proposition: Lemma CokernelOutsEq {x y : C} {f : x --> y} (CK : Cokernel f) {w : C} (φ1 φ2 : C⟦CK, w⟧) (H' : (CokernelArrow CK) · φ1 = (CokernelArrow CK) · φ2) : φ1 = φ2.
proof: Proof. assert (H1 : f · ((CokernelArrow CK) · φ1) = ZeroArrow Z _ _). { rewrite assoc. rewrite CokernelCompZero. apply ZeroArrow_comp_left. } rewrite (CokernelOutUnique (CokernelisCokernel CK) H1 (idpath _)). apply pathsinv0. set (tmp := pr2 (CokernelisCokernel CK w (CokernelArrow CK · φ1) H1) (tpair _ φ2 (! H'))). exact (base_paths _ _ tmp). Qed.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Epis UniMath.CategoryTheory.Limits.Coequalizers UniMath.CategoryTheory.Limits.Zero