Section FrobeniusProperties.
Variables G H K : {group gT}.
Hypothesis frobG : [Frobenius G = K ><| H].
End FrobeniusProperties.
End FrobeniusBasics.
Arguments normedTI_P {gT A G L}.
Arguments normedTI_memJ_P {gT A G L}.
Arguments Frobenius_kerP {gT G K}.

Lemma Frobenius_coprime_quotient (gT : finGroupType) (G K H N : {group gT}) :
K ><| H = G -> N <| G -> coprime #|K| #|H| /\ H :!=: 1%g ->
N \proper K /\ {in H^#, forall x, 'C_K[x] \subset N} ->
[Frobenius G / N = (K / N) ><| (H / N)]%g.