-- Module: Mathlib.CategoryTheory.Sites.DenseSubsite.OneHypercoverDense
Goal:
C₀ : Type u₀
C : Type u
inst : Category.{v₀, u₀} C₀
inst_1 : Category.{v, u} C
F : Functor.{v₀, v, u₀, u} C₀ C
J₀ : GrothendieckTopology.{v₀, u₀} C₀
J : GrothendieckTopology.{v, u} C
A : Type u'
inst_2 : Category.{v', u'} A
inst_3 : IsDenseSubsite J₀ J F
data : (X : C) → OneHypercoverDenseData.{w, v₀, v, u₀, u} F J₀ J X
inst_4 : HasLimitsOfSize.{w, w, v', u'} A
G₀ : Sheaf.{v₀, v', u₀, u'} J₀ A
X₀ W₀ : C₀
a : W₀ ⟶ X₀
ha :
  Sieve.arrows
    (↑(Subtype.mk (p := fun (S : Sieve.{v₀, u₀} X₀) ↦ S ∈ (J₀ : (a : C₀) → Set (Sieve a)) X₀)
          (Sieve.functorPullback F
            (PreZeroHypercover.sieve₀.{w, v, u}
              (PreOneHypercover.toPreZeroHypercover
                (PreOneHypercoverDenseData.toPreOneHypercover (toPreOneHypercoverDenseData (data (F.obj X₀)))))))
          ⋯) :
      Sieve X₀)
    a
T₀ : C₀
b : T₀ ⟶ X₀
hb :
  Sieve.arrows
    (↑(Subtype.mk (p := fun (S : Sieve.{v₀, u₀} X₀) ↦ S ∈ (J₀ : (a : C₀) → Set (Sieve a)) X₀)
          (Sieve.functorPullback F
            (PreZeroHypercover.sieve₀.{w, v, u}
              (PreOneHypercover.toPreZeroHypercover
                (PreOneHypercoverDenseData.toPreOneHypercover (toPreOneHypercoverDenseData (data (F.obj X₀)))))))
          ⋯) :
      Sieve X₀)
    b
U₀ : C₀
p₁ :
  U₀ ⟶
    { Y := W₀, f := a, hf := ha :
        GrothendieckTopology.Cover.Arrow (X := X₀)
          (Subtype.mk (p := fun (S : Sieve.{v₀, u₀} X₀) ↦ S ∈ (J₀ : (a : C₀) → Set (Sieve a)) X₀)
            (Sieve.functorPullback F
              (PreZeroHypercover.sieve₀.{w, v, u}
                (PreOneHypercover.toPreZeroHypercover
                  (PreOneHypercoverDenseData.toPreOneHypercover (toPreOneHypercoverDenseData (data (F.obj X₀)))))))
            ⋯) }.Y
p₂ :
  U₀ ⟶
    { Y := T₀, f := b, hf := hb :
        GrothendieckTopology.Cover.Arrow (X := X₀)
          (Subtype.mk (p := fun (S : Sieve.{v₀, u₀} X₀) ↦ S ∈ (J₀ : (a : C₀) → Set (Sieve a)) X₀)
            (Sieve.functorPullback F
              (PreZeroHypercover.sieve₀.{w, v, u}
                (PreOneHypercover.toPreZeroHypercover
                  (PreOneHypercoverDenseData.toPreOneHypercover (toPreOneHypercoverDenseData (data (F.obj X₀)))))))
            ⋯) }.Y
fac :
  p₁ ≫
      { Y := W₀, f := a, hf := ha :
          GrothendieckTopology.Cover.Arrow (X := X₀)
            (Subtype.mk (p := fun (S : Sieve.{v₀, u₀} X₀) ↦ S ∈ (J₀ : (a : C₀) → Set (Sieve a)) X₀)
              (Sieve.functorPullback F
                (PreZeroHypercover.sieve₀.{w, v, u}
                  (PreOneHypercover.toPreZeroHypercover
                    (PreOneHypercoverDenseData.toPreOneHypercover (toPreOneHypercoverDenseData (data (F.obj X₀)))))))
              ⋯) }.f =
    p₂ ≫ { Y := T₀, f := b, hf := hb }.f
ha' :
  Sieve.ofArrows.h ha ≫
      PreZeroHypercover.f
        (PreOneHypercover.toPreZeroHypercover
          (PreOneHypercoverDenseData.toPreOneHypercover (toPreOneHypercoverDenseData (data (F.obj X₀)))))
        (Sieve.ofArrows.i ha) =
    F.map a
⊢ Sieve.ofArrows.h hb ≫
      PreZeroHypercover.f
        (PreOneHypercover.toPreZeroHypercover
          (PreOneHypercoverDenseData.toPreOneHypercover (toPreOneHypercoverDenseData (data (F.obj X₀)))))
        (Sieve.ofArrows.i hb) =
    F.map b

Tactic:
have hb' := Sieve.ofArrows.fac hb