proposition: Lemma IsoArrowFrom_isaprop (M : category) {A B B':M} (g : A --> B) (g' : A --> B') : isEpi g -> isaprop (IsoArrowFrom g g').
proof: Proof. intros i. apply invproofirrelevance; intros k k'. apply subtypePath. { intros j. apply homset_property. } induction k as [[k K] e], k' as [[k' K'] e']; cbn; cbn in e, e'. apply subtypePath; cbn. { intros f. apply isaprop_is_z_isomorphism. } use i. exact (e @ !e'). Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.Notations UniMath.MoreFoundations.PartA UniMath.Algebra.BinaryOperations UniMath.Algebra.Monoids UniMath.Algebra.Groups UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Monics UniMath.CategoryTheory.Epis UniMath.CategoryTheory.Limits.Zero UniMath.CategoryTheory.Limits.Kernels UniMath.CategoryTheory.Limits.Cokernels UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Limits.Pullbacks UniMath.CategoryTheory.Limits.Pushouts UniMath.CategoryTheory.Limits.BinDirectSums UniMath.CategoryTheory.Limits.Opp UniMath.CategoryTheory.CategoriesWithBinOps UniMath.CategoryTheory.opp_precat UniMath.CategoryTheory.PrecategoriesWithAbgrops UniMath.CategoryTheory.PreAdditive UniMath.CategoryTheory.Morphisms UniMath.CategoryTheory.Additive UniMath.CategoryTheory.Subcategory.Full UniMath.MoreFoundations.Propositions