cases c.left
V : Type u
E : Type v
inst✝¹ : DecidableEq V
inst✝ : DecidableEq E
G : Graph V E
x₀ : V
H : Subgroup (π₁ G x₀)
τ₀ τ₁ : V
e : EdgeBetween G τ₀ τ₁
p : EdgePath G x₀ τ₀
is_reduced✝¹ : reduced p
τ₀' τ₁' : V
e' : EdgeBetween G τ₀' τ₁'
p' : EdgePath G x₀ τ₀'
is_reduced✝ : reduced p'
c : τ₀ = τ₀' ∧ τ₁ = τ₁'
⊢ Setoid.r { τ₀ := τ₀, τ₁ := τ₁, nxt := e, p := p, is_reduced := is_reduced✝¹ }
      { τ₀ := τ₀', τ₁ := τ₁', nxt := e', p := p', is_reduced := is_reduced✝ } →
    { τ₀ := τ₀, τ₁ := τ₁, nxt := e, p := p, is_reduced := is_reduced✝¹ }.nxt.edge =
      { τ₀ := τ₀', τ₁ := τ₁', nxt := e', p := p', is_reduced := is_reduced✝ }.nxt.edge
case refl
V : Type u
E : Type v
inst✝¹ : DecidableEq V
inst✝ : DecidableEq E
G : Graph V E
x₀ : V
H : Subgroup (π₁ G x₀)
τ₀ τ₁ : V
e : EdgeBetween G τ₀ τ₁
p : EdgePath G x₀ τ₀
is_reduced✝¹ : reduced p
τ₁' : V
e' : EdgeBetween G τ₀ τ₁'
p' : EdgePath G x₀ τ₀
is_reduced✝ : reduced p'
c : τ₀ = τ₀ ∧ τ₁ = τ₁'
⊢ Setoid.r { τ₀ := τ₀, τ₁ := τ₁, nxt := e, p := p, is_reduced := is_reduced✝¹ }
      { τ₀ := τ₀, τ₁ := τ₁', nxt := e', p := p', is_reduced := is_reduced✝ } →
    { τ₀ := τ₀, τ₁ := τ₁, nxt := e, p := p, is_reduced := is_reduced✝¹ }.nxt.edge =
      { τ₀ := τ₀, τ₁ := τ₁', nxt := e', p := p', is_reduced := is_reduced✝ }.nxt.edge