proposition: Lemma presented_abgr_extend_comp {X : hSet} {R : hrel (free_abgr X)} {Y : abgr} (g : monoidfun (presented_abgr X R) Y) (H : iscomprelfun R (free_abgr_extend (g ∘ presented_abgr_intro))) : presented_abgr_extend (g ∘ presented_abgr_intro) H ~ g.
proof: Proof. unfold homot. apply setquotunivprop'. + intro. apply isasetmonoid. + intro x. refine (setquotunivcomm _ _ _ _ _ @ _). exact (free_abgr_extend_comp (monoidfuncomp (presented_abgr_pr R) g) x). Defined.
imports: UniMath.MoreFoundations.Subtypes UniMath.MoreFoundations.Sets UniMath.Algebra.Monoids UniMath.Algebra.Groups UniMath.Algebra.IteratedBinaryOperations UniMath.Combinatorics.Lists