Section InternalGroupAction.
Variable gT : finGroupType.
Implicit Types A B : {set gT}.
Implicit Types G H : {group gT}.
Implicit Type x : gT.
(*  Various identities for actions on groups. *)

Lemma sub_afixRs_norm G x : (G :* x \in 'Fix_('Rs)(G)) = (x \in 'N(G)).