proposition: Proposition lift_poset_functor_laws : is_functor lift_poset_functor_data.
proof: Proof. split. - intros X. use eq_mor_hset_struct ; cbn. intro x. induction x as [ x | ] ; cbn. + apply idpath. + apply idpath. - intros X Y Z f g. use eq_mor_hset_struct ; cbn. intro x. induction x as [ x | ] ; cbn. + apply idpath. + apply idpath. Qed.
imports: UniMath.MoreFoundations.All UniMath.OrderTheory.Posets UniMath.CategoryTheory.Core.Prelude UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.DisplayedCats.Structures.CartesianStructure UniMath.CategoryTheory.DisplayedCats.Structures.StructureLimitsAndColimits UniMath.CategoryTheory.DisplayedCats.Structures.StructuresSmashProduct UniMath.CategoryTheory.DisplayedCats.Examples.PointedPosetStrict UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors UniMath.CategoryTheory.Monoidal.Categories UniMath.CategoryTheory.Monoidal.Functors UniMath.CategoryTheory.Monoidal.FunctorCategories UniMath.CategoryTheory.Monoidal.Structure.Symmetric UniMath.CategoryTheory.Monoidal.Structure.Closed UniMath.CategoryTheory.Monoidal.Examples.SmashProductMonoidal UniMath.CategoryTheory.Monoidal.Examples.PosetsMonoidal UniMath.CategoryTheory.DisplayedCats.Examples.CategoryOfPosets UniMath.CategoryTheory.Monads.Comonads UniMath.CategoryTheory.Monoidal.Comonoids.Category