x : SimplexCategory
i : x ⟶ x
inst✝ : Epi i
⊢ IsIso i
x : SimplexCategory
i : x ⟶ x
inst✝ : Epi i
⊢ i = 𝟙 x
suffices IsIso i by
  haveI := this
  apply eq_id_of_isIso
case hf
x : SimplexCategory
i : x ⟶ x
inst✝ : Epi i
⊢ Function.Bijective ↑(Hom.toOrderHom i)
x : SimplexCategory
i : x ⟶ x
inst✝ : Epi i
⊢ IsIso i
apply isIso_of_bijective
case hf
x : SimplexCategory
i : x ⟶ x
inst✝ : Epi i
⊢ Function.Bijective ↑(Hom.toOrderHom i)
case hf
x : SimplexCategory
i : x ⟶ x
inst✝ : Epi i
⊢ Function.Bijective ↑(Hom.toOrderHom i)
dsimp
case hf
x : SimplexCategory
i : x ⟶ x
inst✝ : Epi i
⊢ Epi i
case hf
x : SimplexCategory
i : x ⟶ x
inst✝ : Epi i
⊢ Function.Bijective ↑(Hom.toOrderHom i)
rw [Fintype.bijective_iff_surjective_and_card i.toOrderHom, ← epi_iff_surjective,
  eq_self_iff_true, and_true_iff]
no goals
case hf
x : SimplexCategory
i : x ⟶ x
inst✝ : Epi i
⊢ Epi i
infer_instance
x : SimplexCategory
i : x ⟶ x
inst✝ : Epi i
this✝ this : IsIso i
⊢ i = 𝟙 x
x : SimplexCategory
i : x ⟶ x
inst✝ : Epi i
this : IsIso i
⊢ i = 𝟙 x
haveI := this
no goals
x : SimplexCategory
i : x ⟶ x
inst✝ : Epi i
this✝ this : IsIso i
⊢ i = 𝟙 x
apply eq_id_of_isIso