proposition: 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: Proof. refine (setquotunivcomm _ _ _ _ _ @ _). rewrite free_monoid_extend_funcomp. apply free_monoid_extend_comp. Defined.
imports: UniMath.MoreFoundations.Subtypes UniMath.MoreFoundations.Sets UniMath.Algebra.Monoids UniMath.Algebra.Groups UniMath.Algebra.IteratedBinaryOperations UniMath.Combinatorics.Lists