∀ (ctx : Int.Linear.Context) (k₁ : ℤ) (p₁ : Int.Linear.Poly) (k₂ : ℤ) (p₂ : Int.Linear.Poly) (g : ℤ),
  Int.Linear.dvd_coeff_cert k₁ p₁ k₂ p₂ g = true →
    k₁ ∣ Int.Linear.Poly.denote' ctx p₁ → k₂ ∣ Int.Linear.Poly.denote' ctx p₂