∀ {X Y : TopCat} {f g : C(↑X, ↑Y)} (H : f.Homotopy g) {x₀ x₁ : ↑X}
  (p : FundamentalGroupoid.fromTop x₀ ⟶ FundamentalGroupoid.fromTop x₁),
  CategoryTheory.CategoryStruct.comp ((FundamentalGroupoid.fundamentalGroupoidFunctor.map (TopCat.ofHom f)).map p)
        ⟦H.evalAt x₁⟧ =
      H.diagonalPath' p ∧
    CategoryTheory.CategoryStruct.comp ⟦H.evalAt x₀⟧
        ((FundamentalGroupoid.fundamentalGroupoidFunctor.map (TopCat.ofHom g)).map p) =
      H.diagonalPath' p