Lemma merely_split_monic_to_split_monic {X : UU} (m : A --> B) : isaprop X -> (is_split_monic m -> X) -> is_merely_split_monic m -> X. Proof. intros isx impl mere. refine (factor_through_squash isx _ mere). assumption. Qed.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Monics. Require Import UniMath.CategoryTheory.Epis. Require Import UniMath.CategoryTheory.Retracts.