intro ⟨h, heqn⟩
case mk.mpr
V : Type u
E : Type v
inst✝¹ : DecidableEq V
inst✝ : DecidableEq E
G : Graph V E
x₀ : V
H : Subgroup (π₁ G x₀)
η : EdgePath G x₀ x₀
η' : EdgePath G x₀ x₀ := reduction η
⊢ (∃ h',
      Quot.mk Reduction η =
        (Morphism.π₁map (basepoint H) x₀ (groupCoverProj H)
            (_ : (groupCoverProj H).toFuncV (basepoint H) = (groupCoverProj H).toFuncV (basepoint H)))
          h') →
    Quot.mk Reduction η ∈ H
case mk.mpr
V : Type u
E : Type v
inst✝¹ : DecidableEq V
inst✝ : DecidableEq E
G : Graph V E
x₀ : V
H : Subgroup (π₁ G x₀)
η : EdgePath G x₀ x₀
η' : EdgePath G x₀ x₀ := reduction η
h : π₁ (groupCover H) (basepoint H)
heqn :
  Quot.mk Reduction η =
    (Morphism.π₁map (basepoint H) x₀ (groupCoverProj H)
        (_ : (groupCoverProj H).toFuncV (basepoint H) = (groupCoverProj H).toFuncV (basepoint H)))
      h
⊢ Quot.mk Reduction η ∈ H