Proposition idtoiso_twosided_disp_inv {C₁ C₂ : category} {D : twosided_disp_cat C₁ C₂} {x : C₁} {y : C₂} {xy xy' : D x y} (p : xy = xy') : pr1 (idtoiso_twosided_disp (idpath _) (idpath _) (!p)) = iso_inv_twosided_disp (idtoiso_twosided_disp (idpath _) (idpath _) p). Proof. induction p ; cbn. apply idpath. Qed.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Core.Setcategories. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.DisplayedFunctor. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Isos. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Univalence. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Strictness.