proposition: Lemma cosetpre1 : coset H @*^-1 1 = H.
proof: Proof. by rewrite -kerE ker_coset. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq div) mathcomp(choice fintype prime finset fingroup morphism) mathcomp(automorphism)