proposition: Lemma CokernelEndo_is_identity {x y : C} {f : x --> y} {CK : Cokernel f} (φ : C⟦CK, CK⟧) (H : (CokernelArrow CK) · φ = CokernelArrow CK) : identity CK = φ.
proof: Proof. set (H1 := tpair ((fun φ' : C⟦CK, CK⟧ => _ · φ' = _)) φ H). assert (H2 : identity_is_CokernelOut CK = H1). - apply proofirrelevancecontr. apply (CokernelisCokernel CK). apply CokernelCompZero. - apply (base_paths _ _ H2). 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