no goals
V : Type u
V' : Type v
V'' : Type w
G : SimpleGraph V
G' : SimpleGraph V'
G'' : SimpleGraph V''
f : G →g G'
f' : G' →g G''
u v u' v' : V
p : Walk G u v
⊢ edges (Walk.map f p) = List.map (Sym2.map ↑f) (edges p)
induction p with
| nil => rfl
| cons _ _ ih =>
  simp only [Walk.map_cons, edges_cons, List.map_cons, Sym2.map_pair_eq, List.cons.injEq,
    true_and, ih]
no goals
case nil
V : Type u
V' : Type v
V'' : Type w
G : SimpleGraph V
G' : SimpleGraph V'
G'' : SimpleGraph V''
f : G →g G'
f' : G' →g G''
u v u' v' : V
p : Walk G u v
u✝ : V
⊢ edges (Walk.map f nil) = List.map (Sym2.map ↑f) (edges nil)
rfl
no goals
case cons
V : Type u
V' : Type v
V'' : Type w
G : SimpleGraph V
G' : SimpleGraph V'
G'' : SimpleGraph V''
f : G →g G'
f' : G' →g G''
u v u' v' : V
p : Walk G u v
u✝ v✝ w✝ : V
h✝ : Adj G u✝ v✝
p✝ : Walk G v✝ w✝
ih : edges (Walk.map f p✝) = List.map (Sym2.map ↑f) (edges p✝)
⊢ edges (Walk.map f (cons h✝ p✝)) = List.map (Sym2.map ↑f) (edges (cons h✝ p✝))
simp only [Walk.map_cons, edges_cons, List.map_cons, Sym2.map_pair_eq, List.cons.injEq,
  true_and, ih]