proposition: Proposition spans_double_cat_runitor_laws : double_runitor_laws spans_double_cat_runitor_data.
proof: Proof. intros x₁ x₂ y₁ y₂ h₁ h₂ v₁ v₂ sq. use span_sqr_eq. rewrite transportb_disp_mor2_span ; cbn. unfold span_runitor_mor, mor_of_comp_span_mor. rewrite PullbackArrow_PullbackPr1. apply idpath. Qed.
imports: UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Prelude UniMath.CategoryTheory.Core.Setcategories UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat UniMath.CategoryTheory.TwoSidedDisplayedCats.DisplayedFunctor UniMath.CategoryTheory.TwoSidedDisplayedCats.Isos UniMath.CategoryTheory.TwoSidedDisplayedCats.Univalence UniMath.CategoryTheory.TwoSidedDisplayedCats.Strictness UniMath.CategoryTheory.TwoSidedDisplayedCats.Examples.Spans UniMath.CategoryTheory.Limits.Pullbacks UniMath.Bicategories.Core.Bicat UniMath.Bicategories.Core.Examples.BicatOfUnivCats UniMath.Bicategories.DoubleCategories.Basics.DoubleCategoryBasics UniMath.Bicategories.DoubleCategories.Core.DoubleCats UniMath.Bicategories.DoubleCategories.Core.UnivalentDoubleCats UniMath.Bicategories.DoubleCategories.Core.PseudoDoubleSetCats UniMath.Bicategories.DoubleCategories.Core.CompanionsAndConjoints