induction p with
| nil => simp
| cons _ _ ih => simp only [Walk.transfer, cons_append, cons.injEq, heq_eq_eq, true_and, 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
w : V
H : Digraph V
q : Walk G v w
hpq : ∀ (e : V × V), e ∈ edges (append p q) → e ∈ edgeSet H
⊢ Walk.transfer (append p q) H hpq =
    append (Walk.transfer p H (_ : ∀ (e : V × V), e ∈ edges p → e ∈ edgeSet H))
      (Walk.transfer q H (_ : ∀ (e : V × V), e ∈ edges q → e ∈ edgeSet H))
no goals