proposition: Lemma cosetpre_set1_coset xbar : coset H @*^-1 [set xbar] = xbar.
proof: Proof. by case: (cosetP xbar) => x Nx ->; rewrite cosetpre_set1 ?val_coset. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq div) mathcomp(choice fintype prime finset fingroup morphism) mathcomp(automorphism)