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 age1_res_option: forall phi phi' loc,
age1 phi = Some phi' -> res_option (phi @ loc) = res_option (phi' @ loc).