Definition internal_istrans_weq_internal_istrans_mor {C : category} (PB : Pullbacks C) {x : C} (R : internal_relation x) : internal_istrans R ≃ internal_istrans_mor PB R. Proof. use weqimplimpl. - exact (internal_istrans_to_internal_istrans_mor PB). - exact (internal_istrans_mor_to_internal_istrans PB). - apply isaprop_internal_istrans. - apply isaprop_internal_istrans_mor. Defined.
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.