proposition: Proposition lift_poset_comonad_laws : disp_Comonad_laws (lift_poset_dupl,, lift_poset_extract).
proof: Proof. repeat split. - intro X. use eq_mor_hset_struct. intros [ x | [] ] ; cbn. + apply idpath. + apply idpath. - intro X. use eq_mor_hset_struct. intros [ x | [] ] ; cbn. + apply idpath. + apply idpath. - intro X. use eq_mor_hset_struct. intros [ 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