Proposition isaprop_internal_istrans_mor {C : category} (PB : Pullbacks C) {x : C} (R : internal_relation x) : isaprop (internal_istrans_mor PB R). Proof. use invproofirrelevance. intros t₁ t₂. use subtypePath. { intro. apply isapropdirprod ; apply homset_property. } use internal_relation_monic. - exact (pr12 t₁ @ !(pr12 t₂)). - exact (pr22 t₁ @ !(pr22 t₂)). 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.