-- Lean 4 proof step from Mathlib.CategoryTheory.Sites.ConcreteSheafification (goal)
Goal:
C : Type u
inst : Category.{v, u} C
J : GrothendieckTopology.{v, u} C
D : Type w
inst_1 : Category.{w', w} D
FD : D → D → Type u_1
CD : D → Type t
inst_2 : (X Y : D) → FunLike.{u_1 + 1, t + 1, t + 1} (FD X Y) (CD X) (CD Y)
instCC : ConcreteCategory.{t, w', w, u_1} D FD (CC := CD)
inst_3 : ∀ {X : C} (S : J.Cover X), PreservesLimitsOfShape (WalkingMulticospan S.shape) (forget D (FC := FD) (CC := CD))
inst_4 : ∀ (X : C), HasColimitsOfShape (J.Cover X)ᵒᵖ D
inst_5 : ∀ (P : Functor.{v, w', u, w} Cᵒᵖ D) (X : C) (S : J.Cover X), HasMultiequalizer (S.index P)
Y X : C
P : Functor.{v, w', u, w} Cᵒᵖ D
S : J.Cover X
x : Meq (FD := FD) (CD := CD) P S
f : Y ⟶ X
⊢ Eq (α := Meq (FD := FD) (CD := CD) P (unop ((J.pullback f).op.obj (op S))))
    ((Meq.equiv (FD := FD) (CD := CD) P (unop ((J.pullback f).op.obj (op S))) :
          (a : ToType (multiequalizer ((unop ((J.pullback f).op.obj (op S))).index P))) →
            Meq P (unop ((J.pullback f).op.obj (op S))))
        ((ConcreteCategory.hom (FC := FD) (CC := CD) (NatTrans.app (J.diagramPullback P f) (op S)) :
            (a : CD (multiequalizer (S.index P))) → CD (((J.pullback f).op ⋙ J.diagram P Y).obj (op S)))
          ((Equiv.symm (Meq.equiv (FD := FD) (CD := CD) P S) : (a : Meq P S) → ToType (multiequalizer (S.index P))) x :
            ToType.{t, w', w, u_1} (FC := FD) (CC := CD) (multiequalizer (S.index P)))) :
      Meq (FD := FD) (CD := CD) P (unop ((J.pullback f).op.obj (op S))))
    ((Meq.equiv (FD := FD) (CD := CD) P (unop ((J.pullback f).op.obj (op S))) :
          (a : ToType (multiequalizer ((unop ((J.pullback f).op.obj (op S))).index P))) →
            Meq P (unop ((J.pullback f).op.obj (op S))))
        ((Equiv.symm (Meq.equiv (FD := FD) (CD := CD) P (S.pullback f)) :
            (a : Meq P (S.pullback f)) → ToType (multiequalizer ((S.pullback f).index P)))
          (x.pullback (FD := FD) (CD := CD) f)) :
      Meq (FD := FD) (CD := CD) P (unop ((J.pullback f).op.obj (op S))))
have h : Eq (α := Meq (FD := FD) (CD := CD) P (S.pullback f))
  ((Meq.equiv (FD := FD) (CD := CD) P (S.pullback f) :
        (a : ToType (multiequalizer ((S.pullback f).index P))) → Meq P (S.pullback f))
      ((ConcreteCategory.hom (FC := FD) (CC := CD)
            (Multiequalizer.lift ((S.pullback f).index P) (multiequalizer (S.index P))
              (fun (I : (S.pullback f).Arrow) ↦ Multiequalizer.ι (S.index P) I.base) sorry) :
          (a : CD (multiequalizer (S.index P))) → CD (multiequalizer ((S.pullback f).index P)))
        ((Equiv.symm (Meq.equiv (FD := FD) (CD := CD) P S) : (a : Meq P S) → ToType (multiequalizer (S.index P))) x :
          ToType.{t, w', w, u_1} (FC := FD) (CC := CD) (multiequalizer (S.index P)))) :
    Meq (FD := FD) (CD := CD) P (S.pullback f))
  ((Meq.equiv (FD := FD) (CD := CD) P (S.pullback f) :
        (a : ToType (multiequalizer ((S.pullback f).index P))) → Meq P (S.pullback f))
      ((Equiv.symm (Meq.equiv (FD := FD) (CD := CD) P (S.pullback f)) :
          (a : Meq P (S.pullback f)) → ToType (multiequalizer ((S.pullback f).index P)))
        (x.pullback (FD := FD) (CD := CD) f)) :
    Meq (FD := FD) (CD := CD) P (S.pullback f))
Tactic: dsimp