∀ {n : ℕ} {X Y : SSet.Truncated (n + 1)} {m : ℕ} (f : X.Path m) (σ : X ⟶ Y) (i : Fin m),
  ((SSet.Truncated.trunc (n + 1) 1 ⋯).obj Y).map
      (SimplexCategory.Truncated.Hom.tr (SimplexCategory.δ 1) SSet.Truncated.Path₁._proof_1
          SSet.Truncated.Path₁._proof_5).op
      (σ.app (Opposite.op { obj := { len := 1 }, property := ⋯ }) (f.arrow i)) =
    σ.app (Opposite.op { obj := { len := 0 }, property := ⋯ }) (f.vertex i.castSucc)