Lemma presented_gr_extend_comp {X : hSet} {R : hrel (free_gr X)} {Y : gr} (g : monoidfun (presented_gr X R) Y) (H : iscomprelfun R (free_gr_extend (g ∘ presented_gr_intro))) : presented_gr_extend (g ∘ presented_gr_intro) H ~ g. Proof. unfold homot. apply setquotunivprop'. + intro. apply isasetmonoid. + intro x. refine (setquotunivcomm _ _ _ _ _ @ _). exact (free_gr_extend_comp (monoidfuncomp (presented_gr_pr R) g) _). 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.