proposition: Lemma iscomprelfun_presented_abgrfun {X : hSet} {R : hrel (free_abgr X)} {Y : abgr} (g : monoidfun (presented_abgr X R) Y) : iscomprelfun R (free_abgr_extend (g ∘ presented_abgr_intro)).
proof: Proof. intros x x' r. rewrite !(free_abgr_extend_comp (monoidfuncomp (presented_abgr_pr R) g)). apply (maponpaths (pr1 g)). apply iscompsetquotpr. exact (generated_binopeqrel_intro r). Defined.
imports: UniMath.MoreFoundations.Subtypes UniMath.MoreFoundations.Sets UniMath.Algebra.Monoids UniMath.Algebra.Groups UniMath.Algebra.IteratedBinaryOperations UniMath.Combinatorics.Lists