∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] [inst_1 : CategoryTheory.MonoidalCategory C]
  [inst_2 : CategoryTheory.BraidedCategory C] (A : CategoryTheory.CommMon C)
  {X Y : CategoryTheory.Discrete PUnit.{u + 1}} (x : X ⟶ Y),
  (CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.commMonToLaxBraidedObj A).map x =
    CategoryTheory.CategoryStruct.id A.X