Section NaryDirect.
Context {I : finType} {P : pred I}.
End NaryDirect.
(* Free generator sequences. *)

Lemma free_span X v (sumX := fun k => \sum_(x <- X) k x *: x) :
free X -> v \in <<X>>%VS ->
{k | v = sumX k & forall k1, v = sumX k1 -> {in X, k1 =1 k}}.