proposition: Proposition isaprop_has_dependent_sums (C : cat_with_terminal_cleaving) : isaprop (has_dependent_sums (cleaving_of_types C)).
proof: Proof. use isaproptotal2. - intro. do 10 (use impred ; intro). apply isaprop_left_beck_chevalley. - intros. do 3 (use funextsec ; intro). apply isaprop_dependent_sum. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Prelude UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Univalence UniMath.CategoryTheory.DisplayedCats.Functors UniMath.CategoryTheory.DisplayedCats.Fiber UniMath.CategoryTheory.DisplayedCats.Fibrations UniMath.CategoryTheory.DisplayedCats.DependentSums UniMath.CategoryTheory.Limits.Pullbacks UniMath.Bicategories.Core.Bicat UniMath.Bicategories.Core.AdjointUnique UniMath.Bicategories.Core.UnivalenceOp UniMath.Bicategories.Core.Examples.BicatOfUnivCats UniMath.Bicategories.Core.Examples.OpMorBicat UniMath.Bicategories.Morphisms.Adjunctions UniMath.Bicategories.Morphisms.Examples.MorphismsInBicatOfUnivCats UniMath.Bicategories.Morphisms.Examples.MorphismsInOp1Bicat UniMath.Bicategories.DisplayedBicats.DispBicat UniMath.Bicategories.DisplayedBicats.DispUnivalence UniMath.Bicategories.DisplayedBicats.Examples.LiftDispBicat UniMath.Bicategories.DisplayedBicats.Examples.FullSub UniMath.Bicategories.ComprehensionCat.BicatOfCompCat UniMath.Bicategories.ComprehensionCat.CompCatNotations