proposition: Lemma Quotcategory_comp_iscontr {A B C : ob PA} (f : Quotcategory_ob_mor⟦A, B⟧) (g : Quotcategory_ob_mor⟦B, C⟧) : iscontr (QuotcategoryComp f g).
proof: Proof. use (squash_to_prop (Quotcategory_surj f) (isapropiscontr _)). intros f'. use (squash_to_prop (Quotcategory_surj g) (isapropiscontr _)). intros g'. use make_iscontr. - use make_QuotcategoryComp. + exact (setquotpr (binopeqrel_subgr_eqrel (PAS A C)) ((hfiberpr1 _ _ f') · (hfiberpr1 _ _ g'))). + exact (Quotcategory_comp_iscontr_eq f g (hfiberpr1 _ _ f') (hfiberpr2 _ _ f') (hfiberpr1 _ _ g') (hfiberpr2 _ _ g')). - exact (QuotPrecatetgory_comp_iscontr_univ f g f' g'). Defined.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.MoreFoundations.PartA UniMath.Algebra.BinaryOperations UniMath.Algebra.Monoids UniMath.Algebra.Groups UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Monics UniMath.CategoryTheory.Epis UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.CategoriesWithBinOps UniMath.CategoryTheory.PrecategoriesWithAbgrops UniMath.CategoryTheory.opp_precat UniMath.CategoryTheory.Limits.Zero UniMath.CategoryTheory.Limits.Kernels UniMath.CategoryTheory.Limits.Cokernels