intro c
case mk.mk.mk
V : Type u
E : Type v
G : Graph V E
u✝ v✝ w✝ : V
e : EdgeBetween G v✝ w✝
v w u u' : V
a : EdgePath G v w
b : EdgePath G w u
⊢ ∀ (a_1 : EdgePath G u u'),
    mul (mul (Quot.mk Reduction a) (Quot.mk Reduction b)) (Quot.mk Reduction a_1) =
      mul (Quot.mk Reduction a) (mul (Quot.mk Reduction b) (Quot.mk Reduction a_1))
case mk.mk.mk
V : Type u
E : Type v
G : Graph V E
u✝ v✝ w✝ : V
e : EdgeBetween G v✝ w✝
v w u u' : V
a : EdgePath G v w
b : EdgePath G w u
c : EdgePath G u u'
⊢ mul (mul (Quot.mk Reduction a) (Quot.mk Reduction b)) (Quot.mk Reduction c) =
    mul (Quot.mk Reduction a) (mul (Quot.mk Reduction b) (Quot.mk Reduction c))