proposition: Lemma rcoset_kercosetP x y : x \in 'N(H) -> y \in 'N(H) -> reflect (coset H x = coset H y) (x \in H :* y).
proof: Proof. by rewrite -{6}ker_coset; apply: rcoset_kerP. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq div) mathcomp(choice fintype prime finset fingroup morphism) mathcomp(automorphism)