Instance Cross_rmap:
      @Cross_alg _ (Join_prop _ Join_trace AV.valid) ->
      Cross_alg rmap.

(* Specifications: *)
Lemma Cross_rmap_simple: (forall f, AV.valid f) -> Cross_alg rmap.
Lemma identity_resource: forall r: resource, identity r <-> match r with YES _ _ _ => False | _ => True end.
Lemma YES_inj: forall sh k pp sh' k' pp', YES sh k pp = YES sh' k' pp' -> sh=sh' /\ k=k' /\ pp=pp'.
Lemma SomeP_inj1: forall t t' a a', SomeP t a = SomeP t' a' -> t=t'.
Lemma SomeP_inj2: forall t a a', SomeP t a = SomeP t a' -> a=a'.
Lemma SomeP_inj: forall T a b, SomeP T a = SomeP T b -> a=b.
Lemma PURE_inj: forall T x x' y y', PURE x (SomeP T y) = PURE x' (SomeP T y') -> x=x' /\ y=y'.