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 resource_at_join_sub:
forall phi1 phi2 l,
join_sub phi1 phi2 -> join_sub (phi1@l) (phi2@l).