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).