apply homotopic_of_liftTerminal_eq lem
case a
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
e₁ e₂ : EdgePath (univ G x₀) (basepoint G x₀) vert
lem : liftTerminal (proj G x₀) (basepoint G x₀)
    (_ : (proj G x₀).toFuncV (basepoint G x₀) = (proj G x₀).toFuncV (basepoint G x₀)) (EdgePath.map e₁ (proj G x₀)) =
  liftTerminal (proj G x₀) (basepoint G x₀)
    (_ : (proj G x₀).toFuncV (basepoint G x₀) = (proj G x₀).toFuncV (basepoint G x₀)) (EdgePath.map e₂ (proj G x₀)) :=
  Eq.mpr
    (id
      (congrArg (fun _a => _a = liftTerminal (proj G x₀) (basepoint G x₀) rfl (EdgePath.map e₂ (proj G x₀)))
        (proj_liftTerminal e₁)))
    (Eq.mpr (id (congrArg (fun _a => vert = _a) (proj_liftTerminal e₂))) (Eq.refl vert))
⊢ [[EdgePath.map e₁ (proj G x₀)]] = [[EdgePath.map e₂ (proj G x₀)]]
no goals