proposition: Proposition dependent_sum_map_eq {C : comp_cat} (D : has_dependent_sums (cleaving_of_types C)) {Γ : C} (A : ty Γ) (B : ty (Γ & A)) : dependent_sum_map D A B · π (dep_sum D (π A) B) = π B · π A.
proof: Proof. unfold dependent_sum_map, comp_cat_extend_over. rewrite !assoc'. etrans. { apply maponpaths. apply comprehension_functor_mor_comm. } rewrite !assoc. etrans. { apply maponpaths_2. apply comprehension_functor_mor_comm. } rewrite id_right. apply idpath. 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