if c:τ₀=τ₀' ∧ τ₁ = τ₁' then
  cases c.left
  cases c.right
  simp [Setoid.r, relH]
  intro _ h
  rw [h]
else
  simp [Setoid.r, relH, c]
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'
⊢ 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
no goals