simp [lift_of_proj]
V : Type u
E : Type v
inst✝¹ : DecidableEq V
inst✝ : DecidableEq E
G✝ : Graph V E
x₀✝ : V
G : Graph V E
x₀ : V
vert : Vert G x₀
e : EdgePath (univ G x₀) (basepoint G x₀) vert
⊢ (PathLift.pathClass
        (lift (EdgePath.map e (proj G x₀)) (proj G x₀) (basepoint G x₀)
          (_ : (proj G x₀).toFuncV (basepoint G x₀) = (proj G x₀).toFuncV (basepoint G x₀)))).τ =
    vert
V : Type u
E : Type v
inst✝¹ : DecidableEq V
inst✝ : DecidableEq E
G✝ : Graph V E
x₀✝ : V
G : Graph V E
x₀ : V
vert : Vert G x₀
e : EdgePath (univ G x₀) (basepoint G x₀) vert
⊢ (PathLift.pathClass
        { τ := vert, path := e, term_pushdown := (_ : (proj G x₀).toFuncV vert = (proj G x₀).toFuncV vert),
          list_pushdown :=
            (_ : List.map (proj G x₀).toFuncE (EdgePath.toList e) = EdgePath.toList (EdgePath.map e (proj G x₀))) }).τ =
    vert