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 dtuple_onP t :
reflect (injective (tnth t) /\ forall i, tnth t i \in S) (t \in dtuple_on).