Lemma iscomprelfun_presented_grfun {X : hSet} {R : hrel (free_gr X)} {Y : gr} (g : monoidfun (presented_gr X R) Y) : iscomprelfun R (free_gr_extend (g ∘ presented_gr_intro)). Proof. intros x x' r. rewrite !(free_gr_extend_comp (monoidfuncomp (presented_gr_pr R) g)). apply (maponpaths (pr1 g)). apply iscompsetquotpr. exact (generated_binopeqrel_intro r). 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.