rewrite [show m.succ • g = g + m • g from AddMonoid.nsmul_succ ..,
         show ↑(m.succ) * f g = f g + m * f g
           by rewrite [Nat.succ_eq_add_one, Nat.cast_succ]; linarith]
G : Type u_1
inst✝ : AddCommGroup G
f : G → ℤ
bound : ℕ
h : AlmostAdditive f bound
n : ℤ
g : G
m : ℕ
hᵢ : |f (m • g) - ↑m * f g| ≤ bound * (|↑m| + 1)
⊢ |f (Nat.succ m • g) - ↑(Nat.succ m) * f g| ≤ bound * (|↑(Nat.succ m)| + 1)
G : Type u_1
inst✝ : AddCommGroup G
f : G → ℤ
bound : ℕ
h : AlmostAdditive f bound
n : ℤ
g : G
m : ℕ
hᵢ : |f (m • g) - ↑m * f g| ≤ bound * (|↑m| + 1)
⊢ |f (g + m • g) - (f g + ↑m * f g)| ≤ bound * (|↑(Nat.succ m)| + 1)