Definition mono_codomain_exists_elim : mono_codomain_exists --> zh. Proof. use make_mono_cod_fib_mor. - simple refine (pr11 (He _ _ h _ _ _ (MonicisMonic _ h))). + exact (φf · PullbackPr1 _). + exact m. + abstract (refine (!p @ !_) ; rewrite <- q ; rewrite !assoc' ; apply maponpaths ; cbn ; apply PullbackSqrCommutes). - abstract (exact (pr121 (He _ _ h _ _ _ (MonicisMonic _ h)))). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Monics. Require Import UniMath.CategoryTheory.Limits.Pullbacks. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Fibrations. Require Import UniMath.CategoryTheory.DisplayedCats.Examples.MonoCodomain. Require Import UniMath.CategoryTheory.DisplayedCats.MonoCodomain.FiberMonoCod. Require Import UniMath.CategoryTheory.DisplayedCats.Fiberwise.DependentSums. Require Import UniMath.CategoryTheory.RegularAndExact.RegularCategory. Require Import UniMath.CategoryTheory.RegularAndExact.RegularEpi. Require Import UniMath.CategoryTheory.RegularAndExact.RegularEpiFacts.