-- Module: Mathlib.CategoryTheory.Monoidal.Action.Opposites
Goal:
C : Type u_1
D : Type u_2
inst : Category.{v_1, u_1} C
inst_1 : MonoidalCategory.{v_1, u_1} C
inst_2 : Category.{v_2, u_2} D
inst_3 : MonoidalRightAction.{v_1, u_1, v_2, u_2} Cᵒᵖ Dᵒᵖ
x x_1 x_2 : C
x_3 : D
a :
  Eq.{v_2 + 1} (α :=
    op
        (unop
          (@actionObj.{v_1, u_1, v_2, u_2} _ _ Category.opposite Category.opposite toMonoidalCategoryStruct _ (op x_3)
            (op (tensorObj.{v_1, u_1} (𝒞 := inst) (tensorObj.{v_1, u_1} (𝒞 := inst) x x_1) x_2)))) ⟶
      op
        (unop
          (@actionObj.{v_1, u_1, v_2, u_2} _ _ Category.opposite Category.opposite toMonoidalCategoryStruct _
            (op
              (unop
                (@actionObj.{v_1, u_1, v_2, u_2} _ _ Category.opposite Category.opposite toMonoidalCategoryStruct _
                  (op
                    (unop
                      (@actionObj.{v_1, u_1, v_2, u_2} _ _ Category.opposite Category.opposite toMonoidalCategoryStruct
                        _ (op x_3) (op x))))
                  (op x_1))))
            (op x_2))))
    (inv
      (Quiver.Hom.op
        (Quiver.Hom.unop (op x_3 ⊴ᵣ Quiver.Hom.op (Iso.hom (α_ x x_1 x_2))) ≫
          Iso.hom (Iso.unop (Iso.symm (αᵣ (op x_3) (op x) (op (tensorObj.{v_1, u_1} (𝒞 := inst) x_1 x_2))))) ≫
            Iso.hom
              (Iso.unop
                (Iso.symm
                  (αᵣ
                    (op
                      (unop
                        (@actionObj.{v_1, u_1, v_2, u_2} _ _ Category.opposite Category.opposite
                          toMonoidalCategoryStruct _ (op x_3) (op x))))
                    (op x_1) (op x_2)))))))
    (inv
      (Quiver.Hom.op
        (Iso.hom (Iso.unop (Iso.symm (αᵣ (op x_3) (op (tensorObj.{v_1, u_1} (𝒞 := inst) x x_1)) (op x_2)))) ≫
          Quiver.Hom.unop (Quiver.Hom.op (Iso.hom (Iso.unop (Iso.symm (αᵣ (op x_3) (op x) (op x_1))))) ⊵ᵣ op x_2))))
⊢ Eq.{v_2 + 1} (α :=
    op
        (unop
          (@actionObj.{v_1, u_1, v_2, u_2} _ _ Category.opposite Category.opposite toMonoidalCategoryStruct _
            (op
              (unop
                (@actionObj.{v_1, u_1, v_2, u_2} _ _ Category.opposite Category.opposite toMonoidalCategoryStruct _
                  (op
                    (unop
                      (@actionObj.{v_1, u_1, v_2, u_2} _ _ Category.opposite Category.opposite toMonoidalCategoryStruct
                        _ (op x_3) (op x))))
                  (op x_1))))
            (op x_2))) ⟶
      op
        (unop
          (@actionObj.{v_1, u_1, v_2, u_2} _ _ Category.opposite Category.opposite toMonoidalCategoryStruct _ (op x_3)
            (op (tensorObj.{v_1, u_1} (𝒞 := inst) (tensorObj.{v_1, u_1} (𝒞 := inst) x x_1) x_2)))))
    (Quiver.Hom.op
      (Quiver.Hom.unop (op x_3 ⊴ᵣ Quiver.Hom.op (Iso.hom (α_ x x_1 x_2))) ≫
        Iso.hom (Iso.unop (Iso.symm (αᵣ (op x_3) (op x) (op (tensorObj.{v_1, u_1} (𝒞 := inst) x_1 x_2))))) ≫
          Iso.hom
            (Iso.unop
              (Iso.symm
                (αᵣ
                  (op
                    (unop
                      (@actionObj.{v_1, u_1, v_2, u_2} _ _ Category.opposite Category.opposite toMonoidalCategoryStruct
                        _ (op x_3) (op x))))
                  (op x_1) (op x_2))))))
    (Quiver.Hom.op
      (Iso.hom (Iso.unop (Iso.symm (αᵣ (op x_3) (op (tensorObj.{v_1, u_1} (𝒞 := inst) x x_1)) (op x_2)))) ≫
        Quiver.Hom.unop (Quiver.Hom.op (Iso.hom (Iso.unop (Iso.symm (αᵣ (op x_3) (op x) (op x_1))))) ⊵ᵣ op x_2)))

Tactic:
apply IsIso.inv_eq_inv.mp

Premises used: CategoryTheory.IsIso.inv_eq_inv, Iff.mp