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_YES':
forall phi phi' loc rsh sh k,
necR phi phi' -> (phi@loc = YES rsh sh k NoneP <-> phi'@loc = YES rsh sh k NoneP).