proposition: Lemma cprod_normal2 A B G : A \* B = G -> A <| G /\ B <| G.
proof: Proof. case/cprodP=> [[K H -> ->] <- cKH]; rewrite -cent_joinEr //. by rewrite normalYl normalYr !cents_norm // centsC. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq div) mathcomp(choice fintype bigop finset fingroup morphism) mathcomp(quotient action)