simp [reduction_cons, ←cons_homotopic_redCons]
case cons
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 : [[reduction p]] = [[p]]
⊢ [[reduction (cons e p)]] = [[cons e p]]
case cons
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 : [[reduction p]] = [[p]]
⊢ [[cons e (reduction p)]] = [[cons e p]]