Hint Rewrite PROP_LOCAL_SEP_f: norm2.
Definition global_funspec Delta id argsig retty cc A Pre Post NEPre NEPost :=
(var_types Delta) ! id = None /\
(glob_specs Delta) ! id = Some (mk_funspec (argsig,retty) cc A Pre Post NEPre NEPost) /\
(glob_types Delta) ! id = Some (type_of_funspec (mk_funspec (argsig,retty) cc A Pre Post NEPre NEPost)).

Lemma lookup_funspec:
forall Delta id argsig retty cc A Pre Post NEPre NEPost,
(var_types Delta) ! id = None ->
(glob_specs Delta) ! id = Some (mk_funspec (argsig,retty) cc A Pre Post NEPre NEPost) ->
(glob_types Delta) ! id = Some (type_of_funspec (mk_funspec (argsig,retty) cc A Pre Post NEPre NEPost)) ->
global_funspec Delta id argsig retty cc A Pre Post NEPre NEPost.