Definition is_double_terminal_spans_double_cat {C : category} (T : Terminal C) (PC : Pullbacks C) : is_double_terminal (spans_double_cat PC) T. Proof. intros x₁ x₂ s. use iscontraprop1. - abstract (use invproofirrelevance ; intros φ₁ φ₂ ; use span_sqr_eq ; apply TerminalArrowEq). - use make_span_sqr. + apply TerminalArrow. + abstract (split ; apply TerminalArrowEq). Defined.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Examples.EnrichedRels. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Examples.Spans. Require Import UniMath.CategoryTheory.Categories.HSET.All. Require Import UniMath.CategoryTheory.EnrichedCats.BenabouCosmos. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.Structure.Symmetric. Require Import UniMath.CategoryTheory.Monoidal.Structure.Closed. Require Import UniMath.CategoryTheory.Monoidal.Structure.Cartesian. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.Limits.Pullbacks. Require Import UniMath.CategoryTheory.Limits.Coproducts. Require Import UniMath.Bicategories.DoubleCategories.Basics.DoubleCategoryBasics. Require Import UniMath.Bicategories.DoubleCategories.Core.DoubleCats. Require Import UniMath.Bicategories.DoubleCategories.Examples.RelationsDoubleCat. Require Import UniMath.Bicategories.DoubleCategories.Examples.EnrichedRelDoubleCat. Require Import UniMath.Bicategories.DoubleCategories.Examples.SpansDoubleCat.