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_NO:
forall phi phi' l sh nsh, necR phi phi' ->
(phi@l = NO sh nsh <-> phi'@l = NO sh nsh).