f.
move=> a /morphpreP[Ba Dfa]; apply: etrans (actperm_Aut to Dfa(setI_group G 'C_(|to)[a]) : Group_scope.End MorphAction.Section MorphGroupAction.Variable gT : finGroupType.
Implicit Type A : {set gT}.
Implicit Type G : {group gT}.

(* This is not a Canonical action because it is seldom used, and it would     *)
(* cause too many spurious matches (any group product would be viewed as an   *)
(* action!).