induction p with
| nil _ => 
  simp [nil_toList]
| cons e p' ih =>
  simp [cons_toList, reverse_cons, concat_toList]
  simp [ih, EdgeBetween.bar]
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 : V
p : EdgePath G v w
⊢ List.reverse (toList p) = List.map G.bar (toList (reverse p))
no goals