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

Lemma Frobenius_action_kernel_def G H K sT S to :
K ><| H = G -> @Frobenius_action _ G H sT S to ->
K :=: 1 :|: [set x in G | 'Fix_(S | to)[x] == set0].