proposition: Lemma cardIg_divn G H : #|G :&: H| = (#|G| * #|H|) %/ #|G * H|.
proof: Proof. by rewrite mul_cardG mulKn // (cardD1 (1 * 1)) mem_mulg. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq choice) mathcomp(fintype div path tuple bigop prime finset)