Section SecondIsomorphism.
Variables (gT : finGroupType) (H K : {group gT}).
Hypothesis nKH : H \subset 'N(K).

Lemma second_isom : {f : {morphism H / (K :&: H) >-> coset_of K} |
'injm f & forall A : {set gT}, A \subset H -> f @* (A / (K :&: H)) = A / K}.