fact: Definition in_same_coset_test (x1 x2 : X) : (Y ((grinv _ x1) * x2)) ≃ in_same_left_coset Y x1 x2.
imports: UniMath.MoreFoundations.Orders UniMath.MoreFoundations.Tactics UniMath.MoreFoundations.Subtypes UniMath.Algebra.BinaryOperations UniMath.Algebra.Monoids