Definition dfl_ext_identity_sub_mor {Γ Δ : C} (s : Δ --> Γ) {A : ty Γ} (t₁ t₂ : comp_cat_tm Γ A) : dfl_ext_identity_type (sub_comp_cat_tm t₁ s) (sub_comp_cat_tm t₂ s) -->[ identity _ ] dfl_ext_identity_type t₁ t₂ [[s]]. Proof. use (EqualizerIn (preserves_equalizer_equalizer (pr2 (fiberwise_equalizers_dfl_full_comp_cat C) _ _ s) (dfl_ext_identity t₁ t₂))). - exact (dfl_ext_identity_sub_mor_mor s t₁ t₂). - exact (dfl_ext_identity_sub_mor_eq s t₁ t₂). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Equivalences.Core. Require Import UniMath.CategoryTheory.Limits.Preservation. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.Limits.Equalizers. Require Import UniMath.CategoryTheory.Limits.Pullbacks. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Univalence. Require Import UniMath.CategoryTheory.DisplayedCats.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.NaturalTransformations. Require Import UniMath.CategoryTheory.DisplayedCats.Fiber. Require Import UniMath.CategoryTheory.DisplayedCats.Fibrations. Require Import UniMath.CategoryTheory.DisplayedCats.Fiberwise.FiberwiseTerminal. Require Import UniMath.CategoryTheory.DisplayedCats.Fiberwise.FiberwiseProducts. Require Import UniMath.CategoryTheory.DisplayedCats.Fiberwise.FiberwiseEqualizers. Require Import UniMath.CategoryTheory.DisplayedCats.Fiberwise.DependentSums. Require Import UniMath.CategoryTheory.DisplayedCats.Codomain. Require Import UniMath.CategoryTheory.DisplayedCats.FullyFaithfulDispFunctor. Require Import UniMath.CategoryTheory.Monics. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.ComprehensionCat.BicatOfCompCat. Require Import UniMath.Bicategories.ComprehensionCat.CompCatNotations. Require Import UniMath.Bicategories.ComprehensionCat.DFLCompCat.