induction p with
| nil => simp
| cons _ _ ih =>
  simp only [Walk.transfer, cons.injEq, heq_eq_eq, true_and]
  apply ih
V : Type u
V' : Type v
V'' : Type w
G : Digraph V
G' : Digraph V'
G'' : Digraph V''
u v : V
p : Walk G u v
H : Digraph V
hp : ∀ (e : V × V), e ∈ edges p → e ∈ edgeSet H
K : Digraph V
hp' : ∀ (e : V × V), e ∈ edges (Walk.transfer p H hp) → e ∈ edgeSet K
⊢ Walk.transfer (Walk.transfer p H hp) K hp' = Walk.transfer p K (_ : ∀ (e : V × V), e ∈ edges p → e ∈ edgeSet K)
no goals