proposition: Lemma mul_cardG G H : (#|G| * #|H| = #|G * H|%g * #|G :&: H|)%N.
proof: Proof. by rewrite -LagrangeMr -(LagrangeI G H) -mulnA mulnC. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq choice) mathcomp(fintype div path tuple bigop prime finset)