Proposition isaprop_strict_double_cat_laws {C : category} {D : strict_twosided_disp_cat C C} (I : hor_id D) (Cm : hor_comp D) : isaprop (strict_double_cat_laws I Cm). Proof. use (@isaprop_total2 (make_hProp _ _) (λ _, make_hProp _ _)). { repeat (use impred ; intro). apply is_strict_strict_twosided_disp_cat. } use (@isaprop_total2 (make_hProp _ _) (λ _, make_hProp _ _)). { repeat (use impred ; intro). apply is_strict_strict_twosided_disp_cat. } use (@isaprop_total2 (make_hProp _ _) (λ _, make_hProp _ _)). { repeat (use impred ; intro). apply is_strict_strict_twosided_disp_cat. } cbn -[isaprop] in *. repeat (use isapropdirprod) ; repeat (use impred ; intro) ; apply isaset_disp_mor. Qed.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Core.Setcategories. Require Import UniMath.CategoryTheory.Categories.CategoryOfSetCategories. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.DisplayedFunctor. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.DisplayedNatTrans. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Isos. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Univalence. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Strictness. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.TransportLaws. Require Import UniMath.Bicategories.DoubleCategories.Basics.DoubleCategoryBasics.