(*Qed.*)

Ltac extract_set_reif_type :=
repeat
match goal with
| [ H : exprD' ?tus ?tvs (typtree ?t) (set_reif _ _ _ _) = _ |- _] => fail 1
| [ H : exprD' ?tus ?tvs ?t (set_reif ?i ?vr ?e ?t0) = Some ?x |- _] =>
pose proof (set_reif_istree i tus tvs t vr e t0 x H); subst; try congruence
end.Ltac set_reif_ex :=
match goal with
|  [ H : exprD' ?tus ?tvs (typtree ?t) (set_reif ?i ?vr ?e ?t) = None |- _ ] =>
      edestruct (set_reif_exprD tus tvs t i vr e); eauto; fold func in *;
try congruence
| [ H : context[match typeof_expr ?tus ?tvs (set_reif ?i ?vr ?e ?t) with _ => _ end ] |- _ ] =>
  edestruct (set_reif_exprD tus tvs t i vr e); eauto; pose_types; fold func in *;  forward
end.

(* Specifications: *)
Lemma typeof_set_reif_None_F : forall tus tvs i e t ev vr v, exprD' tus tvs (typtree t) e = Some ev -> exprD' tus tvs t vr = Some v -> typeof_expr tus tvs (set_reif i vr e t) = None -> False.