Section GLOBALENV_PRINCIPLES.
Variable P: t -> Prop.

Lemma add_globals_ensures:
forall id g gl ge,
(forall ge id g, P ge -> In (id, g) gl -> P (add_global ge (id, g))) ->
(forall ge, P (add_global ge (id, g))) ->
In (id, g) gl -> P (add_globals ge gl).