proposition: Lemma quotientGK G : H <| G -> coset H @*^-1 (G / H) = G.
proof: Proof. by case/andP; rewrite -{1}ker_coset; apply: morphimGK. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq div) mathcomp(choice fintype prime finset fingroup morphism) mathcomp(automorphism)