Proposition is_regular_to_isEffective_unique : isaprop (∑ ζ, f · ζ = h). Proof. use invproofirrelevance. intros ζ₁ ζ₂. use subtypePath. { intro. apply homset_property. } use (CoequalizerOutsEq Coeq). cbn. exact (pr2 ζ₁ @ !(pr2 ζ₂)). Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Limits.Coequalizers. Require Import UniMath.CategoryTheory.Limits.Pullbacks. Require Import UniMath.CategoryTheory.Epis. Require Import UniMath.CategoryTheory.EpiFacts. Require Import UniMath.CategoryTheory.Monics. Require Import UniMath.CategoryTheory.RegularAndExact.RegularEpi. Require Import UniMath.CategoryTheory.RegularAndExact.RegularCategory.