proposition: Proposition is_z_iso_from_isTerminal_codomain {x : C} (yf : C/x) (H : isTerminal (C/x) yf) : is_z_isomorphism (pr2 yf).
proof: Proof. pose (T := (_ ,, H) : Terminal _). pose (φ := TerminalArrow T (cod_fib_id x)). use make_is_z_isomorphism. - exact (dom_mor φ). - split. + abstract (use (maponpaths dom_mor (TerminalArrowEq (T := T) (_ · _ ,, _) (identity _))) ; cbn ; rewrite !assoc' ; apply maponpaths ; exact (mor_eq φ)). + abstract (exact (mor_eq φ)). 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