proposition: Lemma isConeOverCoalg {u v : nat} (e : S v = u) : an u · dmor Fcochain e = an v.
proof: Proof. destruct e. induction v as [| n IHn]. - apply TerminalArrowUnique. - simpl ; rewrite assoc' ; apply cancel_precomposition. etrans. 2: { apply maponpaths ; exact IHn. } rewrite functor_comp. simpl. do 2 rewrite functor_comp. apply maponpaths. unfold dmor. cbn. rewrite ! id_left. apply idpath. Qed.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.MoreFoundations.Tactics UniMath.MoreFoundations.Propositions UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Limits.Graphs.Limits UniMath.CategoryTheory.Limits.Graphs.Colimits UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.FunctorCoalgebras UniMath.CategoryTheory.Chains.Chains UniMath.CategoryTheory.Chains.Cochains