proposition: Proposition comprehension_eso_inv_mor_mor : comprehension_eso_inv_mor · comprehension_eso_mor = identity _.
proof: Proof. unfold comprehension_eso_mor, comprehension_eso_inv_mor. rewrite !assoc'. etrans. { apply maponpaths. rewrite !assoc. rewrite z_iso_inv_after_z_iso. apply id_left. } unfold comprehension_eso_mor_help, comprehension_eso_inv_mor_help. unfold sub_to_extension. unfold dfl_ext_identity_sub_tm. simpl. rewrite !assoc'. etrans. { apply maponpaths. etrans. { apply maponpaths. rewrite !assoc. do 2 apply maponpaths_2. exact (PullbackSqrCommutes (comp_cat_pullback comprehension_eso_ty_help comprehension_eso_inv_mor_help_sub)). } rewrite !assoc. etrans. { do 3 apply maponpaths_2. unfold comp_cat_comp_mor. apply comprehension_functor_mor_comm. } rewrite id_right. rewrite !assoc'. etrans. { apply maponpaths. rewrite !assoc. apply maponpaths_2. apply comprehension_eso_inv_mor_help_sub_pr1. } rewrite z_iso_inv_after_z_iso. apply id_right. } apply comp_cat_tm_eq. 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