[GOAL]
C : Type u
inst✝ : Category.{v, u} C
X : TopCat
F✝ : Presheaf C X
ι : Type v
U✝ : ι → Opens ↑X
F : Presheaf (Discrete Unit) X
x✝² : Discrete Unit
U : Opens ↑X
S : Sieve U
x✝¹ : S ∈ GrothendieckTopology.sieves (Opens.grothendieckTopology ↑X) U
x : Presieve.FamilyOfElements (F ⋙ coyoneda.obj (op x✝²)) S.arrows
x✝ : Presieve.FamilyOfElements.Compatible x
⊢ (fun t => Presieve.FamilyOfElements.IsAmalgamation x t) (eqToHom (_ : (op x✝²).unop = F.obj (op U)))
[PROOFSTEP]
aesop_cat
[GOAL]
C : Type u
inst✝ : Category.{v, u} C
X : TopCat
F✝ : Presheaf C X
ι : Type v
U✝ : ι → Opens ↑X
F : Presheaf (Discrete Unit) X
x✝³ : Discrete Unit
U : Opens ↑X
S : Sieve U
x✝² : S ∈ GrothendieckTopology.sieves (Opens.grothendieckTopology ↑X) U
x : Presieve.FamilyOfElements (F ⋙ coyoneda.obj (op x✝³)) S.arrows
x✝¹ : Presieve.FamilyOfElements.Compatible x
x✝ : (F ⋙ coyoneda.obj (op x✝³)).obj (op U)
⊢ (fun t => Presieve.FamilyOfElements.IsAmalgamation x t) x✝ → x✝ = eqToHom (_ : (op x✝³).unop = F.obj (op U))
[PROOFSTEP]
aesop_cat
