Theorem: Graph.reverse_step (Lectures/Graph.lean)

State before:
V : Type u
E : Type v
G : Graph V E
u v✝ w✝ : V
e : EdgeBetween G v✝ w✝
v w : V
a₁ a₂ : EdgePath G v w
rel : Reduction a₁ a₂
⊢ [[reverse a₁]] = [[reverse a₂]]
Tactic:
induction rel
State after:
case step
V : Type u
E : Type v
G : Graph V E
u v✝ w✝ : V
e : EdgeBetween G v✝ w✝
v w : V
a₁ a₂ : EdgePath G v w
u✝ u'✝ : V
e✝ : EdgeBetween G u✝ u'✝
p₁✝ : EdgePath G v u✝
p₂✝ : EdgePath G u✝ w
⊢ [[reverse (p₁✝ ++ cons e✝ (cons (EdgeBetween.bar e✝) p₂✝))]] = [[reverse (p₁✝ ++ p₂✝)]]

State before:
case step
V : Type u
E : Type v
G : Graph V E
u v✝ w✝ : V
e : EdgeBetween G v✝ w✝
v w : V
a₁ a₂ : EdgePath G v w
u✝ u'✝ : V
e✝ : EdgeBetween G u✝ u'✝
p₁✝ : EdgePath G v u✝
p₂✝ : EdgePath G u✝ w
⊢ [[reverse (p₁✝ ++ cons e✝ (cons (EdgeBetween.bar e✝) p₂✝))]] = [[reverse (p₁✝ ++ p₂✝)]]
Tactic:
aesop (add norm simp [reverse_append, reverse_cons])
State after:
no goals