Implicit Types (x y z : gT) (A B C D : {set gT}) (G H K P Q R : {group gT}).Definition Sylow A B := p_group B && Hall A B.Notation "''O_' pi ( G )" := (pcore pi G)
  (at level 8, pi at level 2, format "''O_' pi ( G )") : group_scope.Implicit Types (pi rho : nat_pred) (G H : {group gT}).

Lemma Hall1 G : Hall G 1.