-- Module: Mathlib.Topology.Sheaves.SheafCondition.UniqueGluing
Goal:
C : Type u_1
inst : Category.{v_1, u_1} C
FC : C → C → Type u_2
CC : C → Type u_3
inst_1 : (X Y : C) → FunLike.{u_2 + 1, u_3 + 1, u_3 + 1} (FC X Y) (CC X) (CC Y)
inst_2 : ConcreteCategory.{u_3, v_1, u_1, u_2} C FC (CC := CC)
inst_3 : HasLimitsOfSize.{x, x, v_1, u_1} C
inst_4 : Functor.ReflectsIsomorphisms.{v_1, u_1, u_3, u_3 + 1} (CategoryTheory.forget C (FC := FC) (CC := CC))
inst_5 : PreservesLimitsOfSize.{x, x, v_1, u_3, u_1, u_3 + 1} (CategoryTheory.forget C (FC := FC) (CC := CC))
X : TopCat
F : Sheaf.{x, v_1, u_1} C X
U₁ U₂ V : Opens (↑X : Type x)
i₁ : U₁ ⟶ V
i₂ : U₂ ⟶ V
hcover : V ≤ U₁ ⊔ U₂
s t :
  ToType.{u_3, v_1, u_1, u_2} (FC := FC) (CC := CC)
    (F.obj (P := CategoryTheory.Presheaf.IsSheaf (Opens.grothendieckTopology (↑X : Type x))).obj (op V))
h₁ :
  Eq (α := CC (F.obj (P := CategoryTheory.Presheaf.IsSheaf (Opens.grothendieckTopology (↑X : Type x))).obj (op U₁)))
    ((ConcreteCategory.hom (FC := FC) (CC := CC)
            (F.obj (P := CategoryTheory.Presheaf.IsSheaf (Opens.grothendieckTopology (↑X : Type x))).map i₁.op) :
          (a : CC (F.obj.obj (op V))) → CC (F.obj.obj (op U₁)))
        s :
      CC (F.obj (P := CategoryTheory.Presheaf.IsSheaf (Opens.grothendieckTopology (↑X : Type x))).obj (op U₁)))
    ((ConcreteCategory.hom (FC := FC) (CC := CC)
            (F.obj (P := CategoryTheory.Presheaf.IsSheaf (Opens.grothendieckTopology (↑X : Type x))).map i₁.op) :
          (a : CC (F.obj.obj (op V))) → CC (F.obj.obj (op U₁)))
        t :
      CC (F.obj (P := CategoryTheory.Presheaf.IsSheaf (Opens.grothendieckTopology (↑X : Type x))).obj (op U₁)))
h₂ :
  Eq (α := CC (F.obj (P := CategoryTheory.Presheaf.IsSheaf (Opens.grothendieckTopology (↑X : Type x))).obj (op U₂)))
    ((ConcreteCategory.hom (FC := FC) (CC := CC)
            (F.obj (P := CategoryTheory.Presheaf.IsSheaf (Opens.grothendieckTopology (↑X : Type x))).map i₂.op) :
          (a : CC (F.obj.obj (op V))) → CC (F.obj.obj (op U₂)))
        s :
      CC (F.obj (P := CategoryTheory.Presheaf.IsSheaf (Opens.grothendieckTopology (↑X : Type x))).obj (op U₂)))
    ((ConcreteCategory.hom (FC := FC) (CC := CC)
            (F.obj (P := CategoryTheory.Presheaf.IsSheaf (Opens.grothendieckTopology (↑X : Type x))).map i₂.op) :
          (a : CC (F.obj.obj (op V))) → CC (F.obj.obj (op U₂)))
        t :
      CC (F.obj (P := CategoryTheory.Presheaf.IsSheaf (Opens.grothendieckTopology (↑X : Type x))).obj (op U₂)))
⊢ Eq (α :=
    CC
      (F.obj (P := CategoryTheory.Presheaf.IsSheaf (Opens.grothendieckTopology (↑X : Type x))).obj
        (op (if false = true then U₁ else U₂))))
    ((ConcreteCategory.hom (FC := FC) (CC := CC)
            (F.obj (P := CategoryTheory.Presheaf.IsSheaf (Opens.grothendieckTopology (↑X : Type x))).map
              (Quiver.Hom.op (if h : false = true then eqToHom ⋯ ≫ i₁ else eqToHom ⋯ ≫ i₂))) :
          (a : CC (F.obj.obj (op V))) → CC (F.obj.obj (op (if false = true then U₁ else U₂))))
        s :
      CC
        (F.obj (P := CategoryTheory.Presheaf.IsSheaf (Opens.grothendieckTopology (↑X : Type x))).obj
          (op (if false = true then U₁ else U₂))))
    ((ConcreteCategory.hom (FC := FC) (CC := CC)
            (F.obj (P := CategoryTheory.Presheaf.IsSheaf (Opens.grothendieckTopology (↑X : Type x))).map
              (Quiver.Hom.op (if h : false = true then eqToHom ⋯ ≫ i₁ else eqToHom ⋯ ≫ i₂))) :
          (a : CC (F.obj.obj (op V))) → CC (F.obj.obj (op (if false = true then U₁ else U₂))))
        t :
      CC
        (F.obj (P := CategoryTheory.Presheaf.IsSheaf (Opens.grothendieckTopology (↑X : Type x))).obj
          (op (if false = true then U₁ else U₂))))

Tactic:
h₂

Premises used: Set.Mem, dite, ite