∀ {α : Type u_1} [inst : Lean.Grind.CommRing α] [inst_1 : LE α] [inst_2 : LT α] [Std.LawfulOrderLT α]
  [inst_4 : Std.IsPreorder α] [Lean.Grind.OrderedRing α] (ctx : Lean.Grind.CommRing.Context α)
  (p₁ : Lean.Grind.CommRing.Poly) (k : ℤ) (p : Lean.Grind.CommRing.Poly),
  Lean.Grind.CommRing.mul_ineq_cert p₁ k p = true →
    Lean.Grind.CommRing.Poly.denote ctx p₁ < 0 → Lean.Grind.CommRing.Poly.denote ctx p < 0