(* 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 return_regs_lessdef:
forall caller1 callee1 caller2 callee2,
locmap_lessdef caller1 caller2 ->
locmap_lessdef callee1 callee2 ->
locmap_lessdef (return_regs caller1 callee1) (return_regs caller2 callee2).