Module: Mathlib.NumberTheory.ModularForms.LFunction

Goal state before:
pp: case «0».«0»
Γ : Subgroup (GL (Fin 2) ℝ)
inst✝¹ : Γ.IsArithmetic
k : ℤ
hk : 0 < k
F : Type u_1
inst✝ : FunLike F ℍ ℂ
f : F
s : ℂ
⊢ ↑(Matrix.SpecialLinearGroup.toGL ((Matrix.SpecialLinearGroup.map (Int.castRingHom ℝ)) (-ModularGroup.S)))
      ((fun i ↦ i) ⟨0, ⋯⟩) ((fun i ↦ i) ⟨0, ⋯⟩) =
    ↑((Matrix.GeneralLinearGroup.map (Rat.castHom ℝ))
          (Matrix.SpecialLinearGroup.toGL ((Matrix.SpecialLinearGroup.map (Int.castRingHom ℚ)) (-ModularGroup.S))))
      ((fun i ↦ i) ⟨0, ⋯⟩) ((fun i ↦ i) ⟨0, ⋯⟩)

pp: case «0».«1»
Γ : Subgroup (GL (Fin 2) ℝ)
inst✝¹ : Γ.IsArithmetic
k : ℤ
hk : 0 < k
F : Type u_1
inst✝ : FunLike F ℍ ℂ
f : F
s : ℂ
⊢ ↑(Matrix.SpecialLinearGroup.toGL ((Matrix.SpecialLinearGroup.map (Int.castRingHom ℝ)) (-ModularGroup.S)))
      ((fun i ↦ i) ⟨0, ⋯⟩) ((fun i ↦ i) ⟨1, ⋯⟩) =
    ↑((Matrix.GeneralLinearGroup.map (Rat.castHom ℝ))
          (Matrix.SpecialLinearGroup.toGL ((Matrix.SpecialLinearGroup.map (Int.castRingHom ℚ)) (-ModularGroup.S))))
      ((fun i ↦ i) ⟨0, ⋯⟩) ((fun i ↦ i) ⟨1, ⋯⟩)

pp: case «1».«0»
Γ : Subgroup (GL (Fin 2) ℝ)
inst✝¹ : Γ.IsArithmetic
k : ℤ
hk : 0 < k
F : Type u_1
inst✝ : FunLike F ℍ ℂ
f : F
s : ℂ
⊢ ↑(Matrix.SpecialLinearGroup.toGL ((Matrix.SpecialLinearGroup.map (Int.castRingHom ℝ)) (-ModularGroup.S)))
      ((fun i ↦ i) ⟨1, ⋯⟩) ((fun i ↦ i) ⟨0, ⋯⟩) =
    ↑((Matrix.GeneralLinearGroup.map (Rat.castHom ℝ))
          (Matrix.SpecialLinearGroup.toGL ((Matrix.SpecialLinearGroup.map (Int.castRingHom ℚ)) (-ModularGroup.S))))
      ((fun i ↦ i) ⟨1, ⋯⟩) ((fun i ↦ i) ⟨0, ⋯⟩)

pp: case «1».«1»
Γ : Subgroup (GL (Fin 2) ℝ)
inst✝¹ : Γ.IsArithmetic
k : ℤ
hk : 0 < k
F : Type u_1
inst✝ : FunLike F ℍ ℂ
f : F
s : ℂ
⊢ ↑(Matrix.SpecialLinearGroup.toGL ((Matrix.SpecialLinearGroup.map (Int.castRingHom ℝ)) (-ModularGroup.S)))
      ((fun i ↦ i) ⟨1, ⋯⟩) ((fun i ↦ i) ⟨1, ⋯⟩) =
    ↑((Matrix.GeneralLinearGroup.map (Rat.castHom ℝ))
          (Matrix.SpecialLinearGroup.toGL ((Matrix.SpecialLinearGroup.map (Int.castRingHom ℚ)) (-ModularGroup.S))))
      ((fun i ↦ i) ⟨1, ⋯⟩) ((fun i ↦ i) ⟨1, ⋯⟩)

Tactic:
<;>

Goal state after:
case «0».«0»
Γ : Subgroup (GL (Fin 2) ℝ)
inst✝¹ : Γ.IsArithmetic
k : ℤ
hk : 0 < k
F : Type u_1
inst✝ : FunLike F ℍ ℂ
f : F
s : ℂ
⊢ ↑(Matrix.SpecialLinearGroup.toGL ((Matrix.SpecialLinearGroup.map (Int.castRingHom ℝ)) (-ModularGroup.S)))
      ((fun i ↦ i) ⟨0, ⋯⟩) ((fun i ↦ i) ⟨0, ⋯⟩) =
    ↑((Matrix.GeneralLinearGroup.map (Rat.castHom ℝ))
          (Matrix.SpecialLinearGroup.toGL ((Matrix.SpecialLinearGroup.map (Int.castRingHom ℚ)) (-ModularGroup.S))))
      ((fun i ↦ i) ⟨0, ⋯⟩) ((fun i ↦ i) ⟨0, ⋯⟩)

case «0».«1»
Γ : Subgroup (GL (Fin 2) ℝ)
inst✝¹ : Γ.IsArithmetic
k : ℤ
hk : 0 < k
F : Type u_1
inst✝ : FunLike F ℍ ℂ
f : F
s : ℂ
⊢ ↑(Matrix.SpecialLinearGroup.toGL ((Matrix.SpecialLinearGroup.map (Int.castRingHom ℝ)) (-ModularGroup.S)))
      ((fun i ↦ i) ⟨0, ⋯⟩) ((fun i ↦ i) ⟨1, ⋯⟩) =
    ↑((Matrix.GeneralLinearGroup.map (Rat.castHom ℝ))
          (Matrix.SpecialLinearGroup.toGL ((Matrix.SpecialLinearGroup.map (Int.castRingHom ℚ)) (-ModularGroup.S))))
      ((fun i ↦ i) ⟨0, ⋯⟩) ((fun i ↦ i) ⟨1, ⋯⟩)

case «1».«0»
Γ : Subgroup (GL (Fin 2) ℝ)
inst✝¹ : Γ.IsArithmetic
k : ℤ
hk : 0 < k
F : Type u_1
inst✝ : FunLike F ℍ ℂ
f : F
s : ℂ
⊢ ↑(Matrix.SpecialLinearGroup.toGL ((Matrix.SpecialLinearGroup.map (Int.castRingHom ℝ)) (-ModularGroup.S)))
      ((fun i ↦ i) ⟨1, ⋯⟩) ((fun i ↦ i) ⟨0, ⋯⟩) =
    ↑((Matrix.GeneralLinearGroup.map (Rat.castHom ℝ))
          (Matrix.SpecialLinearGroup.toGL ((Matrix.SpecialLinearGroup.map (Int.castRingHom ℚ)) (-ModularGroup.S))))
      ((fun i ↦ i) ⟨1, ⋯⟩) ((fun i ↦ i) ⟨0, ⋯⟩)

case «1».«1»
Γ : Subgroup (GL (Fin 2) ℝ)
inst✝¹ : Γ.IsArithmetic
k : ℤ
hk : 0 < k
F : Type u_1
inst✝ : FunLike F ℍ ℂ
f : F
s : ℂ
⊢ ↑(Matrix.SpecialLinearGroup.toGL ((Matrix.SpecialLinearGroup.map (Int.castRingHom ℝ)) (-ModularGroup.S)))
      ((fun i ↦ i) ⟨1, ⋯⟩) ((fun i ↦ i) ⟨1, ⋯⟩) =
    ↑((Matrix.GeneralLinearGroup.map (Rat.castHom ℝ))
          (Matrix.SpecialLinearGroup.toGL ((Matrix.SpecialLinearGroup.map (Int.castRingHom ℚ)) (-ModularGroup.S))))
      ((fun i ↦ i) ⟨1, ⋯⟩) ((fun i ↦ i) ⟨1, ⋯⟩)