proposition: Lemma is_nat_trans_post_whisker (B C D : precategory_data) (G H : functor_data B C) (gamma : nat_trans G H) (K : functor C D): is_nat_trans (functor_composite_data G K) (functor_composite_data H K) (λ b : B, #K (gamma b)).
proof: Proof. unfold is_nat_trans. simpl in *. intros; repeat rewrite <- functor_comp. rewrite (nat_trans_ax gamma). apply idpath. Qed.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.FunctorCategory