proposition: Lemma setquotpr_linear {x y : PA} (f g : PA⟦x, y⟧) : to_quot_mor (@to_binop PA _ _ f g) = @to_binop Quotcategory_PreAdditive _ _ (to_quot_mor f) (to_quot_mor g).
proof: Proof. exact (pr1 (abgrquotpr_ismonoidfun (binopeqrel_subgr_eqrel (PAS x y))) f g). Qed.
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