proposition: Lemma ismonoidfuninvmap {X Y : monoid} (f : monoidiso X Y) : ismonoidfun (invmap (pr1 f)).
proof: Proof. split with (isbinopfuninvmap f). apply (invmaponpathsweq (pr1 f)). rewrite (homotweqinvweq (pr1 f)). apply (pathsinv0 (pr2 (pr2 f))). Defined.
imports: UniMath.Algebra.BinaryOperations UniMath.MoreFoundations.Subtypes UniMath.MoreFoundations.Sets UniMath.MoreFoundations.Orders