proposition: Lemma dprodE G H : H \subset 'C(G) -> G :&: H = 1 -> G \x H = G * H.
proof: Proof. by move=> cGH trGH; rewrite /dprod trGH sub1G cprodE. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq div) mathcomp(choice fintype bigop finset fingroup morphism) mathcomp(quotient action)