induction p with
| nil => simp
| cons _ _ ih =>
  rw [map_cons, Walk.cons_isPath_iff, support_map] at hp
  rw [Walk.cons_isPath_iff]
  cases' hp with hp1 hp2
  refine' ⟨ih hp1, _⟩
  contrapose! hp2
  exact List.mem_map_of_mem f hp2
V : Type u
V' : Type v
V'' : Type w
G : Digraph V
G' : Digraph V'
G'' : Digraph V''
f✝ : G →g G'
f' : G' →g G''
u v u' v' : V
p : Walk G u v
f : G →g G'
hp : IsPath (Walk.map f p)
⊢ IsPath p
no goals