proposition: Proposition is_z_iso_span_runitor_mor_eqs : is_inverse_in_precat span_runitor_mor span_rinvunitor.
proof: Proof. split ; unfold span_runitor_mor, span_rinvunitor ; cbn. - use (MorphismsIntoPullbackEqual (isPullback_Pullback (PC _ _ _ _ _))) ; cbn. + rewrite !assoc'. rewrite PullbackArrow_PullbackPr1. rewrite id_left. apply id_right. + rewrite !assoc'. rewrite PullbackArrow_PullbackPr2. rewrite id_left. rewrite PullbackSqrCommutes. apply id_right. - apply PullbackArrow_PullbackPr1. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Prelude UniMath.CategoryTheory.Core.Setcategories UniMath.CategoryTheory.Limits.Pullbacks UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Constructions UniMath.CategoryTheory.DisplayedCats.Isos UniMath.CategoryTheory.DisplayedCats.Univalence UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat 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