proposition: Lemma presented_abmonoid_extend_comp {X : hSet} {R : hrel (free_abmonoid X)} {Y : abmonoid} (g : monoidfun (presented_abmonoid X R) Y) (H : iscomprelfun R (free_abmonoid_extend (g ∘ presented_abmonoid_intro))) : presented_abmonoid_extend (g ∘ presented_abmonoid_intro) H ~ g.
proof: Proof. unfold homot. apply setquotunivprop'. + intro. apply isasetmonoid. + intro x. refine (setquotunivcomm _ _ _ _ _ @ _). exact (free_abmonoid_extend_comp (monoidfuncomp (presented_abmonoid_pr R) g) x). Defined.
imports: UniMath.MoreFoundations.Subtypes UniMath.MoreFoundations.Sets UniMath.Algebra.Monoids UniMath.Algebra.Groups UniMath.Algebra.IteratedBinaryOperations UniMath.Combinatorics.Lists