proposition: Proposition is_invertible_dfl_full_comp_cat_nat_trans_left : τ • is_invertible_dfl_full_comp_cat_nat_trans_inv = id₂ F.
proof: Proof. use dfl_full_comp_cat_nat_trans_eq. - intro x. apply (z_iso_inv_after_z_iso (_ ,, Hτ x)). - intros x xx. etrans. { apply maponpaths. exact (disp_nat_z_iso_iso_inv ττiso x xx). } unfold transportb. rewrite transport_f_f. use transportf_set. apply homset_property. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Prelude UniMath.CategoryTheory.Equivalences.Core UniMath.CategoryTheory.Equivalences.CompositesAndInverses UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Isos UniMath.CategoryTheory.DisplayedCats.Univalence UniMath.CategoryTheory.DisplayedCats.Functors UniMath.CategoryTheory.DisplayedCats.NaturalTransformations UniMath.CategoryTheory.DisplayedCats.Equivalences UniMath.CategoryTheory.DisplayedCats.Fiber UniMath.CategoryTheory.DisplayedCats.Fibrations UniMath.CategoryTheory.DisplayedCats.FiberwiseTerminal UniMath.CategoryTheory.DisplayedCats.FiberwiseProducts UniMath.CategoryTheory.DisplayedCats.FiberwiseEqualizers UniMath.CategoryTheory.DisplayedCats.DependentSums UniMath.CategoryTheory.DisplayedCats.Codomain UniMath.CategoryTheory.DisplayedCats.Codomain.FiberCod UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.Limits.Pullbacks UniMath.CategoryTheory.Limits.Preservation UniMath.Bicategories.Core.Bicat UniMath.Bicategories.DisplayedBicats.DispBicat UniMath.Bicategories.DisplayedBicats.DispUnivalence UniMath.Bicategories.DisplayedBicats.Examples.Prod UniMath.Bicategories.DisplayedBicats.Examples.FullSub UniMath.Bicategories.DisplayedBicats.Examples.Sub1Cell UniMath.Bicategories.ComprehensionCat.BicatOfCompCat UniMath.Bicategories.ComprehensionCat.CompCatNotations UniMath.Bicategories.ComprehensionCat.TypeFormers.UnitTypes UniMath.Bicategories.ComprehensionCat.TypeFormers.ProductTypes UniMath.Bicategories.ComprehensionCat.TypeFormers.EqualizerTypes UniMath.Bicategories.ComprehensionCat.TypeFormers.Democracy UniMath.Bicategories.ComprehensionCat.TypeFormers.SigmaTypes