Implicit Types (A B : {set gT}) (G H K L R X : {group gT}).Notation "[ 'Frobenius' G = K ><| H ]" :=
  (Frobenius_group_with_kernel_and_complement G K H)
  (at level 0, G at level 50, K, H at level 35,
   format "[ 'Frobenius'  G  =  K  ><|  H ]") : group_scope.

Lemma Frobenius_ker_Hall : Hall G K.