proposition: Lemma dprod_modr A B G H : A \x B = G -> B \subset H -> (H :&: A) \x B = H :&: G.
proof: Proof. by rewrite -!(dprodC B) !(setIC H); apply: dprod_modl. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq div) mathcomp(choice fintype bigop finset fingroup morphism) mathcomp(quotient action)