proposition: Proposition struct_cospan_lunitor_laws : struct_cospan_laws L (identity x) (identity y) (comp_struct_cospan (id_struct_cospan x) h) h struct_cospan_lunitor_mor.
proof: Proof. split ; cbn ; unfold struct_cospan_lunitor_mor. - rewrite functor_id. rewrite !id_left. rewrite PushoutArrow_PushoutIn1. apply idpath. - rewrite functor_id. rewrite id_left. rewrite !assoc'. rewrite PushoutArrow_PushoutIn2. rewrite id_right. apply idpath. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Prelude UniMath.CategoryTheory.Core.Setcategories UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Constructions UniMath.CategoryTheory.DisplayedCats.Isos UniMath.CategoryTheory.DisplayedCats.Univalence UniMath.CategoryTheory.Limits.Pushouts UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat UniMath.CategoryTheory.TwoSidedDisplayedCats.DisplayedFunctor UniMath.CategoryTheory.TwoSidedDisplayedCats.Isos UniMath.CategoryTheory.TwoSidedDisplayedCats.Univalence UniMath.CategoryTheory.TwoSidedDisplayedCats.Total UniMath.CategoryTheory.TwoSidedDisplayedCats.Strictness UniMath.CategoryTheory.TwoSidedDisplayedCats.Examples.Constant UniMath.CategoryTheory.TwoSidedDisplayedCats.Examples.DispCatOnTwoSidedDispCat