induction p with
| nil _ =>
  simp [reduction_nil, reduced_nil]
| cons e p ih =>
  apply reduced_redCons
  assumption
V : Type u
E : Type v
inst✝¹ : DecidableEq V
inst✝ : DecidableEq E
G : Graph V E
v w : V
p : EdgePath G v w
⊢ reduced (reduction p)
no goals