proposition: 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: 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.
imports: UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Prelude UniMath.CategoryTheory.Core.Setcategories UniMath.CategoryTheory.Categories.CategoryOfSetCategories UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat UniMath.CategoryTheory.TwoSidedDisplayedCats.DisplayedFunctor UniMath.CategoryTheory.TwoSidedDisplayedCats.DisplayedNatTrans UniMath.CategoryTheory.TwoSidedDisplayedCats.Isos UniMath.CategoryTheory.TwoSidedDisplayedCats.Univalence UniMath.CategoryTheory.TwoSidedDisplayedCats.Strictness UniMath.CategoryTheory.TwoSidedDisplayedCats.TransportLaws UniMath.Bicategories.DoubleCategories.Basics.DoubleCategoryBasics