Definition dest_below (dst: destination) (g: generator) : Prop :=
match dst with
| For_set sd => Plt (sd_temp sd) g.(gen_next)
| _ => True
end.
Remark dest_for_val_below: forall g, dest_below For_val g.

(* Specifications: *)
Lemma dest_for_set_seqbool_set:
forall sd ty g, dest_below (For_set sd) g -> dest_below (For_set (sd_seqbool_set ty sd)) g.
Lemma dest_for_set_condition_val:
forall tmp tycast ty g1 g2, within tmp g1 g2 -> dest_below (For_set (SDbase tycast ty tmp)) g2.
Lemma dest_for_set_condition_set:
forall sd tmp tycast ty g1 g2, dest_below (For_set sd) g2 -> within tmp g1 g2 -> dest_below (For_set (SDcons tycast ty tmp sd)) g2.
Lemma sd_temp_notin:
forall sd g1 g2 l, dest_below (For_set sd) g1 -> contained l g1 g2 -> ~In (sd_temp sd) l.
Lemma dest_below_le:
forall dst g1 g2,
dest_below dst g1 -> Ple g1.(gen_next) g2.(gen_next) -> dest_below dst g2.