Definition para_sqr_inv : para_sqr (identity _) (identity _) g f. Proof. use make_para_sqr. - exact (inv_from_z_iso i). - abstract (unfold para_sqr_laws ; rewrite id_right ; pose (eq_of_para_sqr φ) as p ; rewrite id_right in p ; rewrite <- p ; rewrite !assoc ; rewrite <- tensor_comp_mor ; rewrite id_right ; refine (_ @ id_left _) ; apply maponpaths_2 ; refine (_ @ tensor_id_id _ _) ; apply maponpaths_2 ; exact (z_iso_after_z_iso_inv i)). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Core.Setcategories. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Univalence. Require Import UniMath.CategoryTheory.DisplayedCats.Constructions. Require Import UniMath.CategoryTheory.DisplayedCats.Univalence. Require Import UniMath.CategoryTheory.DisplayedCats.Projection. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Isos. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Strictness. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Discrete. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Univalence. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Total. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Examples.Constant. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Examples.DispCatOnTwoSidedDispCat. Import MonoidalNotations.