proposition: Proposition struct_cospan_associator_laws : struct_cospan_laws L (identity _) (identity _) (comp_struct_cospan h₁ (comp_struct_cospan h₂ h₃)) (comp_struct_cospan (comp_struct_cospan h₁ h₂) h₃) struct_cospan_associator_mor.
proof: Proof. split ; cbn. - rewrite functor_id, id_left. unfold struct_cospan_associator_mor. rewrite !assoc'. rewrite PushoutArrow_PushoutIn1. apply idpath. - rewrite functor_id, id_left. unfold struct_cospan_associator_mor. rewrite !assoc'. rewrite !PushoutArrow_PushoutIn2. 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