Theorem: Graph.SubgroupCover.Quot.bar_bar (GroupComp/Graph/SubgroupCover.lean)

State before:
V : Type u
E : Type v
inst✝¹ : DecidableEq V
inst✝ : DecidableEq E
G : Graph V E
x₀ : V
H : Subgroup (π₁ G x₀)
⊢ ∀ (ebar : Quotient (edgeSetoid H)), bar H (bar H ebar) = ebar
Tactic:
apply Quotient.ind
State after:
case a
V : Type u
E : Type v
inst✝¹ : DecidableEq V
inst✝ : DecidableEq E
G : Graph V E
x₀ : V
H : Subgroup (π₁ G x₀)
⊢ ∀ (a : Edge G x₀), bar H (bar H ⟦a⟧) = ⟦a⟧

State before:
case a
V : Type u
E : Type v
inst✝¹ : DecidableEq V
inst✝ : DecidableEq E
G : Graph V E
x₀ : V
H : Subgroup (π₁ G x₀)
⊢ ∀ (a : Edge G x₀), bar H (bar H ⟦a⟧) = ⟦a⟧
Tactic:
intro e
State after:
case a
V : Type u
E : Type v
inst✝¹ : DecidableEq V
inst✝ : DecidableEq E
G : Graph V E
x₀ : V
H : Subgroup (π₁ G x₀)
e : Edge G x₀
⊢ bar H (bar H ⟦e⟧) = ⟦e⟧

State before:
case a
V : Type u
E : Type v
inst✝¹ : DecidableEq V
inst✝ : DecidableEq E
G : Graph V E
x₀ : V
H : Subgroup (π₁ G x₀)
e : Edge G x₀
⊢ bar H (bar H ⟦e⟧) = ⟦e⟧
Tactic:
simp [bar_eq_barn]
State after:
no goals