proposition: Lemma coalgebra_mor_commutes {X Y : coalgebra_ob} (f : coalgebra_mor X Y) : coalg_map X · #F f = pr1 f · coalg_map Y.
proof: Proof. exact (pr2 f). Qed.
imports: UniMath.Foundations.Propositions UniMath.MoreFoundations.PartA UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Total