-- Lean 4 proof step from Mathlib.CategoryTheory.Shift.ShiftedHomOpposite (goal)
Goal:
C : Type u_1
inst : Category.{v_1, u_1} C
inst_1 : HasShift.{v_1, u_1, 0} C ℤ
X Y Z : C
a b : ℤ
f : ShiftedHom (Opposite.op Z) (Opposite.op Y) a
g : ShiftedHom (Opposite.op Y) (Opposite.op X) b
c : ℤ
h : b + a = c
⊢ Eq.{v_1 + 1} (α := ShiftedHom X Z c)
    (CategoryStruct.comp (Y :=
      Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor C b)
        (Opposite.unop (Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor Cᵒᵖ b) (Opposite.op X))))
      (Quiver.Hom.unop (NatTrans.app (Iso.inv (Equivalence.unitIso (opShiftFunctorEquivalence C b))) (Opposite.op X)) :
        Opposite.unop (Opposite.op X) ⟶
          Opposite.unop
            (Opposite.op
              (Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor C b)
                (Opposite.unop (Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor Cᵒᵖ b) (Opposite.op X))))))
      (CategoryStruct.comp (Y :=
          Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor C b)
            (Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor C a)
              (Opposite.unop
                (Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor Cᵒᵖ a)
                  (Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor Cᵒᵖ b) (Opposite.op X))))))
          (Functor.map (shiftFunctor C b)
              (Quiver.Hom.unop
                (NatTrans.app (Iso.inv (Equivalence.unitIso (opShiftFunctorEquivalence C a)))
                  (Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor Cᵒᵖ b) (Opposite.op X)))) :
            Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor C b)
                (Opposite.unop (Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor Cᵒᵖ b) (Opposite.op X))) ⟶
              Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor C b)
                (Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor C a)
                  (Opposite.unop
                    (Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor Cᵒᵖ a)
                      (Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor Cᵒᵖ b) (Opposite.op X))))))
          (NatTrans.app (Iso.inv (shiftFunctorAdd' C a b c ⋯))
                (Opposite.unop
                  (Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor Cᵒᵖ a)
                    (Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor Cᵒᵖ b) (Opposite.op X)))) ≫
              Functor.map (shiftFunctor C c)
                (𝟙
                    (Opposite.unop
                      (Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor Cᵒᵖ a)
                        (Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor Cᵒᵖ b) (Opposite.op X)))) ≫
                  Quiver.Hom.unop (Functor.map (shiftFunctor Cᵒᵖ a) g) ≫ Quiver.Hom.unop f) :
            Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor C b)
                (Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor C a)
                  (Opposite.unop
                    (Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor Cᵒᵖ a)
                      (Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor Cᵒᵖ b) (Opposite.op X))))) ⟶
              Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor C c) Z) :
        Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor C b)
            (Opposite.unop (Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor Cᵒᵖ b) (Opposite.op X))) ⟶
          Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor C c) Z))
    (CategoryStruct.comp (Y := Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor C b) Y)
      (CategoryStruct.comp (Y :=
          Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor C b)
            (Opposite.unop (Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor Cᵒᵖ b) (Opposite.op X))))
          (Quiver.Hom.unop
              (NatTrans.app (Iso.inv (Equivalence.unitIso (opShiftFunctorEquivalence C b))) (Opposite.op X)) :
            Opposite.unop (Opposite.op X) ⟶
              Opposite.unop
                (Opposite.op
                  (Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor C b)
                    (Opposite.unop (Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor Cᵒᵖ b) (Opposite.op X))))))
          (Functor.map (shiftFunctor C b) (Quiver.Hom.unop g) :
            Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor C b)
                (Opposite.unop (Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor Cᵒᵖ b) (Opposite.op X))) ⟶
              Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor C b) Y) :
        X ⟶ Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor C b) Y)
      (Functor.map (shiftFunctor C b)
            ((Equiv.symm (opEquiv a) : (a_1 : ShiftedHom (Opposite.op Z) (Opposite.op Y) a) → ShiftedHom Y Z a) f) ≫
          NatTrans.app (Iso.inv (shiftFunctorAdd' C a b c ⋯)) Z :
        Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor C b) Y ⟶ Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor C c) Z))
have rw : Eq.{v_1 + 1} (α := ShiftedHom X Z c)
  (CategoryStruct.comp (Y :=
    Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor C b)
      (Opposite.unop (Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor Cᵒᵖ b) (Opposite.op X))))
    (Quiver.Hom.unop (NatTrans.app (Iso.inv (Equivalence.unitIso (opShiftFunctorEquivalence C b))) (Opposite.op X)) :
      Opposite.unop (Opposite.op X) ⟶
        Opposite.unop
          (Opposite.op
            (Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor C b)
              (Opposite.unop (Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor Cᵒᵖ b) (Opposite.op X))))))
    (CategoryStruct.comp (Y :=
        Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor C b)
          (Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor C a)
            (Opposite.unop
              (Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor Cᵒᵖ a)
                (Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor Cᵒᵖ b) (Opposite.op X))))))
        (Functor.map (shiftFunctor C b)
            (Quiver.Hom.unop
              (NatTrans.app (Iso.inv (Equivalence.unitIso (opShiftFunctorEquivalence C a)))
                (Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor Cᵒᵖ b) (Opposite.op X)))) :
          Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor C b)
              (Opposite.unop (Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor Cᵒᵖ b) (Opposite.op X))) ⟶
            Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor C b)
              (Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor C a)
                (Opposite.unop
                  (Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor Cᵒᵖ a)
                    (Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor Cᵒᵖ b) (Opposite.op X))))))
        (Functor.map (shiftFunctor C a ⋙ shiftFunctor C b) (Quiver.Hom.unop (Functor.map (shiftFunctor Cᵒᵖ a) g)) ≫
            Functor.map (shiftFunctor C a ⋙ shiftFunctor C b) (Quiver.Hom.unop f) ≫
              NatTrans.app (Iso.inv (shiftFunctorAdd' C a b c sorry)) Z :
          Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor C a ⋙ shiftFunctor C b)
              (Opposite.unop
                (Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor Cᵒᵖ a)
                  (Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor Cᵒᵖ b) (Opposite.op X)))) ⟶
            Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor C c) Z) :
      Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor C b)
          (Opposite.unop (Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor Cᵒᵖ b) (Opposite.op X))) ⟶
        Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor C c) Z))
  (CategoryStruct.comp (Y :=
    Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor C b)
      (Opposite.unop (Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor Cᵒᵖ b) (Opposite.op X))))
    (Quiver.Hom.unop (NatTrans.app (Iso.inv (Equivalence.unitIso (opShiftFunctorEquivalence C b))) (Opposite.op X)) :
      Opposite.unop (Opposite.op X) ⟶
        Opposite.unop
          (Opposite.op
            (Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor C b)
              (Opposite.unop (Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor Cᵒᵖ b) (Opposite.op X))))))
    (Functor.map (shiftFunctor C b) (Quiver.Hom.unop g) ≫
        Functor.map (shiftFunctor C b)
            (CategoryStruct.comp (Y :=
              Opposite.unop
                (Functor.obj.{v_1, v_1, u_1, u_1}
                  (Equivalence.functor (opShiftFunctorEquivalence C a) ⋙
                    Equivalence.inverse (opShiftFunctorEquivalence C a))
                  (Opposite.op Y)))
              (Quiver.Hom.unop
                (NatTrans.app (Iso.inv (Equivalence.unitIso (opShiftFunctorEquivalence C a))) (Opposite.op Y)))
              (Functor.map (shiftFunctor C a) (Quiver.Hom.unop f))) ≫
          NatTrans.app (Iso.inv (shiftFunctorAdd' C a b c sorry)) Z :
      Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor C b)
          (Opposite.unop (Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor Cᵒᵖ b) (Opposite.op X))) ⟶
        Functor.obj.{v_1, v_1, u_1, u_1} (shiftFunctor C c) Z))
Tactic: rw [assoc, id_comp, Functor.map_comp, ← NatTrans.naturality_assoc,
    ← NatTrans.naturality, opEquiv_symm_apply]