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 level_later_fash:
forall m m': rmap, (level m > level m')%nat  -> exists m1, laterR m m1 /\ level m1 = level m'.