calc |f (g + m • g) - (f g + m * f g)|
    = |(f (g + m • g) - f g - f (m • g)) + (f (m • g) - m * f g)|
        := congrArg Int.natAbs <| by linarith
  _ ≤ |f (g + m • g) - f g - f (m • g)| + |f (m • g) - m * f g|
        := Int.natAbs_add_le ..
  _ ≤ bound + bound * (m + 1)
        := Nat.add_le_add (h.almost_additive ..) hᵢ
  _ = bound * (m.succ + 1)
        := by 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 (g + m • g) - (f g + ↑m * f g)| ≤ bound * (|↑(Nat.succ m)| + 1)
no goals