Proposition isaprop_internal_relation_to_arr_relation {C : category} {x : C} (R : internal_relation x) {w : C} (f g : w --> x) : isaprop (internal_relation_to_arr_relation R f g). Proof. use invproofirrelevance. intros h₁ h₂. use subtypePath. { intro. apply isapropdirprod ; apply homset_property. } use internal_relation_monic. - exact (pr12 h₁ @ !(pr12 h₂)). - exact (pr22 h₁ @ !(pr22 h₂)). Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Limits.Pullbacks. Require Import UniMath.CategoryTheory.Limits.Coequalizers. Require Import UniMath.CategoryTheory.RegularAndExact.RegularCategory.