proposition: Lemma action_binproduct_is_object : is_monoid_action action_binproduct_object_data.
proof: Proof. use make_is_monoid_action. - intro. use pathsdirprod; apply action_unel. - intros. use pathsdirprod; apply action_op. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.Algebra.Monoids UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.Categories.HSET.Core UniMath.CategoryTheory.Categories.HSET.MonoEpiIso UniMath.CategoryTheory.Core.Prelude UniMath.CategoryTheory.exponentials UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.Limits.Preservation UniMath.CategoryTheory.DisplayedCats.Constructions UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Total