proposition: Lemma sub_der1_normal G H : G^`(1) \subset H -> H \subset G -> H <| G.
proof: Proof. by move=> sG'H sHG; rewrite /(H <| G) sHG sub_der1_norm. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat fintype) mathcomp(bigop finset binomial fingroup morphism) mathcomp(automorphism quotient gfunctor)