Proposition isTerminal_codomain_fib {x : C} (yf : C/x) (H : is_z_isomorphism (pr2 yf)) : isTerminal (C/x) yf. Proof. pose (f := (_ ,, H) : z_iso _ _). intro zg. use iscontraprop1. - abstract (use invproofirrelevance ; intros φ₁ φ₂ ; use eq_mor_cod_fib ; use (cancel_z_iso _ _ f) ; exact (pr2 φ₁ @ !(pr2 φ₂))). - use make_cod_fib_mor. + exact (cod_mor zg · inv_from_z_iso f). + abstract (rewrite assoc' ; refine (_ @ id_right _) ; apply maponpaths ; exact (z_iso_after_z_iso_inv f)). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.Limits.BinProducts. Require Import UniMath.CategoryTheory.Limits.Equalizers. Require Import UniMath.CategoryTheory.Limits.Pullbacks. Require Import UniMath.CategoryTheory.Limits.PullbackConstructions. Require Import UniMath.CategoryTheory.Limits.Preservation. 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.Fiberwise.FiberwiseTerminal. Require Import UniMath.CategoryTheory.DisplayedCats.Fiberwise.FiberwiseProducts. Require Import UniMath.CategoryTheory.DisplayedCats.Fiberwise.FiberwiseEqualizers. Require Import UniMath.CategoryTheory.DisplayedCats.Codomain.FiberCod. Require Import UniMath.CategoryTheory.DisplayedCats.Codomain.CodLeftAdjoint. Section FromEqCodFib. End FromEqCodFib. Section FromUMP. End FromUMP.