proposition: Proposition comprehension_eso_mor_eq : comprehension_eso_mor · δ = π fib.
proof: Proof. unfold comprehension_eso_mor. rewrite !assoc'. use z_iso_inv_on_right. refine (_ @ !(dependent_sum_map_eq _ _ _)). unfold comprehension_eso_mor_help. use (cancel_z_iso _ _ γΓ). rewrite !assoc'. pose (maponpaths (λ z, z · PullbackPr1 HΓ) (!(dfl_ext_identity_eq left_tm right_tm))) as p. cbn -[left_tm right_tm PullbackPr1] in p. rewrite !assoc' in p. rewrite left_tm_pr1, right_tm_pr1 in p. rewrite !assoc' in p. exact p. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Prelude UniMath.CategoryTheory.Equivalences.Core UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.Limits.Equalizers UniMath.CategoryTheory.Limits.Pullbacks UniMath.CategoryTheory.Limits.Preservation UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Isos UniMath.CategoryTheory.DisplayedCats.Univalence UniMath.CategoryTheory.DisplayedCats.Functors UniMath.CategoryTheory.DisplayedCats.NaturalTransformations UniMath.CategoryTheory.DisplayedCats.Equivalences UniMath.CategoryTheory.DisplayedCats.EquivalenceOverId UniMath.CategoryTheory.DisplayedCats.Fiber UniMath.CategoryTheory.DisplayedCats.Fibrations UniMath.CategoryTheory.DisplayedCats.FiberwiseTerminal UniMath.CategoryTheory.DisplayedCats.FiberwiseProducts UniMath.CategoryTheory.DisplayedCats.FiberwiseEqualizers UniMath.CategoryTheory.DisplayedCats.DependentSums UniMath.CategoryTheory.DisplayedCats.Codomain UniMath.CategoryTheory.DisplayedCats.FullyFaithfulDispFunctor UniMath.Bicategories.Core.Bicat UniMath.Bicategories.ComprehensionCat.BicatOfCompCat UniMath.Bicategories.ComprehensionCat.CompCatNotations UniMath.Bicategories.ComprehensionCat.DFLCompCat UniMath.Bicategories.ComprehensionCat.DFLCompCatNotations