proposition: Lemma precompWithBinCoproductArrow {a b : C} (CCab : BinCoproduct a b) {c d : C} (CCcd : BinCoproduct c d) (f : a --> c) (g : b --> d) {x : C} (k : c --> x) (h : d --> x) : BinCoproductOfArrows CCab CCcd f g · BinCoproductArrow CCcd k h = BinCoproductArrow CCab (f · k) (g · h).
proof: Proof. apply BinCoproductArrowUnique. - rewrite assoc. rewrite BinCoproductOfArrowsIn1. rewrite <- assoc, BinCoproductIn1Commutes. apply idpath. - rewrite assoc, BinCoproductOfArrowsIn2. rewrite <- assoc, BinCoproductIn2Commutes. apply idpath. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.Limits.Zero UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.Limits.Graphs.Colimits UniMath.CategoryTheory.Limits.Coproducts UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.ProductCategory