-- Module: Mathlib.Topology.Sheaves.Stalks
Goal:
C : Type u
inst : Category.{v, u} C
inst_1 : HasColimits.{v, u} C
X : TopCat
FC : C → C → Type u_1
CC : C → Type v
inst_2 : (X Y : C) → FunLike.{u_1 + 1, v + 1, v + 1} (FC X Y) (CC X) (CC Y)
instCC : ConcreteCategory C FC (CC := CC)
inst_3 : PreservesFilteredColimits (forget C (FC := FC) (CC := CC))
F G : Presheaf C X
f : F ⟶ G
h :
  ∀ (U : Opens (↑X : Type v)),
    Function.Injective.{v + 1, v + 1} (α := CC (F.obj (op U))) (β := CC (G.obj (op U)))
      (⇑(ConcreteCategory.hom (FC := FC) (CC := CC) (f.app (op U))) : (a : CC (F.obj (op U))) → CC (G.obj (op U)))
x : (↑X : Type v)
U₁ : Opens (↑X : Type v)
hxU₁ : x ∈ U₁
s : ToType (FC := FC) (CC := CC) (F.obj (op U₁))
U₂ : Opens (↑X : Type v)
hxU₂ : x ∈ U₂
t : ToType (FC := FC) (CC := CC) (F.obj (op U₂))
hst :
  Eq (α := CC (obj (stalkFunctor C x) G))
    ((ConcreteCategory.hom (FC := FC) (CC := CC) (G.germ U₁ x hxU₁) : (a : CC (G.obj (op U₁))) → CC (G.stalk x))
        ((ConcreteCategory.hom (FC := FC) (CC := CC) (f.app (op U₁)) : (a : CC (F.obj (op U₁))) → CC (G.obj (op U₁)))
            s :
          CC (G.obj (op U₁))) :
      CC (G.stalk x))
    ((ConcreteCategory.hom (FC := FC) (CC := CC) (G.germ U₂ x hxU₂) : (a : CC (G.obj (op U₂))) → CC (G.stalk x))
        ((ConcreteCategory.hom (FC := FC) (CC := CC) (f.app (op U₂)) : (a : CC (F.obj (op U₂))) → CC (G.obj (op U₂)))
            t :
          CC (G.obj (op U₂))) :
      CC (G.stalk x))
W : Opens (↑X : Type v)
hxW : x ∈ W
iWU₁ : W ⟶ U₁
iWU₂ : W ⟶ U₂
heq :
  Eq (α := CC (F.obj (op W)))
    ((ConcreteCategory.hom (FC := FC) (CC := CC) (F.map iWU₁.op) : (a : CC (F.obj (op U₁))) → CC (F.obj (op W))) s :
      CC (F.obj (op W)))
    ((ConcreteCategory.hom (FC := FC) (CC := CC) (F.map iWU₂.op) : (a : CC (F.obj (op U₂))) → CC (F.obj (op W))) t :
      CC (F.obj (op W)))
h₁ :
  CC (obj (stalkFunctor C x) F) = CC (F.stalk x) →
    Eq (α := CC (obj (stalkFunctor C x) F))
      ((ConcreteCategory.hom (FC := FC) (CC := CC) (F.germ U₁ x hxU₁) : (a : CC (F.obj (op U₁))) → CC (F.stalk x)) s :
        CC (F.stalk x))
      ((ConcreteCategory.hom (FC := FC) (CC := CC) (F.germ W x hxW) : (a : CC (F.obj (op W))) → CC (F.stalk x))
          ((ConcreteCategory.hom (FC := FC) (CC := CC) (F.map iWU₁.op) : (a : CC (F.obj (op U₁))) → CC (F.obj (op W)))
              s :
            CC (F.obj (op W))) :
        CC (F.stalk x))
h₂ :
  CC (obj (stalkFunctor C x) F) = CC (F.stalk x) →
    Eq (α := CC (obj (stalkFunctor C x) F))
      ((ConcreteCategory.hom (FC := FC) (CC := CC) (F.germ U₂ x hxU₂) : (a : CC (F.obj (op U₂))) → CC (F.stalk x)) t :
        CC (F.stalk x))
      ((ConcreteCategory.hom (FC := FC) (CC := CC) (F.germ W x hxW) : (a : CC (F.obj (op W))) → CC (F.stalk x))
          ((ConcreteCategory.hom (FC := FC) (CC := CC) (F.map iWU₂.op) : (a : CC (F.obj (op U₂))) → CC (F.obj (op W)))
              t :
            CC (F.obj (op W))) :
        CC (F.stalk x))
⊢ Eq (α := CC (obj (stalkFunctor C x) F))
    ((ConcreteCategory.hom (FC := FC) (CC := CC) (F.germ U₁ x hxU₁) : (a : CC (F.obj (op U₁))) → CC (F.stalk x)) s :
      CC (F.stalk x))
    ((ConcreteCategory.hom (FC := FC) (CC := CC) (F.germ U₂ x hxU₂) : (a : CC (F.obj (op U₂))) → CC (F.stalk x)) t :
      CC (F.stalk x))

Tactic:
convert! congr_arg (F.germ _ x hxW) heq using 1

Premises used: CategoryTheory.ConcreteCategory.hom, TopCat.Presheaf.germ, congr_arg, DFunLike.coe