proposition: Lemma move_action_through_vector {n m : nat} (f : vec (T m : hSet) n) (a : stn m → A): weqvecfun _ (vec_map (λ fi, action fi a) f) = λ i, action (weqvecfun _ f i) a.
proof: Proof. apply funextfun. intro. simpl. now rewrite el_vec_map. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.Combinatorics.StandardFiniteSets UniMath.Combinatorics.Vectors UniMath.AlgebraicTheories.AlgebraicTheories UniMath.AlgebraicTheories.AlgebraCategoryCore