Theorem: Graph.SubgroupCover.liftTermFactors (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)
w₂ : V
e : EdgePath G x₀ w₂
⊢ (lift e (groupCoverProj H) (basepoint H)
        (_ : (groupCoverProj H).toFuncV (basepoint H) = (groupCoverProj H).toFuncV (basepoint H))).τ =
    ⟦liftTerminal (proj G x₀) (UniversalCover.basepoint G x₀)
        (_ : (proj G x₀).toFuncV (UniversalCover.basepoint G x₀) = (proj G x₀).toFuncV (UniversalCover.basepoint G x₀))
        e⟧
Tactic:
rw [liftFactors]
State after:
V : Type u
E : Type v
inst✝¹ : DecidableEq V
inst✝ : DecidableEq E
G : Graph V E
x₀ : V
H : Subgroup (π₁ G x₀)
w₂ : V
e : EdgePath G x₀ w₂
⊢ (liftViaUniv H e).τ =
    ⟦liftTerminal (proj G x₀) (UniversalCover.basepoint G x₀)
        (_ : (proj G x₀).toFuncV (UniversalCover.basepoint G x₀) = (proj G x₀).toFuncV (UniversalCover.basepoint G x₀))
        e⟧

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)
w₂ : V
e : EdgePath G x₀ w₂
⊢ (liftViaUniv H e).τ =
    ⟦liftTerminal (proj G x₀) (UniversalCover.basepoint G x₀)
        (_ : (proj G x₀).toFuncV (UniversalCover.basepoint G x₀) = (proj G x₀).toFuncV (UniversalCover.basepoint G x₀))
        e⟧
Tactic:
rfl
State after:
no goals