proposition: Lemma precompWithCoproductArrow {a : I -> C} (CCab : Coproduct a) {c : I -> C} (CCcd : Coproduct c) (f : ∏ i, a i --> c i) {x : C} (k : ∏ i, c i --> x) : CoproductOfArrows CCab CCcd f · CoproductArrow CCcd k = CoproductArrow CCab (λ i, f i · k i).
proof: Proof. apply CoproductArrowUnique; intro i. now rewrite assoc, CoproductOfArrowsIn, <- assoc, CoproductInCommutes. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.ProductCategory UniMath.CategoryTheory.Limits.Graphs.Colimits UniMath.CategoryTheory.whiskering