Theorem: Graph.EdgePath.eq_of_edge_eq (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 w : V
e₁ e₂ : EdgeBetween G v w
⊢ e₁.edge = e₂.edge → e₁ = e₂
Tactic:
intro h
State after:
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 w : V
e₁ e₂ : EdgeBetween G v w
h : e₁.edge = e₂.edge
⊢ e₁ = e₂

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 w : V
e₁ e₂ : EdgeBetween G v w
h : e₁.edge = e₂.edge
⊢ e₁ = e₂
Tactic:
ext
State after:
case edge
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 w : V
e₁ e₂ : EdgeBetween G v w
h : e₁.edge = e₂.edge
⊢ e₁.edge = e₂.edge

State before:
case edge
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 w : V
e₁ e₂ : EdgeBetween G v w
h : e₁.edge = e₂.edge
⊢ e₁.edge = e₂.edge
Tactic:
exact h
State after:
no goals