∀ {ctx : Int.Linear.Context} {p₁ p₂ : Int.Linear.Poly} {k : ℤ},
  k > 0 →
    Int.Linear.Poly.divCoeffs k p₁ = true →
      p₂ = Int.Linear.Poly.div k p₁ → (Int.Linear.Poly.denote ctx p₁ ≤ 0 ↔ Int.Linear.Poly.denote ctx p₂ ≤ 0)