fact: Definition gr_merely_invertible_elements : monoid -> gr := fun X => (carrierofasubsetwithbinop (submonoidtosubsetswithbinop _ (invertible_submonoid X)),, invertible_submonoid_grop X).
imports: UniMath.MoreFoundations.Orders UniMath.MoreFoundations.Tactics UniMath.MoreFoundations.Subtypes UniMath.Algebra.BinaryOperations UniMath.Algebra.Monoids