induction p₁ with
| nil v => 
  simp [nil_toList]
| cons e p' ih =>
  simp [cons_toList]
  apply ih
V : Type u
E : Type v
inst✝¹ : DecidableEq V
inst✝ : DecidableEq E
G✝ : Graph V E
u✝ v✝ w✝ : V
e : EdgeBetween G✝ v✝ w✝
G : Graph V E
v w u : V
p₁ : EdgePath G v w
p₂ : EdgePath G w u
⊢ toList (p₁ ++ p₂) = toList p₁ ++ toList p₂
no goals