∀ {motive : (a : Lean.Grind.Linarith.Poly) → a.NonnegCoeffs → Prop} {a : Lean.Grind.Linarith.Poly} (t : a.NonnegCoeffs),
  motive Lean.Grind.Linarith.Poly.nil Lean.Grind.Linarith.Poly.NonnegCoeffs.nil →
    (∀ (a : ℤ) (x : Lean.Grind.Linarith.Var) (p : Lean.Grind.Linarith.Poly) (a_1 : a ≥ 0) (a_2 : p.NonnegCoeffs),
        motive (Lean.Grind.Linarith.Poly.add a x p) ⋯) →
      motive a t