Lemma free_abgrfun_setquotpr {X Y : hSet} (f : X → Y) (x : free_gr X) : free_abgrfun f (setquotpr _ x) = setquotpr _ (free_grfun f x). Proof. refine (setquotunivcomm _ _ _ _ _ @ _). rewrite free_gr_extend_funcomp. exact (free_gr_extend_comp _ (free_grfun f x)). 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.