proposition: Lemma morphim_norms A B : A \subset 'N(B) -> f @* A \subset 'N(f @* B).
proof: Proof. by move=> nBA; apply: subset_trans (morphim_norm B); apply: morphimS. Qed.
imports: mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq choice) mathcomp(fintype finfun bigop finset fingroup)