J K : Type v
inst✝⁵ : SmallCategory J
inst✝⁴ : SmallCategory K
C : Type u
inst✝³ : Category C
F : J ⥤ K ⥤ C
inst✝² : HasLimitsOfShape K C
inst✝¹ : HasLimit (uncurry.obj F)
inst✝ : HasLimit (F ⋙ lim)
j : J
k : K
⊢ limit.lift (F ⋙ lim) (coneOfConeUncurry (fun j => limit.isLimit (F.obj j)) (limit.cone (uncurry.obj F))) ≫
      limit.π (F ⋙ lim) j ≫ limit.π (F.obj j) k =
    limit.π (uncurry.obj F) (j, k)
J K : Type v
inst✝⁵ : SmallCategory J
inst✝⁴ : SmallCategory K
C : Type u
inst✝³ : Category C
F : J ⥤ K ⥤ C
inst✝² : HasLimitsOfShape K C
inst✝¹ : HasLimit (uncurry.obj F)
inst✝ : HasLimit (F ⋙ lim)
j : J
k : K
⊢ (limitUncurryIsoLimitCompLim F).hom ≫ limit.π (F ⋙ lim) j ≫ limit.π (F.obj j) k = limit.π (uncurry.obj F) (j, k)
dsimp [limitUncurryIsoLimitCompLim, IsLimit.conePointUniqueUpToIso, IsLimit.uniqueUpToIso]
no goals
J K : Type v
inst✝⁵ : SmallCategory J
inst✝⁴ : SmallCategory K
C : Type u
inst✝³ : Category C
F : J ⥤ K ⥤ C
inst✝² : HasLimitsOfShape K C
inst✝¹ : HasLimit (uncurry.obj F)
inst✝ : HasLimit (F ⋙ lim)
j : J
k : K
⊢ limit.lift (F ⋙ lim) (coneOfConeUncurry (fun j => limit.isLimit (F.obj j)) (limit.cone (uncurry.obj F))) ≫
      limit.π (F ⋙ lim) j ≫ limit.π (F.obj j) k =
    limit.π (uncurry.obj F) (j, k)
simp