proposition: Lemma comonads_category_id_subproof {F : functor C C} (T : disp_Comonad_data F) (Tlaws : disp_Comonad_laws T) : disp_Comonad_Mor_laws T T (nat_trans_id F).
proof: Proof. split; intros a; simpl. - now rewrite id_left, id_right, functor_id, id_right. - now apply id_left. Qed.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.MoreFoundations.Tactics UniMath.MoreFoundations.Notations UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Total UniMath.CategoryTheory.DisplayedCats.Constructions UniMath.CategoryTheory.DisplayedCats.Isos UniMath.CategoryTheory.DisplayedCats.SIP UniMath.CategoryTheory.DisplayedCats.Univalence UniMath.CategoryTheory.Core.Univalence