proposition: Lemma pgroupP pi G : reflect (forall p, prime p -> p %| #|G| -> p \in pi) (pi.-group G).
proof: Proof. exact: pnatP. Qed.
imports: mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq div) mathcomp(fintype bigop finset prime fingroup morphism) mathcomp(gfunctor automorphism quotient action gproduct) mathcomp(cyclic)