∀ (G : Type u_1) [inst : Group G] (n : ℕ) (x : G),
  CategoryTheory.CategoryStruct.comp
      ((Action.trivial G
            (CategoryTheory.MonoidalCategoryStruct.tensorObj (Action.leftRegular G) (Action.trivial G (Fin n → G))).V).ρ
        x)
      (Fin.insertNthEquiv (fun x => G) 0).toIso.hom =
    CategoryTheory.CategoryStruct.comp
      ((Action.trivial G
            (CategoryTheory.MonoidalCategoryStruct.tensorObj (Action.leftRegular G) (Action.trivial G (Fin n → G))).V).ρ
        x)
      (Fin.insertNthEquiv (fun x => G) 0).toIso.hom