-- Module: Mathlib.CategoryTheory.Triangulated.Yoneda
Goal:
C : Type u_1
inst : Category.{v_1, u_1} C
inst_1 : Preadditive.{v_1, u_1} C
inst_2 : HasShift.{v_1, u_1, 0} C ℤ
inst_3 : ∀ (n : ℤ), Functor.Additive.{v_1, u_1, v_1, u_1} (shiftFunctor C n)
B : C
n m a a' a'' : ℤ
ha' : n + a = a'
ha'' : m + a' = a''
w :
  ∀ (x : Cᵒᵖ)
    (x_1 :
      (↑(Functor.obj
            (shiftFunctor Cᵒᵖ (m + n) ⋙
              Functor.obj preadditiveYoneda (Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor C a) B))
            x) :
        Type v_1)),
    Eq (α :=
      (↑(Functor.obj (Functor.obj preadditiveYoneda (Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor C a'') B)) x) :
        Type v_1))
      ((AddCommGrpCat.Hom.hom
              (NatTrans.app
                (Iso.hom
                  (NatIso.ofComponents
                    (fun (A : Cᵒᵖ) ↦
                      AddEquiv.toAddCommGrpIso
                        (let __Equiv :
                          (↑(Functor.obj
                                  (shiftFunctor Cᵒᵖ (m + n) ⋙
                                    Functor.obj preadditiveYoneda
                                      (Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor C a) B))
                                  A) :
                              Type v_1) ≃
                            (↑(Functor.obj
                                  (Functor.obj preadditiveYoneda
                                    (Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor C a'') B))
                                  A) :
                              Type v_1) :=
                          Equiv.trans Quiver.Hom.opEquiv (Equiv.symm (ShiftedHom.opEquiv' (m + n) a a'' ⋯));
                        { toEquiv := __Equiv, map_add' := ⋯ }))
                    ⋯))
                x) :
            (a : (↑((shiftFunctor Cᵒᵖ (m + n) ⋙ preadditiveYoneda.obj ((shiftFunctor C a).obj B)).obj x) : Type v_1)) →
              (↑((preadditiveYoneda.obj ((shiftFunctor C a'').obj B)).obj x) : Type v_1))
          x_1 :
        (↑(Functor.obj (Functor.obj preadditiveYoneda (Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor C a'') B)) x) :
          Type v_1))
      ((AddCommGrpCat.Hom.hom
              (NatTrans.app
                (Iso.hom
                  (Functor.isoWhiskerRight (shiftFunctorAdd Cᵒᵖ m n)
                      (Functor.obj preadditiveYoneda (Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor C a) B)) ≪≫
                    Functor.associator (shiftFunctor Cᵒᵖ m) (shiftFunctor Cᵒᵖ n)
                        (Functor.obj preadditiveYoneda (Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor C a) B)) ≪≫
                      Functor.isoWhiskerLeft (shiftFunctor Cᵒᵖ m)
                          (NatIso.ofComponents
                            (fun (A : Cᵒᵖ) ↦
                              AddEquiv.toAddCommGrpIso
                                (let __Equiv :
                                  (↑(Functor.obj
                                          (shiftFunctor Cᵒᵖ n ⋙
                                            Functor.obj preadditiveYoneda
                                              (Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor C a) B))
                                          A) :
                                      Type v_1) ≃
                                    (↑(Functor.obj
                                          (Functor.obj preadditiveYoneda
                                            (Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor C a') B))
                                          A) :
                                      Type v_1) :=
                                  Equiv.trans Quiver.Hom.opEquiv (Equiv.symm (ShiftedHom.opEquiv' n a a' ha'));
                                { toEquiv := __Equiv, map_add' := ⋯ :
                                  (↑(Functor.obj
                                          (shiftFunctor Cᵒᵖ n ⋙
                                            Functor.obj preadditiveYoneda
                                              (Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor C a) B))
                                          A) :
                                      Type v_1) ≃+
                                    (↑(Functor.obj
                                          (Functor.obj preadditiveYoneda
                                            (Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor C a') B))
                                          A) :
                                      Type v_1) }))
                            ⋯) ≪≫
                        NatIso.ofComponents
                          (fun (A : Cᵒᵖ) ↦
                            AddEquiv.toAddCommGrpIso
                              (let __Equiv :
                                (↑(Functor.obj
                                        (shiftFunctor Cᵒᵖ m ⋙
                                          Functor.obj preadditiveYoneda
                                            (Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor C a') B))
                                        A) :
                                    Type v_1) ≃
                                  (↑(Functor.obj
                                        (Functor.obj preadditiveYoneda
                                          (Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor C a'') B))
                                        A) :
                                    Type v_1) :=
                                Equiv.trans Quiver.Hom.opEquiv (Equiv.symm (ShiftedHom.opEquiv' m a' a'' ha''));
                              { toEquiv := __Equiv, map_add' := ⋯ }))
                          ⋯))
                x) :
            (a : (↑((shiftFunctor Cᵒᵖ (m + n) ⋙ preadditiveYoneda.obj ((shiftFunctor C a).obj B)).obj x) : Type v_1)) →
              (↑((preadditiveYoneda.obj ((shiftFunctor C a'').obj B)).obj x) : Type v_1))
          x_1 :
        (↑(Functor.obj (Functor.obj preadditiveYoneda (Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor C a'') B)) x) :
          Type v_1))
⊢ Eq (α :=
    Iso (C := Functor.{v_1, v_1, u_1, v_1 + 1} Cᵒᵖ AddCommGrpCat)
      (shiftFunctor Cᵒᵖ (m + n) ⋙ Functor.obj preadditiveYoneda (Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor C a) B))
      (Functor.obj preadditiveYoneda (Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor C a'') B)))
    (NatIso.ofComponents
      (fun (A : Cᵒᵖ) ↦
        AddEquiv.toAddCommGrpIso
          (let __Equiv :
            (↑(Functor.obj
                    (shiftFunctor Cᵒᵖ (m + n) ⋙
                      Functor.obj preadditiveYoneda (Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor C a) B))
                    A) :
                Type v_1) ≃
              (↑(Functor.obj (Functor.obj preadditiveYoneda (Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor C a'') B))
                    A) :
                Type v_1) :=
            Equiv.trans Quiver.Hom.opEquiv (Equiv.symm (ShiftedHom.opEquiv' (m + n) a a'' ⋯));
          { toEquiv := __Equiv, map_add' := ⋯ }))
      ⋯)
    (Functor.isoWhiskerRight (shiftFunctorAdd Cᵒᵖ m n)
        (Functor.obj preadditiveYoneda (Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor C a) B)) ≪≫
      Functor.associator (shiftFunctor Cᵒᵖ m) (shiftFunctor Cᵒᵖ n)
          (Functor.obj preadditiveYoneda (Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor C a) B)) ≪≫
        Functor.isoWhiskerLeft (shiftFunctor Cᵒᵖ m)
            (NatIso.ofComponents
              (fun (A : Cᵒᵖ) ↦
                AddEquiv.toAddCommGrpIso
                  (let __Equiv :
                    (↑(Functor.obj
                            (shiftFunctor Cᵒᵖ n ⋙
                              Functor.obj preadditiveYoneda (Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor C a) B))
                            A) :
                        Type v_1) ≃
                      (↑(Functor.obj
                            (Functor.obj preadditiveYoneda (Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor C a') B))
                            A) :
                        Type v_1) :=
                    Equiv.trans Quiver.Hom.opEquiv (Equiv.symm (ShiftedHom.opEquiv' n a a' ha'));
                  { toEquiv := __Equiv, map_add' := ⋯ :
                    (↑(Functor.obj
                            (shiftFunctor Cᵒᵖ n ⋙
                              Functor.obj preadditiveYoneda (Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor C a) B))
                            A) :
                        Type v_1) ≃+
                      (↑(Functor.obj
                            (Functor.obj preadditiveYoneda (Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor C a') B))
                            A) :
                        Type v_1) }))
              ⋯) ≪≫
          NatIso.ofComponents
            (fun (A : Cᵒᵖ) ↦
              AddEquiv.toAddCommGrpIso
                (let __Equiv :
                  (↑(Functor.obj
                          (shiftFunctor Cᵒᵖ m ⋙
                            Functor.obj preadditiveYoneda (Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor C a') B))
                          A) :
                      Type v_1) ≃
                    (↑(Functor.obj
                          (Functor.obj preadditiveYoneda (Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor C a'') B)) A) :
                      Type v_1) :=
                  Equiv.trans Quiver.Hom.opEquiv (Equiv.symm (ShiftedHom.opEquiv' m a' a'' ha''));
                { toEquiv := __Equiv, map_add' := ⋯ }))
            ⋯)

Tactic:
ext _ x