Section NTransitive.
Variables (gT : finGroupType) (sT : finType).
Variables (n :  nat) (A : {set gT}) (S : {set sT}) (to : {action gT &-> sT}).
Definition dtuple_on := [set t : n.-tuple sT | uniq t & t \subset S].
Definition ntransitive := [transitive A, on dtuple_on | to * n].

Lemma n_act_dtuple t a :
a \in 'N(S | to) -> t \in dtuple_on -> n_act to t a \in dtuple_on.