proposition: Lemma Ff_l_leftwhisker_comp (F : Ff C) {G G' G'' : Ff C} (τ : G --> G') (τ' : G' --> G'') : (F ⊗pre (τ · τ')) = (F ⊗pre τ) · (F ⊗pre τ').
proof: Proof. use section_nat_trans_eq; intro f. apply subtypePath; [intro; apply isapropdirprod; apply homset_property|]. apply pathsinv0. etrans. use (pr1_transportf_const). etrans. use (pr1_section_disp_on_morphisms_comp F). use (section_disp_on_eq_morphisms F). - apply pathsinv0. etrans. use (pr1_transportf_const). reflexivity. - apply id_left. Qed.
imports: UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Prelude UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.opp_precat UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Total UniMath.CategoryTheory.DisplayedCats.Functors UniMath.CategoryTheory.DisplayedCats.Constructions UniMath.Combinatorics.StandardFiniteSets UniMath.CategoryTheory.Limits.Graphs.Colimits UniMath.CategoryTheory.Limits.Graphs.Coequalizers UniMath.CategoryTheory.Chains.Chains UniMath.CategoryTheory.DisplayedCats.Examples.Arrow UniMath.CategoryTheory.DisplayedCats.Examples.Three UniMath.ModelCategories.NWFS UniMath.ModelCategories.Helpers