∀ {X₁ X₂ X₃ X₄ : Type u_1} (t : X₁ ⟶ X₂) (r : X₂ ⟶ X₄) (l : X₁ ⟶ X₃) (b : X₃ ⟶ X₄)
  (w : CategoryTheory.CategoryStruct.comp t r = CategoryTheory.CategoryStruct.comp l b),
  (∀ (x₁ y₁ : X₁), t x₁ = t y₁ ∧ l x₁ = l y₁ → x₁ = y₁) →
    (∀ (x₂ : X₂) (x₃ : X₃), r x₂ = b x₃ → ∃ x₁, t x₁ = x₂ ∧ l x₁ = x₃) → Function.Bijective fun x₁ => ⟨(t x₁, l x₁), ⋯⟩