conv in f₁ (f₂ (x + y)) =>
  
  rw [show f₂ (x + y) = (f₂ (x + y) - f₂ x - f₂ y) + (f₂ x + f₂ y)
      by linarith]
G : Type u_1
inst✝ : AddCommGroup G
f₁ : ℤ → ℤ
bound₁ : ℕ
h₁ : AlmostAdditive f₁ bound₁
f₂ : G → ℤ
bound₂ : ℕ
h₂ : AlmostAdditive f₂ bound₂
x y : G
⊢ |f₁ (f₂ (x + y)) - f₁ (f₂ (x + y) - f₂ x - f₂ y) - f₁ (f₂ x + f₂ y)| + |f₁ (f₂ (x + y) - f₂ x - f₂ y)| +
      |f₁ (f₂ x + f₂ y) - f₁ (f₂ x) - f₁ (f₂ y)| ≤
    bound₁ + ((bound₁ + |f₁ 1|) * |f₂ (x + y) - f₂ x - f₂ y| + bound₁) + bound₁
G : Type u_1
inst✝ : AddCommGroup G
f₁ : ℤ → ℤ
bound₁ : ℕ
h₁ : AlmostAdditive f₁ bound₁
f₂ : G → ℤ
bound₂ : ℕ
h₂ : AlmostAdditive f₂ bound₂
x y : G
⊢ |f₁ (f₂ (x + y) - f₂ x - f₂ y + (f₂ x + f₂ y)) - f₁ (f₂ (x + y) - f₂ x - f₂ y) - f₁ (f₂ x + f₂ y)| +
        |f₁ (f₂ (x + y) - f₂ x - f₂ y)| +
      |f₁ (f₂ x + f₂ y) - f₁ (f₂ x) - f₁ (f₂ y)| ≤
    bound₁ + ((bound₁ + |f₁ 1|) * |f₂ (x + y) - f₂ x - f₂ y| + bound₁) + bound₁