Theorem: Graph.PathClass.mul_inv (Lectures/Graph.lean)

State before:
V : Type u
E : Type v
G : Graph V E
u✝ v✝ w : V
e : EdgeBetween G v✝ w
u v : V
⊢ ∀ (p : PathClass G u v), mul p (inv p) = PathClass.id u
Tactic:
apply Quot.ind
State after:
case mk
V : Type u
E : Type v
G : Graph V E
u✝ v✝ w : V
e : EdgeBetween G v✝ w
u v : V
⊢ ∀ (a : EdgePath G u v), mul (Quot.mk Reduction a) (inv (Quot.mk Reduction a)) = PathClass.id u

State before:
case mk
V : Type u
E : Type v
G : Graph V E
u✝ v✝ w : V
e : EdgeBetween G v✝ w
u v : V
⊢ ∀ (a : EdgePath G u v), mul (Quot.mk Reduction a) (inv (Quot.mk Reduction a)) = PathClass.id u
Tactic:
aesop
State after:
no goals