Definition mono_cod_implication_elim : zχ --> mono_cod_implication. Proof. use make_mono_cod_fib_mor. - refine (mono_dom_mor (mono_cod_forall_elim φ _ zχ _)). use make_mono_cod_fib_mor. + use PullbackArrow. * exact (PullbackPr2 _). * exact (mono_cod_impl_pb_map _ _ · ζ). * abstract (cbn ; refine (!_) ; etrans ; [ rewrite !assoc' ; apply maponpaths ; exact (mono_mor_eq l) | ] ; cbn ; unfold mono_cod_impl_pb_map ; rewrite !assoc ; rewrite PullbackArrow_PullbackPr1 ; apply idpath). + abstract (cbn ; apply PullbackArrow_PullbackPr1). - abstract (exact (mono_mor_eq (mono_cod_forall_elim _ _ _ _))). 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.Adjunctions.Core. Require Import UniMath.CategoryTheory.Adjunctions.AdjunctionMonics. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.Limits.BinProducts. Require Import UniMath.CategoryTheory.Limits.Pullbacks. Require Import UniMath.CategoryTheory.Limits.Preservation. Require Import UniMath.CategoryTheory.LocallyCartesianClosed.LocallyCartesianClosed. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Fibrations. Require Import UniMath.CategoryTheory.DisplayedCats.Fiber. Require Import UniMath.CategoryTheory.DisplayedCats.Codomain. Require Import UniMath.CategoryTheory.DisplayedCats.Codomain.FiberCod. Require Import UniMath.CategoryTheory.DisplayedCats.Codomain.CodMorphisms. Require Import UniMath.CategoryTheory.DisplayedCats.Codomain.CodLimits. Require Import UniMath.CategoryTheory.DisplayedCats.Examples.MonoCodomain. Require Import UniMath.CategoryTheory.DisplayedCats.MonoCodomain.FiberMonoCod. Require Import UniMath.CategoryTheory.DisplayedCats.MonoCodomain.MonoCodLeftAdjoint. Require Import UniMath.CategoryTheory.DisplayedCats.MonoCodomain.MonoCodLimits. Require Import UniMath.CategoryTheory.DisplayedCats.MonoCodomain.Inclusion. Require Import UniMath.CategoryTheory.DisplayedCats.Fiberwise.DependentSums. Require Import UniMath.CategoryTheory.DisplayedCats.Fiberwise.DependentProducts. Require Import UniMath.CategoryTheory.DisplayedCats.Fiberwise.FiberwiseProducts. Require Import UniMath.CategoryTheory.DisplayedCats.Fiberwise.FiberwiseCartesianClosed. Require Import UniMath.CategoryTheory.DisplayedCats.Fiberwise.DualBeckChevalley. Require Import UniMath.CategoryTheory.RegularAndExact.RegularCategory.