Theorem: Digraph.Walk.map_map (GraphProjects/DigraphConnectivity.lean)

State before:
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
⊢ Walk.map f' (Walk.map f p) = Walk.map (Hom.comp f' f) p
Tactic:
induction p with
| nil => rfl
| cons _ _ ih => simp [ih]
State after:
no goals

State before:
case nil
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
u✝ : V
⊢ Walk.map f' (Walk.map f nil) = Walk.map (Hom.comp f' f) nil
Tactic:
rfl
State after:
no goals

State before:
case cons
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
u✝ v✝ w✝ : V
h✝ : G.Adj u✝ v✝
p✝ : Walk G v✝ w✝
ih : Walk.map f' (Walk.map f p✝) = Walk.map (Hom.comp f' f) p✝
⊢ Walk.map f' (Walk.map f (cons h✝ p✝)) = Walk.map (Hom.comp f' f) (cons h✝ p✝)
Tactic:
simp [ih]
State after:
no goals