Definition PEq_Im {c d : A} (P1 P2 : PseudoElem c) (f : c --> d) (H : PEq P1 P2) : PEq (PseudoIm P1 f) (PseudoIm P2 f). Proof. use make_PEq. - exact (PEqOb H). - exact (PEqEpi1 H). - exact (PEqEpi2 H). - exact (PEq_Im_Eq P1 P2 f H). Defined.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.Sets. Require Import UniMath.Algebra.BinaryOperations. Require Import UniMath.Algebra.Monoids. Require Import UniMath.CategoryTheory.Limits.Zero. Require Import UniMath.CategoryTheory.Limits.Pushouts. Require Import UniMath.CategoryTheory.Limits.Pullbacks. Require Import UniMath.CategoryTheory.Limits.Equalizers. Require Import UniMath.CategoryTheory.Limits.Coequalizers. Require Import UniMath.CategoryTheory.Limits.Opp. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.opp_precat. Require Import UniMath.CategoryTheory.Morphisms. Require Import UniMath.CategoryTheory.CategoriesWithBinOps. Require Import UniMath.CategoryTheory.PrecategoriesWithAbgrops. Require Import UniMath.CategoryTheory.PreAdditive. Require Import UniMath.CategoryTheory.Additive. Require Import UniMath.CategoryTheory.Abelian. Require Import UniMath.CategoryTheory.AbelianToAdditive. Require Import UniMath.CategoryTheory.AbelianPushoutPullback. Require Import UniMath.CategoryTheory.ShortExactSequences. Require Import UniMath.CategoryTheory.Monics. Require Import UniMath.CategoryTheory.Epis. Require Import UniMath.CategoryTheory.Limits.Kernels. Require Import UniMath.CategoryTheory.Limits.Cokernels. Require Import UniMath.CategoryTheory.Limits.BinDirectSums.