proposition: Lemma sub_quotient_pre A C : A \subset 'N(H) -> (A / H \subset C) = (A \subset coset H @*^-1 C).
proof: Proof. exact: sub_morphim_pre. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq div) mathcomp(choice fintype prime finset fingroup morphism) mathcomp(automorphism)