proposition: Theorem unicity_univ_prop_reindexing_forward : ∏ DH' :disp_functor H D' D'', disp_nat_z_iso (disp_functor_composite DF DH') DG (nat_z_iso_id (F ∙ H)) -> disp_nat_z_iso DH' DH (nat_z_iso_id H).
proof: Proof. intros DH' µ'. apply DH0_DH1_disp_nat_z_iso. apply (transportf _ (comp_nat_z_iso_id_left (nat_z_iso_id (F ∙ H)))). apply (disp_nat_z_iso_comp µ'). apply (transportf _ nat_z_iso_inv_id). exact (disp_nat_z_iso_inv univ_prop_reindexing_forward). Defined.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Functors UniMath.CategoryTheory.DisplayedCats.NaturalTransformations UniMath.CategoryTheory.DisplayedCats.Isos UniMath.CategoryTheory.DisplayedCats.Univalence UniMath.CategoryTheory.DisplayedCats.Fibrations UniMath.CategoryTheory.DisplayedCats.StreetFibration