Lemma free_abmonoidfun_setquotpr {X Y : hSet} (f : X → Y) (x : free_monoid X) : free_abmonoidfun f (setquotpr _ x) = setquotpr _ (free_monoidfun f x). Proof. refine (setquotunivcomm _ _ _ _ _ @ _). rewrite free_monoid_extend_funcomp. apply free_monoid_extend_comp. Defined.
Require Import UniMath.MoreFoundations.Subtypes. Require Import UniMath.MoreFoundations.Sets. Require Import UniMath.Algebra.Monoids. Require Import UniMath.Algebra.Groups. Require Import UniMath.Algebra.IteratedBinaryOperations. Require Import UniMath.Combinatorics.Lists.