proposition: Lemma BinCoproductIn1Commutes_right_in_double_ctx_dir (g0 : x --> a) (f : a --> c) (g : b --> c) (h : c --> d) (h' : x --> d) : h' = g0 · f · h -> h' = g0 · BinCoproductIn1 (CC _ _) · (BinCoproductArrow (CC _ _) f g · h).
proof: Proof. intro Hyp. rewrite Hyp. repeat rewrite <- assoc. apply maponpaths. rewrite assoc. rewrite BinCoproductIn1Commutes. 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