Definition contained (l: list ident) (g1 g2: generator) : Prop :=
forall id, In id l -> within id g1 g2.

Lemma contained_widen:
forall l g1 g2 g1' g2',
contained l g1 g2 ->
Ple (gen_next g1') (gen_next g1) ->
Ple (gen_next g2) (gen_next g2') ->
contained l g1' g2'.