simp [cons_toList] at h
case cons.cons
V : Type u
E : Type v
G✝ : Graph V E
u v✝² w✝² : V
e : EdgeBetween G✝ v✝² w✝²
G : Graph V E
v w v✝¹ w✝¹ u✝¹ v✝ w✝ u✝ : V
e₂ : EdgeBetween G v✝ w✝
p₂' : EdgePath G w✝ u✝
a_ih✝ :
  ∀ (e₁ : EdgeBetween G w✝ w✝¹) (p₁' : EdgePath G w✝¹ u✝),
    (∀ (p₂ : EdgePath G w✝¹ u✝), toList p₁' = toList p₂ → p₁' = p₂) →
      toList (cons e₁ p₁') = toList p₂' → cons e₁ p₁' = p₂'
e₁ : EdgeBetween G v✝ w✝¹
p₁' : EdgePath G w✝¹ u✝
ih : ∀ (p₂ : EdgePath G w✝¹ u✝), toList p₁' = toList p₂ → p₁' = p₂
h : toList (cons e₁ p₁') = toList (cons e₂ p₂')
⊢ cons e₁ p₁' = cons e₂ p₂'
case cons.cons
V : Type u
E : Type v
G✝ : Graph V E
u v✝² w✝² : V
e : EdgeBetween G✝ v✝² w✝²
G : Graph V E
v w v✝¹ w✝¹ u✝¹ v✝ w✝ u✝ : V
e₂ : EdgeBetween G v✝ w✝
p₂' : EdgePath G w✝ u✝
a_ih✝ :
  ∀ (e₁ : EdgeBetween G w✝ w✝¹) (p₁' : EdgePath G w✝¹ u✝),
    (∀ (p₂ : EdgePath G w✝¹ u✝), toList p₁' = toList p₂ → p₁' = p₂) →
      toList (cons e₁ p₁') = toList p₂' → cons e₁ p₁' = p₂'
e₁ : EdgeBetween G v✝ w✝¹
p₁' : EdgePath G w✝¹ u✝
ih : ∀ (p₂ : EdgePath G w✝¹ u✝), toList p₁' = toList p₂ → p₁' = p₂
h : e₁.edge = e₂.edge ∧ toList p₁' = toList p₂'
⊢ cons e₁ p₁' = cons e₂ p₂'