fact: Definition lcoset_in_rcoset {X : gr} (N : subgr X) : UU := ∏ g : X, ∏ n1 : N, ∑ n2 : N, g * (pr1 n1) = (pr1 n2) * g.
imports: UniMath.MoreFoundations.Orders UniMath.MoreFoundations.Tactics UniMath.MoreFoundations.Subtypes UniMath.Algebra.BinaryOperations UniMath.Algebra.Monoids