proposition: Lemma dprodEcp A B : A :&: B = 1 -> A \x B = A \* B.
proof: Proof. by move=> trAB; rewrite /dprod trAB subxx. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq div) mathcomp(choice fintype bigop finset fingroup morphism) mathcomp(quotient action)