proposition: Lemma presheaf_mor_comp {T : algebraic_theory} {P P' P'' : presheaf T} (F : presheaf_morphism P P') (F' : presheaf_morphism P' P'') (n : nat) : (F · F' : presheaf_morphism _ _) n = funcomp (F n) (F' n).
proof: Proof. refine (maponpaths (λ z, z _) (pr1_transportf (B := λ _, ∏ n, P n → P'' n) _ _) @ _). exact (maponpaths (λ z, (z _) _) (transportf_const _ _)). Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.Combinatorics.StandardFiniteSets UniMath.AlgebraicTheories.AlgebraicTheories UniMath.AlgebraicTheories.Presheaves UniMath.AlgebraicTheories.PresheafCategoryCore UniMath.AlgebraicTheories.IndexedSetCategory