Theorem: Graph.liftClass_eq_of_homotopic (GroupComp/Graph/Covering.lean)

State before:
V : Type u
E : Type v
V₁ : Type u_1
E₁ : Type u_2
V₂ : Type u_3
E₂ : Type u_4
G₁ : Graph V₁ E₁
G₂ : Graph V₂ E₂
p : Morphism G₁ G₂
inst✝ : CoveringMap p
v₁ : V₁
v₂ w₂ : V₂
h : p.toFuncV v₁ = v₂
e₁ e₂ : EdgePath G₂ v₂ w₂
red : [[e₁]] = [[e₂]]
⊢ liftClass p v₁ v₂ w₂ h e₁ = liftClass p v₁ v₂ w₂ h e₂
Tactic:
simp [liftClass, ← homotopyLift_of_path]
State after:
V : Type u
E : Type v
V₁ : Type u_1
E₁ : Type u_2
V₂ : Type u_3
E₂ : Type u_4
G₁ : Graph V₁ E₁
G₂ : Graph V₂ E₂
p : Morphism G₁ G₂
inst✝ : CoveringMap p
v₁ : V₁
v₂ w₂ : V₂
h : p.toFuncV v₁ = v₂
e₁ e₂ : EdgePath G₂ v₂ w₂
red : [[e₁]] = [[e₂]]
⊢ homotopyLift p v₁ h [[e₁]] = homotopyLift p v₁ h [[e₂]]

State before:
V : Type u
E : Type v
V₁ : Type u_1
E₁ : Type u_2
V₂ : Type u_3
E₂ : Type u_4
G₁ : Graph V₁ E₁
G₂ : Graph V₂ E₂
p : Morphism G₁ G₂
inst✝ : CoveringMap p
v₁ : V₁
v₂ w₂ : V₂
h : p.toFuncV v₁ = v₂
e₁ e₂ : EdgePath G₂ v₂ w₂
red : [[e₁]] = [[e₂]]
⊢ homotopyLift p v₁ h [[e₁]] = homotopyLift p v₁ h [[e₂]]
Tactic:
congr
State after:
no goals