Theorem: Graph.EdgePath.toList_shiftEnds (GroupComp/Graph.lean)

State before:
V : Type u
E : Type v
inst✝¹ : DecidableEq V
inst✝ : DecidableEq E
G✝ : Graph V E
u v✝ w✝ : V
e : EdgeBetween G✝ v✝ w✝
G : Graph V E
v v' w w' : V
p : EdgePath G v w
eqlv : v = v'
eqlw : w = w'
⊢ toList (shiftEnds p eqlv eqlw) = toList p
Tactic:
match p, w', eqlv, eqlw with
| nil _, _, rfl, rfl =>
  simp only [shiftEnds]
| cons e p', w', rfl,  eqlw =>
  simp only [shiftEnds, cons_toList, toList_shiftTarget]
State after:
no goals

State before:
V : Type u
E : Type v
inst✝¹ : DecidableEq V
inst✝ : DecidableEq E
G✝ : Graph V E
u v✝ w✝ : V
e : EdgeBetween G✝ v✝ w✝
G : Graph V E
v v' w w' : V
p : EdgePath G v w
eqlv : v = v'
eqlw : w = w'
⊢ toList (shiftEnds (nil v) (_ : v = v) (_ : v = v)) = toList (nil v)
Tactic:
simp only [shiftEnds]
State after:
no goals

State before:
V : Type u
E : Type v
inst✝¹ : DecidableEq V
inst✝ : DecidableEq E
G✝ : Graph V E
u v✝ w✝² : V
e✝ : EdgeBetween G✝ v✝ w✝²
G : Graph V E
v v' w✝¹ w'✝ : V
p : EdgePath G v w✝¹
eqlv : v = v'
eqlw✝ : w✝¹ = w'✝
w w✝ : V
e : EdgeBetween G v w✝
p' : EdgePath G w✝ w
w' : V
eqlw : w = w'
⊢ toList (shiftEnds (cons e p') (_ : v = v) eqlw) = toList (cons e p')
Tactic:
simp only [shiftEnds, cons_toList, toList_shiftTarget]
State after:
no goals