∀ {n : Type u_1} {R : Type u_2} [inst : Ring R] [inst_1 : LinearOrder R] {A : Matrix n n R} (i j : n)
  (p : Quiver.Path i j) (motive : (∃ v p₁ p₂, p = p₁.comp p₂ ∧ p₁.length = 1) → Prop)
  (x : ∃ v p₁ p₂, p = p₁.comp p₂ ∧ p₁.length = 1),
  (∀ (v : n) (p₁ : Quiver.Path i v) (p₂ : Quiver.Path v j) (_hp_eq : p = p₁.comp p₂) (hp₁_len : p₁.length = 1),
      motive ⋯) →
    motive x