apply proj_injective
case refl.mk.mk
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
η₁ η₂ : EdgePath G₁ v₁ v₁
⊢ PathClass.map p (Quot.mk Reduction η₁) = PathClass.map p (Quot.mk Reduction η₂) →
    Quot.mk Reduction η₁ = Quot.mk Reduction η₂
no goals