proposition: Lemma precompRU_ff : disp_functor_ff precompRU.
proof: Proof. intro ; intros. apply isweqinclandsurj. - do 3 intro. assert (p : isaset ( hfiber (λ ff : unit, ♯ precompRU ff) y0)). { use isaset_hfiber ; use isasetaprop ; apply isapropunit. } use tpair. + use total2_paths_f. { apply isapropunit. } use proofirrelevance. use hlevelntosn. apply isapropunit. + intro ; apply p. - intro ; intros. apply hinhpr. exists tt. apply isapropunit. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.Equivalences.Core UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.PrecompEquivalence UniMath.CategoryTheory.catiso UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.Monoidal.AlternativeDefinitions.MonoidalCategoriesTensored UniMath.CategoryTheory.Monoidal.AlternativeDefinitions.MonoidalFunctorCategory UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Functors UniMath.CategoryTheory.DisplayedCats.Total UniMath.CategoryTheory.DisplayedCats.TotalCategoryFacts UniMath.CategoryTheory.Monoidal.RezkCompletion.LiftedTensor UniMath.CategoryTheory.Monoidal.RezkCompletion.LiftedTensorUnit