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 necR_PURE':
forall phi phi' loc k,
necR phi phi' ->
((exists pp, phi@loc = PURE k pp) <->
(exists pp, phi'@loc = PURE k pp)).