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