Section Dfs.
Variable g : T -> seq T.
Implicit Type v w a : seq T.
Fixpoint dfs n v x :=
if x \in v then v else
if n is n'.+1 then foldl (dfs n') (x :: v) (g x) else v.

Lemma subset_dfs n v a : v \subset foldl (dfs n) v a.