(* 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_setpair_lessdef:
forall p ls1 ls2 v1 v2,
locmap_lessdef ls1 ls2 -> Val.lessdef v1 v2 -> locmap_lessdef (Locmap.setpair p v1 ls1) (Locmap.setpair p v2 ls2).