(* Lemma locmap_undef_lessdef: forall ll ls1 ls2, locmap_lessdef ls1 ls2 -> locmap_lessdef (Locmap.undef ll ls1) (Locmap.undef ll ls2).  Lemma locmap_undef_lessdef_1: forall ll ls1 ls2, locmap_lessdef ls1 ls2 -> locmap_lessdef (Locmap.undef ll ls1) ls2. *)

Lemma locmap_getpairs_lessdef:
forall pl ls1 ls2,
locmap_lessdef ls1 ls2 ->
Val.lessdef_list (map (fun p => Locmap.getpair p ls1) pl) (map (fun p => Locmap.getpair p ls2) pl).