apply c
V : Type u
E : Type v
inst✝¹ : DecidableEq V
inst✝ : DecidableEq E
G : Graph V E
u'' v w' : V
e'' : EdgeBetween G u'' v
p : EdgePath G v w'
w w'' : V
e' : EdgeBetween G v w''
p' : EdgePath G w'' w
hyp : reduced (cons e' p')
c : ¬w'' = u''
p'' : EdgePath G u'' w
red' : Reduction (cons e'' (cons e' p')) p''
u u' : V
p₁ : EdgePath G u'' u
e : EdgeBetween G u'' u'
p₂ : EdgePath G u'' w
eqn : cons e (cons (EdgeBetween.bar e) p₂) = cons e'' (cons e' p')
leqn : e.edge = e''.edge ∧ G.bar e.edge = e'.edge ∧ toList p₂ = toList p'
⊢ False
V : Type u
E : Type v
inst✝¹ : DecidableEq V
inst✝ : DecidableEq E
G : Graph V E
u'' v w' : V
e'' : EdgeBetween G u'' v
p : EdgePath G v w'
w w'' : V
e' : EdgeBetween G v w''
p' : EdgePath G w'' w
hyp : reduced (cons e' p')
c : ¬w'' = u''
p'' : EdgePath G u'' w
red' : Reduction (cons e'' (cons e' p')) p''
u u' : V
p₁ : EdgePath G u'' u
e : EdgeBetween G u'' u'
p₂ : EdgePath G u'' w
eqn : cons e (cons (EdgeBetween.bar e) p₂) = cons e'' (cons e' p')
leqn : e.edge = e''.edge ∧ G.bar e.edge = e'.edge ∧ toList p₂ = toList p'
⊢ w'' = u''