Section FrobeniusProperties.
Variables G H K : {group gT}.
Hypothesis frobG : [Frobenius G = K ><| H].
End FrobeniusProperties.

Lemma Frobenius_kerS G K G1 :
G1 \subset G -> K \proper G1 ->
[Frobenius G with kernel K] -> [Frobenius G1 with kernel K].