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.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_ghost_of: forall phi phi', necR phi phi' -> ghost_of phi' = ghost_fmap (approx (level phi')) (approx (level phi')) (ghost_of phi).