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.

Lemma necR_PURE:
forall phi phi' loc k pp,
necR phi phi' ->
phi @ loc = PURE k pp ->
phi' @ loc = PURE k (preds_fmap (approx (level phi')) pp).