proposition: Proposition isTerminal_codomain_fib {x : C} (yf : C/x) (H : is_z_isomorphism (pr2 yf)) : isTerminal (C/x) yf.
proof: 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.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Prelude UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.Equalizers UniMath.CategoryTheory.Limits.Pullbacks UniMath.CategoryTheory.Limits.PullbackConstructions UniMath.CategoryTheory.Limits.Preservation UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Fibrations UniMath.CategoryTheory.DisplayedCats.Fiber UniMath.CategoryTheory.DisplayedCats.Codomain UniMath.CategoryTheory.DisplayedCats.FiberwiseTerminal UniMath.CategoryTheory.DisplayedCats.FiberwiseProducts UniMath.CategoryTheory.DisplayedCats.FiberwiseEqualizers UniMath.CategoryTheory.DisplayedCats.Codomain.FiberCod UniMath.CategoryTheory.DisplayedCats.Codomain.CodLeftAdjoint