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

Lemma Frobenius_subr G K H H1 :
H1 :!=: 1 -> H1 \subset H -> [Frobenius G = K ><| H] ->
[Frobenius K <*> H1 = K ><| H1].