Program Definition empty_genv (pub: list ident): t :=
@mkgenv pub (PTree.empty _) (PTree.empty _) 1%positive _ _ _.
Next Obligation.
rewrite PTree.gempty in H. discriminate.
Qed.
Next Obligation.
rewrite PTree.gempty in H. discriminate.
Qed.
Next Obligation.
rewrite PTree.gempty in H. discriminate.
Qed.
Definition globalenv (p: program F V) :=
add_globals (empty_genv p.(prog_public)) p.(prog_defs).
(** Proof principles *)
Section GLOBALENV_PRINCIPLES.
Variable P: t -> Prop.

Lemma add_globals_unique_preserves:
forall id gl ge,
(forall ge id1 g, P ge -> In (id1, g) gl -> id1 <> id -> P (add_global ge (id1, g))) ->
~In id (map fst gl) -> P ge -> P (add_globals ge gl).