assumption
case a
V : Type u
E : Type v
inst✝¹ : DecidableEq V
inst✝ : DecidableEq E
G : Graph V E
v w v✝ w✝ u✝ : V
e : EdgeBetween G v✝ w✝
p : EdgePath G w✝ u✝
ih : reduced p → reduction p = p
hyp : reduced (cons e p)
⊢ reduced (cons ?e p)

case u
V : Type u
E : Type v
inst✝¹ : DecidableEq V
inst✝ : DecidableEq E
G : Graph V E
v w v✝ w✝ u✝ : V
e : EdgeBetween G v✝ w✝
p : EdgePath G w✝ u✝
ih : reduced p → reduction p = p
hyp : reduced (cons e p)
⊢ V

case e
V : Type u
E : Type v
inst✝¹ : DecidableEq V
inst✝ : DecidableEq E
G : Graph V E
v w v✝ w✝ u✝ : V
e : EdgeBetween G v✝ w✝
p : EdgePath G w✝ u✝
ih : reduced p → reduction p = p
hyp : reduced (cons e p)
⊢ EdgeBetween G ?u w✝
no goals