∀ {ι : Type u_1} [inst : Preorder ι] {G : ι → Type u_2} [inst_1 : (i : ι) → CommRing (G i)]
  {f' : (i j : ι) → i ≤ j → G i →+* G j} (q₂ : Polynomial (Ring.DirectLimit G fun i j h => ⇑(f' i j h)))
  (motive : (∃ i p, Polynomial.map (Ring.DirectLimit.of G (fun i j h => ⇑(f' i j h)) i) p = q₂) → Prop)
  (x : ∃ i p, Polynomial.map (Ring.DirectLimit.of G (fun i j h => ⇑(f' i j h)) i) p = q₂),
  (∀ (i₂ : ι) (p₂ : Polynomial (G i₂))
      (ih₂ : Polynomial.map (Ring.DirectLimit.of G (fun i j h => ⇑(f' i j h)) i₂) p₂ = q₂), motive ⋯) →
    motive x