proposition: Lemma classes_gt1 : (#|classes G| > 1) = (G :!=: 1).
proof: Proof. rewrite (cardsD1 1) classes1 ltnS lt0n cards_eq0. apply/set0Pn/trivgPn=> [[xG /setD1P[nt_xG]] | [x Gx ntx]]. by case/imsetP=> x Gx def_xG; rewrite def_xG classG_eq1 in nt_xG; exists x. by exists (x ^: G); rewrite !inE classG_eq1 ntx; apply: imset_f. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq choice) mathcomp(fintype div path tuple bigop prime finset)