Ltac inv H := (apply join_YES_pfullshare1 in H || apply join_YES_pfullshare2 in H || idtac);
(inversion H; clear H; subst).
Definition empty_rmap' : rmap'.
set (f:= fun _: AV.address => NO).
assert (R.valid f).
red; unfold f; simpl.
apply AV.valid_empty.
exact (exist _ f H).
Defined.
Definition empty_rmap (n:nat) : rmap := R.squash (n, empty_rmap').

Lemma empty_rmap_level:
forall lev, level (empty_rmap lev) = lev.