Module R := R0.
Hint Resolve (@subp_sepcon _ Join_rmap Perm_rmap Sep_rmap): contractive.
Ltac do_map_arg :=
match goal with |- ?a = ?b =>
match a with context [map ?x _] =>
match b with context [map ?y _] => replace y with x; auto end end end.
Arguments resource_at_empty [phi] _ _.
Ltac inj_pair_tac :=
match goal with H: (@existT ?U ?P ?p ?x = @existT _ _ _ ?y) |- _ =>
generalize (@inj_pair2 U P p x y H); clear H; intro; try (subst x || subst y)
end.

Lemma resource_at_join_sub:
forall phi1 phi2 l,
join_sub phi1 phi2 -> join_sub (phi1@l) (phi2@l).