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

Lemma bigcat_basis Us (U := (\sum_(i | P i) Us i)%VS) :
directv U -> (forall i, P i -> basis_of (Us i) (Xs i)) ->
basis_of U (\big[cat/[::]]_(i | P i) Xs i).