ℂ) → ℂ) p4 : ℂ) (240 : ℂ)

Tactic:
simp_all only [PowerSeries.coeff_zero_eq_constantCoeff]

Premises used: PowerSeries.coeff_zero_eq_constantCoeff
-- Module: Mathlib.NumberTheory.ModularForms.LevelOne.DimensionFormula
Goal:
p p4 p6 : PowerSeries ℂ
c4 c6 : ℂ
hp4_0 : Eq (α := ℂ) ((PowerSeries.coeff 0 : (a : PowerSeries ℂ) → ℂ) p4 : ℂ) (1 : ℂ)
hp6_0 : Eq (α := ℂ) ((PowerSeries.coeff 0 : (a : PowerSeries ℂ) → ℂ) p6 : ℂ) (1 : ℂ)
hp4_1 : Eq (α := ℂ) ((PowerSeries.coeff 1 : (a : PowerSeries ℂ) → ℂ) p4 : ℂ) (240 : ℂ)
hp6_1 : Eq (α := ℂ) ((PowerSeries.coeff 1 : (a : PowerSeries ℂ) → ℂ) p6 : ℂ) (-504 : ℂ)
hqc4 : c4 • p4 = HPow.hPow (β := ℕ) p 2
hqc6 : c6 • p6 = HPow.hPow (β := ℕ) p 3
hp4_0₁ : Eq (α := ℂ) ((PowerSeries.constantCoeff : (a : PowerSeries ℂ) → ℂ) p4 : ℂ) (1 : ℂ)
hp6_0₁ : Eq (α := ℂ) ((PowerSeries.constantCoeff : (a : PowerSeries ℂ) → ℂ) p6 : ℂ) (1 : ℂ)
hp4_1₁ : Eq (α := ℂ) ((PowerSeries.coeff 1 : (a : PowerSeries ℂ) → ℂ) p4 : ℂ) (240 : ℂ)
⊢ Eq (α := ℂ) ((PowerSeries.coeff 1 : (a : PowerSeries ℂ) → ℂ) p6 : ℂ) (-504 : ℂ)

Tactic:
simp_all only [PowerSeries.coeff_zero_eq_constantCoeff]

Premises used: PowerSeries.coeff_zero_eq_constantCoeff
-- Module: Mathlib.NumberTheory.ModularForms.LevelOne.DimensionFormula
Goal:
p p4 p6 : PowerSeries ℂ
c4 c6 : ℂ
hp4_0 : Eq (α := ℂ) ((PowerSeries.coeff 0 : (a : PowerSeries ℂ) → ℂ) p4 : ℂ) (1 : ℂ)
hp6_0 : Eq (α := ℂ) ((PowerSeries.coeff 0 : (a : PowerSeries ℂ) → ℂ) p6 : ℂ) (1 : ℂ)
hp4_1 : Eq (α := ℂ) ((PowerSeries.coeff 1 : (a : PowerSeries ℂ) → ℂ) p4 : ℂ) (240 : ℂ)
hp6_1 : Eq (α := ℂ) ((PowerSeries.coeff 1 : (a : PowerSeries ℂ) → ℂ) p6 : ℂ) (-504 : ℂ)
hqc4 : c4 • p4 = HPow.hPow (β := ℕ) p 2
hqc6 : c6 • p6 = HPow.hPow (β := ℕ) p 3
hp4_0₁ : Eq (α := ℂ) ((PowerSeries.constantCoeff : (a : PowerSeries ℂ) → ℂ) p4 : ℂ) (1 : ℂ)
hp6_0₁ : Eq (α := ℂ) ((PowerSeries.constantCoeff : (a : PowerSeries ℂ) → ℂ) p6 : ℂ) (1 : ℂ)
hp4_1₁ : Eq (α := ℂ) ((PowerSeries.coeff 1 : (a : PowerSeries ℂ) → ℂ) p4 : ℂ) (240 : ℂ)
hp6_1₁ : Eq (α := ℂ) ((PowerSeries.coeff 1 : (a : PowerSeries ℂ) → ℂ) p6 : ℂ) (-504 : ℂ)
⊢ c4 • p4 = HPow.hPow (β := ℕ) p 2

Tactic:
simp_all only [PowerSeries.coeff_zero_eq_constantCoeff]

Premises used: PowerSeries.coeff_zero_eq_constantCoeff
-- Module: Mathlib.NumberTheory.ModularForms.LevelOne.DimensionFormula
Goal:
p p4 p6 : PowerSeries ℂ
c4 c6 : ℂ
hp4_0 : Eq (α := ℂ) ((PowerSeries.coeff 0 : (a : PowerSeries ℂ) → ℂ) p4 : ℂ) (1 : ℂ)
hp6_0 : Eq (α := ℂ) ((PowerSeries.coeff 0 : (a : PowerSeries ℂ) → ℂ) p6 : ℂ) (1 : ℂ)
hp4_1 : Eq (α := ℂ) ((PowerSeries.coeff 1 : (a : PowerSeries ℂ) → ℂ) p4 : ℂ) (240 : ℂ)
hp6_1 : Eq (α := ℂ) ((PowerSeries.coeff 1 : (a : PowerSeries ℂ) → ℂ) p6 : ℂ) (-504 : ℂ)
hqc4 : c4 • p4 = HPow.hPow (β := ℕ) p 2
hqc6 : c6 • p6 = HPow.hPow (β := ℕ) p 3
hp4_0₁ : Eq (α := ℂ) ((PowerSeries.constantCoeff : (a : PowerSeries ℂ) → ℂ) p4 : ℂ) (1 : ℂ)
hp6_0₁ : Eq (α := ℂ) ((PowerSeries.constantCoeff : (a : PowerSeries ℂ) → ℂ) p6 : ℂ) (1 : ℂ)
hp4_1₁ : Eq (α := ℂ) ((PowerSeries.coeff 1 : (a : PowerSeries ℂ) → ℂ) p4 : ℂ) (240 : ℂ)
hp6_1₁ : Eq (α := ℂ) ((PowerSeries.coeff 1 : (a : PowerSeries ℂ) → ℂ) p6 : ℂ) (-504 : ℂ)
hqc4₁ : c4 • p4 = HPow.hPow (β := ℕ) p 2
⊢ c6 • p6 = HPow.hPow (β := ℕ) p 3

Tactic:
simp_all only [PowerSeries.coeff_zero_eq_constantCoeff]

Premises used: PowerSeries.coeff_zero_eq_constantCoeff
-- Module: Mathlib.NumberTheory.ModularForms.LevelOne.DimensionFormula
Goal:
p p4 p6 : PowerSeries ℂ
c4 c6 : ℂ
hp4_0 : Eq (α := ℂ) ((PowerSeries.constantCoeff : (a : PowerSeries ℂ) → ℂ) p4 : ℂ) (1 : ℂ)
hp6_0 : Eq (α := ℂ) ((PowerSeries.constantCoeff : (a : PowerSeries ℂ) → ℂ) p6 : ℂ) (1 : ℂ)
hp4_1 : Eq (α := ℂ) ((PowerSeries.coeff 1 : (a : PowerSeries ℂ) → ℂ) p4 : ℂ) (240 : ℂ)
hp6_1 : Eq (α := ℂ) ((PowerSeries.coeff 1 : (a : PowerSeries ℂ) → ℂ) p6 : ℂ) (-504 : ℂ)
hqc4 : c4 • p4 = HPow.hPow (β := ℕ) p 2
hqc6 : c6 • p6 = HPow.hPow (β := ℕ) p 3
D : PowerSeries ℂ := HPow.hPow (β := ℕ) (c4 • p4) 3 - HPow.hPow (β := ℕ) (c6 • p6) 2
⊢ (PowerSeries.coeff 0 : (a : PowerSeries ℂ) → ℂ) D = HPow.hPow (β := ℕ) c4 3 - HPow.hPow (β := ℕ) c6 2

Tactic:
simp [D, hp4_0, hp6_0]
-- Module: Mathlib.NumberTheory.ModularForms.LevelOne.DimensionFormula
Goal:
p p4 p6 : PowerSeries ℂ
c4 c6 : ℂ
hp4_0 : Eq (α := ℂ) ((PowerSeries.constantCoeff : (a : PowerSeries ℂ) → ℂ) p4 : ℂ) (1 : ℂ)
hp6_0 : Eq (α := ℂ) ((PowerSeries.constantCoeff : (a : PowerSeries ℂ) → ℂ) p6 : ℂ) (1 : ℂ)
hp4_1 : Eq (α := ℂ) ((PowerSeries.coeff 1 : (a : PowerSeries ℂ) → ℂ) p4 : ℂ) (240 : ℂ)
hp6_1 : Eq (α := ℂ) ((PowerSeries.coeff 1 : (a : PowerSeries ℂ) → ℂ) p6 : ℂ) (-504 : ℂ)
hqc4 : c4 • p4 = HPow.hPow (β := ℕ) p 2
hqc6 : c6 • p6 = HPow.hPow (β := ℕ) p 3
D : PowerSeries ℂ := HPow.hPow (β := ℕ) (c4 • p4) 3 - HPow.hPow (β := ℕ) (c6 • p6) 2
⊢ (PowerSeries.coeff 0 : (a : PowerSeries ℂ) → ℂ) D = HPow.hPow (β := ℕ) c4 3 - HPow.hPow (β := ℕ) c6 2

Tactic:
have hD0 : D.coeff 0 = c4 ^ 3 - c6 ^ 2 := by simp [D, hp4_0, hp6_0]
-- Module: Mathlib.NumberTheory.ModularForms.LevelOne.DimensionFormula
Goal:
p p4 p6 : PowerSeries ℂ
c4 c6 : ℂ
hp4_0 : Eq (α := ℂ) ((PowerSeries.constantCoeff : (a : PowerSeries ℂ) → ℂ) p4 : ℂ) (1 : ℂ)
hp6_0 : Eq (α := ℂ) ((PowerSeries.constantCoeff : (a : PowerSeries ℂ) → ℂ) p6 : ℂ) (1 : ℂ)
hp4_1 : Eq (α := ℂ) ((PowerSeries.coeff 1 : (a : PowerSeries ℂ) → ℂ) p4 : ℂ) (240 : ℂ)
hp6_1 : Eq (α := ℂ) ((PowerSeries.coeff 1 : (a : PowerSeries ℂ) → ℂ) p6 : ℂ) (-504 : ℂ)
hqc4 : c4 • p4 = HPow.hPow (β := ℕ) p 2
hqc6 : c6 • p6 = HPow.hPow (β := ℕ) p 3
D : PowerSeries ℂ := HPow.hPow (β := ℕ) (c4 • p4) 3 - HPow.hPow (β := ℕ) (c6 • p6) 2
hD0 : (PowerSeries.coeff 0 : (a : PowerSeries ℂ) → ℂ) D = HPow.hPow (β := ℕ) c4 3 - HPow.hPow (β := ℕ) c6 2
simp :
  c4 *
        (c4 *
          (c4 *
            (HMul.hMul (β := ℂ)
                (HMul.hMul (α := ℂ) (β := ℂ) ((PowerSeries.constantCoeff : (a : PowerSeries ℂ) → ℂ) p4 : ℂ)
                  ((PowerSeries.constantCoeff : (a : PowerSeries ℂ) → ℂ) p4 : ℂ))
                ((PowerSeries.coeff 1 : (a : PowerSeries ℂ) → ℂ) p4 : ℂ) +
              HMul.hMul (β := ℂ)
                (HMul.hMul (α := ℂ) (β := ℂ) ((PowerSeries.constantCoeff : (a : PowerSeries ℂ) → ℂ) p4 : ℂ)
                    ((PowerSeries.coeff 1 : (a : PowerSeries ℂ) → ℂ) p4 : ℂ) +
                  HMul.hMul (α := ℂ) (β := ℂ) ((PowerSeries.coeff 1 : (a : PowerSeries ℂ) → ℂ) p4 : ℂ)
                    ((PowerSeries.constantCoeff : (a : PowerSeries ℂ) → ℂ) p4 : ℂ))
                ((PowerSeries.constantCoeff : (a : PowerSeries ℂ) → ℂ) p4 : ℂ)))) -
      c6 *
        (c6 *
          (HMul.hMul (α := ℂ) (β := ℂ) ((PowerSeries.constantCoeff : (a : PowerSeries ℂ) → ℂ) p6 : ℂ)
              ((PowerSeries.coeff 1 : (a : PowerSeries ℂ) → ℂ) p6 : ℂ) +
            HMul.hMul (α := ℂ) (β := ℂ) ((PowerSeries.coeff 1 : (a : PowerSeries ℂ) → ℂ) p6 : ℂ)
              ((PowerSeries.constantCoeff : (a : PowerSeries ℂ) → ℂ) p6 : ℂ))) =
    720 * (c4 * c4 * c4) + 1008 * (c6 * c6)
⊢ (PowerSeries.coeff 1 : (a : PowerSeries ℂ) → ℂ) D = 720 * HPow.hPow (β := ℕ) c4 3 + 1008 * HPow.hPow (β := ℕ) c6 2

Tactic:
simp [D, pow_succ, PowerSeries.coeff_mul, Finset.Nat.antidiagonal_succ]

Premises used: Finset.Nat.antidiagonal_succ, pow_succ, PowerSeries.coeff_mul
-- Module: Mathlib.NumberTheory.ModularForms.LevelOne.DimensionFormula
Goal:
p p4 p6 : PowerSeries ℂ
c4 c6 : ℂ
hp4_0 : Eq (α := ℂ) ((PowerSeries.constantCoeff : (a : PowerSeries ℂ) → ℂ) p4 : ℂ) (1 : ℂ)
hp6_0 : Eq (α := ℂ) ((PowerSeries.constantCoeff : (a : PowerSeries ℂ) → ℂ) p6 : ℂ) (1 : ℂ)
hp4_1 : Eq (α := ℂ) ((PowerSeries.coeff 1 : (a : PowerSeries ℂ) → ℂ) p4 : ℂ) (240 : ℂ)
hp6_1 : Eq (α := ℂ) ((PowerSeries.coeff 1 : (a : PowerSeries ℂ) → ℂ) p6 : ℂ) (-504 : ℂ)
hqc4 : c4 • p4 = HPow.hPow (β := ℕ) p 2
hqc6 : c6 • p6 = HPow.hPow (β := ℕ) p 3
D : PowerSeries ℂ := HPow.hPow (β := ℕ) (c4 • p4) 3 - HPow.hPow (β := ℕ) (c6 • p6) 2
hD0 : (PowerSeries.coeff 0 : (a : PowerSeries ℂ) → ℂ) D = HPow.hPow (β := ℕ) c4 3 - HPow.hPow (β := ℕ) c6 2
⊢ c4 *
        (c4 *
          (c4 *
            (HMul.hMul (β := ℂ)
                (HMul.hMul (α := ℂ) (β := ℂ) ((PowerSeries.constantCoeff : (a : PowerSeries ℂ) → ℂ) p4 : ℂ)
                  ((PowerSeries.constantCoeff : (a : PowerSeries ℂ) → ℂ) p4 : ℂ))
                ((PowerSeries.coeff 1 : (a : PowerSeries ℂ) → ℂ) p4 : ℂ) +
              HMul.hMul (β := ℂ)
                (HMul.hMul (α := ℂ) (β := ℂ) ((PowerSeries.constantCoeff : (a : PowerSeries ℂ) → ℂ) p4 : ℂ)
                    ((PowerSeries.coeff 1 : (a : PowerSeries ℂ) → ℂ) p4 : ℂ) +
                  HMul.hMul (α := ℂ) (β := ℂ) ((PowerSeries.coeff 1 : (a : PowerSeries ℂ) → ℂ) p4 : ℂ)
                    ((PowerSeries.constantCoeff : (a : PowerSeries ℂ) → ℂ) p4 : ℂ))
                ((PowerSeries.constantCoeff : (a : PowerSeries ℂ) → ℂ) p4 : ℂ)))) -
      c6 *
        (c6 *
          (HMul.hMul (α := ℂ) (β := ℂ) ((PowerSeries.constantCoeff : (a : PowerSeries ℂ) → ℂ) p6 : ℂ)
              ((PowerSeries.coeff 1 : (a : PowerSeries ℂ) → ℂ) p6 : ℂ) +
            HMul.hMul (α := ℂ) (β := ℂ) ((PowerSeries.coeff 1 : (a : PowerSeries ℂ) → ℂ) p6 : ℂ)
              ((PowerSeries.constantCoeff : (a : PowerSeries ℂ) → ℂ) p6 : ℂ))) =
    720 * (c4 * c4 * c4) + 1008 * (c6 * c6)

Tactic:
grind
-- Module: Mathlib.NumberTheory.ModularForms.LevelOne.DimensionFormula
Goal:
p p4 p6 : PowerSeries ℂ
c4 c6 : ℂ
hp4_0 : Eq (α := ℂ) ((PowerSeries.constantCoeff : (a : PowerSeries ℂ) → ℂ) p4 : ℂ) (1 : ℂ)
hp6_0 : Eq (α := ℂ) ((PowerSeries.constantCoeff : (a : PowerSeries ℂ) → ℂ) p6 : ℂ) (1 : ℂ)
hp4_1 : Eq (α := ℂ) ((PowerSeries.coeff 1 : (a : PowerSeries ℂ) → ℂ) p4 : ℂ) (240 : ℂ)
hp6_1 : Eq (α := ℂ) ((PowerSeries.coeff 1 : (a : PowerSeries ℂ) → ℂ) p6 : ℂ) (-504 : ℂ)
hqc4 : c4 • p4 = HPow.hPow (β := ℕ) p 2
hqc6 : c6 • p6 = HPow.hPow (β := ℕ) p 3
D : PowerSeries ℂ := HPow.hPow (β := ℕ) (c4 • p4) 3 - HPow.hPow (β := ℕ) (c6 • p6) 2
hD0 : (PowerSeries.coeff 0 : (a : PowerSeries ℂ) → ℂ) D = HPow.hPow (β := ℕ) c4 3 - HPow.hPow (β := ℕ) c6 2
⊢ (PowerSeries.coeff 1 : (a : PowerSeries ℂ) → ℂ) D = 720 * HPow.hPow (β := ℕ) c4 3 + 1008 * HPow.hPow (β := ℕ) c6 2

Tactic:
have hD1 : D.coeff 1 = 720 * c4 ^ 3 + 1008 * c6 ^ 2 := by
    simp [D, pow_succ, PowerSeries.coeff_mul, Finset.Nat.antidiagonal_succ]
    grind
-- Module: Mathlib.NumberTheory.ModularForms.LevelOne.DimensionFormula
Goal:
p p4 p6 : PowerSeries ℂ
c4 c6 : ℂ
hp4_0 : Eq (α := ℂ) ((PowerSeries.constantCoeff : (a : PowerSeries ℂ) → ℂ) p4 : ℂ) (1 : ℂ)
hp6_0 : Eq (α := ℂ) ((PowerSeries.constantCoeff : (a : PowerSeries ℂ) → ℂ) p6 : ℂ) (1 : ℂ)
hp4_1 : Eq (α := ℂ) ((PowerSeries.coeff 1 : (a : PowerSeries ℂ) → ℂ) p4 : ℂ) (240 : ℂ)
hp6_1 : Eq (α := ℂ) ((PowerSeries.coeff 1 : (a : PowerSeries ℂ) → ℂ) p6 : ℂ) (-504 : ℂ)
hqc4 : c4 • p4 = HPow.hPow (β := ℕ) p 2
hqc6 : c6 • p6 = HPow.hPow (β := ℕ) p 3
D : PowerSeries ℂ := HPow.hPow (β := ℕ) (c4 • p4) 3 - HPow.hPow (β := ℕ) (c6 • p6) 2
hD0 : (PowerSeries.coeff 0 : (a : PowerSeries ℂ) → ℂ) D = HPow.hPow (β := ℕ) c4 3 - HPow.hPow (β := ℕ) c6 2
hD1 : (PowerSeries.coeff 1 : (a : PowerSeries ℂ) → ℂ) D = 720 * HPow.hPow (β := ℕ) c4 3 + 1008 * HPow.hPow (β := ℕ) c6 2
⊢ p = 0

Tactic:
grind [pow_eq_zero_iff, zero_smul]

Premises used: pow_eq_zero_iff, zero_smul
-- Module: Mathlib.NumberTheory.ModularForms.LevelOne.DimensionFormula
Goal:
f : ModularForm (MonoidHom.range (G := SL(2, ℤ)) (Matrix.SpecialLinearGroup.mapGL ℝ)) 2
⊢ ∃ (c4 : ℂ), c4 • E₄ = f.mul f

Tactic:
(finrank_eq_one_iff_of_nonzero' E₄ (E_ne_zero _ ⟨2, rfl⟩)).mp
      (Module.rank_eq_one_iff_finrank_eq_one.mp levelOne_weight_four_rank_one) _

Premises used: EisensteinSeries.E_ne_zero, ModularForm.E₄, Module.rank_eq_one_iff_finrank_eq_one, Exists.intro, Iff.mp, ModularForm.levelOne_weight_four_rank_one, OfNat.ofNat, Int.add, finrank_eq_one_iff_of_nonzero', rfl
-- Module: Mathlib.NumberTheory.ModularForms.LevelOne.DimensionFormula
Goal:
f : ModularForm (MonoidHom.range (G := SL(2, ℤ)) (Matrix.SpecialLinearGroup.mapGL ℝ)) 2
obtain : ∀ (c4 : ℂ) (hc4 : c4 • E₄ = f.mul f), qExpansion 1 (⇑f : (a : ℍ) → ℂ) = 0
⊢ qExpansion 1 (⇑f : (a : ℍ) → ℂ) = 0

Tactic:
obtain ⟨c4, hc4⟩ : ∃ c4, c4 • E₄ = f.mul f :=
    (finrank_eq_one_iff_of_nonzero' E₄ (E_ne_zero _ ⟨2, rfl⟩)).mp
      (Module.rank_eq_one_iff_finrank_eq_one.mp levelOne_weight_four_rank_one) _

Premises used: EisensteinSeries.E_ne_zero, ModularForm.mul, ModularForm.E₄, Module.rank_eq_one_iff_finrank_eq_one, Exists.intro, Iff.mp, ModularForm.levelOne_weight_four_rank_one, OfNat.ofNat, finrank_eq_one_iff_of_nonzero', rfl
-- Module: Mathlib.NumberTheory.ModularForms.LevelOne.DimensionFormula
Goal:
f : ModularForm (MonoidHom.range (G := SL(2, ℤ)) (Matrix.SpecialLinearGroup.mapGL ℝ)) 2
c4 : ℂ
hc4 : c4 • E₄ = f.mul f
⊢ ∃ (c6 : ℂ), c6 • E₆ = (f.mul f).mul f

Tactic:
(finrank_eq_one_iff_of_nonzero' E₆ (E_ne_zero _ ⟨3, rfl⟩)).mp
      (Module.rank_eq_one_iff_finrank_eq_one.mp levelOne_weight_six_rank_one) _

Premises used: EisensteinSeries.E_ne_zero, Module.rank_eq_one_iff_finrank_eq_one, Exists.intro, Iff.mp, OfNat.ofNat, Int.add, finrank_eq_one_iff_of_nonzero', ModularForm.E₆, rfl, ModularForm.levelOne_weight_six_rank_one
-- Module: Mathlib.NumberTheory.ModularForms.LevelOne.DimensionFormula
Goal:
f : ModularForm (MonoidHom.range (G := SL(2, ℤ)) (Matrix.SpecialLinearGroup.mapGL ℝ)) 2
c4 : ℂ
hc4 : c4 • E₄ = f.mul f
obtain : ∀ (c6 : ℂ) (hc6 : c6 • E₆ = (f.mul f).mul f), qExpansion 1 (⇑f : (a : ℍ) → ℂ) = 0
⊢ qExpansion 1 (⇑f : (a : ℍ) → ℂ) = 0

Tactic:
obtain ⟨c6, hc6⟩ : ∃ c6, c6 • E₆ = (f.mul f).mul f :=
    (finrank_eq_one_iff_of_nonzero' E₆ (E_ne_zero _ ⟨3, rfl⟩)).mp
      (Module.rank_eq_one_iff_finrank_eq_one.mp levelOne_weight_six_rank_one) _

Premises used: EisensteinSeries.E_ne_zero, ModularForm.mul, Module.rank_eq_one_iff_finrank_eq_one, Exists.intro, Iff.mp, OfNat.ofNat, finrank_eq_one_iff_of_nonzero', ModularForm.E₆, rfl, ModularForm.levelOne_weight_six_rank_one
-- Module: Mathlib.NumberTheory.ModularForms.LevelOne.DimensionFormula
Goal:
f : ModularForm (MonoidHom.range (G := SL(2, ℤ)) (Matrix.SpecialLinearGroup.mapGL ℝ)) 2
c4 : ℂ
hc4 : c4 • E₄ = f.mul f
c6 : ℂ
hc6 : c6 • E₆ = (f.mul f).mul f
rw : c4 • qExpansion 1 (⇑E₄ : (a : ℍ) → ℂ) = qExpansion 1 (⇑f : (a : ℍ) → ℂ) * qExpansion 1 (⇑f : (a : ℍ) → ℂ)
rw₁ : c4 • qExpansion 1 (⇑E₄ : (a : ℍ) → ℂ) = qExpansion 1 (⇑(f.mul f) : (a : ℍ) → ℂ)
rw₂ : qExpansion 1 (HSMul.hSMul (β := (a : ℍ) → ℂ) c4 (⇑E₄ : (a : ℍ) → ℂ)) = qExpansion 1 (⇑(f.mul f) : (a : ℍ) → ℂ)
rw₃ rw₄ : qExpansion 1 (⇑(f.mul f) : (a : ℍ) → ℂ) = qExpansion 1 (⇑(f.mul f) : (a : ℍ) → ℂ)
⊢ c4 • qExpansion 1 (⇑E₄ : (a : ℍ) → ℂ) = HPow.hPow (β := ℕ) (qExpansion 1 (⇑f : (a : ℍ) → ℂ)) 2

Tactic:
rw [pow_two, ← ModularForm.qExpansion_mul one_pos one_mem_strictPeriods_SL f f,
      ← ModularForm.qExpansion_smul one_pos one_mem_strictPeriods_SL c4 E₄,
      show (c4 • E₄ : ℍ → ℂ) = (f.mul f) from congrArg DFunLike.coe hc4]

Premises used: pow_two, congrArg, one_mem_strictPeriods_SL, ModularForm.qExpansion_smul, ModularForm.E₄, ModularForm.qExpansion_mul, DFunLike.coe, one_pos
-- Module: Mathlib.NumberTheory.ModularForms.LevelOne.DimensionFormula
Goal:
f : ModularForm (MonoidHom.range (G := SL(2, ℤ)) (Matrix.SpecialLinearGroup.mapGL ℝ)) 2
c4 : ℂ
hc4 : c4 • E₄ = f.mul f
c6 : ℂ
hc6 : c6 • E₆ = (f.mul f).mul f
⊢ c4 • qExpansion 1 (⇑E₄ : (a : ℍ) → ℂ) = HPow.hPow (β := ℕ) (qExpansion 1 (⇑f : (a : ℍ) → ℂ)) 2

Tactic:
have hqc4 : c4 • qExpansion 1 (E₄ : ℍ → ℂ) = qExpansion 1 (f : ℍ → ℂ) ^ 2 := by
    rw [pow_two, ← ModularForm.qExpansion_mul one_pos one_mem_strictPeriods_SL f f,
      ← ModularForm.qExpansion_smul one_pos one_mem_strictPeriods_SL c4 E₄,
      show (c4 • E₄ : ℍ → ℂ) = (f.mul f) from congrArg DFunLike.coe hc4]
-- Module: Mathlib.NumberTheory.ModularForms.LevelOne.DimensionFormula
Goal:
f : ModularForm (MonoidHom.range (G := SL(2, ℤ)) (Matrix.SpecialLinearGroup.mapGL ℝ)) 2
c4 : ℂ
hc4 : c4 • E₄ = f.mul f
c6 : ℂ
hc6 : c6 • E₆ = (f.mul f).mul f
hqc4 : c4 • qExpansion 1 (⇑E₄ : (a : ℍ) → ℂ) = HPow.hPow (β := ℕ) (qExpansion 1 (⇑f : (a : ℍ) → ℂ)) 2
rw :
  c6 • qExpansion 1 (⇑E₆ : (a : ℍ) → ℂ) =
    HPow.hPow (β := ℕ) (qExpansion 1 (⇑f : (a : ℍ) → ℂ)) 2 * qExpansion 1 (⇑f : (a : ℍ) → ℂ)
rw₁ :
  c6 • qExpansion 1 (⇑E₆ : (a : ℍ) → ℂ) =
    qExpansion 1 (⇑f : (a : ℍ) → ℂ) * qExpansion 1 (⇑f : (a : ℍ) → ℂ) * qExpansion 1 (⇑f : (a : ℍ) → ℂ)
rw₂ : c6 • qExpansion 1 (⇑E₆ : (a : ℍ) → ℂ) = qExpansion 1 (⇑(f.mul f) : (a : ℍ) → ℂ) * qExpansion 1 (⇑f : (a : ℍ) → ℂ)
rw₃ : c6 • qExpansion 1 (⇑E₆ : (a : ℍ) → ℂ) = qExpansion 1 (⇑((f.mul f).mul f) : (a : ℍ) → ℂ)
rw₄ :
  qExpansion 1 (HSMul.hSMul (β := (a : ℍ) → ℂ) c6 (⇑E₆ : (a : ℍ) → ℂ)) = qExpansion 1 (⇑((f.mul f).mul f) : (a : ℍ) → ℂ)
rw₅ rw₆ : qExpansion 1 (⇑((f.mul f).mul f) : (a : ℍ) → ℂ) = qExpansion 1 (⇑((f.mul f).mul f) : (a : ℍ) → ℂ)
⊢ c6 • qExpansion 1 (⇑E₆ : (a : ℍ) → ℂ) = HPow.hPow (β := ℕ) (qExpansion 1 (⇑f : (a : ℍ) → ℂ)) 3

Tactic:
rw [pow_succ, pow_two, ← ModularForm.qExpansion_mul one_pos one_mem_strictPeriods_SL f f,
      ← ModularForm.qExpansion_mul one_pos one_mem_strictPeriods_SL (f.mul f) f,
      ← ModularForm.qExpansion_smul one_pos one_mem_strictPeriods_SL c6 E₆,
      show (c6 • E₆ : ℍ → ℂ) = (f.mul f).mul f from congrArg DFunLike.coe hc6]

Premises used: pow_two, congrArg, pow_succ, one_mem_strictPeriods_SL, ModularForm.mul, ModularForm.qExpansion_smul, ModularForm.qExpansion_mul, DFunLike.coe, one_pos, ModularForm.E₆
-- Module: Mathlib.NumberTheory.ModularForms.LevelOne.DimensionFormula
Goal:
f : ModularForm (MonoidHom.range (G := SL(2, ℤ)) (Matrix.SpecialLinearGroup.mapGL ℝ)) 2
c4 : ℂ
hc4 : c4 • E₄ = f.mul f
c6 : ℂ
hc6 : c6 • E₆ = (f.mul f).mul f
hqc4 : c4 • qExpansion 1 (⇑E₄ : (a : ℍ) → ℂ) = HPow.hPow (β := ℕ) (qExpansion 1 (⇑f : (a : ℍ) → ℂ)) 2
⊢ c6 • qExpansion 1 (⇑E₆ : (a : ℍ) → ℂ) = HPow.hPow (β := ℕ) (qExpansion 1 (⇑f : (a : ℍ) → ℂ)) 3

Tactic:
have hqc6 : c6 • qExpansion 1 E₆ = qExpansion 1 (f : ℍ → ℂ) ^ 3 := by
    rw [pow_succ, pow_two, ← ModularForm.qExpansion_mul one_pos one_mem_strictPeriods_SL f f,
      ← ModularForm.qExpansion_mul one_pos one_mem_strictPeriods_SL (f.mul f) f,
      ← ModularForm.qExpansion_smul one_pos one_mem_strictPeriods_SL c6 E₆,
      show (c6 • E₆ : ℍ → ℂ) = (f.mul f).mul f from congrArg DFunLike.coe hc6]