fact: Definition lcoset_in_rcoset_witness {X : gr} {N : subgr X} : lcoset_in_rcoset N -> (X -> N -> N) := fun H g n1 => pr1 (H g n1).
imports: UniMath.MoreFoundations.Orders UniMath.MoreFoundations.Tactics UniMath.MoreFoundations.Subtypes UniMath.Algebra.BinaryOperations UniMath.Algebra.Monoids