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.

(* Specifications: *)
Lemma semiregular1l H : semiregular 1 H.
Lemma semiregular1r K : semiregular K 1.
Lemma semiregular_sym H K : semiregular K H -> semiregular H K.
Lemma semiregular_prime H K : semiregular K H -> semiprime K H.
Lemma Frobenius_reg_ker : semiregular K H.
Lemma Frobenius_reg_compl : semiregular H K.
Lemma Frobenius_ker_Hall : Hall G K.
Lemma Frobenius_compl_Hall : Hall G H.