induction p with
| nil _ =>
  simp [reduction_nil]
| cons e p ih =>
  simp [reduction_cons, ←cons_homotopic_redCons]
  apply cons_equiv_of_equiv
  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
⊢ [[reduction p]] = [[p]]
no goals