cases prepend_cases e p with
| inl h =>
    rw [h]
| inr h =>
    let ⟨t, h₁, h₂⟩ := h
    rw [h₁] at hyp
    have split :
      cons e (cons e.bar t) =
        (nil u : EdgePath G u u) ++
          cons e (cons e.bar t) := by
        simp [nil_append]
    have :¬ reduced (cons e (cons e.bar t)) := by
            apply not_reduced_of_split split
    contradiction
V : Type u
E : Type v
inst✝¹ : DecidableEq V
inst✝ : DecidableEq E
G : Graph V E
u v w : V
e : EdgeBetween G u v
p : EdgePath G v w
hyp : reduced (cons e p)
⊢ redCons e p = cons e p
no goals