fact: Definition lcoset_equal_rcoset {X : gr} (N : subgr X) : UU := lcoset_in_rcoset N × rcoset_in_lcoset N.
imports: UniMath.MoreFoundations.Orders UniMath.MoreFoundations.Tactics UniMath.MoreFoundations.Subtypes UniMath.Algebra.BinaryOperations UniMath.Algebra.Monoids