∀ {X : SSet.Truncated 1} {n : ℕ}
  (vertex : Fin (n + 1) → X.obj (Opposite.op { obj := { len := 0 }, property := SSet.Truncated.Path₁._proof_1 }))
  (arrow : Fin n → X.obj (Opposite.op { obj := { len := 1 }, property := SSet.Truncated.Path₁._proof_2 }))
  (arrow_src :
    ∀ (i : Fin n),
      X.map
          (SimplexCategory.Truncated.Hom.tr (SimplexCategory.δ 1) SSet.Truncated.Path₁._proof_1
              SSet.Truncated.Path₁._proof_5).op
          (arrow i) =
        vertex i.castSucc)
  (arrow_tgt :
    ∀ (i : Fin n),
      X.map
          (SimplexCategory.Truncated.Hom.tr (SimplexCategory.δ 0) SSet.Truncated.Path₁._proof_1
              SSet.Truncated.Path₁._proof_5).op
          (arrow i) =
        vertex i.succ)
  (vertex_1 : Fin (n + 1) → X.obj (Opposite.op { obj := { len := 0 }, property := SSet.Truncated.Path₁._proof_1 }))
  (arrow_1 : Fin n → X.obj (Opposite.op { obj := { len := 1 }, property := SSet.Truncated.Path₁._proof_2 }))
  (arrow_src_1 :
    ∀ (i : Fin n),
      X.map
          (SimplexCategory.Truncated.Hom.tr (SimplexCategory.δ 1) SSet.Truncated.Path₁._proof_1
              SSet.Truncated.Path₁._proof_5).op
          (arrow_1 i) =
        vertex_1 i.castSucc)
  (arrow_tgt_1 :
    ∀ (i : Fin n),
      X.map
          (SimplexCategory.Truncated.Hom.tr (SimplexCategory.δ 0) SSet.Truncated.Path₁._proof_1
              SSet.Truncated.Path₁._proof_5).op
          (arrow_1 i) =
        vertex_1 i.succ),
  ({ vertex := vertex, arrow := arrow, arrow_src := arrow_src, arrow_tgt := arrow_tgt } =
      { vertex := vertex_1, arrow := arrow_1, arrow_src := arrow_src_1, arrow_tgt := arrow_tgt_1 }) =
    (vertex = vertex_1 ∧ arrow = arrow_1)