Theorem: Digraph.Walk.map_id (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✝ p : Walk G u v
⊢ Walk.map Hom.id p = p
Tactic:
induction p with
| nil => rfl
| cons _ p' ih => simp [ih p']
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' u✝ : V
p : Walk G u✝ u✝
⊢ Walk.map Hom.id nil = 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' u✝ v✝ w✝ : V
h✝ : G.Adj u✝ v✝
p' : Walk G v✝ w✝
ih : Walk G v✝ w✝ → Walk.map Hom.id p' = p'
p : Walk G u✝ w✝
⊢ Walk.map Hom.id (cons h✝ p') = cons h✝ p'
Tactic:
simp [ih p']
State after:
no goals