Inductive match_specs: forall (p: program) (G: funspecs), Prop :=
| match_specs_nil: match_specs nil nil
| match_specs_cons: forall i vars f p' P G',
not (In i (map (@fst _ _) p')) ->
match_specs p' G' ->
typecheck vars f = true ->
match_specs ((i,(vars,f))::p') ((i,P)::G').

Lemma cohere_make_world:
forall p G n,
match_specs p G ->
app_pred (cohere (initial_heap p)) (make_world G (initial_heap p) n).